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Nelson 1.11.0.0

Nelson is a powerful, open-source numerical computational language, developed to provide a comprehensive and intuitive environment for engineers, scientists, and students. With over 1,200 built-in functions, Nelson supports a wide range of tasks, from basic algebra to advanced numerical simulations.

Originally inspired by languages like MATLAB© and GNU Octave, Nelson offers users a lightweight yet feature-rich experience. It is designed to be easy to learn and use, with an emphasis on performance and flexibility.

Try it now!

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Features

Data Types Managed by Nelson

Double and Complex Double: Supports scalars, vectors, 2D matrices, N-dimensional arrays, and sparse matrices.
Single and Complex Single: Includes scalars, vectors, 2D matrices, N-dimensional arrays, and sparse matrices.
Logical: Handles scalars, vectors, 2D matrices, N-dimensional arrays, and sparse matrices.
Character Arrays: Supports UNICODE characters.
String Arrays: Fully supports UNICODE.
Integers: 8, 16, 32, and 64-bit signed and unsigned scalars, vectors, 2D matrices, and N-dimensional arrays.
Handle Objects: For object-oriented functionality.
Anonymous Functions: Allows creation and manipulation of functions without names.
Data Structures: Supports dictionaries and tables.
Overloading: All types can be overloaded for custom behavior.

Performance Enhancements

OpenMP and SIMD: Utilizes parallel processing and vectorization for faster computations.

Visualization & Interface

2D and 3D Plotting: High-level commands for visualizations.
User Interface Controls: Built-in controls for creating custom interfaces.
Desktop Environment: Comes with history tracking, a file explorer, and workspace browser.

Advanced Modules

Parallel Computing: Enables efficient use of multi-core processors.
Fast Fourier Transform (FFT): High-performance FFT functions based on FFTW and MKL.
SLICOT Interface: Optional support for the Systems and Control Theory subroutine library.
Control System Module: Tools for control theory and system design.
MPI (Message Passing Interface): Functions for distributed parallel computing.

Data Formats & Interfacing

JSON Support: Read and write JSON files.
HDF5 Functions: High-level I/O functions, with HDF5 as the default file format for .nh5 workspaces.
MAT-File Compatibility: Load and save workspaces in MAT-file format.
Foreign Function Interface (FFI): Build and load C/Fortran code on the fly.
MEX C API Compatibility: Interfacing with MEX-compatible C APIs.
Nelson Engine API: Use Nelson as a backend engine within C code, compatible with the MEX Engine API.
Python Interfacing: Call Python scripts and functions from Nelson.
RESTful API: Enables Nelson to interact with web services.

Additional Capabilities

Inter-Process Communication: Communicate between Nelson processes.
QML Engine: Use Qt’s QML framework to display and manipulate graphical content.
Component Object Model (COM): Interface with COM components, especially on Windows.
Excel File Support: Write and read .xlsx files using COM on Windows.
Embedded Code Editor: Integrated editor for Nelson scripts.

Help & Testing Tools

Help Engine: Generate and view help files in various formats like HTML, Markdown, PDF, or GitBook.
Test Engine: Validate algorithms using built-in functions, with support for xUnit report export.

Profiling & Code Coverage

Profiler: Built-in profiler to analyze and optimize code performance.
Code Coverage: Measure the coverage of your tests to ensure thorough validation.

Cloud & Extensibility

Nelson Cloud: Instant access to Nelson from any web browser via Nelson Cloud.
Module Skeleton: Templates for extending Nelson:
- Template with Macros and Builtins.
- Basic Macros Template.
Nelson Modules Manager (nmm): A package manager to install and manage extensions for Nelson.

Changelogs

License

Nelson license

Functions manager

Description

functions manager

addpath - Add directories to functions search path.
builtin - Executes built-in function.
clearfun - Clear an built-in function.
feval - Evaluates function.
inmem - Names of functions, MEX-files.
isbuiltin - Check for the existence of a builtin.
ismacro - Check for the existence of a macro (function).
ismex - Check for the existence of a mex function.
macroargs - Returns variables names of a function.
path - Modify or display Nelson’s load path.
private functions - Private functions.
rehash - Reinitialize Nelson’s search path directory cache.
restoredefaultpath - Restore Nelson’s path to its initial state at startup.
rmpath - Remove directory from search path.
userpath - Displays or modify default user functions directory.
what - Get Nelson builtin and macro list.
which - Locates functions and built-in.

addpath

Add directories to functions search path.

Syntax

addpath(dirname)
addpath(dirname, ..., dirname)
addpath(dirname, ..., dirname, '-begin')
addpath(dirname, ..., dirname, '-end')
addpath(dirname, ..., dirname, '-frozen')
previous = addpath(dirname)
previous = addpath(dirname, ..., dirname)
previous = addpath(dirname, ..., dirname, '-begin')
previous = addpath(dirname, ..., dirname, '-end')

Input argument

dirname - a string: a directory
'-end' or '-begin' - append dirname at the end or begin of the list.
'-frozen' - disables folder change detection for the folders being added or modified.

Output argument

previous - returns previous path before adding

Description

addpath add directories to search path.

It is also possible to add lists of directory names separated by pathsep.

Non-existent path will not be added and a warning will be issued.

files watchers is disabled for internal modules.

Example

path()
addpath(tempdir())
path
rmpath(tempdir())
path

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

builtin

Executes built-in function.

Syntax

builtin(function_name; x1, ..., xn)
builtin(function_handle; x1, ..., xn)
[r1, ..., rn] = builtin(function_name, x1, ..., xn)
[r1, ..., rn] = builtin(function_handle, x1, ..., xn)

Input argument

function_name - a string: function name.
function_handle - a function handle.
x1, ..., xn - input arguments of the builtin.

Output argument

r1, ..., rn - output arguments returned by the builtin

Description

builtin calls the base built-in described by its name or function handle and input arguments.

Example

a = builtin('cos', 0)
b = builtin(str2func('cos'), 0)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

clearfun

Clear an built-in function.

Syntax

l = clearfun(function_name)
l = clearfun(function_handle)

Input argument

function_name - a string: function name.
function_handle - a function handle.

Output argument

l - a logical

Description

clearfun clears built-in.

Example

cos(3)
a = clearfun('cos')
cos(3)

sin(3)
b = clearfun(str2func('sin'))
sin(3)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

feval

Evaluates function.

Syntax

feval(function_name; x1, ..., xn)
feval(function_handle; x1, ..., xn)
[r1, ..., rn] = feval(function_name, x1, ..., xn)
[r1, ..., rn] = feval(function_handle, x1, ..., xn)

Input argument

function_name - a string: function name.
function_handle - a function handle.
x1, ..., xn - input arguments of the function.

Output argument

r1, ..., rn - output arguments returned by the function

Description

function calls the base function or built-in described by its name or function handle and input arguments.

Example

a = feval('cos', 0)
b = feval(str2func('cos'), 0)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

inmem

Names of functions, MEX-files.

Syntax

F = inmem()
[F, M] = inmem()
F = inmem('-completenames')
[F, M] = inmem('-completenames')

Input argument

'-completenames' - a string: mex function name.

Output argument

F - cell array of character vectors containing the names of the macros that are loaded.
M - cell array of character vectors containing the names of the mex that are loaded.

Description

inmem returns cells array of names of functions and mex currently loaded.

Example

clear all
tand(3)
inmem()
inmem('-completenames')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

isbuiltin

Check for the existence of a builtin.

Syntax

tf = isbuiltin(name)

Input argument

name - a string: builtin name.

Output argument

tf - a logical: true if builtin exists.

Description

isbuiltin checks for the existence of a builtin.

Example

isbuiltin('isbuiltin')
isbuiltin('exist')
ismacro('exist')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

ismacro

Check for the existence of a macro (function).

Syntax

tf = ismacro(name)

Input argument

name - a string: macro name.

Output argument

tf - a logical: true if macro exists.

Description

isbuiltin checks for the existence of a macro.

Example

ismacro('isbuiltin')
ismacro('exist')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

ismex

Check for the existence of a mex function.

Syntax

tf = ismex(name)

Input argument

name - a string: mex function name.

Output argument

tf - a logical: true if mex exists.

Description

ismex checks for the existence of a mex function.

Example

ismex('isbuiltin')
ismex('exist')
ismex('exist')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

macroargs

Returns variables names of a function.

Syntax

[argOut, argIn] = macroarg(function_name)

Input argument

function_name - a string: function name.

Output argument

argOut - a cell with output arguments.
argIn - a cell with input arguments.

Description

macroargs returns input and output variables used by the function.

Example

[out_args, in_args] = macroarg('getfield')
[out_args, in_args] = macroarg('deal')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

path

Modify or display Nelson’s load path.

Syntax

path()
p = path()
path(dirname)
path(path(), dirname)
path(dirname, path())

Input argument

dirname - a directory name or an suite of directory names using pathsep()

Output argument

p - string: the specified paths

Description

path modifies or displays Nelson’s load path.

Example

path
p = path()
path(p, tempdir())
path
path(p)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

private functions

Private functions.

Description

Private functions serve a valuable purpose when you wish to restrict the accessibility of a function.

In numerous instances, a single function may require access to one or more auxiliary functions.

when a solitary auxiliary function is utilized by multiple functions, it becomes necessary to relocate these auxiliary functions to a dedicated subdirectory named "private", positioned within the directory where the functions that require access to these auxiliary functions are located.

To illustrate this concept, consider a function, let's call it function1, that relies on a helper function, function2, to perform a substantial portion of its tasks, as shown in below example.

In this scenario, if the path to func1 is directory/function1.m and function2 is found in the directory directory/private/function2.m, then function2 is only accessible to functions within directory, such as function1.

Examples

directory/function1.m

function y = function1(x)
  y = function2(x)  +  1;
end

directory/private/function2.m

function y = function2(x)
  y = 41;
end

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

rehash

Reinitialize Nelson’s search path directory cache.

Syntax

rehash

Description

rehash() reinitializes Nelson’s search path directory cache.

This happens each time Nelson displays the prompt.

You should use rehash() only when you run a .m file that updates another .m file

Example

rehash()

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

restoredefaultpath

Restore Nelson’s path to its initial state at startup.

Syntax

restoredefaultpath

Description

restoredefaultpath restores Nelson's search path to its startup state.

Example

path
path('')
path
restoredefaultpath
path

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

rmpath

Remove directory from search path.

Syntax

rmpath(dirname)
previouspaths = rmpath(dirname)

Input argument

dirname - name of directory to remove

Output argument

previouspaths - a string: path prior to removing the specified paths

Description

rmpath removes directory from search path.

Example

path
addpath(tempdir())
path
rmpath(tempdir())
path

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

userpath

Displays or modify default user functions directory.

Syntax

p = userpath()
userpath(dirname)
userpath('reset')
userpath('clear')

Input argument

dirname - an existing directory name
'clear' - removes the first directory for current and next sessions of Nelson.
'reset' - resets the first directory to the default for your platform.

Output argument

p - string: the specified user path

Description

userpath modifies or displays user’s load path.

By default, userpath directory is platform-dependant:

Windows platforms: %USERPROFILE%/Documents/Nelson

Others platforms: $home/Documents/Nelson

It is possible to force userpath by define an environment variable: NELSON_USERPATH with an existing path.

Example

path
userpath

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

what

Get Nelson builtin and macro list.

Syntax

list_builtin = what()
[list_builtin, list_macro] = what()

Output argument

list_builtin - a cell of strings
list_macro - a cell of strings

Description

what returns the list of all builtin and macro available in current Nelson's session.

Example

l = what()
[l, m] = what()

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

which

Locates functions and built-in.

Syntax

which(function_name)
p = which(function_name)
c = which(function_name, '-all')
m = which(function_name, '-module')

Input argument

function_name - a string: function name.

Output argument

p - a string: path of the function or built-in
c - a cell of strings: paths of the function or built-in.
m - a cell of strings: name of the modules where function or built-in is available.

Description

which returns the path of a function or a built-in.

Example

which('cos')
p = which('cos')
c = which('cos', '-all')
m = which('cos', '-module')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

Modules manager

Description

modules manager functions

addgateway - Adds dynamically builtin at runtime.
addmodule - Add module to Nelson.
gatewayinfo - Returns information about an gateway.
getmodules - Returns list of modules loaded in Nelson.
ismodule - Checks if a module is loaded.
module.json - module.json description
modulepath - Returns path of a module.
nmm - Nelson Modules Manager.
nmm_build_help - helper's function to build help of an external module
nmm_build_loader - helper's function to build main loader.m of an external module
removegateway - Removes dynamically builtin at runtime.
removemodule - remove a module from Nelson.
requiremodule - Returns an error if module is not loaded in Nelson.
semver - semantic versioner.
toolboxdir - Returns path of a module.
usermodulesdir - Returns path where external modules are saved.

addgateway

Adds dynamically builtin at runtime.

Syntax

addgateway(dyn_lib_path)

Input argument

dyn_lib_path - a string: path of a dynamic library prepared for Nelson.

Description

addgateway(dyn_lib_path) adds dynamically builtin at runtime.

The dynamic library loaded must have at least an C entry point AddGateway.

If gateway was already loaded, no error or warning will be raised.

Example

Add gateway for string module:

addgateway(modulepath('time', 'builtin'))

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

addmodule

Add module to Nelson.

Syntax

addmodule(module_path, module_short_name)

Input argument

module_path - a string: root path of a module. path must exist.
module_short_name - a string: short module's name. This name must not be already used.

Description

addmodule registers a new module designed by his path and short name.

Example

See module skeleton for example

ismodule('module_skeleton')
addmodule([nelsonroot(), '/module_skeleton'], 'module_skeleton')
ismodule('module_skeleton')
removemodule('module_skeleton')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

gatewayinfo

Returns information about an gateway.

Syntax

[gateway_name, builtin_list] = gatewayinfo(dyn_lib_path)

Input argument

dyn_lib_path - a string: path of a dynamic library prepared for Nelson.

Output argument

gateway_name - a string: gateway name
builtin_list - a cell of strings: list of builtin in this gateway

Description

[gateway_name, builtin_list] = gatewayinfo(dyn_lib_path) get information about an gateway.

The dynamic library must have at least an C entry point GetGatewayInfo.

If file does not exist an error is raised.

Example

[gateway_name, builtin_list] = gatewayinfo(modulepath('time', 'builtin'))

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

getmodules

Returns list of modules loaded in Nelson.

Syntax

modules_name = getmodules()
[modules_name, modules_root_path, modules_version, modules_protected] = getmodules()

Output argument

modules_name - a cell of strings: modules names.
modules_root_path - a cell of strings: path of modules.
modules_version - a cell of vector: [major, minor, patch].
modules_protected - a vector of logical: true if module can be removed or not.

Description

getmodules returns list of modules loaded in Nelson.

all core's modules are protected and cannot removed during an nelson's session.

Example

[modules_name, modules_root_path, modules_version, modules_protected] = getmodules()

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

ismodule

Checks if a module is loaded.

Syntax

state = ismodule(module_short_name)
state = ismodule(module_short_name, 'isprotected')

Input argument

module_short_name - a string: short module's name to test.
'isprotected' - check module isprotected (ie. internal module).

Output argument

state - a logical.

Description

ismodule returns true if module is loaded otherwise false.

Example

ismodule('core')
ismodule('mymodule')

History

Version	Description
1.0.0	initial version
1.11.0	'isprotected' second argument.

Author

Allan CORNET

module.json

module.json description

Description

A module.json file is required for each nelson's external module, it allows to manager easily with nmm function.

module: unique identifier module short name (alphanumeric characters), example: "module_skeleton_basic"

title: complete module name (human friendly name), example: "Module skeleton basic"

summary: one line description, example: "Skeleton of a basic nelson package"

version: version number using semantic versioning, example: "1.0.0"

platforms: platforms supported.

"all" for all platforms

others platforms:

"win32": windows 32 bits

"win64": windows 64 bits

"maci64": macos 64 bits build

"maci32": macos 32 bits build

"glnxa64": linux 64 bits build

"glnxa32": linux 64 bits build

example: ["win64", "glnxa64"], module will be available only on windows and linux 64 bits platforms.

nelson: nelson's supported versions, example: "<2.0.0" (default)

builtin: true if module requires C/C++ compiler, false if module have only macros.

author: Author information: name, email and website

Example:

{

"name": "Allan CORNET",

"email": "nelson.numerical.computation@gmail.com",

"url": "https://nelson-lang.github.io/nelson-website/"

}

homepage: homepage of the module, example "https://github.com/nelson-lang/module_skeleton_basic"

description: full description of the module, markdown format supported, example: "nelson's module skeleton (macros only)"

license: License under which the toolbox will be published, example: "BSD" or "LGPLv2", ...

keywords: keywords describing your module.

Example:

["interpreter", "scientific-computing", "programming-language", "matrix-functions", "skeleton"]

dependencies: list of modules dependencies {} (default) or name : url values

{

"module_a": "https://module_a.git#v1.0.0",

"module_b": "https://module_b.git#v1.0.0"

}

Example

Deploy module_skeleton and module_skeleton_basic template

if ~ismodule('module_skeleton_basic')
    nmm('install', 'https://github.com/nelson-lang/module_skeleton_basic.git#v1.0.0');
end
if ~ismodule('module_skeleton')
    nmm('install', 'https://github.com/nelson-lang/module_skeleton.git#v1.0.0');
end
modules_installed = nmm('list');
edit([modules_installed.module_skeleton.path, 'module.json']);
edit([modules_installed.module_skeleton_basic.path, 'module.json']);

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

modulepath

Returns path of a module.

Syntax

p = modulepath(module_short_name)
p = modulepath(module_short_name, option)

Input argument

module_short_name or 'nelson' - a string: short module's name. module must exist in nelson session.
option - a string: 'etc', 'bin', 'root', 'builtin', 'tests'.

Output argument

p - a string: path or subpath of the module.

Description

modulepath is an helper's function to return module root path or a subdirectory.

modulepath('nelson') is equivalent to modulepath('nelson', 'root')

modulepath('nelson', 'bin') return path of nelson's executables.

modulepath('nelson', 'builtin') returns path of nelson's dynamic libraries.

Example

modulepath('core')
modulepath('core', 'root')
modulepath('core', 'etc')
modulepath('core', 'bin')
modulepath('core', 'builtin')
modulepath('core', 'tests')
modulepath('nelson', 'root')
modulepath('nelson', 'bin')
modulepath('nelson', 'builtin')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

nmm

Nelson Modules Manager.

Syntax

st = nmm('list')
nmm('load', module_name)
l = nmm('autoload', module_name)
nmm('autoload', module_name, state)
nmm('install', git_url)
nmm('uninstall', module_name)
package_filename = nmm('package', module_name, destination_dir)

Input argument

module_name - a string: short module's name.
state - a logical: true will autoload module at startup, false disable autoload for this module.
git_url - a string: a git url (http/https protocol).
destination_dir - a string: an existing destination directory where archive will be created.

Output argument

st - a struct: list of installed modules.
l - a logical: current state of autoload.
package_filename - a string: filename.

Description

nmm is the Nelson Modules Manager.

Source-based distribution packages allows to have optimized packages for your computer and allows to have distributed repositories.

Installed modules are locally built and can require an C/C++.

st = nmm('list') get list of installed modules.

nmm('install', git_url) install a distant module.

About git_url, in this example 'https://github.com/nelson-lang/module_skeleton_basic.git#v1.0.0'

'#v1.0.0' is defined as #<commit-ish>, it allows to clone exactly an commit.

The commit-ish can be a tag (exact version), and an sha1 (exac commit) or an branch name.

Without commit-ish, master branch will be used.

nmm('install', filename_nmz) install an prebuilt external module.

nmm('load', module_name) load an installed module for current session.

l = nmm('autoload', module_name returns current state autoload for module_name.

nmm('autoload', module_name, state) marks an installed modules "marked" as autoload at startup.

By default modules are marked as autoload.

nmm('uninstall', module_name) uninstall an installed module.

nmm('package', module_name, destination_dir) packages an module as a zip file.

Examples

Deploy module_skeleton_basic template

if ~ismodule('module_skeleton_basic')
    nmm('install', 'https://github.com/nelson-lang/module_skeleton_basic.git#v1.0.0');
    macro_sum(3, 4)
    nmm('uninstall', 'module_skeleton_basic')
end

Package easily a module

if ~ismodule('module_skeleton_basic')
    nmm('install', 'https://github.com/nelson-lang/module_skeleton_basic.git#v1.0.0');
end
package_filename = nmm('package', 'module_skeleton_basic', tempdir())

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

nmm_build_help

helper's function to build help of an external module

Syntax

nmm_build_help(module_short_name, module_root_path)

Input argument

module_short_name - a string: short module's name.
module_root_path - a string: path of the module named 'module_short_name'.

Description

nmm_build_help generates help of an external module.

Example

See module skeleton for example

% see builder.m

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

nmm_build_loader

helper's function to build main loader.m of an external module

Syntax

nmm_build_loader(module_short_name, module_root_path)

Input argument

module_short_name - a string: short module's name.
module_root_path - a string: path of the module named 'module_short_name'.

Description

nmm_build_loader generates main loader.m of an external module.

Example

See module skeleton for example

% see builder.m

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

removegateway

Removes dynamically builtin at runtime.

Syntax

removegateway(dyn_lib_path)

Input argument

dyn_lib_path - a string: path of a dynamic library prepared for Nelson.

Description

removegateway(dyn_lib_path) removes dynamically builtin at runtime.

The dynamic library loaded must have at least an C entry point RemoveGateway.

If gateway was not loaded, no error or warning will be raised. If file does not exist an error is raised.

Example

removes time builtin

calendar
removegateway(modulepath('time', 'builtin'))
calendar

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

removemodule

remove a module from Nelson.

Syntax

removemodule(module_short_name)

Input argument

module_short_name - a string: short module's name.

Description

removemodule remove a module designed by his short name.

all core's modules are protected and cannot removed during an nelson's session.

Example

See module skeleton for example

ismodule('module_skeleton')
addmodule([nelsonroot(), '/module_skeleton'], 'module_skeleton')
ismodule('module_skeleton')
removemodule('module_skeleton')
ismodule('module_skeleton')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

requiremodule

Returns an error if module is not loaded in Nelson.

Syntax

requiremodule(module_short_name)

Input argument

module_short_name - a string: short module's name.

Description

requiremodule returns an error if desired module is not loaded.

This function is usefull to verify a dependency on another module.

Example

See module skeleton for example

ismodule('module_skeleton')
requiremodule('module_skeleton')
addmodule([nelsonroot(), '/module_skeleton'], 'module_skeleton')
ismodule('module_skeleton')
requiremodule('module_skeleton')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

semver

semantic versioner.

Syntax

r = semver(version_str, version_range)

Input argument

version_str - a string: current version.
version_range - a string: version to compare or range.

Output argument

r - a double: -1, 0 or 1.

Description

semver compares a version string to an version or an range version.

if an range version is used, r return 0 (not satisfied) or 1 (satisfied).

if an simple version is used, an comparaison value r is returned -1 (inferior), 0 (equal) or 1 (superior).

supported range operators:

= - Equality

>= - Higher or equal to

<= - Lower or equal to

< - Lower than

> - Higher than

^ - Caret operator comparison

~ - Tilde operator comparison

Used function(s)

semver.c

Bibliography

https://semver.org/

Example

semver('1.5.10', '2.3.0')
semver('2.3.0', '1.5.10');
semver('1.5.10', '1.5.10')
semver('1.2.3', '~1.2.3')
semver('1.5.3', '~1.2.3')
semver('1.0.3', '~1')
semver('2.0.3', '~1')
semver('1.2.3-alpha', '>1.2.3-beta')
semver('1.2.3-alpha', '<1.2.3-beta')
semver('1.2.3', '^1.2.3')
semver('1.2.2', '^1.2.3')
semver('1.9.9', '^1.2.3')
semver('2.0.1', '^1.2.3')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

toolboxdir

Returns path of a module.

Syntax

p = toolboxdir(module_short_name)

Input argument

module_short_name - a string: short module's name.

Output argument

p - a string: path of the module.

Description

toolboxdir is an helper's function to return module root path.

Example

toolboxdir('core')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

usermodulesdir

Returns path where external modules are saved.

Syntax

p = usermodulesdir()

Output argument

p - a string: path where are external modules.

Description

usermodulesdir is an helper's function to return path where users modules are saved.

This path can be overloaded by defining NELSON_EXTERNAL_MODULES_PATH environment variable on your system.

Example

usermodulesdir()

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

Core

Description

core functions

banner - Shows Nelson banner.
eval - Evaluate Nelson code in string.
evalc - Evaluate Nelson code with console capture.
evalin - Evaluate Nelson code in string in an specified scope.
execstr - Execute Nelson code in strings.
exist - Check for the existence.
exit - Terminate Nelson program (same as quit)
feature - undocumented features.
inputname - Get variable name of function input.
isunicodesupported - Detect whether the current terminal supports Unicode.
license - Get license information for Nelson.
maxNumCompThreads - Set/Get maximum number of computional threads.
namelengthmax - Return the maximum variable name length.
nargin - Returns the number of input arguments.
narginchk - Checks the number of input arguments.
nargout - Returns the number of output arguments.
nargoutchk - Checks the number of output arguments.
nelsonroot - Returns Nelson's root folder.
nfilename - Returns the name of the currently executing file.
pause - Pauses script execution.
prefdir - Return the preferences directory used by Nelson.
quit - Terminate Nelson application
run - Executes a script file (.m).
sha256 - Get sha256 checksum.
version - Return the version of Nelson.

Shows Nelson banner.

Syntax

banner

Description

banner shows Nelson banner.

Example

clc();banner

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

eval

Evaluate Nelson code in string.

Syntax

eval(str)
eval(str, catch_str)
[r1, ... rn] = eval(str)
[r1, ... rn] = eval(str, catch_str)

Input argument

str - a string: Nelson instruction to execute
catch_str - a string: Nelson instruction to execute if an error is detected.

Output argument

[r1, ... rn] - results: output variables

Description

eval executes Nelson instructions given in a string.

Please use try catch end block instead than eval, if you need to capture an error message for higher performance.

Examples

eval('B=4')

This example will fail and returns an error message.

C = eval('B=4')

D = eval(4)

This example will not fail and return false.

eval('error(''blabla'')', 'l = lasterror(); disp([''lasterror message: '', l.message])')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

evalc

Evaluate Nelson code with console capture.

Syntax

t = evalc(str)
t = evalc(str)
[t, r1, ... rn] = evalc(str)

Input argument

str - a string: Nelson instruction to execute

Output argument

T - output text captured in t variable
[r1, ... rn] - results: output variables

Description

evalc executes Nelson instructions given in a string.

console display is redirected into a variable.

diary, more, and input are disabled when evalc is used.

Examples

evalc('B=4')

t = evalc('dir')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

evalin

Evaluate Nelson code in string in an specified scope.

Syntax

evalin(scope, str)
[r1, ... rn] = evalin(scope, str)

Input argument

scope - a string: 'base' or 'caller'.
str - a string: Nelson instruction to execute

Output argument

[r1, ... rn] - results: output variables

Description

eval executes Nelson instructions given in a string in 'base' or 'caller' scope.

Example

R = evalin('base', 'evalin(''caller'',''pi'')')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

execstr

Execute Nelson code in strings.

Syntax

execstr(str)
execstr(str, 'nocatch')
bSuccess = execstr(str, 'errcatch')

Input argument

str - a string: Nelson instruction to execute

Output argument

bSuccess - a logical: true or false if command fails

Description

execstr executes Nelson instructions given in a string.

execstr(str, 'nocatch') is equivalent to execstr(str)

execstr can be used as alternative to try ... catch ... end block.

Examples

execstr('b = ''hello''; disp(b);')

This example will fail and returns an error message.

execstr('b = yyyy')

This example will fail and returns an error message.

execstr('b = yyyy', 'nocatch')

This example will not fail and return false.

r = execstr('b = yyyy', 'errcatch')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

exist

Check for the existence.

Syntax

res = exist(name)
res = exist(name, category)

Input argument

name - a string: name of variable, function, file or directory.
category - a string: 'var', 'builtin', 'file', or 'dir'.

Output argument

res - a integer value.

Description

exists checks for the existence of variable, builtin, file or directory.

exists returns:

0 does not exist

1 is an variable

2 is a file

3 is a mex function

5 is a builtin or function

7 is a directory

Example

exist('fileread')
fileread = 3;
exist('fileread')
clear fileread
exist('fileread')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

exit

Terminate Nelson program (same as quit)

Syntax

exit
exit(status)
exit('force')
exit('cancel')
exit(status, 'force')

Description

This function is equivalent to the quit function.

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

feature

undocumented features.

Syntax

ret = feature(name)
ret = feature(name, newValue)

Input argument

name - a string: name of the feature.
newValue - a variable

Output argument

ret - result: result returned

Description

feature is an entirely undocumented and unsupported Nelson function.

It is a helper function for debugging Nelson.

featurecan change without prior notice between Nelson releases, so be very careful when using this function in your code.

History

Version	Description
1.2.0	initial version

Author

Allan CORNET

inputname

Get variable name of function input.

Syntax

s = inputname(argNumber)

Input argument

argNumber - a scalar, real, positive integer value: Number of function input argument

Output argument

s - character vector: variable name

Description

inputname get variable name of function input.

inputname is only useable within a function

Example

function R = getinputname(varargin)
    R = string([]);
    for i = 1:nargin
        R = [R, string(inputname(i))];
    end
end

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

isunicodesupported

Detect whether the current terminal supports Unicode.

Syntax

tf = isunicodesupported()

Output argument

tf - a logical: true or false.

Description

isunicodesupported: returns if current terminal supports Unicode.

value returned can be overloaded if environment variable 'NELSON_TERM_IS_UNICODE_SUPPORTED' is 'TRUE'

Example

isunicodesupported()

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

license

Get license information for Nelson.

Syntax

license
r = license
[r, txt] = license

Output argument

r - a string: minimal string description about license
txt - a string: complete license text.

Description

license get license information for Nelson.

Example

license()
r = license()
[r,txt] = license()

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

maxNumCompThreads

Set/Get maximum number of computional threads.

Syntax

T = maxNumCompThreads()
PREVIOUS_T = maxNumCompThreads(T)
PREVIOUS_T = maxNumCompThreads('automatic')

Input argument

T - an integer value: number of threads used by Nelson for computations.

Output argument

T - an integer value: number of threads used by Nelson for computations.
PREVIOUS_T - an integer value: previous number of threads used by Nelson for computations.

Description

maxNumCompThreads returns the number of threads used by Nelson for computations.

maxNumCompThreads(T) sets the maximum number of computational threads. This modification is only available for current session.

By default, maxNumCompThreads uses OMP_NUM_THREADS environment variable or numbers of detected physical cores on Windows and logical cores on others platforms.

Limitation: On Windows 32 bits, due to MKL and OpenMP, maxNumCompThreads returns 4 max even if there is more core.

Example

maxNumCompThreads

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

namelengthmax

Return the maximum variable name length.

Syntax

R = namelengthmax

Output argument

R - a double: the maximum variable name length

Description

namelengthmax: Nelson allows 4096 as maximum length for variables and structures field names.

Examples

Working: identifier length 4096 characters

ID = ['A', char(double('0') * ones(1, namelengthmax -1 ))];
length(ID)
STR = [ID, ' = 3'];
execstr(STR)

Not Working: identifier length 4097 characters

ID = ['A', char(double('0') * ones(1, namelengthmax))];
length(ID)
STR = [ID, ' = 3'];
execstr(STR)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

nargin

Returns the number of input arguments.

Syntax

R = nargin()
R = nargin(function_name)
R = nargin(function_handle)

Input argument

function_name - a string: function name
function_handle - a function handle

Output argument

R - an integer value: number of input argument

Description

nargin returns the number of input arguments of an function.

If the last input argument of the function is varargin the returned value is negative.

Examples

With an macro function:

nargin('getfield')

With an builtin function:

nargin('cos')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

narginchk

Checks the number of input arguments.

Syntax

narginchk(minArgs, maxArgs)

Input argument

minArgs - minimum number of accepted inputs (scalar integer value).
maxArgs - maximum number of accepted inputs (scalar integer value).

Description

narginchk checks the number of input arguments of an function.

To ensure that a minimum number of arguments is provided, while allowing an unlimited maximum number by setting maxArgs to inf. For instance, use narginchk(2, inf) to throw an error if fewer than two inputs are supplied.

Example

With an macro function:

narginchk(1, 2)

History

Version	Description
1.0.0	initial version
1.10.0	narginchk(3, Inf) managed

Author

Allan CORNET

nargout

Returns the number of output arguments.

Syntax

R = nargout()
R = nargout(function_name)
R = nargout(function_handle)

Input argument

function_name - a string: function name
function_handle - a function handle

Output argument

R - an integer value: number of output argument

Description

nargout returns the number of output arguments of an function.

If the last output argument of the function is varargout the returned value is negative.

Examples

With an macro function:

nargout('cellstr')

With an builtin function:

nargout('cos')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

nargoutchk

Checks the number of output arguments.

Syntax

nargoutchk(minArgs, maxArgs)
msg = nargoutchk(minArgs, maxArgs, numArgs)
st = nargoutchk(minArgs, maxArgs, numArgs, 'struct')

Input argument

minArgs - minimum number of accepted outputs (scalar integer value).
maxArgs - maximum number of accepted outputs (scalar integer value).
numArgs - number of function outputs (scalar integer value).

Output argument

msg - a string: error message.
st - a struct with error message and identifier.

Description

nargoutchk checks the number of output arguments of an function.

To ensure a minimum number of outputs while imposing no maximum limit, set maxArgs to inf. For example, nargoutchk(2, inf) generates an error if fewer than two outputs are specified.

Example

With an macro function:

nargoutchk(1, 2, 3)
nargoutchk(1, 2, 3, 'struct')

History

Version	Description
1.0.0	initial version
1.10.0	nargoutchk(3, Inf) managed

Author

Allan CORNET

nelsonroot

Returns Nelson's root folder.

Syntax

nelson_path = nelsonroot

Output argument

nelson_path - a string: the root folder of Nelson.

Description

nelsonroot returns the root folder of Nelson.

Example

pwd
cd(nelsonroot)
pwd

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

nfilename

mfilename

Returns the name of the currently executing file.

Syntax

R = nfilename()
R = nfilename('fullpath')
R = nfilename('fullpathext')

Output argument

R - a string: the path of current function

Description

R = nfilename() returns the name of the currently executing file.

nfilename() called from outside an nlf file returns an empty string.

With the input argument 'fullpathext', the string includes the directory part of the macro filename, and the filename extension.

With the input argument 'fullpath', the string includes the directory part of the macro filename, but not the extension.

mfilename is an alias on nfilename added for basic script compatibility.

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

pause

Pauses script execution.

Syntax

state = pause()
pause(t)
pause(newState)
previousState = pause(newState)
currentState = pause('query')

Input argument

t - t: double value. time (seconds) before to continue.
newState - a string: 'on' (enable pause) or 'off' (disable pause setting)

Output argument

previousState, currentState - a string: 'on' or 'off'

Description

pause(t) suspends execution for t seconds.

pause without input argument wait until return key is pressed.

Example

an example

state = pause
echo('press return to continue.')
pause
pause('off')
pause
pause('on')
pause(5)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

prefdir

Return the preferences directory used by Nelson.

Syntax

pref_path = prefdir

Output argument

pref_path - a string: the preferences directory

Description

pref_path = prefdir() returns the preferences directory used by Nelson.

Example

an example

cd(prefdir)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

quit

Terminate Nelson application

Syntax

quit
quit(status)
quit('force')
quit('cancel')
quit(status, 'force')

Description

quit terminates current Nelson application.

quit('cancel') command is designed specifically for utilization within a finish.m script, preventing the termination process.

Its functionality is restricted to this context.

On the other hand, quit('force') disregards the finish.m script and immediately concludes Nelson.

Employ this syntax when you need to override the finish script, ensuring a smooth exit in case the script poses obstacles to quitting.

When you utilize quit(code), Nelson exits with the specified value as the exit code.

If you append "force" to this command quit(code, 'force') it enforces an immediate termination, bypassing finish.m and incorporating the provided exit code.

The exit code, denoted by "code" and specified as a signed integer, determines the status of Nelson termination.

On Windows® platforms, Nelson furnishes exit codes within the range of INT_MIN to INT_MAX (-2147483647 to 2147483647).

On Linux® and macOS platforms, Nelson confines exit codes to the range of 0 to 255.

This distinction should be considered when interpreting or handling exit codes in Nelson scripts or processes.

Example

Beware this example will close Nelson

quit

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

run

Executes a script file (.m).

Syntax

run(script_file)
run(script_file, 'nocatch')
bsuccess = run(script_file, 'errcatch')

Input argument

script_file - a string: path of a script
'nocatch' - a string: default option (no error catch)
'errcatch' - a string: error catched

Output argument

bsuccess - a logical: true if no error detected during script execution

Description

run(script_file) executes a Nelson's script file (.m file extension).

Examples

Creates two .m in temp directory to use as example:

fd = fopen([tempdir(), 'example_run_ok.m'], 'wt');
fprintf(fd, ['A = 1;', char(10)]);
fprintf(fd, ['B = 2;', char(10)]);
fprintf(fd, ['C = A + B', char(10)]);
fclose(fd);

fd = fopen([tempdir(), 'example_run_not_ok.m'], 'wt');
fprintf(fd, ['AA = 1;', char(10)]);
fprintf(fd, ['CC = AA + BB', char(10)]);
fclose(fd);

run a script without error.

run([tempdir(), 'example_run_ok.m']);

run a script and catch error (no error).

bsuccess = run([tempdir(), 'example_run_ok.m'], 'errcatch')

run a script and catch error (with error).

bsuccess = run([tempdir(), 'example_run_not_ok.m'], 'errcatch')

run a script and no catch error.

run([tempdir(), 'example_run_not_ok.m'], 'nocatch');

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

sha256

Get sha256 checksum.

Syntax

hexa_hash = sha256(str)
hexa_hash = sha256(filename)
hexa_hash = sha256(str, '-file')
hexa_hash = sha256(str, '-string')

Input argument

str - a character vector, cell of string or array of strings: content of string will be hashed.
filename - a string: existing filename: content of the file will be hashed.
'-file' or '-string' - force to hash as file or string content.

Output argument

hexa_hash - a character vector, cell of string or array of strings: hashed result (checksum).

Description

sha256 get sha256 checksum.

Examples

R = sha256('Nelson')

R = sha256({'Hello', 'World'})

R = sha256(["Hello"; "World"])

R = sha256([modulepath('matio', 'tests'), '/mat/test_char_array_unicode_7.4_GLNX86.mat'])

R = sha256([modulepath('matio', 'tests'), '/mat/test_char_array_unicode_7.4_GLNX86.mat'], '-file')

R = sha256([modulepath('matio', 'tests'), '/mat/test_char_array_unicode_7.4_GLNX86.mat'], '-string')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

version

Return the version of Nelson.

Syntax

ver_str = version
ver_date = version('-date')
ver_desc = version('-description')
ver_comp = version('-compiler')
ver_hash = version('-commit_hash')
ver_number = version('-number')
ver_release = version('-release')
[ver_str, ver_release] = version()

Input argument

'-date' - a string to get release date
'-description' - a string to get release description
'-semantic' - a string to get semantic version
'-release' - a string to get release number
'-compiler' - a string to get compiler used to build Nelson
'-number' - a string to get semantic version
'-commit_hash' - a string to get commit hash

Output argument

ver_str - a string : version
ver_date - a string: version date
ver_desc - a string: version description
ver_release - a string: release info
ver_commit - a string: commit hash
ver_compiler - a cell of string: {compiler used, arch}
ver_number - a matrix of integer values: [MAJOR, MINOR, MAINTENANCE, BUILD]

Description

version the version of Nelson.

Examples

ver = version

ver_date = version('-date')

ver_date = version('-description')

ver_date = version('-release')

ver_version_vector] = version('-semantic')

ver_version_vector = version('-number')

compiler_info = version('-compiler')

[ver, release] = version()

History

Version	Description
1.0.0	initial version
1.2.0	`-semantic` option added.

Author

Allan CORNET

Engine

Description

nelson engine functions

argv - Nelson command line arguments.
executable - Executables to start Nelson software.
finish - User-defined termination script for Nelson.
getnelsonmode - Returns current Nelson mode.
isquietmode - Return true if Nelson started with --quiet option.
#! shebang - On Unix, Linux operating systems, Parses the rest of the script's initial line as an interpreter directive.
startup - User-defined startup script for Nelson.

argv

Nelson command line arguments.

Syntax

args = argv()

Output argument

args - a cell array of strings.

Description

argv() returns a cell array of strings containing the arguments of the Nelson command line.

The first element of the cell returned contains the path of the launched executable.

Example

argv()

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

executable

Executables to start Nelson software.

Syntax

nelson arg1 ... argn
nelson-cli arg1 ... argn
nelson-adv-cli arg1 ... argn
nelson-gui arg1 ... argn

Input argument

-cli - equivalent to call 'nelson-cli'.
-adv-cli - equivalent to call 'nelson-adv-cli'.
-gui - equivalent to call 'nelson-gui'.
-e "nelson instructions" - If this option is present then Nelson instruction is executed just after startup file execution into Nelson. -e and -f options are mutually exclusive.
-f filename - Nelson script file is executed just after startup file execution) into Nelson. -e and -f options are mutually exclusive.
-F filename - If this option is present then Nelson script file is executed just after startup file execution) into an existing Nelson's process or creates it.
--help - help about program options.
--version - Return Nelson version.
--vscode - enable Visual Studio Code mode.
--open - opens files arg2 ... argN must be valid/existing filenames.
--mat - load files arg2 ... argN must be valid/existing .nh5 or .mat filenames.
--nostartup - disable the main Nelson script file executed at startup.
--nousermodules - disable the load of user's modules. loaded before user's script.
--nouserstartup - disable the user script file executed at startup after the main startup file.
--minimize - minimize main GUI Windows (GUI mode only).
--noipc - disable interprocess features (files association, ipc builtin).
--withoutfilewatcher - disable file watcher feature for this session.
--noaudio - disable audio module.
--without_python - disable python_engine module.
--language lang - If this option is present it fixes the user language. Currently, lang can be: fr_FR en_US.
--quiet - If this option is present no banner and version displayed.

Description

nelson-cli: basic terminal, no gui (no dependency to gui framework), no history, no completion (iso latin encoding)

nelson-adv-cli: advanced terminal, no graphical console, history, completion available (UTF-16 support)

nelson-gui: graphical console, history, completion available (UTF-16 support)

If you have installed Nelson on Windows, the NELSON_RUNTIME_PATH environment variable will be defined.

It allows to call easily Nelson "%NELSON_RUNTIME_PATH%\nelson.bat".

Examples

nelson-adv-cli -q -e "a = 1 + 2"

nelson-gui -v

nelson-gui --help

History

Version	Description
1.0.0	initial version
1.4.0	--without_python added
1.11.0	About NELSON_RUNTIME_PATH environment variable added
1.11.0	--vsocde argument

Author

Allan CORNET

finish

User-defined termination script for Nelson.

Description

startup.m in Nelson initiates user-specified commands upon Nelson startup.

It executes any file named startup.m that is located on the search path.

To leverage this feature, create a file named startup.m in the userpath folder, which is included in the Nelson search path.

Embed commands within this file that you wish to be executed during Nelson startup.

This could involve setting physical constants, defining defaults for graphics properties, incorporating engineering conversion factors, or predefining any other elements desired in your workspace.

Customizing the startup.m file allows you to establish a tailored environment every time Nelson is launched.

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

getnelsonmode

Returns current Nelson mode.

Syntax

m = getnelsonmode()

Output argument

m - a string.

Description

getnelsonmode() returns current Nelson mode used.

There are 5 modes:

BASIC_ENGINE: Nelson used as engine without any graphics.

ADVANCED_ENGINE: Nelson used as engine with graphics/gui.

BASIC_TERMINAL: Nelson launched as terminal without graphics.

ADVANCED_TERMINAL: Nelson launched as terminal with graphics/gui.

BASIC_SIO_CLIENT: Nelson launched as socket IO client.

ADVANCED_SIO_CLIENT: Nelson launched as socket IO client with graphics/gui.

GUI: Nelson launched as a graphical application (default).

Example

getnelsonmode()

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

isquietmode

Return true if Nelson started with --quiet option.

Syntax

res = isquietmode()

Output argument

res - a logical true or false

Description

isquietmode returns a logical 1 if Nelson started with --quiet option and a logical 0 otherwise.

Example

disp(isquietmode());

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

#! shebang

On Unix, Linux operating systems, Parses the rest of the script's initial line as an interpreter directive.

Description

On Unix, Linux and MacOs X, shebang allows to execute directly a NelSon script.

Example

#!nelson-adv-cli -q -f
argv()
disp('shebang example line 1')
disp('shebang example line 2')
exit()

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

startup

User-defined startup script for Nelson.

Description

startup.m in Nelson initiates user-specified commands upon Nelson startup.

It executes any file named startup.m that is located on the search path.

To leverage this feature, create a file named startup.m in the userpath folder, which is included in the Nelson search path.

Embed commands within this file that you wish to be executed during Nelson startup.

This could involve setting physical constants, defining defaults for graphics properties, incorporating engineering conversion factors, or predefining any other elements desired in your workspace.

Customizing the startup.m file allows you to establish a tailored environment every time Nelson is launched.

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

Interpreter functions

Description

interpreter functions

abort - stop evaluation.
break - exit evaluation loop.
continue - continue evaluation in loop.
for - for loop.
function - function declaration.
if - conditional statement.
iskeyword - Returns all Nelson keywords.
keyboard - Stops script execution and enter in debug mode.
max_recursion_depth - Internal limit on the number of times a function may be called recursively.
numeric types - About integer and floating-point data.
parsefile - Parse a Nelson file.
parsestring - Parse a string.
switch - switch statement.
try - try/catch statement.
while - while loop.

abort

return

stop evaluation.

Syntax

abort
return

Description

return or abort stops current evaluation.

Example

for i=1:10,a = i,abort,end
a

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

break

exit evaluation loop.

Syntax

break

Description

break statement is used to exit a loop prematurely.

break statement can be used inside a for or a while loop.

Example

for i = 1:10
  if i == 5
   disp('i == 5');
   break;
  end
  disp(i)
end

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

continue

continue evaluation in loop.

Syntax

continue

Description

continue statement can be used inside a for or a while loop.

continue statement is used to pass control to the next iteration of a loop.

Example

for i=1:10
  if (i == 5)
    continue;
    disp('never here')
    disp(i)
  else
    disp(i)
  end
end

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

for

parfor

for loop.

Syntax

for variable = expression, statements, end
for variable, statements, end

Description

for loop executes a set of statements with an index variable looping through each element in a vector.

parfor is currently an alias on for keyword.

Examples

for i = 1:10, disp(i), end

for i = [1, 2; 3 4], disp(i), disp('next'), end

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

function

endfunction

function declaration.

Syntax

function [out_1,...,out_M,varargout] = fname(in_1, ... , in_N, varargin)
function fname(in_1, ... , in_N, varargin)
function [out_1,...,out_M,varargout] = fname()
function fname()

Description

function opens a function definition.

endfunction closes a function definition (optional, but strongly recommended).

Example

in a file: demo_function.m

function r = demo_function(a, b)
  r = a + b;
endfunction

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

if

conditional statement.

Syntax

if conditional_expression_1, statements_1, elseif conditional_expression_2, statements_2, else statements_N end

Description

if and else statements form a control structure for conditional execution.

Example

i = 0;
if i == 0
  disp('ok')
elseif i == 1
  disp('not ok 1')
else
  disp('not ok 2')
end

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

iskeyword

Returns all Nelson keywords.

Syntax

state = iskeyword(name)
ce = iskeyword()

Input argument

name - a string.

Output argument

state - a logical: true if is an Nelson keyword.
ce - a cell of strings: list of Nelson's keywords.

Description

iskeyword returns a list of all Nelson keywords.

Example

iskeyword('for')
ce = iskeyword()

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

keyboard

Stops script execution and enter in debug mode.

Syntax

keyboard()

Description

keyboard stops script execution and enter in debug mode. prompt is modified and displays debug level.

Example

keyboard()

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

max_recursion_depth

Internal limit on the number of times a function may be called recursively.

Syntax

current_val = max_recursion_depth()
previous_val = max_recursion_depth(new_val)

Input argument

new_val - a integer value: new value

Output argument

current_val - a integer value.
previous_val - a integer value.

Description

max_recursion_depth specifies the recursion depth max to prevent Nelson from recursing infinitely.

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

numeric types

About integer and floating-point data.

Description

In Nelson you can specify the data type of a numeric literal by using a suffix or a type specifier.

Here are some common suffixes for specifying the data type of numeric literals:

literal number suffix	Nelson type
f32	single (float single precision)
f64	double (float double precision)
i8	int8 (8-bit signed integer)
i16	int16 (16-bit signed integer)
i32	int32 (32-bit signed integer)
i64	int64 (64-bit signed integer)
u8	uint8 (8-bit unsigned integer)
u16	uint16 (16-bit unsigned integer)
u32	uint32 (32-bit unsigned integer)
u64	uint64 (64-bit unsigned integer)

i64: To specify a 64-bit signed integer, you can use the i64 suffix. example: A = 42i64

f32: To specify a 32-bit floating-point number (single precision), you can use the f64 suffix. example: 3.14f32

These suffixes help the Nelson infer the correct data type for the literal.

Nelson automatically infer data type by default as double and you don't need to specify this suffixe explicitly. example: A = 3.14

Unless you have specific requirements or need to disambiguate between data types, you often don't need to explicitly specify the type of numeric literals.

But when you create a numeric array of large integers in Nelson, especially when they exceed the maximum precision representable by double (larger than flintmax), Nelson initially stores these values as double-precision floating-point numbers by default.

Examples

explicit single number

single(3.1415)
3.1415f32

implicit-explicit double number

3.1415
3.1415f64

values exceed maximum precision representable by double

R1 = uint64([72057594035891654 81997179153022975])
R2 = [72057594035891654u64 81997179153022975u64]

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

parsefile

Parse a Nelson file.

Syntax

status = parsefile(filename)

Input argument

filename - a string: a filename to parse.

Output argument

status - a string: 'script', 'function', 'error'.

Description

parsefile parse a file and returns if it is a valid script, a valid function or an error.

Example

parsefile([nelsonroot(), '/etc/startup.m'])
parsefile([nelsonroot(), '/modules/data_structures/functions/cellstr.m'])

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

parsestring

Parse a string.

Syntax

status = parsestring(str)

Input argument

str - a string: a string to parse.

Output argument

status - a string: 'script', 'function', 'error'.

Description

parsestring parse a string and returns if it is a valid script, a valid function or an error.

Example

parsestring('1 + 1')
parsestring('1 +++ 1')
parsestring('1 +*+ 1')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

switch

switch statement.

Syntax

switch(expression), case test_expression_1, statements, case test_expression_2, statements, otherwise statements, end

Description

switch statement is used to selective execute code based on the value of either scalar value or a string.

otherwise clause is optional.

Examples

demo_switch.m

function c = demo_switch(a)
 switch(a)
    case {'hello', 'world'}
      c = 'message';
    case {'red', 'green', 'blue'}
      c = 'color';
    otherwise
      c = 'not sure';
  end
end

demo_switch('hello')
demo_switch('red')
demo_switch('?')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

try

catch

try/catch statement.

Syntax

try, statements_1, catch, statements_2, end
try, statements_1, catch exception, statements_2, end

Description

try and catch statements are used for error handling and control in files.

exception is an MException object that allows you to identify the error.

The catch block assigns the current exception object to the variable in exception.

Examples

try/catch in a script file

try
error('an error')
catch
  disp('error catched')
end

try/catch in a script file

try
error('an error')
catch ME
  ME
end

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

while

while loop.

Syntax

while test_expression, statements, end

Description

while loop executes a set of statements as long as a the test condition remains true.

Example

i = 0;
while lt(i, 10)
  disp(i)
  i = i + 1;
end

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

Display format

Description

output display format functions

disp - Display a variable.
display - Show information about variable or result of expression.
echo - Controls the echoing during their execution.
format - Display format and number printing.
formattedDisplayText - Capture display output as string.

disp

Display a variable.

Syntax

disp(V)

Input argument

V - a variable

Description

disp(V) displays the value of the variable V.

disp uses current format setting to display numeric values.

Examples

disp('Hello Nelson')

disp(pi)

disp(eye(3, 3))

disp always ends with a newline.

disp('')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

display

Show information about variable or result of expression.

Syntax

display(V)
display(V, name)

Input argument

V - Result of executing a statement or expression
name - a character vector: variable name displayed.

Description

display(V) displays information about the variable V.

Nelson calls display function whenever an object is referred to in a statement that is not terminated by a semicolon.

Examples

display(33, 'Hello')

display('Hello Nelson')

display(pi)

A = eye(3, 3); disp(A)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

echo

Controls the echoing during their execution.

Syntax

state = echo()
echo()
echo('on')
echo('off')

Input argument

'on' - enable echo mode (default)
'off' - disable echo mode

Output argument

state - a string: 'on' or 'off'

Description

echo('off') disable echo mode.

Without input and output arguments, echo toggles the current echo state.

Example

an example

R = echo
echo('on')
A = 1+1
echo('off')
A = A+1
echo(R)
A

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

format

Display format and number printing.

Syntax

fmt = format()
format()
format('default')
format(new_style)

Input argument

new_style - a string

Output argument

fmt - DisplayFormatOptions object: format used

Description

format(new_style) changes the display format and number printing of the current session.

format('default') will reset to default format (short, loose).

Styles supported:

short

long

shortE

longE

shortEng

longEng

plus

rational

hex

Line Spacing Format supported:

loose

compact

Example

an example

current_style = format()
pi
format('short')
pi
format('long')
pi
format('shortE')
pi
format('longE')
pi
format('hex')
pi
format('+')
pi
format('rational')
pi
format('compact')
pi
format(current_style)
pi

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

formattedDisplayText

Capture display output as string.

Syntax

str = formattedDisplayText(V)
str = formattedDisplayText(V, Name, Value)

Input argument

V - Variable to return as string
Name, Value - Name-Value Pair Arguments, Name: 'NumericFormat' or 'LineSpacing'.

Output argument

str - a string

Description

str = formattedDisplayText(V) returns the display output of V as a string.

The string contains equivalent to disp(V).

Example

R = eye(3, 3)
str = formattedDisplayText(R)
R = rand(3, 3);
disp(R)
str = formattedDisplayText(R)
str = formattedDisplayText(R, 'NumericFormat', 'bank', 'LineSpacing', 'compact')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

Localization functions

Description

localization functions

getavailablelanguages - Returns available languages in Nelson.
getdefaultlanguage - Returns the default language used in Nelson.
getlanguage - Returns the current language in Nelson.
setlanguage - Changes the language used in Nelson.

getavailablelanguages

Returns available languages in Nelson.

Syntax

ce = getavailablelanguages()

Output argument

ce - a cell of strings: supported languages.

Description

getavailablelanguages returns the list of currently supported languages in Nelson.

Example

getavailablelanguages()

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

getdefaultlanguage

Returns the default language used in Nelson.

Syntax

lang = getdefaultlanguage()

Output argument

lang - a string: 'en_US' by default.

Description

getdefaultlanguage returns the default language used by Nelson.

Example

getdefaultlanguage()

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

getlanguage

Returns the current language in Nelson.

Syntax

lang = getlanguage()

Output argument

lang - a string: current language used in Nelson.

Description

getlanguage returns the current language used in Nelson.

Example

l = getlanguage()

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

setlanguage

Changes the language used in Nelson.

Syntax

setlanguage(language)

Input argument

language - a string: 'en_US', 'fr_FR' or others by default.

Description

setlanguage changes the language used by Nelson and saves this changes for subsequent runs of Nelson.

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

I18n functions

Description

internalization functions

gettext - Get text translated into the current locale.
i18nHelpers - Internationalization (i18n) utility functions
poheader - Generates po file header.

gettext

_

Get text translated into the current locale.

Syntax

translated_string = gettext(your_string)
translated*string = *(your_string))

Input argument

your_string - a string: message to be translated.

Output argument

translated_string - a string: message translated.

Description

translated_string = gettext(your_string) gets the translation of a string your_string to the current locale in the Nelson domain.

_(your_string) is an alias of gettext(your_string).

Example

disp(_('function not found.'))

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

i18nHelpers

Internationalization (i18n) utility functions

Syntax

i18nHelpers('convert', potFile, jsonFile)
i18nHelpers('merge', jsonFile1, jsonFile2)
i18nHelpers('sort', jsonFileA, jsonFileB)

Input argument

potFile - String: Path to the source .po/.pot translation template file
jsonFile - String: Path to JSON translation file destination
jsonFile1 - String: Path to the source JSON translation file
jsonFile2 - String: Path to the destination JSON translation file
jsonFileA - String: Path to the source JSON file to sort
jsonFileB - String: Path to the sorted JSON file

Description

i18nHelpers provides essential utility functions for managing internationalization files. The main functions include:

- 'convert': Converts a .po/.pot translation template file into JSON format for easier manipulation.

- 'merge': Merges two JSON translation files. The entries from jsonFile1 are added to jsonFile2, and entries exclusive to jsonFile2 are removed.

- 'sort': Sorts and organizes entries in a JSON translation file. jsonFileA and jsonFileB may refer to the same file if in-place sorting is desired.

This utility is intended for internal use and may be updated over time.

History

Version	Description
1.10.0	Initial version

Author

Allan CORNET

poheader

Generates po file header.

Syntax

ce = poheader(domain, language)

Input argument

domain - a string: domain message.
language - a string: language, examples 'en_US' or 'fr_FR'.

Output argument

ce - a cell of string: po file header.

Description

ce = poheader(domain, language) generates po file header.

Example

poheader('nelson', 'en_US')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

Characters encoding

Description

characters encoding functions

native2unicode - Converts bytes representation to unicode characters
nativecharset - Find all charset matches that appear to be consistent with the input
unicode2native - Converts unicode characters representation to bytes

native2unicode

Converts bytes representation to unicode characters

Syntax

str = native2unicode(bytes, charset)

Input argument

bytes - a uint8 vector
charset - an scalar string or vector characters array.

Output argument

str - an vector characters array.

Description

native2unicode converts an uint8 vector to unicode characters.

str = native2unicode(bytes) converts an uint8 vector to unicode characters (using the native character set of the machine).

str = native2unicode(bytes, charset) converts an uint8 vector to unicode characters (character set charset instead of the native character set).

List of characters set: http://www.iana.org/assignments/character-sets/character-sets.xhtml

Bibliography

ICU library

Example

native2unicode(uint8([149   208   137   188   150   188]), 'SHIFT_JIS')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

nativecharset

Find all charset matches that appear to be consistent with the input

Syntax

ce = nativecharset(bytes)

Input argument

bytes - a uint8 vector, or string or row characters array

Output argument

ce - a cell of strings.

Description

nativecharset find all charset matches that appear to be consistent with the input, returning a cell of string with results.

The results are ordered with the best quality match first.

List of characters set: http://www.iana.org/assignments/character-sets/character-sets.xhtml

Bibliography

ICU library

Example

C = uint8([194   232   240   242   243   224   235   252   237   224   255]);
nativecharset(R)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

unicode2native

Converts unicode characters representation to bytes

Syntax

bytes = unicode2native(str, charset)

Input argument

str - an scalar string or vector characters array.
charset - an scalar string or vector characters array.

Output argument

bytes - a uint8 vector

Description

unicode2native converts unicode characters to an numeric array.

bytes = unicode2native(str) converts unicode characters to an numeric array (the native character set of the machine).

bytes = unicode2native(str, charset) converts unicode characters to an numeric array (character set charset instead of the native character set).

List of characters set: http://www.iana.org/assignments/character-sets/character-sets.xhtml

Bibliography

ICU library

Example

R = unicode2native('片仮名', 'SHIFT_JIS')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

Types module

Description

module about types management.

class - Return classname of object or creates a named object.
isa - Return true if var is an object from the class str.
iscell - Return true if variable var is a cell array.
ischar - Return true if variable var is a char array.
isclass - Return true if variable var is a class object.
isdouble - Return true if variable var is a double matrix.
isempty - Return true if variable var is an empty matrix.
isfloat - Return true if variable var is a single or double matrix.
ishandle - Return true if variable var is a handle object.
isint16 - Return true if variable var is a signed 16-bit integer type array.
isint32 - Return true if variable var is a signed 32-bit integer type array.
isint64 - Return true if variable var is a signed 64-bit integer type array.
isint8 - Return true if variable var is a signed 8-bit integer type array.
isinteger - Return true if variable var is a integer type array.
islogical - Return true if variable var is a logical.
isnumeric - Return true if variable var is a numeric array.
isobject - Return true if variable var is an object.
isreal - Return true if all imaginary part is a zero array.
issingle - Return true if variable var is a single matrix.
issparse - Return true if variable var is a sparse array.
isstring - Return true if variable var is a string array.
isstruct - Return true if variable var is a structure.
isuint16 - Return true if variable var is an unsigned 16-bit integer type array.
isuint32 - Return true if variable var is an unsigned 32-bit integer type array.
isuint64 - Return true if variable var is an unsigned 64-bit integer type array.
isuint8 - Return true if variable var is an unsigned 8-bit integer type array.
isvarname - Return true if input is valid variable name.

class

Return classname of object or creates a named object.

Syntax

name = class(var)
obj = class(st, strname)

Input argument

var - a variable
st - a struct
strname - a string: classname desired

Output argument

name - a string
obj - an object of type 'strname' based on struct 'st'

Description

name = class(var) returns the class of var variable.

Standard classes are:

'cell'

'struct'

'single'

'double'

'logical'

'char'

'int8'

'int16'

'int32'

'int64'

'uint8'

'uint16'

'uint32'

'uint64'

'function_handle'

Examples

A = 3;
res = class(A)

C = [1 ; 3];
res = class(C)

addpath([nelsonroot(), '/modules/overload/examples/complex']);
c = complexObj(3,4);
class(c)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

isa

Return true if var is an object from the class str.

Syntax

res = isa(var, str)

Input argument

var - a variable
str - a string: classname expected

Output argument

res - a logical: true or false

Description

isa returns a logical 1 if the argument is a cell array and a logical 0 otherwise.

str can also be 'numeric', 'float', or 'integer':

numeric: floating point or integer array: double, single, int8, uint8, int16, uint16, int32, uint32, int64, uint64

float: single or double precision floating-point array: double, single

integer: unsigned or signed integer array: int8, uint8, int16, uint16, int32, uint32, int64, uint64

If var is a handle object, str can be 'handle' or type name of the handle.

Examples

A = 3;
res = isa(A, 'double')

B = {'NelSon', 3, true};
res = isa(B, 'cell')

B = {'NelSon', 3, true};
res = isa(B, 'cell')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

iscell

Return true if variable var is a cell array.

Syntax

res = iscell(var)

Input argument

var - a variable

Output argument

res - a logical: true or false

Description

iscell returns a logical 1 if the argument is a cell array and a logical 0 otherwise.

Examples

A = 3;
res = iscell(A)

B = {'NelSon', 3, true};
res = iscell(B)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

ischar

Return true if variable var is a char array.

Syntax

res = ischar(var)

Input argument

var - a variable

Output argument

res - a logical: true or false

Description

ischar returns a logical 1 if the argument is a char array and a logical 0 otherwise.

Examples

A = 3;
res = ischar(A)

B = 'NelSon';
res = ischar(B)

C = [1 ; 3];
res = ischar(C)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

isclass

Return true if variable var is a class object.

Syntax

res = isclass(var)

Input argument

var - a variable

Output argument

res - a logical: true or false

Description

isclass returns a logical 1 if the argument is a class object and a logical 0 otherwise.

Example

A = 3;
res = isclass(A)
addpath([nelsonroot(), '/modules/overload/examples/complex']);
c = complexObj(3,4);
res = isclass(c)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

isdouble

Return true if variable var is a double matrix.

Syntax

res = isdouble(var)

Input argument

var - a variable

Output argument

res - a logical: true or false

Description

isdouble returns a logical 1 if the argument is a double matrix and a logical 0 otherwise.

Examples

A = 3;
res = isdouble(A)

A = single(3);
res = isdouble(A)

A = single([3, i]);
res = isdouble(A)

A = [3, i];
res = isdouble(A)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

isempty

Return true if variable var is an empty matrix.

Syntax

res = isempty(var)

Input argument

var - a variable

Output argument

res - a logical: true or false

Description

isempty returns a logical true if the argument is an empty matrix.

Any one of its dimensions is zero.

Examples

A = rand(3, 3, 3);
res = isempty(A)
A(:, :, :) = [];
res = isempty(A)

B = {};
res = isempty(B)
C = struct()
res = isempty(C)
C = struct([])
res = isempty(C)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

isfloat

Return true if variable var is a single or double matrix.

Syntax

res = isfloat(var)

Input argument

var - a variable

Output argument

res - a logical: true or false

Description

isfloat returns a logical 1 if the argument is a single or double matrix and a logical 0 otherwise.

Examples

A = 3;
res = isfloat(A)

A = single(3);
res = isfloat(A)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

ishandle

Return true if variable var is a handle object.

Syntax

res = ishandle(var)

Input argument

var - a variable

Output argument

res - a logical: true or false

Description

ishandle returns a logical 1 if the argument is a handle object and a logical 0 otherwise.

Example

A = 3;
res = ishandle(A)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

isint16

Return true if variable var is a signed 16-bit integer type array.

Syntax

res = isint16(var)

Input argument

var - a variable

Output argument

res - a logical: true or false

Description

isint16 returns a logical 1if the argument is a signed 16-bit integer array and a logical 0 otherwise.

Examples

A = 3;
res = isint16(A)

B = int16(3);
res = isint16(B)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

isint32

Return true if variable var is a signed 32-bit integer type array.

Syntax

res = isint32(var)

Input argument

var - a variable

Output argument

res - a logical: true or false

Description

isint32 returns a logical 1if the argument is a signed 32-bit integer array and a logical 0 otherwise.

Examples

A = 3;
res = isint32(A)

B = int32(3);
res = isint32(B)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

isint64

Return true if variable var is a signed 64-bit integer type array.

Syntax

res = isint64(var)

Input argument

var - a variable

Output argument

res - a logical: true or false

Description

isint64 returns a logical 1if the argument is a signed 64-bit integer array and a logical 0 otherwise.

Examples

A = 3;
res = isint64(A)

B = int64(3);
res = isint64(B)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

isint8

Return true if variable var is a signed 8-bit integer type array.

Syntax

res = isint8(var)

Input argument

var - a variable

Output argument

res - a logical: true or false

Description

isint8 returns a logical 1if the argument is a signed 8-bit integer array and a logical 0 otherwise.

Examples

A = 3;
res = isint8(A)

B = int8(3);
res = isint8(B)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

isinteger

Return true if variable var is a integer type array.

Syntax

res = isinteger(var)

Input argument

var - a variable

Output argument

res - a logical: true or false

Description

isinteger returns a logical 1 if the argument is a integer type (int8, int16 ...) array and a logical 0 otherwise.

Examples

A = 3;
res = isinteger(A)

B = uint8(3);
res = isinteger(B)

A = single([3, i]);
res = isinteger(A)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

islogical

Return true if variable var is a logical.

Syntax

res = islogical(var)

Input argument

var - a variable

Output argument

res - a logical: true or false

Description

islogical returns a logical 1 if the argument is a logical array and a logical 0 otherwise.

Examples

A = 1;
res = islogical(A)

B = logical(1);
res = islogical(B)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

isnumeric

Return true if variable var is a numeric array.

Syntax

res = isnumeric(var)

Input argument

var - a variable

Output argument

res - a logical: true or false

Description

isnumeric returns a logical 1 if the argument is a numeric array and a logical 0 otherwise.

List of numeric types:

single : single precision

double : double precision

int8 : 8 bit signed integer

int16 : 16 bit signed integer

int32 : 32 bit signed integer

int64 : 64 bit signed integer

uint8 : 8 bit unsigned integer

uint16 : 16 bit unsigned integer

uint32 : 32 bit unsigned integer

uint64 : 64 bit unsigned integer

Examples

A = 1;
res = isnumeric(A)

B = single(1+i);
res = isnumeric(B)

C = logical(1);
res = isnumeric(C)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

isobject

Return true if variable var is an object.

Syntax

res = isobject(var)

Input argument

var - a variable

Output argument

res - a logical: true or false

Description

ishandle returns a logical 1 if the argument is an object and a logical 0 otherwise.

Example

A = 3;
res = isobject(A)

addpath([modulepath('overload', 'root'), '/examples/complex']);
A = complexObj(1, 2);
res = isobject(A)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

isreal

Return true if all imaginary part is a zero array.

Syntax

res = isreal(var)

Input argument

var - a variable

Output argument

res - a logical: true or false

Description

isreal returns a logical true if var is a non-complex matrix or scalar and a logical false otherwise.

Examples

A = 1 + 0i;
res = isreal(A)

B = uint8(3);
res = isreal(B)

A = single([3, i]);
res = isreal(A)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

issingle

Return true if variable var is a single matrix.

Syntax

res = issingle(var)

Input argument

var - a variable

Output argument

res - a logical: true or false

Description

issingle returns a logical 1 if the argument is a single matrix and a logical 0 otherwise.

Examples

A = 3.6;
res = issingle(A)

B = single([1 ; 3]);
res = issingle(B)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

issparse

Return true if variable var is a sparse array.

Syntax

res = issparse(var)

Input argument

var - a variable

Output argument

res - a logical: true or false

Description

issparse returns a logical 1 if the argument is a sparse array and a logical 0 otherwise.

Examples

A = 1;
res = issparse(A)

B = sparse(1);
res = issparse(B)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

isstring

Return true if variable var is a string array.

Syntax

res = isstring(var)

Input argument

var - a variable

Output argument

res - a logical: true or false

Description

isstring returns a logical 1 if the argument is a string array and a logical 0 otherwise.

Examples

A = 3;
res = isstring(A)

B = "NelSon";
res = isstring(B)

C = [1 ; 3];
res = isstring(C)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

isstruct

Return true if variable var is a structure.

Syntax

res = isstruct(var)

Input argument

var - a variable

Output argument

res - a logical: true or false

Description

isstruct returns a logical 1 if the argument is a struct (structure) and a logical 0 otherwise.

Examples

A = 1;
res = isstruct(A)

B = struct();
res = isstruct(B)

C.a = 1;
C.B = 'hello';
res = isstruct(C)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

isuint16

Return true if variable var is an unsigned 16-bit integer type array.

Syntax

res = isuint16(var)

Input argument

var - a variable

Output argument

res - a logical: true or false

Description

isuint16 returns a logical 1if the argument is an unsigned 16-bit integer array and a logical 0 otherwise.

Examples

A = 3;
res = isuint16(A)

B = uint16(3);
res = isuint16(B)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

isuint32

Return true if variable var is an unsigned 32-bit integer type array.

Syntax

res = isuint32(var)

Input argument

var - a variable

Output argument

res - a logical: true or false

Description

isuint32 returns a logical 1if the argument is an unsigned 32-bit integer array and a logical 0 otherwise.

Examples

A = 3;
res = isuint32(A)

B = uint32(3);
res = isuint32(B)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

isuint64

Return true if variable var is an unsigned 64-bit integer type array.

Syntax

res = isuint64(var)

Input argument

var - a variable

Output argument

res - a logical: true or false

Description

isuint64 returns a logical 1if the argument is an unsigned 64-bit integer array and a logical 0 otherwise.

Examples

A = 3;
res = isuint64(A)

B = uint64(3);
res = isuint64(B)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

isuint8

Return true if variable var is an unsigned 8-bit integer type array.

Syntax

res = isuint8(var)

Input argument

var - a variable

Output argument

res - a logical: true or false

Description

isuint8 returns a logical 1if the argument is an unsigned 8-bit integer array and a logical 0 otherwise.

Examples

A = 3;
res = isuint8(A)

B = uint8(3);
res = isuint8(B)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

isvarname

Return true if input is valid variable name.

Syntax

res = isvarname(var)

Input argument

var - a variable

Output argument

res - a logical: true or false

Description

isvarname returns a logical 1 if the argument is a valid variable name and a logical 0 otherwise.

Example

isvarname(4)
isvarname('t')
isvarname('8t')
isvarname('t8t')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

Overloading

Description

Overloading capabilities on functions and operators.

overloading - Customizing Operators and Functions

overloading

Customizing Operators and Functions

Description

In various scenarios, you may find it necessary to modify the behavior of Nelson's operators and functions when they operate on objects or basic types.

This customization can be achieved by overloading the relevant functions, allowing them to handle diverse types and quantities of input arguments and execute the appropriate operation for the highest-priority object.

Overloading Operators:

Each built-in operator corresponds to a specific function name (e.g., the - operator is associated with the minus.m function).

You can overload any operator by creating an M-file with the appropriate name within the class directory.

For instance, if either A or B is an object of type classname, the expression A - B triggers a call to a function @classname/minus.m, provided it exists.

When A and B belong to different classes, Nelson employs precedence rules to determine which method to apply.

The table below provides a list of function names associated with most of the Nelson operators:

Description	Operator	Function
Binary addition	a + b	plus(a, b)
Binary subtraction	a - b	minus(a, b)
Unary minus	-a	uminus(a)
Unary plus	+a	uplus(a)
Element-wise multiplication	a .* b	times(a, b)
Matrix multiplication	a * b	mtimes(a, b)
Right element-wise division	a ./ b	rdivide(a, b)
Left element-wise division	a .\ b	ldivide(a, b)
Matrix right division	a / b	mrdivide(a, b)
Matrix left division	a \ b	mldivide(a, b)
Element-wise power	a .^ b	power(a, b)
Matrix power	a ^ b	mpower(a, b)
Less than	a < b	lt(a, b)
Greater than	a > b	gt(a, b)
Less than or equal to	a <= b	le(a, b)
Greater than or equal to	a >= b	ge(a, b)
Not equal to	a ~= b	ne(a, b)
Equality	a == b	eq(a, b)
Logical AND	a & b	and(a, b)
Logical OR	a \| b	or(a, b)
Logical NOT	~a	not(a)
Colon operator	a:d:b	colon(a, d, b)
Complex conjugate transpose	a'	ctranspose(a)
Matrix transpose	a.'	transpose(a)
Display method	command window output	display(a)
Horizontal concatenation	[a, b]	horzcat(a, b, ...)
Vertical concatenation	[a; b]	vertcat(a, b, ...)
Subscripted reference	a(s1, s2, ... , sn)	subsref(a, s)
Subscripted assignment	a(s1, ... , sn) = b	subsasgn(a, s, b)
Subscript index	b(a)	subsindex(a)

Example

Overload minus operator with double

% save in @double directory, as minus.m
function r = minus(A, B)
  disp('minus was called')
  % to call minus builtin
  r = builtin('minus', A, B)
end

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

Logical type functions

Description

logical type functions

false - Logical false.
logical - Converts a numeric value to logical type.
true - Logical true.
xor - Exclusive or.

false

Logical false.

Syntax

false
l = false(n)
l = false(sz)
l = false(n, m, ..., k)
l = false(n, m, 'like', sp)

Input argument

n - a integer value.
sz - a size vector.
n, m, ..., k - a n -by- m - ... -by- k array to indicate size.
sp - a sparse or array.

Output argument

l - a logical value: false.

Description

false build a matrix of false.

Example

false
false(4)
false(4, 1, 4)
L = logical(sparse(1, 2))
L2 = false(3,'like', L);

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

logical

Converts a numeric value to logical type.

Syntax

Y = logical(X)

Input argument

X - a numeric value.

Output argument

Y - a logical value.

Description

logical converts a numeric value to logical type.

Nonzero value converted to true and zeros values converted to false.

Complex numbers returns an error.

Example

A = eye(2, 2)
B = logical(A)
islogical(B)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

true

Logical true.

Syntax

true
l = true(n)
l = true(sz)
l = true(n, m, ..., k)
l = true(n, m, 'like', sp)

Input argument

n - a integer value.
sz - a size vector.
n, m, ..., k - a n -by- m - ... -by- k array to indicate size.
sp - a sparse or array.

Output argument

l - a logical value: true.

Description

true build a matrix of true.

Example

true
true(4)
true(4, 1, 4)
L = logical(sparse(1, 2))
L2 = true(3,'like', L);

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

xor

Exclusive or.

Syntax

R = xor(V1, V2)
R = xor(V1, V2, ... , VN)

Input argument

V1 - a matrix.
V2 - a matrix, same dimensions than V1.
VN - a matrix, same dimensions than V1.

Output argument

R - a logical matrix.

Description

xor performs a logical exclusive-OR.

Example

x = [0 1 0 1];
y = [0 0 1 1];
R = xor(x, y)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

Single type

Description

single type functions

single - Converts a variable to single precision type.

single

Converts a variable to single precision type.

Syntax

S = single(V)

Input argument

V - a variable.

Output argument

S - a single.

Description

single(V) converts to the single-precision type.

Examples

single('Nelson')

A = single(pi)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

Double

Description

double type functions

double - Converts a variable to double precision type.
flintmax - Largest consecutive integer in floating-point format.
realmax - Largest positive floating-point number.
realmin - Smallest positive floating-point number.

double

Converts a variable to double precision type.

Syntax

D = double(V)

Input argument

V - a variable.

Output argument

D - a double.

Description

double(V) converts to the double-precision type.

Examples

double('Nelson')

A = single(pi)
B = double(A)
B - A

A = ["3.134", "NaN"; "Inf", "-5"];
B = double(A)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

flintmax

Largest consecutive integer in floating-point format.

Syntax

R = flintmax()
R = flintmax('double')
R = flintmax('single')
R = flintmax('like', V)

Input argument

V - a double or single variable.

Output argument

R - a double or single.

Description

flintmax returns largest consecutive integer in floating-point format.

Example

flintmax
flintmax('double')
flintmax('like', pi)
flintmax('single')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

realmax

Largest positive floating-point number.

Syntax

R = realmax()
R = realtmax('double')
R = realmax('single')

Output argument

R - a double or single.

Description

realmax returns largest positive floating-point number.

Example

realmax
realmax('double')
realmax('single')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

realmin

Smallest positive floating-point number.

Syntax

R = realmin()
R = realmin('double')
R = realmin('single')

Output argument

R - a double or single.

Description

realmin returns smallest positive floating-point number.

Example

realmin
realmin('double')
realmin('single')

History

Version	Description
1.10.0	initial version

Author

Allan CORNET

Data structures

Description

data structures functions

cell - Create cell array of empty matrices.
cell2mat - Transform a cell array containing matrices into a single, concatenated matrix.
cell2struct - Creates a struct from a cell.
celldisp - Display cell array contents.
cellfun - Evaluates an function on a cell.
cellstr - Converts to cell of character array.
fieldnames - Returns field names of a structure or an handle.
getfield - Returns value of a field in a struct.
iscellstr - Returns if a variable is a cell of strings.
isfield - Checks if a fieldname exists in a struct.
namedargs2cell - Converts a struct containing name-value pairs to a cell.
num2cell - Convert array to cell array with consistently sized cells.
orderfields - Reorganize the fields of a structured array.
rmfield - Remove fields from structure.
setfield - Set structure field contents.
struct - Creates a struct.
struct2cell - Creates a cell from a structure.

cell

Create cell array of empty matrices.

Syntax

C = cell()
C = cell(m)
C = cell(m, n)
C = cell(m, n, ... , p)
C = cell(sz)
C = cell(A)

Input argument

m, n, ... , p - dimensions of the cell to create.
sz - a vector of integer values (dimensions of the cell to create).
A - a string array.

Output argument

C - a cell

Description

cell returns a cell array of empty matrices.

cell() is equivalent to cell(0)

cell(A) with A a string array converts to cell.

Examples

A = eye(2, 4);
sz = size(A)
C = cell(sz)

A = ["Nel", "son"; "open", "source"];
C = cell(A)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

cell2mat

Transform a cell array containing matrices into a single, concatenated matrix.

Syntax

M = cell2smat(ce)

Input argument

ce - a cell.

Output argument

M - array.

Description

M = cell2smat(ce) creates a single matrix by merging all elements within the cell array ce into a multi-dimensional array. The elements in c can consist of numeric, logical, or character matrices, cell arrays, or structs, and they must be compatible for concatenation using cat function.

Example

C = {[10], [20 30 40]; [90; 50], [60 76 88; 110 111 112]};
 M = cell2mat(C)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

cell2struct

Creates a struct from a cell.

Syntax

st = cell2struct(ce, fields)
st = cell2struct(ce, fields, dim)

Input argument

ce - a cell.
fields - a cell of strings.
dim - dimension along cell is converted.

Output argument

st - a struct array.

Description

st = cell2struct(ce, fields) creates a struct from a cell.

Example

ce = {85, 50, 68; 'Pierre', 'Anna', 'Roberto'}
fields = {'Height','Name'}
A = cell2struct (ce, fields, 1)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

celldisp

Display cell array contents.

Syntax

celldisp(C)
celldisp(C, name)

Input argument

C - cell array.
name - displayed name of cell array.

Description

celldisp recursively display the contents of a cell array.

Example

C = {2, 22, 'ff', {331, 332}};
celldisp(C)
celldisp(C, 'var_name')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

cellfun

Evaluates an function on a cell.

Syntax

R = cellfun(function_name, ce)
R = cellfun(function_handle, ce)
[R1, ... , Rp] = cellfun(function_handle, ce1, ..., cep)
[R1, ... , Rp] = cellfun(function_handle, ce1, ..., cep, name, value)

Input argument

function_handle - a function handle.
ce1, ... , cep - cells with p inputs required for function_handle.
name, value pair - 'UniformOutput': true or false, 'ErrorHandler': a error function.

Output argument

R1, ... , Rp - Outputs from function

Description

cellfun applies function to each cell elements.

Examples

greetings = {'Hello', 'Guten Tag', 'Sawadee', 'Bonjour', 'Namaste', ''};
R = cellfun('size', greetings, 1)
R1 = cellfun('size', greetings, 2)

C = {1:10, eye(3,4), eye(5,6)};
f = str2func('size');
[nrows_1, ncols_1] = cellfun(f, C,'UniformOutput', false)
[nrows_2, ncols_2] = cellfun(f, C,'UniformOutput', true)

functions to define for next example:

function r = fun1(x, y)
r = x > y;
end

function result = errorfun(S, varargin)
	disp(nargin())
	disp(S)
	disp(class(varargin))
	disp(size(varargin))
	disp(varargin{1})
	disp(varargin{2})
	result = false;
end

R = str2func('fun1');
H =  str2func('errorfun');
A = {rand(3)};
B = {rand(5)};
AgtA = cellfun(R, A, B, 'ErrorHandler', H, 'UniformOutput', true)
AgtB = cellfun(R, A, B, 'ErrorHandler', H, 'UniformOutput', false)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

cellstr

Converts to cell of character array.

Syntax

ce = cellstr(A)

Input argument

A - a string, a string array, cell of character array.

Output argument

ce - a cell of character array

Description

cellstr(A) converts to cell of character array.

Examples

cellstr('Nelson')

cellstr({'Nelson'})

cellstr({})

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

fieldnames

Returns field names of a structure or an handle.

Syntax

names = fieldnames(st)
names = fieldnames(h)
names = fieldnames(h, '-full')

Input argument

st - a structure
h - a handle object

Output argument

names - a cell of strings

Description

names = fieldnames(st) returns a cell of strings with the names of the fields in the input structure.

names = fieldnames(h) returns a cell of strings with the names of the properties in the handle (without hidden).

names = fieldnames(h, '-full') returns a cell of strings with the names of the all properties in the handle.

Example

fieldnames(dir())

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

getfield

Returns value of a field in a struct.

Syntax

value = getfield(st, field)

Input argument

st - a structure.
field - a string.

Output argument

value - the value of a field from a structure.

Description

value = getfield(st, field) returns the value of the field named field from a structure.

Example

example.a = 1
example.b = 'nelson'
example.c = []
getfield(example, 'b')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

iscellstr

Returns if a variable is a cell of strings.

Syntax

true_or_false = iscellstr(A)

Input argument

A - a variable

Output argument

true_or_false - a logical

Description

iscellstr(A) returns true if A is a cell of strings or an empty cell).

Examples

iscellstr('Nelson')

iscellstr({'Nelson'})

iscellstr({})

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

isfield

Checks if a fieldname exists in a struct.

Syntax

res = isfield(S, name)
res = isfield(S, C)

Input argument

S - a struct
name - a string
C - a cell

Output argument

res - a logical

Description

isfield(A) returns true if name is a fieldname of S.

Examples

S.Nelson = 1;
isfield(S, 'Nel')
isfield(S, 'Nelson')

S.nel = 1;
S.son = 2;
isfield(S,{ 1, 'nel'; 2, 'son'})

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

namedargs2cell

Converts a struct containing name-value pairs to a cell.

Syntax

ce = namedargs2cell(st)

Input argument

st - a scalar structure.

Output argument

ce - a cell.

Description

ce = namedargs2cell(st) returns an cell containing name-value pairs.

Example

S = struct();
S.CharacterEncoding = 'auto';
S.Timeout = 5;
S.Username = "";
S.logical = false;
R = namedargs2cell(S)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

num2cell

Convert array to cell array with consistently sized cells.

Syntax

C = num2cell(A)
C = num2cell(A, dim)

Input argument

A - any type of multidimensional array.
dim - positive integer value or positive vector of integers.

Output argument

C - a cell array.

Description

num2cell function converts a numeric array into a cell array, where each element of the numeric array is placed in its own cell in the resulting cell array.

If A is a character array, num2cell will convert each row of the array into a separate cell in the resulting cell array.

Example

A = [1 2; 3 4; 5 6];
C = num2cell(A)
C = num2cell(A, 1)
C = num2cell(A, 2)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

orderfields

Reorganize the fields of a structured array.

Syntax

S = orderfields(S1)
S = orderfields(S1, S2)
S = orderfields(S1, C)
S = orderfields(S1, P)
[S, Pout] = orderfields(...)

Input argument

S1 - structure array: Input structure.
S2 - structure array: Field order by structure.
C - cell array of character vectors or string array: Field order by name
P - numeric vector: Field order by number.

Output argument

S - structure array: Reordered structure.
Pout - numeric vector: Output field order.

Description

S = orderfields(S1) sorts the fields in S1 alphabetically by their names, considering uppercase letters before lowercase ones, and digits and underscores are also accounted for.

S = orderfields(S1,S2) returns a copy of S1 with its fields rearranged to match the order of fields in S2.Both S1 and S2 must share the same field names.

S = orderfields(S1, C) matches the order specified in the input array C. Each field name from S1 must appear once in C.

S = orderfields(S1, P) reorders fields based on the permutation vector P. P contains integers from 1 to n, where n is the number of fields in S1. This syntax is useful for maintaining consistent ordering across multiple structure arrays.

[S, Pout] = orderfields(...) also returns a permutation vector Pout, indicating the changes in field order. Pout consists of integers from 1 to n, reflecting the rearranged field positions. This syntax is compatible with any of the previously mentioned arguments.

orderfields function exclusively arranges the top-level fields and doesn't operate recursively.

Example

s = struct ("d", 4, "b", 2, "a", 1, "c", 3);
tA = orderfields (s)
t = struct ("d", {}, "c", {}, "b", {}, "a", {});
tB = orderfields (s, tA)

History

Version	Description
1.5.0	initial version

Author

Allan CORNET

rmfield

Remove fields from structure.

Syntax

s = rmfield(st, field)

Input argument

st - a structure.
field - a string, cell of strings, or char.

Output argument

s - a structure without field.

Description

s = rmfield(st, field) removes the specified field from structure array.

Example

example.a = 1
example.b = 'nelson'
example.c = []
rmfield(example, 'b')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

setfield

Set structure field contents.

Syntax

stOut = setfield(stIn, fieldname, fieldvalue)
stOut = setfield(stIn, fieldname1, fieldvalue1, ..., fieldnameN, fieldvalueN)

Input argument

stIn - a structure.
fieldname - a string or characters vector.
fieldvalue - a variable value.

Output argument

stOut - a structure: result.

Description

Set the contents of the specified field to the value.

Alternative syntax: S.(fieldname) = fieldvalue

Alternative syntax: S(idx1, idx2).(fieldname) = fieldvalue

Example

A = {};
setfield(A, 'vv', 3)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

struct

Creates a struct.

Syntax

st = struct()
st = struct([])
st = struct(object)
st = struct(field, value)
st = struct(field, value, field2, value2, ..., fieldn, valuen)

Input argument

field, field2, ... , fieldn - strings : field names, valid names are same than variable identifiers.
value, value2, ..., valuen - all data types supported by Nelson.
object - an object created with 'class' builtin.

Output argument

st - a struct

Description

struct returns a structure.

Examples

struct()

struct([])

date_st = struct('day', 15, 'month' ,'August','year', 1974)

Other way to create a struct:

date_st.day = 15
date_st.month = 'August'
date_st.year = 1974)

History

Version	Description
1.0.0	initial version
1.3.0	Scalar String allowed as field name.

Author

Allan CORNET

struct2cell

Creates a cell from a structure.

Syntax

ce = struct2cell(st)

Input argument

st - a structure.

Output argument

ce - a cell.

Description

ce = struct2cell(st) returns a new cell from the structure.

Example

names = {'Pierre', 'Anna', 'Roberto'}
values =  {45, 42, 13}
st = struct ('name', names, 'age', values);
ce = struct2cell(st)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

Dictionaries

Description

Map data with keys that index values.

configureDictionary - Generate a dictionary with defined key and value types.
dictionary - Object that maps unique keys to values.
entries - Key-value pairs of dictionary.
insert - Add entries to a dictionary.
isConfigured - Check if dictionary has types assigned to keys and values.
isKey - Check if dictionary contains key
keyHash - Create a hash code for a dictionary key.
keyMatch - Check whether two dictionary keys are same.
keys - Keys of dictionary.
lookup - Find value in dictionary by key.
numEntries - Number of key-value pairs in dictionary.
remove - Remove dictionary entries.
types - Types of dictionary keys and values.
values - Values of dictionary.

configureDictionary

Generate a dictionary with defined key and value types.

Syntax

d = configureDictionary(keyType, valueType)

Input argument

keyType - Key data type: string scalar or character vector.
valueType - Value data type: string scalar or character vector.

Output argument

d - scalar: a dictionary object.

Description

d = configureDictionary(keyType, valueType) initializes an empty dictionary that enforces keys of type keyType and values of type valueType.

Example

d1 = configureDictionary("string", "single")
d2 = configureDictionary("cell", "struct")

History

Version	Description
1.5.0	initial version

Author

Allan CORNET

dictionary

Object that maps unique keys to values.

Syntax

d = dictionary()
d = dictionary(d1)
d = dictionary(keys, values)
d = dictionary(key1, value1, ... , keyN, valueN)

Input argument

d1 - a dictionary or py.dict object.
keys - scalar or array
values - scalar, array or cell array
key1, value1, ... , keyN, valueN - Key-value pairs

Output argument

d - scalar: a dictionary object.

Description

d = dictionary(): This command initializes an empty dictionary with no keys or values.

Initially, the dictionary has no specific data types assigned to its keys or values. Once entries are added, the data types for keys and values are determined based on these entries.

d = dictionary(keys, values): This creates a dictionary using the provided keys and values.

The resulting dictionary is a 1-by-1 scalar object. If a key appears multiple times, only the last corresponding value is kept. If the values parameter is a scalar, each key is assigned this value. When keys and values are arrays, they must have matching sizes, resulting in key-value pairs accordingly.

Dictionaries are typed according to their entries. All keys must share the same data type, and all values must share a different, consistent data type. If a new entry has parts that don't match the existing data types, Nelson will attempt to convert them. Keys and values can have different data types, and character row vectors are converted to string scalars.

d = dictionary(key1, value1, ... , keyN, valueN): This syntax creates a dictionary with the specified key-value pairs.

If a key is repeated, only the last key-value pair for that key is kept.

Removing an Entry from a Dictionary:

d(keys) = []: This command removes the entry associated with the specified key from the dictionary.

Assigning Values to Entries:

d(keys) = newValues: This command assigns the elements of newValues to the entries specified by the corresponding keys.

If a specified key does not exist in the dictionary, a new entry is created. If a key appears multiple times, only the last assigned value is kept. Assigning a new value to an existing key overwrites its previous value.

Looking Up a Value:

bvalue = d(keys): This command retrieves the value corresponding to the specified keys from the dictionary.

Storing Multiple Data Types in a Dictionary:

value = d{keys} retrieves the value associated with keys and returns the contents of the cell. If keys is an array, a comma-separated list of the corresponding values is returned. An error is thrown if the dictionary's values are configured to a datatype other than cell.

d{keys} = values assigns cells containing the elements of values to the entries specified by the corresponding keys. An error is thrown if the dictionary's values are configured to a datatype other than cell.

Examples

d = dictionary()
d('apple') = 1
d('banana') = 2
d('kiwi') = 3
d('banana') = []

Values = {{'a','b'},["ff", "cc"],struct,[1 2 3 4]}
Keys = ["letters" "words" "a structure" "numeric array"]
d = dictionary(Keys, Values)
d{"numeric array"}
d{"a new entry"} = 'table'

dictionary conversion nelson -- python

wheels = [1 2 3];
names = ["Monocycle" "Bicycle" "Tricycle"];
d = dictionary(wheels, names)
R = pyrun("A = d", "A", 'd', d)
dictionary(R)

History

Version	Description
1.5.0	initial version

Author

Allan CORNET

entries

Key-value pairs of dictionary.

Syntax

E = entries(d)
E = entries(d, format)

Input argument

d - scalar: dictionary object.
format - format: string scalar or character vector: 'cell', 'struct', 'table' (not yet implemented) .

Output argument

E - table, struct or cell.

Description

E = entries(d) retrieves a table containing the key-value pairs from the given dictionary, d.

E = entries(d) currently not implemented.

E = entries(d, format) specifies the output format as either a table or a structure. For instance, entries(d, "struct") returns a structure containing the key-value pairs of d. This option is useful for data types that are not compatible with tables.

Example

names = ["Biil" "John" "Yann"];
wheels = [1 2 3];
d = dictionary(wheels, names)
E = entries(d, 'struct')
E = entries(d, 'cell')

History

Version	Description
1.5.0	initial version

Author

Allan CORNET

insert

Add entries to a dictionary.

Syntax

db = insert(da, key, value)
db = insert(da, key, value, 'Overwrite', tf)

Input argument

da - scalar: a dictionary object.
key - scalar or array: key
value - scalar or array: value. size of key must be compatible with the size of value.
tf - true force to Overwrite, false do not overwrite and ignore change

Output argument

db - scalar: a dictionary object.

Description

db = insert(da, key, value) adds the key-value pair to the dictionary da.

If the key already exists, its value is updated.

d = insert(d, key, value) is equivalent to d[key] = value.

db = insert(da, key, value, 'overwrite', tf) specifies whether to overwrite an existing value for the key based on the boolean parameter Overwrite.

Example

names = ["Apple" "Banana" "Kiwi"];
wheels = [1 2 3];
d = dictionary(wheels, names)
d = insert(d, [2 4] ,["Orange" "Citra"], 'Overwrite', false)

History

Version	Description
1.5.0	initial version

Author

Allan CORNET

isConfigured

Check if dictionary has types assigned to keys and values.

Syntax

tf = isConfigured(d)

Input argument

d - scalar: dictionary object.

Output argument

tf - scalar logical: true if configured, false if not.

Description

tf = isConfigured(d) returns a logical true if the specified dictionary is configured, and a logical false if it is not.

A dictionary is considered configured when it has assigned types for its keys and values. Adding entries to an unconfigured dictionary will configure it.

Example

names = ["Biil" "John" "Yann"];
wheels = [1 2 3];
d = dictionary(wheels, names)
tf = isConfigured(d)
d2 = dictionary()
tf = isConfigured(d2)

History

Version	Description
1.5.0	initial version

Author

Allan CORNET

isKey

Check if dictionary contains key

Syntax

tf = isKey(d)

Input argument

d - scalar: dictionary object.

Output argument

tf - scalar logical: true if key, false if not.

Description

tf = isKey(d, key) returns a logical true if the specified key exists in the configured dictionary, and a logical false if it does not.

If d is an unconfigured dictionary, isKey throws an error.

If key is an array of multiple keys, then tf is a logical array of the same size.

Example

names = ["Biil" "John" "Yann"];
wheels = [1 2 3];
d = dictionary(wheels, names)
tf = isKey(d, "John")
tf = isKey(d, ["biil" , "Yannis")

History

Version	Description
1.5.0	initial version

Author

Allan CORNET

keyHash

Create a hash code for a dictionary key.

Syntax

H = keyHash(A)

Input argument

A - array

Output argument

H - scalar: uint64, Hash code.

Description

H = keyHash(A) returns a uint64 scalar representing the input array, A.

The keyHash function computes a hash code derived from the characteristics of the input.

For custom classes, keyHash might require overloading to guarantee proper equivalence.

Example

keyHash({'a', 'b', 1})
keyHash({1, 'a', 'b'})

History

Version	Description
1.5.0	initial version

Author

Allan CORNET

keyMatch

Check whether two dictionary keys are same.

Syntax

tf = keyMatch(A, B)

Input argument

A - array
B - array

Output argument

tf - logical: true or false.

Description

tf = keyMatch(A, B) returns true if arrays A and B have identical classes, properties, dimensions, and values, and returns false otherwise.

For custom classes, overloading keyMatch may be necessary to ensure accurate equivalence.

Example

A = {'a', 'b', 1};
B = {1, 'a', 'b'};
C = A;
D = B;
keyMatch(A, B)
keyMatch(A, C)
keyMatch(B, D)

History

Version	Description
1.5.0	initial version

Author

Allan CORNET

keys

Keys of dictionary.

Syntax

k = keys(d)
k = keys(d, 'cell')

Input argument

d - scalar: dictionary object.

Output argument

k - keys.

Description

k = keys(d) retrieves an array containing the keys of the specified dictionary, d.

k = keys(d, 'cell') optionally returns the keys as a cell array.

Example

names = ["Biil" "John" "Yann"];
wheels = [1 2 3];
d = dictionary(wheels, names)
k = keys(d)
k = keys(d, 'cell')

History

Version	Description
1.5.0	initial version

Author

Allan CORNET

lookup

Find value in dictionary by key.

Syntax

value = lookup(d, key)
value = lookup(d, key, 'FallbackValue', fallback)

Input argument

d - scalar: dictionary object.
key - key type must match or be convertible to the data type of keys in d.
fallback - scalar: Fallback value

Output argument

value - value.

Description

value = lookup(d, key) retrieves the value associated with the given key in dictionary d.

If the key does not exist, an error is raised.

value = lookup(d, key) is equivalent to value = d[key].

value = lookup(d, key, 'FallbackValue', fallback) specifies a fallback value to return if the key is not found in d.

lookup function only validates the fallback if it is needed. An error is raised only if the key is not found and no valid fallback is provided.

Example

names = ["Apple" "Banana" "Kiwi"];
wheels = [1 2 3];
d = dictionary(wheels, names)
v = lookup(d,[3,5], 'FallbackValue', "Orange")

History

Version	Description
1.5.0	initial version

Author

Allan CORNET

numEntries

Number of key-value pairs in dictionary.

Syntax

n = numEntries(d)

Input argument

d - scalar: dictionary object.

Output argument

n - scalar: number of entries.

Description

n = numEntries(d) retrieves the number of key-value pairs stored in the dictionary.

If d is an unconfigured dictionary, then numEntries returns 0.

Example

names = ["Biil" "John" "Yann"];
wheels = [1 2 3];
d = dictionary(wheels, names)
n = numEntries(d)

History

Version	Description
1.5.0	initial version

Author

Allan CORNET

remove

Remove dictionary entries.

Syntax

db = remove(da, key)

Input argument

da - scalar: a dictionary object.
key - scalar or array: key

Output argument

db - scalar: a dictionary object.

Description

db = remove(da, key) deletes the entry associated with the key from dictionary da.

d = remove(d, key) is equivalent to d[key] = [].

Example

names = ["Apple" "Banana" "Kiwi"];
wheels = [1 2 3];
d = dictionary(wheels, names)
d = remove(d, 2)

History

Version	Description
1.5.0	initial version

Author

Allan CORNET

types

Types of dictionary keys and values.

Syntax

[keyType, valueType] = types(d)
keyType = types(d)

Input argument

d - scalar: dictionary object.

Output argument

keyType - string scalar: Data type of dictionary keys.
valueType - string scalar: Data type of dictionary values.

Description

keyType = types(d) returns the data type of the keys in the dictionary.

[keyType, valueType] = types(d) returns the data types of the keys and values in the specified dictionary. If the dictionary d is not configured, types returns a string scalar indicating missing.

Example

names = ["Biil" "John" "Yann"];
wheels = [1 2 3];
d = dictionary(wheels, names)
[keyType, valueType] = types(d)

History

Version	Description
1.5.0	initial version

Author

Allan CORNET

values

Values of dictionary.

Syntax

v = values(d)
v = values(d, 'cell')

Input argument

d - scalar: dictionary object.

Output argument

v - values.

Description

v = values(d) retrieves an array containing the values of the specified dictionary, d.

v = values(d, 'cell') optionally returns the values as a cell array.

Example

names = ["Biil" "John" "Yann"];
wheels = [1 2 3];
d = dictionary(wheels, names)
v = values(d)
v = values(d, 'cell')

History

Version	Description
1.5.0	initial version

Author

Allan CORNET

Tables

Description

Tables of arrays with named columns, each potentially containing different data types.

Accessing and Manipulating Tables in Nelson
Direct computation with Table
Read/Write table to files
array2table - Convert homogeneous array to table.
cell2table - Convert cell array to table.
head - Get top rows of table or array.
height - Number of table rows
istable - Determine if input is table.
removevars - Delete variables from table.
renamevars - Rename variables in table.
struct2table - Convert a structure array into a tabular format.
table - A table-like array with named variables, capable of holding different data types
table2array - Convert table to homogeneous array.
table2cell - Convert table to cell array
table2struct - Convert table to structure array
tail - Get bottom rows of table or array.
width - Number of table variables

Accessing and Manipulating Tables in Nelson

Description

Insertion into a Table

To insert new data into a table, use dot notation or curly braces {} for specific element-wise insertion. You can add new rows, columns, or update existing data.

see examples: Adding a New Column and Updating an Existing Element

Extraction from a Table

You can extract specific rows, columns, or individual elements using indexing or by referencing variable names.

see examples: Extracting Specific Columns and Extracting Specific Rows

Removing Data from a Table

In Nelson, you can remove rows, columns, or specific elements from a table by using indexing or the removevars function. Rows or columns can be removed by setting the indices to empty brackets [].

see examples: Removing Rows and Removing Columns

Horizontal Concatenation (horzcat)

You can concatenate tables horizontally (side by side) using the horzcat function. This function combines tables by appending the columns of one table to the columns of another table.

see examples: Horizontal Concatenation

Vertical Concatenation (vertcat)

You can concatenate tables vertically (one below the other) using the vertcat function. This function combines tables by appending the rows of one table to the rows of another table.

see examples: Vertical Concatenation

Convert variable types

You can convert table variables by using the VariableTypes property.

see examples: VariableTypes example

Summary

In Nelson, tables provide a flexible way to store and manipulate heterogeneous data. You can easily insert data, extract parts of the table, and concatenate tables both horizontally and vertically using built-in functionality like dot notation and concatenation functions (horzcat, vertcat), making table manipulation intuitive and powerful for data analysis.

Examples

Adding a New Column

T = table([1; 2], {'A'; 'B'}, 'VariableNames', {'ID', 'Label'})
% Insert a new column 'Score'
T.Score = [10; 20]

Updating an Existing Element

T = table([1; 2], {'A'; 'B'}, 'VariableNames', {'ID', 'Label'})
% Insert a new column 'Score'
T.Score = [10; 20]
% Update the value in row 1, column 'Score'
T{1, 'Score'} = 15

Extracting Specific Columns

T = table([1; 2], {'A'; 'B'}, 'VariableNames', {'ID', 'Label'})
% Insert a new column 'Score'
T.Score = [10; 20]
% Update the value in row 1, column 'Score'
T{1, 'Score'} = 15
% Extract the 'ID' column from the table
ID_column = T.ID

Extracting Specific Rows

T = table([1; 2], {'A'; 'B'}, 'VariableNames', {'ID', 'Label'})
% Insert a new column 'Score'
T.Score = [10; 20]
% Update the value in row 1, column 'Score'
T{1, 'Score'} = 15
% Extract the first two rows of the table
rows_1_2 = T(1:2, :)

Removing a Column

T = table([1; 2], {'A'; 'B'}, 'VariableNames', {'ID', 'Label'})
% Insert a new column 'Score'
T.Score = [10; 20]
% Remove the 'Score' column from the table
T(:, 'Score') = [];

Removing a Row

T = table([1; 2], {'A'; 'B'}, 'VariableNames', {'ID', 'Label'})
% Insert a new column 'Score'
T.Score = [10; 20]
% Remove the second row from the table
T(2, :) = [];

Horizontal Concatenation

% Create two tables with the same number of rows
T1 = table([1; 2], {'A'; 'B'}, 'VariableNames', {'ID', 'Label'});
T2 = table([10; 20], {'X'; 'Y'}, 'VariableNames', {'Score', 'Grade'});

% Concatenate horizontally
T_horz = [T1, T2]  % or T_horz = horzcat(T1, T2);

Vertical Concatenation

T1 = table([1; 2], {'A'; 'B'}, 'VariableNames', {'ID', 'Label'});
% Create two tables with the same column names
T3 = table([3; 4], {'C'; 'D'}, 'VariableNames', {'ID', 'Label'});

% Concatenate vertically
T_vert = [T1; T3]  % or T_vert = vertcat(T1, T3)

Convert variable types

Names = {'John'; 'Alice'; 'Bob'; 'Diana'};
Age = [28; 34; 22; 30];
Height = [175; 160; 180; 165];
Weight = [70; 55; 80; 60];
T = table(Names, Age, Height, Weight);
T.Properties.VariableTypes
T{:,1}
T{:,2}
T.Properties.VariableTypes = ["string"    "int8"    "double"    "double"];
T{:,1}
T{:,2}
T.Properties.VariableTypes

History

Version	Description
1.8.0	initial version
1.10.0	VariableTypes property

Author

Allan CORNET

Direct computation with Table

Description

You can perform calculations directly on tableswithout needing to index into them.

To perform such operations using the same syntax as you would for arrays, your tables must meet several criteria:

All variables within the table must have data types that support the intended calculations (e.g., numeric or logical types).

When performing an operation where only one operand is a table, the other operand must be either a numeric or logical array.

For operations involving two tables, they must have compatible sizes (i.e., the same number of rows and columns or the operation must make sense for the structures involved).

Below is an example that demonstrates how to perform calculations without explicitly indexing into the table.

Example

Direct computation on Tables

% Create a sample table with sensor data
T = table([1.5; -2.3; 4.7], [0.5; 1.1; -0.7], [-1; 2; 3], ...
          'VariableNames', {'Voltage', 'Current', 'Resistance'});

% Apply functions directly to the table columns
abs(T)
acos(T)
acosh(T)
T > 1
T + 2
T .* T
abs(sin(T)) + 1

History

Version	Description
1.9.0	initial version

Author

Allan CORNET

Read/Write table to files

Description

Nelson provides extensive capabilities for reading and writing tables to files, supporting both text-based and binary storage formats to meet different data management needs.

Text files (.csv, .txt, etc.):

writetable() exports tables to delimited text files with customizable separators
readtable() imports tables from delimited text files with automatic format detection
Text files preserve variable names and data in human-readable format

Binary file:

Nelson HDF5 format (.nh5):
- Efficient binary storage using HDF5 format
- Preserves all table metadata and data types
- Use save -nh5 and load commands

Binary format is recommended for preserving exact numeric precision and working with large datasets.

Examples

Read/Write table to .nh5 file

% Create a sample table with sensor data
T = table([1.5; -2.3; 4.7], [0.5; 1.1; -0.7], [-1; 2; 3], 'VariableNames', {'Voltage', 'Current', 'Resistance'});
R = T;
filename = [tempdir(), 'table_example.nh5'];
save(filename, '-nh5', 'T');
clear T
load(filename, 'T');
assert(isequal(T, R));
T

Read/Write table to text file

% Create a sample table with sensor data
T = table([1.5; -2.3; 4.7], [0.5; 1.1; -0.7], [-1; 2; 3], 'VariableNames', {'Voltage', 'Current', 'Resistance'});
filename = [tempdir(), 'table_example.csv'];
writetable(T, filename);
T2 = readtable(filename);

History

Version	Description
1.10.0	initial version

Author

Allan CORNET

array2table

Convert homogeneous array to table.

Syntax

T = array2table(A)

Input argument

A - matrix: single, double, integer types, logical, char, string, struct, cell.

Output argument

T - Table object.

Description

T = array2table(A) converts an m-by-n array A into an m-by-n table, where each column of A becomes a variable in the resulting table T.

By default, array2table uses the name of the input array, combined with the column number, to create variable names in the table. If these names are not valid identifiers, it assigns default names of the form 'Var1', 'Var2', ... , 'VarN', where N is the number of columns in A.

Example

A = magic(6);
T = array2table(A)
T = array2table(magic(6))

History

Version	Description
1.8.0	initial version

Author

Allan CORNET

cell2table

Convert cell array to table.

Syntax

T = cell2table(C)

Input argument

C - 2-D cell array.

Output argument

T - Table object.

Description

T = cell2table(C) converts the contents of an m-by-n cell array C into an m-by-n table.

Each column of the input cell array becomes the data for a corresponding variable in the output table.

To generate variable names in the output table, cell2table appends the column numbers to the name of the input array.

If the input array does not have a name, cell2table assigns default variable names in the format "Var1", "Var2", ... , "VarN", where N is the number of columns in the cell array.

Example

C = {'John', 28, true; 'Alice', 35, false; 'Bob', 42, true};
% Convert the cell array to a table
T = cell2table(C)

History

Version	Description
1.8.0	initial version

Author

Allan CORNET

head

Get top rows of table or array.

Syntax

head(A)
head(A, k)
B = head(...)

Input argument

A - Input array (table or other).

Output argument

k - a integer value: Number of rows to extract (k = 8 by default).

Description

head(A) displays the first eight rows of an array, or table A in the Command Window without assigning it to a variable.

head(A, k) displays the first k rows of A.

B = head(...) returns the specified rows of A for any of the previous syntaxes, with B having the same data type as A.

Examples

LastName = {'Sanchez';'Johnson';'Li';'Diaz';'Brown'};
Age = [38;43;38;40;49];
Smoker = logical([1;0;1;0;1]);
Height = [71;69;64;67;64];
Weight = [176;163;131;133;119];
BloodPressure = [124 93; 109 77; 125 83; 117 75; 122 80];
T = table(LastName, Age, Smoker, Height, Weight, BloodPressure)
head(T, 2)

A = repmat((1:50)',1, 3);
head(A)

History

Version	Description
1.9.0	initial version

Author

Allan CORNET

height

Number of table rows

Syntax

H = height(T)

Input argument

T - Input array (table or other).

Output argument

H - a integer value: Number of table rows in Table or size(T, 1).

Description

H = height(T) returns the number of rows in the table T.

The function height(T) is equivalent to size(T, 1), which also provides the number of rows in the table.

Example

T = table();
height(T)
C = {'John', 28, true; 'Alice', 35, false; 'Bob', 42, true};
T = cell2table(C);
height(T)

History

Version	Description
1.8.0	initial version

Author

Allan CORNET

istable

Determine if input is table.

Syntax

tf = istable(A)

Input argument

A - Input array.

Output argument

tf - a logical: true if it is a table.

Description

tf = istable(A) returns true if A is a table, and false if it is not.

Example

T = table();
istable(T)
M = magic(6);
istable(M)

History

Version	Description
1.8.0	initial version

Author

Allan CORNET

removevars

Delete variables from table.

Syntax

TB = removevars(TA, varsNames)

Input argument

TA - Input table.
varsNames - Variable names in input table to remove: character vector, string array or cell array of character vectors.

Output argument

TB - Table object modified.

Description

TB = removevars(TA, varsNames) removes the variables specified by varsNames from the table TA and stores the remaining variables in T2.

You can specify the variables by name, position, or using logical indices.

You can also remove variables from a table using T(:, varsNames) = [].

Example

C = {'John', 28, true; 'Alice', 35, false; 'Bob', 42, true};
% Convert the cell array to a table
T1 = cell2table(C)
T2 = removevars(T1, 'C2')

History

Version	Description
1.9.0	initial version

Author

Allan CORNET

renamevars

Rename variables in table.

Syntax

TB = renamevars(TA, varsNames, newNames)

Input argument

TA - Input table.
varsNames - Variable names in input table: character vector, string array or cell array of character vectors.
newNames - New names for variables: character vector, string array or cell array of character vectors.

Output argument

TB - Table object with variable names modified.

Description

TB = renamevars(TA, varsNames, newNames) renames the variables in the table TA as specified by varsNames and assigns them the new names provided in newNames.

You can also rename all the variables in a table by assigning new names to its VariableNames property using T.Properties.VariableNames = newNames.

In this case, newNames must be a string array or a cell array of character vectors.

Example

C = {'John', 28, true; 'Alice', 35, false; 'Bob', 42, true};
% Convert the cell array to a table
T1 = cell2table(C);
T2 = renamevars(T1, {'C1', 'C2'}, {'Name', 'Age'})
T3 = cell2table(C);
T3.Properties.VariableNames = {'Name', 'Age', 'Married'};
T3

History

Version	Description
1.9.0	initial version

Author

Allan CORNET

struct2table

Convert a structure array into a tabular format.

Syntax

T = struct2table(S)

Input argument

S - structure: Array provided as a structure.

Output argument

T - A table object.

Description

T = struct2table(S) transforms a structure array into a table, where each field of the input structure is represented as a variable in the resulting table.

If the input is a scalar structure containing 𝑛 fields, each with 𝑚 rows, the output will be an 𝑚×𝑛 table.

If the input is either an 𝑚×1 or a 1×𝑚 structure array with 𝑛 fields, the output will also be an 𝑚×𝑛 table.

Examples

% Define a structure array
S(1).Name = 'Alice';
S(1).Age = 30;
S(1).Height = 5.5;

S(2).Name = 'Bob';
S(2).Age = 25;
S(2).Height = 6.0;

% Convert the structure array to a table
T = struct2table(S)

S = struct();
S(1).a = [10 20];
S(2).a = [30 40];
S(1).b = 50;
S(2).b = 60;
T = struct2table(S)

S = struct();
S.a = [1;2;3]
S.b = [4 5;6 7;8 9]
T = struct2table(S)

S = struct();
S(1).a = [10 20];
S(2).a = [30 40 50];
S(1).b = 70;
S(2).b = 80;
T = struct2table(S)

History

Version	Description
1.8.0	initial version

Author

Allan CORNET

table

A table-like array with named variables, capable of holding different data types

Syntax

T = table()
T = table(var1, ... , varN)
T = table(... , Name, Value)

Input argument

var1, ... , varN - Input variables: Input variables are specified as arrays that all have the same number of rows. These variables can differ in size and data type.
Name, Value - Optional arguments are specified as pairs in the format Name1, Value1, ... , NameN, ValueN, where Name represents the argument name and Value is its corresponding value. These name-value pairs must come after any other arguments, but the order of the pairs themselves is flexible

Output argument

T - A table object.

Description

Table arrays are designed to store column-oriented, such as columns from text files or spreadsheets.

Each column of data is stored in a variable within the table, and these variables can have different data types and sizes, provided they all share the same number of rows.

Table variables have names, similar to structure fields.

To access data in a table, use the following methods:

- Dot notation (T.varname) to extract a single variable.

- Curly braces (T{rows, vars}) to extract an array from specific rows and variables.

- Parentheses (T(rows, vars)) to return a subset of the table.

T = table(var1, ..., varN) creates a table from the specified input variables var1,...,varN.

The variables can vary in size and data type, but they must all have the same number of rows.

If the inputs are workspace variables, their names are used as the variable names in the resulting table.

Otherwise, the table assigns default names in the format 'Var1', 'Var2', and so on, where N is the total number of variables.

T = table(..., Name, Value) allows you to specify additional options using one or more name-value pair arguments.

For instance, you can set custom variable names by using the 'VariableNames' name-value pair.

This syntax can be used in combination with any of the input arguments from the previous forms.

T = table() creates an empty table with 0 rows and 0 columns.

Examples

Names = {'John'; 'Alice'; 'Bob'; 'Diana'};
Age = [28; 34; 22; 30];
Height = [175; 160; 180; 165];
Weight = [70; 55; 80; 60];
T = table(Names, Age, Height, Weight)
T.Names
T{2, 2}
T{'Alice', 'Age'}
T{2, 'Age'}
T(:, 'Age')
T(2:3,1:3)

N = {'John'; 'Alice'; 'Bob'; 'Diana'};
A = [28; 34; 22; 30];
H = [175; 160; 180; 165];
W = [70; 55; 80; 60];
T = table(N, A, H, W, 'VariableNames', {'Name', 'Age', 'Height', 'Weight'})

N = {'John'; 'Alice'; 'Bob'; 'Diana'};
A = [28; 34; 22; 30];
H = [175; 160; 180; 165];
W = [70; 55; 80; 60];

% Define the row names
RowNames = {'Person1', 'Person2', 'Person3', 'Person4'};

% Create the table with row names
T = table(A, H, W, 'RowNames', RowNames, 'VariableNames', {'Age', 'Height_cm', 'Weight_kg'})
T('Person2', 1:2)

History

Version	Description
1.8.0	initial version

Author

Allan CORNET

table2array

Convert table to homogeneous array.

Syntax

A = table2array(T)

Input argument

T - table object.

Output argument

A - matrix: single, double, integer types, logical, char, string, struct, cell.

Description

A = table2array(T) converts the input table T into a homogeneous array A, where the variables in T become the columns of A.

The output A does not retain the table properties from T.Properties.

If T is a table with row names, these row names will not be included in A.

Example

A = magic(6);
T = array2table(A);
A = table2array(T)

History

Version	Description
1.8.0	initial version

Author

Allan CORNET

table2cell

Convert table to cell array

Syntax

S = table2cell(T)
S = table2cell(T, "ToScalar", true)

Input argument

T - a table object

Output argument

C - Cell array.

Description

C = table2cell(T) converts the table T into a cell array C, where each variable in T is transformed into a column of cells in C.

The output C does not include any properties from T.Properties.

If T contains row names, these will not be included in C.

Example

S = ["Y";"Y";"N";"N";"N"];
A = [38;43;38;40;49];
B = [124 93;109 77; 125 83; 117 75; 122 80];
T = table(S, A, B, 'VariableNames',["Smoker" "Age" "BloodPressure"], 'RowNames',["Chang" "Brown" "Ruiz" "Lee" "Garcia"])
C = table2cell(T)

History

Version	Description
1.8.0	initial version

Author

Allan CORNET

table2struct

Convert table to structure array

Syntax

S = table2struct(T)
S = table2struct(T, "ToScalar", true)

Input argument

T - a table object

Output argument

S - Structure.

Description

S = table2struct(T) converts the table T into a structure array S, where each variable in T is represented as a field in S.

If T is an m-by-n table, S will be an m-by-1 structure array with n fields.

the output S will not contain any table properties from T.Properties.

S = table2struct(T, "ToScalar", true) converts the table T into a scalar structure S, where each variable in T becomes a field in S.

If T is an m-by-n table, S will contain n fields, and each field will have m rows.

Example

Names = {'John'; 'Alice'; 'Bob'; 'Diana'};
Age = [28; 34; 22; 30];
Height = [175; 160; 180; 165];
Weight = [70; 55; 80; 60];
T = table(Names, Age, Height, Weight)
S1 = table2struct(T)
S1 = table2struct(T, "ToScalar", true)

History

Version	Description
1.8.0	initial version

Author

Allan CORNET

tail

Get bottom rows of table or array.

Syntax

tail(A)
tail(A, k)
B = tail(...)

Input argument

A - Input array (table or other).

Output argument

k - a integer value: Number of rows to extract (k = 8 by default).

Description

tail(A) displays the last eight rows of an array, or table A in the Command Window without assigning it to a variable.

tail(A, k) displays the last k rows of A.

B = tail(...) returns the specified rows of A for any of the previous syntaxes, with B having the same data type as A.

Examples

LastName = {'Sanchez';'Johnson';'Li';'Diaz';'Brown'};
Age = [38;43;38;40;49];
Smoker = logical([1;0;1;0;1]);
Height = [71;69;64;67;64];
Weight = [176;163;131;133;119];
BloodPressure = [124 93; 109 77; 125 83; 117 75; 122 80];
T = table(LastName, Age, Smoker, Height, Weight, BloodPressure)
tail(T, 2)

A = repmat((1:50)',1, 3);
tail(A)

History

Version	Description
1.9.0	initial version

Author

Allan CORNET

width

Number of table variables

Syntax

W = width(T)

Input argument

T - Input array (table or other).

Output argument

W - a integer value: Number of Variables in Table or size(T, 2).

Description

W = width(T) returns the number of variables in the table T.

The function width(T) is equivalent to size(T, 2), which also provides the number of columns in the table.

Example

T = table();
width(T)
C = {'John', 28, true; 'Alice', 35, false; 'Bob', 42, true};
T = cell2table(C);
width(T)

History

Version	Description
1.8.0	initial version

Author

Allan CORNET

Integers type

Description

These functions convert and store data to 1, 2 or 4 bytes integers. These data types are especially useful to store big objects such as images.

int16 - Converts to 16-bit signed integer.
int32 - Converts to 32-bit signed integer.
int64 - Converts to 64-bit signed integer.
int8 - Converts to 8-bit signed integer.
intmax - Return the largest integer that can be represented in an integer type.
intmin - Return the smallest integer that can be represented in an integer type.
uint16 - Converts to 16-bit unsigned integer.
uint32 - Converts to 32-bit unsigned integer.
uint64 - Converts to 64-bit unsigned integer.
uint8 - Converts to 8-bit unsigned integer.

int16

Converts to 16-bit signed integer.

Syntax

Y = int16(X)

Input argument

X - a matrix of double, single or integers.

Output argument

Y - a matrix of 16-bit integer.

Description

int16 converts value to 16-bit integer type.

The value is rounded to the nearest int16 value on conversion. A value that is above or below the range for an int16 class is mapped to one of the endpoints of the range [-32768, 32767].

Example

A = [1 -32769 -120 127 32767 32768]
B = int16(A)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

int32

Converts to 32-bit signed integer.

Syntax

Y = int32(X)

Input argument

X - a matrix of double, single or integers.

Output argument

Y - a matrix of 32-bit integer.

Description

int32 converts value to 32-bit integer type.

The value is rounded to the nearest int32 value on conversion. A value that is above or below the range for an int32 class is mapped to one of the endpoints of the range [-2147483648, 2147483647].

Example

A = [1 -2147483649 -120 127 2147483647 2147483648]
B = int32(A)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

int64

Converts to 64-bit signed integer.

Syntax

Y = int64(X)

Input argument

X - a matrix of double, single or integers.

Output argument

Y - a matrix of 64-bit integer.

Description

int64 converts value to 64-bit integer type.

The value is rounded to the nearest int64 value on conversion. A value that is above or below the range for an int64 class is mapped to one of the endpoints of the range [-9223372036854775808,9223372036854775807].

When you create a numeric array of large integers in Nelson, especially when they exceed the maximum precision representable by double (larger than flintmax), Nelson initially stores these values as double-precision floating-point numbers by default.

This default representation can lead to a loss of precision, as floating-point numbers have limited precision.

To maintain the full precision of these large integer values, it's advisable to explicitly convert each scalar element of the array to the int64 or uint64 data type using the i64 or u64 notation (see example).

This way, you ensure that the values are stored with their full precision as 64-bit signed or unsigned integers, respectively, rather than as double-precision floating-point numbers.

Example

A = [1 12 -120 127 -9e24 9e23]
B = int64(A)
R1 = int64([72057594035891654 81997179153022975])
R2 = [72057594035891654i64 81997179153022975i64]

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

int8

Converts to 8-bit signed integer.

Syntax

Y = int8(X)

Input argument

X - a matrix of double, single or integers.

Output argument

Y - a matrix of 8-bit integer.

Description

int8 converts value to 8-bit integer type.

The value is rounded to the nearest int8 value on conversion. A value that is above or below the range for an int8 class is mapped to one of the endpoints of the range [-128, 127].

Example

A = [1 -255 -120 127 128 215]
B = int8(A)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

intmax

Return the largest integer that can be represented in an integer type.

Syntax

imax = intmax()
imax = intmax(classname)

Input argument

classname - a string: by default: int32

Output argument

imax - largest integer

Description

imax = intmax(classname)the largest integer that can be represented in an integer type.

Supported values for the string classname are:

'int8'

'uint8'

'int16'

'uint16'

'int32'

'uint32'

'int64'

'uint64'

Examples

A = intmax('int64')
res = class(A)

A = intmax('uint32')
res = class(C)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

intmin

Return the smallest integer that can be represented in an integer type.

Syntax

imin = intmin()
imin = intmin(classname)

Input argument

classname - a string: by default: int32

Output argument

imin - smallest integer

Description

imin = intmin(classname)the smallest integer that can be represented in an integer type.

Supported values for the string classname are:

'int8'

'uint8'

'int16'

'uint16'

'int32'

'uint32'

'int64'

'uint64'

Examples

A = intmin('int64')
res = class(A)

A = intmin('uint32')
res = class(C)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

uint16

Converts to 16-bit unsigned integer.

Syntax

Y = uint16(X)

Input argument

X - a matrix of double, single or integers.

Output argument

Y - a matrix of 16-bit unsigned integer.

Description

uint16 converts value to 16-bit unsigned integer type.

The value is rounded to the nearest uint16 value on conversion. A value that is above or below the range for an uint16 class is mapped to one of the endpoints of the range [0, 65535].

Example

A = [1 -32769 -120 127 32767 32768]
B = uint16(A)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

uint32

Converts to 32-bit unsigned integer.

Syntax

Y = uint32(X)

Input argument

X - a matrix of double, single or integers.

Output argument

Y - a matrix of 32-bit unsigned integer.

Description

uint32 converts value to 32-bit unsigned integer type.

The value is rounded to the nearest uint32 value on conversion. A value that is above or below the range for an uint32 class is mapped to one of the endpoints of the range [0, 4294967295].

Example

A = [1 -2147483649 -120 127 2147483647 2147483648]
B = uint32(A)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

uint64

Converts to 64-bit unsigned integer.

Syntax

Y = uint64(X)

Input argument

X - a matrix of double, single or integers.

Output argument

Y - a matrix of 64-bit unsigned integer.

Description

uint64 converts value to 64-bit unsigned integer type.

The value is rounded to the nearest uint64 value on conversion. A value that is above or below the range for an uint64 class is mapped to one of the endpoints of the range [0, 18446744073709551616].

This default representation can lead to a loss of precision, as floating-point numbers have limited precision.

This way, you ensure that the values are stored with their full precision as 64-bit signed or unsigned integers, respectively, rather than as double-precision floating-point numbers.

Example

A = [1 12 -120 127 -9e24 9e23]
B = uint64(A)
R1 = uint64([72057594035891654 81997179153022975])
R2 = [72057594035891654u64 81997179153022975u64]

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

uint8

Converts to 8-bit unsigned integer.

Syntax

Y = uint8(X)

Input argument

X - a matrix of double, single or integers.

Output argument

Y - a matrix of 8-bit unsigned integer.

Description

uint8 converts value to 8-bit unsigned integer type.

The value is rounded to the nearest uint8 value on conversion. A value that is above or below the range for an uint8 class is mapped to one of the endpoints of the range [0, 255].

Example

A = [1 256 -120 127 -1 215]
B = uint8(A)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

Sparse type

Description

sparse type functions

IJV - Returns I,J,V triplets from a sparse matrix.
full - Sparse to full matrix conversion.
nnz - Return the number of nonzero elements.
nzmax - Reserved size for nonzero elements.
sparse - Sparse matrix definition.
speye - Sparse identity matrix.
spones - Replaces non zero sparse matrix elements with ones.

IJV

Returns I,J,V triplets from a sparse matrix.

Syntax

[iv, jv, vv, m, n, nzmax] = IJV(sp)

Input argument

sp - a sparse matrix.

Output argument

iv - a vector: row indices of the nonzero elements.
jv - a vector: column indices of the nonzero elements.
vv - a vector: values of the nonzero elements.
m - an integer value: number of rows in the matrix.
n - an integer value: number of columns in the matrix.
nzmax - an integer value: reserved size for nonzero elements..

Description

IJV converts a sparse matrix into its COO format.

Example

sp = sparse(eye(3,3))
[IV, JV, VV, m, n, nzmax] = IJV(sp)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

full

Sparse to full matrix conversion.

Syntax

M = full(sp)

Input argument

sp - a matrix: double or logical, sparse.

Output argument

M - a matrix.

Description

full converts a sparse matrix into its full representation.

If input argument is already full then output argument will be equal to input argument.

Example

sp = sparse(eye(3,3))
F = full(sp)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

nnz

Return the number of nonzero elements.

Syntax

v = nnz(M)

Input argument

M - a matrix: double or logical, sparse or not.

Output argument

v - a integer value.

Description

nnz returns the number of non zero elements in an matrix.

Example

I = [1 2 3];
J = [3 1 2];
V = [32 42 53];
sp = sparse(I, J, V, 5, 4, 10)
size(sp)
nnz(sp)
nzmax(sp)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

nzmax

Reserved size for nonzero elements.

Syntax

v = nzmax(M)

Input argument

M - a matrix: double or logical, sparse or not.

Output argument

v - a integer value.

Description

nzmax returns the amount of storage allocated for nonzero elements.

Example

I = [1 2 3];
J = [3 1 2];
V = [32 42 53];
sp = sparse(I, J, V, 5, 4, 10)
size(sp)
nnz(sp)
nzmax(sp)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

sparse

Sparse matrix definition.

Syntax

sp = sparse(M)
sp = sparse(m, n)
sp = sparse(I, J, V)
sp = sparse(I, J, V, m, n)
sp = sparse(I, J, V, m, n, nz)

Input argument

M - a matrix: double or logical.
m - an integer value: rows dimension.
n - an integer value: columns dimension
I - a vector.
J - a vector.
V - a vector.
nz - an integer value: storage allocation for nonzero elements.

Output argument

S - a single.

Description

sparse is used to build a sparse matrix. Only non-zero entries are stored.

If Mis a full matrix, sparse converts it to a sparse matrix representation, removing all zero values.

If nz is not specified, sparse uses as default value: nz = max([numel(i), numel(j), numel(v)])

If multiple values are specified with the same i, j indices, the associated value will be the sum of the values at the repeated index.

Examples

sp = sparse(eye(3,3))

sp = sparse(3, 3)

I = [1 2 3];
J = [3 1 2];
V = [32 42 53];
sp = sparse(I, J, V)
size(sp)

I = [1 2 3];
J = [3 1 2];
V = [32 42 53];
sp = sparse(I, J, V, 5, 4)
size(sp)
nnz(sp)
nzmax(sp)

I = [1 2 3];
J = [3 1 2];
V = [32 42 53];
sp = sparse(I, J, V, 5, 4, 10)
size(sp)
nnz(sp)
nzmax(sp)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

speye

Sparse identity matrix.

Syntax

S = speye()
S = speye(n)
S = speye(n, m)
S = speye(sz)

Input argument

n, m - dimension sizes: nonnegative integer scalar.
sz - dimension sizes: two-element row vector.

Output argument

S - a sparse matrix.

Description

S = speye() returns a sparse scalar 1.

S = speye(n) returns a sparse n-by-n identity matrix, with ones on the main diagonal.

S = speye(n, m) returns a sparse n-by-m matrix, with ones on the main diagonal.

S = speye(sz) returns a matrix with ones on the main diagonal.

Example

tic();S = speye(5000, 5000);toc()
tic();S = sparse(eye(5000, 5000));toc()

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

spones

Replaces non zero sparse matrix elements with ones.

Syntax

s = spones(S)

Input argument

S - Sparse or 2D matrix.

Output argument

S - a sparse matrix.

Description

s = spones(S) returns a matrix s with the same sparsity structure as S, but with one's in the nonzero positions.

Example

S = sparse([1,0;3,4]);
R = spones(S)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

String type

Description

string type functions

append - combines strings horizontally.
blanks - creates an string of blank characters.
char - Converts to a character array.
contains - checks if string contains with pattern.
convertCharsToStrings - Convert chars arrays to string arrays.
convertStringsToChars - Convert string arrays to character arrays.
count - Computes the number of occurrences of an pattern.
deblank - Remove trailing whitespace.
endsWith - checks if string ends with pattern.
int2str - Convert an integer array to a string
isStringScalar - checks if input is string array with one element.
isletter - Determine which characters are letters.
isspace - Determine which characters are space.
join - Combine strings.
mat2str - Matrix to String.
matches - Determine if pattern matches with strings.
newline - Returns a newline character.
num2str - Converts numbers to character array.
replace - Replaces strings in another.
sprintf - Writes data to a string.
startsWith - checks if string starts with pattern.
str2double - Converts a string to double.
strcat - concatenate strings horizontally.
strcmp - Strings comparaison.
strcmpi - Strings comparaison (case insensitive).
strfind - Find a string in another.
string - string array constructor.
strings - Create string array without characters.
strjust - Justify strings
strlength - Length of strings in cell of strings or string array.
strncmp - Compares first n characters of strings.
strncmpi - Compares first n characters of strings (case sensitive).
strrep - Replaces strings in another.
strtrim - Remove leading and trailing whitespace.
tolower - Lower case conversion.
toupper - Upper case conversion.

append

combines strings horizontally.

Syntax

res = append(s1, s2, ..., sN)

Input argument

s1, s2, ..., sN - a string, string array or cell of strings.

Output argument

res - a string, string array or cell of strings.

Description

strcat combines strings horizontally.

If all inputs are character arrays, then res is a character array.

If any input is a string array, then the res is a string array.

If any input is a cell array, and none are string arrays, then res is a cell array of character vectors.

append does not remove trailing white space.

Example

append("Nelson", 'nelSon')
A = {'abcde','fghi'};
B = {'jkl','mn'};
C = append(A, B)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

blanks

creates an string of blank characters.

Syntax

r = blanks(n)

Input argument

n - an value integer, number of blanks.

Output argument

r - a character array with n blanks

Description

blanks creates an string of blank characters.

Example

blanks(4)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

char

Converts to a character array.

Syntax

res = char(var)
res = char(var1, var2)
res = char(var1, var2, ..., varN)

Input argument

var - a cell of strings, string array or an numeric array.
var1, var2, ..., varN - strings or an numeric arrays.

Output argument

res - a string

Description

char converts numerical input into character data by taking the corresponding unicode character for each element.

Examples

M = [ 104   101   108   108   111;
20320   22909 32    32    32];
char(M)

R = char('these', 'are', 'test', 'strings')

R = char(["these"; "are"; "test"; "strings"])

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

contains

checks if string contains with pattern.

Syntax

tf = contains(str, pattern)
tf = contains(str, pattern,'IgnoreCase', true)
tf = contains(str, pattern,'IgnoreCase', false)

Input argument

str - a string, string array or cell of strings.
pattern - a string to find.

Output argument

tf - a matrix of logical.

Description

contains returns true if str contains pattern.

Example

str = 'To make a mountain out of a molehill';
k = contains (str, 'hill')
k = contains (str, 'molehill')
k = contains (str, 'Hill', 'IgnoreCase', true)

A = {'Nel', 'son'; 'Nelson', 'Modules'}
k = contains(A, 'son')

A = ["Nel", "son"; "Nelson", "Modules"]
k = contains(A, 'son')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

convertCharsToStrings

Convert chars arrays to string arrays.

Syntax

S = convertCharsToStrings(C)
[B1, B2, ..., BN] = convertCharsToStrings(A1, A2, ..., AN)

Input argument

C - if C is a char array, output S will be converted to an string array.
A1, A2, ..., AN - variables to convert to string array if it is a char array.

Output argument

S - a string array or unaltered variable
B1, B2, ..., BN - variables converted to string array if it is a char array or cell of char array.

Description

convertCharsToStrings converts chars arrays to string arrays.

Example

[A, B, C, D] = convertCharsToStrings("one", 2, 'three', {'four' ; 'NaN' ;'five'})
R = convertCharsToStrings(['Nelson' ; '  is  '; '  good'])

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

convertStringsToChars

Convert string arrays to character arrays.

Syntax

C = convertStringsToChars(S)
[B1, B2, ..., BN] = convertStringsToChars(A1, A2, ..., AN)

Input argument

S - if S is a string array, output C will be converted to an cell of strings or an character vector (if S is scalar).
A1, A2, ..., AN - variables to convert to char array if it is a string array.

Output argument

C - a char array or unaltered variable
B1, B2, ..., BN - variables converted to char array if it is a string array.

Description

convertStringsToChars converts string arrays to character arrays.

Example

A = convertStringsToChars("Nelson")
A = convertStringsToChars(["Nelson", string(NaN)])

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

count

Computes the number of occurrences of an pattern.

Syntax

nbocc = count(str, pattern)
nbocc = count(str, pattern,'IgnoreCase', true)
nbocc = count(str, pattern,'IgnoreCase', false)

Input argument

str - a string, string array or cell of strings.
pattern - a string or string array or cell of strings to find.

Output argument

nbocc - a matrix of integer values.

Description

count computes the number of occurrences of an pattern.

Example

str = 'To make a mountain out of a molehill';
k = count(str, 'hill')
k = count(str, 'molehill')
k = count(str, 'Hill', 'IgnoreCase', true)

A = {'Nel', 'son'; 'Nelson', 'Modules'}
k = count(A, 'son')

A = ["Nel", "son"; "Nelson", "Modules"]
k = count(A, 'son')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

deblank

Remove trailing whitespace.

Syntax

res = deblank(str)

Input argument

str - a string, a cell of strings or a string array.

Output argument

res - a string without trailing whitespace.

Description

deblank removes trailing whitespace.

deblank does not remove all significant whitespace (only characters ' \t\n\r\f\v' removed).

Examples

deblank(' Nel Son ')

deblank(" Nel Son ")

deblank([' Nel Son ', char(160)])

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

endsWith

checks if string ends with pattern.

Syntax

tf = endsWith(str, pattern)
tf = endsWith(str, pattern,'IgnoreCase', true)
tf = endsWith(str, pattern,'IgnoreCase', false)

Input argument

str - a string, string array or cell of strings.
pattern - a string to find.

Output argument

tf - a matrix of logical.

Description

endsWith returns true if str ends with pattern.

Example

str = 'To make a mountain out of a molehill';
k = endsWith (str, 'hill')
k = endsWith (str, 'molehill')
k = endsWith (str, 'Hill', 'IgnoreCase', true)

A = {'Nel', 'son'; 'Nelson', 'Modules'}
k = endsWith(A, 'son')

A = ["Nel", "son"; "Nelson", "Modules"]
k = endsWith(A, "son")

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

int2str

Convert an integer array to a string

Syntax

res = int2str(var)

Input argument

var - an numeric array.

Output argument

res - a string

Description

int2str converts an numeric array to a string with integer format. Inputs are rounded before conversion.

Examples

R = int2str ([-Inf, 2, NaN; 4, Inf, 6])

R = int2str(uint64(intmax('uint64')))

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

isStringScalar

checks if input is string array with one element.

Syntax

r = isStringScalar(str)

Input argument

str - a string, string array or cell of strings.

Output argument

r - a logical, true if res is string type and scalar.

Description

isStringScalar checks if input is string array with one element.

Example

r = isStringScalar('hello')
r = isStringScalar("hello")
r = isStringScalar(["hello", "world"])

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

isletter

Determine which characters are letters.

Syntax

res = isletter(str)

Input argument

str - scalar, vector, matrix or multidimensional array.

Output argument

res - logical array

Description

isletter determines which characters are letters.

Examples

isletter('Nel Son')

isletter("六書 six writings")

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

isspace

Determine which characters are space.

Syntax

res = isspace(str)

Input argument

str - scalar, vector, matrix or multidimensional array.

Output argument

res - logical array

Description

isletter determines which characters are space characters.

Examples

isspace('Nel Son')

isspace("六書 six writings")

History

Version	Description
1.3.0	initial version

Author

Allan CORNET

join

Combine strings.

Syntax

res = join(str)
res = join(str, delimiter)
res = join(str, dim)
res = join(str, delimiter, dim)

Input argument

str - a string, string array or cell of strings.
delimiter - a string, string array or cell of strings:Characters used to separate and join strings.
dim - positive integer: Dimension along which to join strings.

Output argument

res - a string, string array or cell of strings.

Description

res = join(str) combines the elements of str into a single text by joining them with a space character as the default delimiter.

The input, str, can be either a string array or a cell array of character vectors. The output, res, has the same data type as str.

If str is a 1-by-N or N-by-1 string array or cell array, res will be a string scalar or a cell array containing a single character vector.

If str is an M-by-N string array or cell array, res will be an M-by-1 string array or cell array.

For arrays of any size, join concatenates elements along the last dimension with a size greater than 1.

res = join(str, delimiter) joins the elements of str using the specified delimiter instead of the default space character.

If delimiter is an array of multiple delimiters, and str has N elements along the joining dimension, delimiter must have N–1 elements along the same dimension. All other dimensions of delimiter must either have size 1 or match the size of the corresponding dimensions of str.

res = join(str, dim) combines the elements of str along the specified dimension dim.

res = join(str, delimiter, dim) joins the elements of str along the specified dimension dim, using delimiter to separate them.

Example

str = ["x","y","z"; "a","b","c"];
delimiters = [" + "," = "; " - "," = "];
R = join(str, delimiters)

History

Version	Description
1.10.0	initial version

Author

Allan CORNET

mat2str

Matrix to String.

Syntax

res = mat2str(M)
res = mat2str(M, 'class')
res = mat2str(M, P, 'class')

Input argument

M - a numerical 2D matrix or logical.
P - an integer value: precision, 15 by default.

Output argument

res - a string

Description

mat2str converts a matrix to a string.

This string may be used to reconstruct the original matrix with execstr function.

Example

R = mat2str(pi)
R = mat2str(pi, 'class')
R = mat2str(pi, 4)
R = mat2str(pi + i, 'class')
execstr(['RB = ', R])

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

matches

Determine if pattern matches with strings.

Syntax

res = matches(str, pattern)
res = matches(str, pattern, 'IgnoreCase', true)

Input argument

str - a string, string array or cell of strings.
pattern - a string, string array or cell of strings.

Output argument

res - a logical: true if the two matches and false otherwise.

Description

matches determines if pattern matches with strings.

Example

matches("Nelson", 'nelSon')
matches("Nelson", 'Nelson')
str = ["yellow", "green", "blue", "brown"];
R = matches(str, ["yellow", "Brown"], 'IgnoreCase', true);

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

newline

Returns a newline character.

Syntax

ch = newline()

Output argument

ch - a char: equivalent to char(10)

Description

newline returns a newline character.

Example

double(newline)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

num2str

Converts numbers to character array.

Syntax

S = num2str(A)
S = num2str(A, precision)
S = num2str(A, formatSpec)

Input argument

A - a numerical matrix or logical.
precision - an positive integer value: Maximum number of significant digits.
formatSpec - a character array: Format of output fields.

Output argument

S - a character array: text representation of input array.

Description

num2str converts numbers to character array.

num2str trims any leading spaces from a character array. For better control over the results, use sprintf.

Example

R = num2str(pi, 4)
R = num2str(magic(3))

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

replace

Replaces strings in another.

Syntax

res = replace(str, old, new)

Input argument

str - a string, string array or cell of strings.
old - a string, string array or cell of strings to find.
new - a string, string array or cell of strings.

Output argument

res - a string, string array or cell of strings.

Description

replace replaces strings in another.

replace and strrep replace strings but replace is recommended.

Example

r = replace('This is a string.', 'is', 'is not')
r = replace({'cccc','ccbbcca'},{'cc','bb'},{'cc'})

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

sprintf

Writes data to a string.

Syntax

sprintf(format, v1, ... , vn)

Input argument

format - a string describing the format to used_function.
v1, ... , vn - data to convert and print according to the previous format parameter.

Description

Write data in text form to a string.

The format follows C fprintf syntax.

Value type	format	comment
Integer	%i	base 10
Integer signed	%d	base 10
Integer unsigned	%u	base 10
Integer	%o	Octal (base 8)
Integer	%x	Hexadecimal (lowercase)
Integer	%X	Hexadecimal (uppercase)
Floating-point number	%f	Fixed-point notation
Floating-point number	%e	Exponential notation (lowercase)
Floating-point number	%E	Exponential notation (uppercase)
Floating-point number	%g	Exponential notation (compact format, lowercase)
Floating-point number	%G	Exponential notation (compact format, uppercase)
Character	%c	Single character
String	%s	Character vector.

To display a percent sign, you need to use a double percent sign (%%) in the format string.

Examples

sprintf('an example of %s.', 'text')

sprintf("an example of %s.", "text")

sprintf('an value %g.', pi)

Display a percent sign

sprintf('%d%%.', 95)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

startsWith

checks if string starts with pattern.

Syntax

tf = startsWith(str, pattern)
tf = startsWith(str, pattern,'IgnoreCase', true)
tf = startsWith(str, pattern,'IgnoreCase', false)

Input argument

str - a string, string array or cell of strings.
pattern - a string to find.

Output argument

tf - a matrix of logical.

Description

startsWith returns true if str starts with pattern.

Example

str = 'To make a mountain out of a molehill';
k = startsWith (str, 'in')
k = startsWith (str, 'to')
k = startsWith (str, 'to', 'IgnoreCase', true)

A = {'Nel', 'son'; 'Nelson', 'Modules'}
k = startsWith(A, 'Nel')

A = ["Nel", "son"; "Nelson", "Modules"];
k = startsWith(A, "Nel")

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

str2double

Converts a string to double.

Syntax

res = str2double(str)

Input argument

str - a cell of strings, string array or a string.

Output argument

res - a double

Description

str2double converts any complex number as a whole into a complex numeric field, converting the real and imaginary parts to the specified numeric type.

If str2double cannot convert string to a number, then it returns a Not An Number value.

Example

R = str2double('2.6 + 3j')
R = str2double('+NaNi')
R = str2double({'2.71' '3.1415'})
R = str2double(["2.71" "3.1415"])

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

strcat

concatenate strings horizontally.

Syntax

res = strcat(s1, s2, ..., sN)

Input argument

s1, s2, ..., sN - a string, string array or cell of strings.

Output argument

res - a string, string array or cell of strings.

Description

strcat concatenate strings horizontally.

If all inputs are character arrays, then res is a character array.

If any input is a string array, then the res is a string array.

If any input is a cell array, and none are string arrays, then res is a cell array of character vectors.

For cell and string array inputs, strcat does not remove trailing white space.

For character array inputs, strcat removes trailing ASCII white-space characters.

Example

strcat("Nelson", 'nelSon')
A = {'abcde','fghi'};
B = {'jkl','mn'};
C = strcat(A, B)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

strcmp

Strings comparaison.

Syntax

res = strcmp(s1, s2)

Input argument

s1 - a string, string array or cell of strings.
s2 - a string, string array or cell of strings.

Output argument

res - a logical: true if the two are identical and false otherwise.

Description

strcmp compares two strings.

Example

strcmp('Nelson', 'nelSon')
strcmp('Nelson', 'Nelson')

A = {'Nel', 'son'; 'Toolboxes', 'Modules'}
B = {'Handle', 'Struct'; 'Toolboxes', 'Modules'}
C = {'C', 'Contents'; 'Nel', 'son'}
strcmp(A, B)
strcmp(A, C)
strcmp(C, 'C')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

strcmpi

Strings comparaison (case insensitive).

Syntax

res = strcmpi(s1, s2)

Input argument

s1 - a string, string array or cell of strings.
s2 - a string, string array or cell of strings.

Output argument

res - a logical: true if the two are identical (case insensitive) and false otherwise.

Description

strcmpi compares two strings (case insensitive).

Example

strcmpi('Nelson', 'nelSon')
strcmpi('Nelson', 'Nelson')

A = {'Nel', 'son'; 'Toolboxes', 'Modules'}
B = {'Handle', 'Struct'; 'Toolboxes', 'Modules'}
C = {'C', 'Contents'; 'Nel', 'son'}
strcmpi(A, B)
strcmpi(A, C)
strcmpi(C, 'C')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

strfind

Find a string in another.

Syntax

occ = strfind(str, pattern)
occ = strfind(str, pattern,'ForceCellOutput', ouput)

Input argument

str - a string or cell of strings.
pattern - a string to find.
output - a logical.

Output argument

occ - a cell or matrix of integer values: occurences position.

Description

strfind find a string in another.

Example

str = 'To make a mountain out of a molehill';
k = strfind (str, 'in')
k= strfind(str, ' ')
k = strfind ({'abababada', 'beabebe', 'ab'}, 'aba')

A = {'Nel', 'son'; 'Toolboxes', 'Modules'}
k = strfind(A, 'o')

str = 'No pain no gain.';
k = strfind(str,'in','ForceCellOutput',true)
k = strfind(str,'in','ForceCellOutput',false)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

string

string array constructor.

Syntax

res = string(var)

Input argument

var - characters, a cell of characters, or an logical or numeric array.

Output argument

res - a string array

Description

string converts input into string array.

Examples

R = string({'these', 'are'; 'test', 'strings'})
R2 = ["these", "are"; "test", "strings"];

M = [ 104   101   108   108   111;
20320   22909 32    32    32];
R = string(M)
D = double(R)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

strings

Create string array without characters.

Syntax

C = strings()
C = strings(m)
C = strings(m, n)
C = strings(m, n, ... , p)
C = strings(sz)

Input argument

m, n, ... , p - dimensions of the string array to create.
sz - a vector of integer values (dimensions of the cell to create).

Output argument

C - a string array

Description

strings returns a cell array of empty matrices.

Example

A = eye(2, 4);
sz = size(A)
C = strings(sz)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

strjust

Justify strings

Syntax

J = strjust(str)
J = strjust(str, side)

Input argument

str - characters vector, cell of characters or string array.
side - 'left', 'center', 'right' (default).

Output argument

J - justified text

Description

J = strjust(str, side) returns the text that is justified on the side specified by side.

Examples

S = ["a"; "ab"; "abc"; "abcd"];
J = strjust (S)
J = strjust (S, 'left')
J = strjust (S, 'center')
J = strjust (S, 'right')

J = strjust('                 text', 'center')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

strlength

Length of strings in cell of strings or string array.

Syntax

len = strlength(ce)

Input argument

ce - a string, string array or cell of strings.

Output argument

len - a matrix of integer values: length of strings.

Description

strlength returns length of strings.

Example

str = 'To make a mountain out of a molehill';
k = strlength(str)

A = {'Nel', 'son'; 'Toolboxes', 'Modules'}
k = strlength(A)

B = ["Nel", NaN, "son"; "is", "open", "source"];
k = strlength(B)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

strncmp

Compares first n characters of strings.

Syntax

res = strncmp(s1, s2, n)

Input argument

s1 - a string, string array or cell of strings.
s2 - a string, string array or cell of strings.
n - an integer value: numbers of characters to compare.

Output argument

res - a logical: true if the two are identical and false otherwise.

Description

strncmp compares the first n characters of two strings (case sensitive).

Example

strncmp('Nelson', 'nelSon', 3)
strncmp('Nelson', 'Nelson', 3)

A = {'Nel', 'son'; 'Toolboxes', 'Modules'}
B = {'Handle', 'Struct'; 'Toolboxes', 'Modules'}
C = {'C', 'Contents'; 'Nel', 'son'}
strncmp(A, B, 2)
strncmp(A, C, 2)
strncmp(C, 'C', 4)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

strncmpi

Compares first n characters of strings (case sensitive).

Syntax

res = strncmpi(s1, s2, n)

Input argument

s1 - a string, string array or cell of strings.
s2 - a string, string array or cell of strings.
n - an integer value: numbers of characters to compare.

Output argument

res - a logical: true if the two are identical and false otherwise.

Description

strncmpi compares the first n characters of two strings (case insensitive).

Example

strncmpi('Nelson', 'nelSon', 3)
strncmpi('Nelson', 'Nelson', 3)

A = {'Nel', 'son'; 'Toolboxes', 'Modules'}
B = {'Handle', 'Struct'; 'Toolboxes', 'Modules'}
C = {'C', 'Contents'; 'Nel', 'son'}
strncmpi(A, B, 2)
strncmpi(A, C, 2)
strncmpi(C, 'C', 4)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

strrep

Replaces strings in another.

Syntax

res = strrep(str, old, new)

Input argument

str - a string, string array or cell of strings.
old - a string, string array or cell of strings to find.
new - a string, string array or cell of strings.

Output argument

res - a string, string array or cell of strings.

Description

replace replaces strings in another.

replace and strrep replace strings but replace is recommended.

Example

r = strrep('This is a string.', 'is', 'is not')
r = strrep({'cccc','ccbbcca'},{'cc','bb'},{'cc'})
r = strrep("This is a string.", "is", 'is not')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

strtrim

Remove leading and trailing whitespace.

Syntax

res = strtrim(str)

Input argument

str - a string, a cell of strings or a string array.

Output argument

res - a string without leading or trailing whitespace.

Description

strtrim removes leading and trailing whitespace.

strtrim does not remove all significant whitespace (only characters ' \t\n\r\f\v' removed).

Examples

strtrim(' Nel Son')

strtrim(" Nel Son")

strtrim([' Nel Son', char(160)])

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

tolower

Lower case conversion.

Syntax

res = tolower(str)

Input argument

str - a row character array, a cell of strings or an string array.

Output argument

res - lower case equivalent

Description

tolower converts a string to lower case.

Examples

tolower('NelSon')

tolower(["NelSon", "is", "open"])

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

toupper

Upper case conversion.

Syntax

res = toupper(str)

Input argument

str - a row character array, a cell of strings or an string array.

Output argument

res - a string upper case

Description

toupper converts a string to upper case.

Examples

toupper('NelSon')

upper(["NelSon", "is", "open"])

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

Function_handle functions

Description

function_handle functions

Anonymous Functions - Anonymous Functions.
func2str - Return a function handle constructed from a string.
isfunction_handle - Checks if value is a function handle.
str2func - Returns a function handle from a string.

Anonymous Functions

Anonymous Functions.

Description

Anonymous functions provide a convenient way to swiftly create straightforward functions without the need to generate separate M-files on every occasion.

These anonymous functions can be built either directly at the command line or within any M-file function or script.

To create an anonymous function from an expression, use the following syntax:

function_handle = @(argument_list) expression

Breaking down this syntax, expression represents the body of the function, which contains the code that performs the primary task of your function.

This part consists of a valid expression. Next, there's argument_list, which is a comma-separated list of input arguments to be passed to the function.

These components are similar to the body and argument list of any regular function.

At the beginning of this syntax statement, you'll notice the @ sign.

This @ sign is the operator that constructs a function handle.

Creating a function handle for an anonymous function allows you to invoke the function and is useful when passing your anonymous function as an argument to another function.

The @ sign is a necessary part of the anonymous function definition.

It's worth noting that function handles not only apply to anonymous functions but also to any function.

The syntax for creating a function handle to a regular function is different and looks like this:

function_handle = @function_name

For example: f = @cos

You have the option to store function handles along with their associated values in a MAT-file.

Later, in a different session, you can retrieve and utilize them using the save and load functions.

for example a = 1;b = 2; f = @(x) a + b + x; save('test.nH5', f);

Only .nh5 files allows to save and load function_handle type as expected.

You can create an anonymous function that takes multiple input arguments, x and y.

Assuming that variables A and B are already defined, you can define the function as follows:

A = 10; B = 100; r = @(x, y) (A*y + B*x);

Examples

A = 10;
f1 = @() sqr(A);
clear A
f1
f1()

f2 = @cos;
f2
f2(0.6)

f3 = @(x)cos(x) + 1;
f2
f3(0.6)

Multiple input arguments

A = 10;
B = 100;
f4 = @(x, y) (A*y + B*x);
f4
f4(0.6, 0.2)

Save/Load function handle

a = 1;
b = 2;
f5 = @(x) a + b + x;
save([tempdir(), 'test.nh5'], 'f5');
clear all
load([tempdir(), 'test.nh5'])
f5
f5(10)

Multiple output arguments

P = pi * 3;
mymeshgrid = @(X, Y) meshgrid((-X:X/P:X),(-Y:Y/P:Y));
[x, y] = mymeshgrid(pi, 2 * pi);
z = cos(x) + sin(y);
mesh(x, y, z)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

func2str

Return a function handle constructed from a string.

Syntax

func_handle = str2func(str)

Input argument

str - a string.

Output argument

func_handle - a function handle

Description

func_handle = str2func(str) returns a function handle constructed from the string str.

Example

fh = str2func('cos')
class(fh)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

isfunction_handle

Checks if value is a function handle.

Syntax

l = isfunction_handle(func_handle)

Input argument

func_handle - a function handle or other variable type.

Output argument

l - a logical

Description

l = isfunction_handle(func_handle) checks if func_handle is a function handle. Returning true if it is.

Example

fh = str2func('cos')
isfunction_handle(fh)
fh = 3
isfunction_handle(fh)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

str2func

Returns a function handle from a string.

Syntax

func_handle = str2func(str)

Input argument

str - a string

Output argument

func_handle - a function handle.

Description

function_handle = str2func(str) returns a function handle function_handle for the function named in the string str

str function name or representation of anonymous function.

Examples

fh = str2func('cos')
str = func2str(fh)

myFind = str2func('@(x, y) find(x > y)')
M = rand(4, 3, 5);
[R, C] = myFind(M, 0.9)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

Handle

Description

handle object functions

delete - delete handle objects.
get - Retrieve a property value from an handle object.
invoke - Invoke method on an handle object.
ismethod - Return true if method of handle object.
isprop - Return true if property of handle object.
isvalid - Return true if variable h is a valid handle.
methods - Returns the methods name of an object handle.
properties - Returns the properties name of an object handle.
set - Set a property value of an handle object.

delete

delete handle objects.

Syntax

delete(h)

Input argument

h - a handle object: scalar or matrix.

Description

delete(h) removes from memory the handle objects referenced by h.

When deleted, any references to the objects in h become invalid.

To remove the handle variables, use the clear function.

See clear function about how to force delete with clear function.

Example

f = figure();
ax = gca();
img = image();
hold on
P = plot(magic(5));
children1 = ax.Children;
delete(img);
size(children1)
children2 = ax.Children;
size(children2)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

get

Retrieve a property value from an handle object.

Syntax

R = get(h, property_name)

Input argument

h - an handle object.
property_name - a string: property name.

Output argument

R - The data type of the return value depends on the invoked method.

Description

R = get(h, property_name) returns the value of property asked.

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

invoke

Invoke method on an handle object.

Syntax

R = invoke(h)
R = invoke(h, 'methodname')
R = invoke(h, 'methodname', arg1, arg2, ... , argN)

Input argument

h - an handle object.

Output argument

R - The data type of the return value depends on the invoked method.

Description

invoke(h) returns a struct with a list of all callable methods.

R = invoke(h, 'methodname') calls the method specified by methodname, and returns an output value.

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

ismethod

Return true if method of handle object.

Syntax

res = ismethod(h, methodname)

Input argument

h - a handle object
methodname - a string

Output argument

res - a logical: true or false

Description

ismethod returns a logical 1 if the argument is a valid handle with method name and a logical 0 otherwise.

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

isprop

Return true if property of handle object.

Syntax

res = isprop(h, propertyname)

Input argument

h - a handle object
propertyname - a string

Output argument

res - a logical: true or false

Description

isprop returns a logical 1 if the argument is a valid handle with property name and a logical 0 otherwise.

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

isvalid

Return true if variable h is a valid handle.

Syntax

res = isvalid(h)

Input argument

h - an handle object

Output argument

res - a logical: true or false

Description

isvalid returns a logical 1 if the argument is a valid handle and a logical 0 otherwise.

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

methods

Returns the methods name of an object handle.

Syntax

c = methods(h)

Input argument

h - a handle object

Output argument

c - a cell of strings

Description

methods returns a cell of strings with methods name.

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

properties

Returns the properties name of an object handle.

Syntax

properties(h)
c = properties(h)

Input argument

h - a handle object

Output argument

c - a cell of strings

Description

properties returns a cell of strings with properties name.

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

set

Set a property value of an handle object.

Syntax

R = set(h, property_name, value)

Input argument

h - an handle object.
property_name - a string: property name.
value - a variable.

Output argument

R - user-settable properties and possible values for the object identified by h.

Description

This routine can be used to modify the value of a specified property from an handle object.

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

Error manager

Description

error handling functions

MException - Matrix Exception information.
error - Raise an error message.
getLastReport - Returns last recorded formatted error message.
lasterror - Returns last recorded error message.
lastwarn - Returns last recorded warning message.
rethrow - rethrow error.
throw - throw error.
throwAsCaller - Throw exception as if occurs within calling function.
warning - Display a warning message.

MException

Matrix Exception information.

Syntax

ME = MException(identifier, message)
ME = MException('last')
MException('reset')

Input argument

identifier - a string: error identifier.
message - a string.

Output argument

ME - a MException object.

Description

All Nelson code that detects an error and throws an exception constructs an MException object.

identifier includes one or more component fields and a mnemonic field (example: 'nelson:matrix:empty')

ME = MException('last') return last exception.

MException('reset') clears last exception.

Example

ME = MException('nelson:identifier', 'your error message.')
throw(ME)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

error

Raise an error message.

Syntax

error(id, msg)
error(msg)
error(error_structure)

Input argument

id - a string: error identifier.
msg - a string.
error_structure - error message structure.

Description

error stops the current script execution.

error('') will be ignored and the script will continue to run.

identifier includes one or more component fields and a mnemonic field (example: 'nelson:matrix:empty')

Examples

error('your error message.')
error('nelson:identifier', 'your error message.')

error('')

1 / [1 2 3]
a = lasterror()
lasterror('reset')
b = lasterror()
error(a)
c = lasterror()

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

getLastReport

Returns last recorded formatted error message.

Syntax

messageText = getLastReport()

Output argument

messageText - a character vector: formatted error message.

Description

getLastReport returns last formatted error message.

Examples

lasterror('reset')
getLastReport()

state = execstr('xxxxxx', 'errcatch')
l = lasterror()
getLastReport

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

lasterror

Returns last recorded error message.

Syntax

last_err = lasterror()
lasterror('reset')
lasterror(error_struct)

Output argument

last_err - error message structure.

Description

l = lasterror() returns a structure containing the last error message and information as an struct.

lasterror('reset') clears last error.

lasterror(error_struct) set last error.

Examples

state = execstr('xxxxxx', 'errcatch')
if ~state
  l = lasterror()
end

state = execstr('xxxxxx', 'errcatch')
l = lasterror();
lasterror('reset');
lasterror()
lasterror(l);
lasterror()

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

lastwarn

Returns last recorded warning message.

Syntax

last_message = lastwarn()
[last_message, last_identifier] = lastwarn()
lastwarn('')
lastwarn(new_message)
lastwarn(new_message, new_identifier)
[last_message, last_identifier] = lastwarn('')
[last_message, last_identifier] = lastwarn(new_message)
[last_message, last_identifier] = lastwarn(new_message, new_identifier)

Output argument

last_message - string: last warning message.
last_identifier - string: identifier.

Description

last_message = lastwarn() returns a string containing the last warning message.

lastwarn('') clears last warning.

Example

[1:3]:3
    lastwarn
    [msg, id] = lastwarn()
    lastwarn('')
    [msg, id] = lastwarn()

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

rethrow

rethrow error.

Syntax

rethrow(MException)

Input argument

MException - MException object

Description

rethrow(MException) reissues the error specified by MException.

Example

try
  a
catch ME
  disp(ME)
  rethrow(ME)
end

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

throw

throw error.

Syntax

throw(MException)

Input argument

MException - MException object

Description

throw(MException) throws an exception based on the information contained in the MException object, exception.

Example

ME = MException('nelson:errorId', 'my error')
throw(ME)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

throwAsCaller

Throw exception as if occurs within calling function.

Syntax

throwAsCaller(MException)

Input argument

MException - MException object

Description

It throws an exception as if it occurs within the calling function.

Example

function test_throwAsCaller()
  ME = MException('n:m', 'your error')
  throwAsCaller(ME)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

warning

Display a warning message.

Syntax

warning()
warning(msg)
warning(id, msg)
warning(state)
warning(state, id)
st = warning()
warning(st)

Input argument

id - a string: identifier for the warning.
msg - a string: message to warn.
state - a string: 'on', 'off', 'aserror', 'all' or 'query'.
st - a struct: set warning settings.

Output argument

st - a struct, warning settings.

Description

warning displays a warning message.

warning('') resets lastwarn state.

Examples

warning('your warning message.')

warning('on', 'myModule:identifier');
warning('myModule:identifier', 'my message 1 on');
warning('off', 'myModule:identifier');
warning('myModule:identifier', 'my message 2 off');
warning('aserror', 'myModule:identifier');
warning('myModule:identifier', 'my message 3 as error');

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

Debugger functions

Description

debugger functions

dbstack - call stack.

dbstack

call stack.

Syntax

dbstack
st = dbstack()
dbstack('-completenames')
st = dbstack('-completenames')
dbstack('-completenames', omit)
st = dbstack('-completenames', omit)

Input argument

omit - an integer value: Number of frames to omit (must be positive).

Output argument

st - a struct

Description

dbstack displays the file names and line numbers of the function calls.

dbstack('-completenames') displays the full file names.

Example

Creates a myfun.m and calls it.

function myfun(x)
dbstack();
end

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

Profiling tools

Description

Profile to Improve Performance

profile - Profile execution time for Macro functions.
profsave - Save profile result to HTML format.

profile

Profile execution time for Macro functions.

Syntax

profile on
profile off
profile resume
profile clear
status = profile('status')
p = profile('info')
profile('show', sortOption)
profile('show', sortOption, nbLines)

Input argument

sortOption - a string: 'nfl' by name file line, 'line' by line, 'percalls', 'totaltime', 'filename', 'function' or 'nbcalls'.
nbLines - a integer value: number of lines to display.

Description

Profiling is a way to measure where Macro function spend times.

s = profile('status') returns a structure with the current status of the profiler.

p = profile('info') returns a structure with collected profiling data.

profile('on') starts profiler.

profile('off') stops profiler. Collected profiling data will be retrieved later with p = profile ('info').

profile('clear') clears collected profiling data.

profile('resume') restarts and continue and extends collected profiling data.

Examples

profile on
sind(5)
profile off
profile('show')
profile('show', 'totaltime')
profile('show', 'totaltime', 4)

profile on
sind(5)
profile off
profsave(profile('info'), [tempdir(), 'profile_results'])
unix([tempdir(), 'profile_results/index.html'])

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

profsave

Save profile result to HTML format.

Syntax

profsave
profsave(profile_info)
profsave(profile_info, dirname)

Input argument

profile_info - a struct: result of profile('info')
dirname - a string: output directory destination.

Description

profsave exports the profiling data into a series of HTML files.

The input profile_info is the structure returned by profile('info').

If unspecified, profsave will use the current profile.

Example

profile on
sind(5)
profile off
profsave(profile('info'), [tempdir(), 'profile_results'])
unix([tempdir(), 'profile_results/index.html'])

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

Constructors functions

Description

Create scalars, vectors, or matrices

Inf - Infinity
NaN - Creates an Not-a-Number
diag - Get diagonal elements of matrix or create diagonal matrix.
eps - Creates an epsilon (machine precision)
eye - Creates an identity matrix.
i - Pure Imaginary number.
ones - Creates an matrix made of ones.
pi - Ratio of circle's circumference to its diameter.
zeros - Creates an matrix made of zeros.

Inf

Infinity

Syntax

Inf
inf
Inf(n)
Inf(n, m)

Input argument

n - a variable: n-by-n matrix
m - a variable: n-by-m matrix

Description

NaN returns the IEEE symbol Inf (Infinity).

Examples

Inf

-Inf + Inf

1.e1000

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

NaN

Creates an Not-a-Number

Syntax

NaN
nan
NaN(n)
NaN(n, m)

Input argument

n - a variable: n-by-n matrix
m - a variable: n-by-m matrix

Description

NaN returns the IEEE symbol NaN (Not a Number).

NaN is the result of operations which do not produce a well defined numerical result.

Beware, you must never compare NaN with NaN, in this case, please use isnan.

Examples

NaN

3 + NaN

NaN != NaN
isnan(NaN)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

diag

Get diagonal elements of matrix or create diagonal matrix.

Syntax

D = diag(V)
X = diag(A)
D = diag(V, k)
X = diag(A, k)

Input argument

V - Diagonal elements
A - Input matrix

Output argument

D - vector
X - matrix

Description

diag returns diagonal elements of matrix or create diagonal matrix.

Example

diag(eye(3))
diag(diag(eye(3)))

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

eps

Creates an epsilon (machine precision)

Syntax

eps
eps
eps(n)
eps(n, m)
eps('double')
eps('single')

Input argument

n - a variable: n-by-n matrix
m - a variable: n-by-m matrix

Description

eps returns the machine precision 2^(-52) for double and 2^(-23) for single.

eps(Inf), eps(-Inf) and eps(NaN) return NaN.

Examples

eps

eps('double')

eps('single')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

eye

Creates an identity matrix.

Syntax

R = eye
R = eye(n)
R = eye(n, m)
R = eye(n, m, ..., z)
R = eye(n, m, ..., z, 'like', V)
R = eye(n, m, ..., z, classname)

Input argument

n - a variable: n-by-n matrix
m - a variable: n-by-m matrix

Description

eye returns an identity matrix.

Examples

eye(3)

eye(3,1,3,'single')

A = single([3 3])
B = eye(2,4,'like', A)

A = eye(0, 4)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

i

Pure Imaginary number.

Syntax

Description

i, or j returns a pure imaginary number equivalent to sqrt(-1).

Beware, i and j can be redefined and used as ordinary variables, in this case, you must use clear to restore default behavior.

Examples

A = 3i

A = single(3i)

i = 33;
disp(i);
clear('i');
disp(i);

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

ones

Creates an matrix made of ones.

Syntax

R = ones
R = ones(n)
R = ones(n, m)
R = ones(n, m, ..., z)
R = ones(n, m, ..., z, 'like', V)
R = ones(n, m, ..., z, classname)

Input argument

n - a variable: n-by-n matrix
m - a variable: n-by-m matrix

Description

ones returns a matrix made of ones.

Examples

ones(3,2)

ones(3,1,3,'single')

A = single([3 3])
B = ones(2,4,'like', A)

tic(); single(1) * ones(1000); toc()
tic();ones(1000,'single'); toc()

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

pi

Ratio of circle's circumference to its diameter.

Syntax

Description

pi eturns the floating-point number nearest the value of π .

Examples

cos(pi)

sin(pi)

4*atan(1) == pi

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

zeros

Creates an matrix made of zeros.

Syntax

R = zeros
R = zeros(n)
R = zeros(n, m)
R = zeros(n, m, ..., z)
R = zeros(n, m, ..., z, 'like', V)
R = zeros(n, m, ..., z, classname)

Input argument

n - a variable
m - a variable

Description

zeros returns a matrix made of zeros.

Examples

zeros(3, 2)

zeros(3, 1, 3, 'single')

A = single([3 3])
B = zeros(2, 4, 'like', A)

tic(); single(1) * zeros(1000); toc()
tic();zeros(1000, 'single'); toc()

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

Operators

Description

Operators

all - all of the elements of a matrix satisfy some condition.
and - logical 'AND' operator, &
any - any of the elements of a matrix satisfy some condition.
bitand - Bit-wise AND
bitor - Bit-wise OR
bitxor - Bit-wise XOR
cat - Concatenate arrays.
colon - colon operator ':'.
ctranspose - Returns complex conjugate transpose: ' operator.
eq - equality, == operator.
ge - greater than or equal, >= operator.
gt - greater than, > operator.
horzcat - Horizontal concatenation.
ismember - Array elements that are members of another array.
ldivide - Left division, .\ operator.
le - less than or equal, ≤ operator.
lt - less than, < operator.
minus - Subtraction, - operator
mldivide - Matrix left division, \ operator.
mpower - Matrix power, ^ operator
mrdivide - Matrix right division, / operator.
mtimes - Matrix multiplication, * operator
ne - Inequality, ~= operator
not - not logical, ~ operator
or - logical 'OR' operator, |
plus - Addition, + operator
power - Element wise power, .^ operator
rdivide - Right division, ./ operator
shortcutand - Short circuit 'AND' operator, &&
shortcutor - Short circuit 'OR' operator, ||
subsasgn - Redefine subscripted assignment.
subsindex - Convert an object to an index vector.
subsref - Subscripted reference.
mtimes - Element wise multiplication, .* operator
transpose - Returns vector or matrix transpose: .' operator.
uminus - Unary minus, - operator
uplus - Unary plus, + operator
vertcat - Vertical concatenation.

all

all of the elements of a matrix satisfy some condition.

Syntax

R = all(M)
R = all(M, dim)
R = all(M, 'all')

Input argument

M - a matrix.
dim - a integer value: dimension along it works.
'all' - tests over all elements of M.

Output argument

R - a logical matrix.

Description

all returns true if all of the elements of a matrix satisfy some condition.

Example

all([33, 22; 11, 0])
all([33, 22; 11, 0], 2)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

and

logical 'AND' operator, &

Syntax

C = and(A, B)
C = A & B

Input argument

A - a variable
B - a variable

Output argument

C - result of A & B

Description

C = and(A, B) performs a logical AND operation.

Example

A = [6 8 0; 0 3 89; 15 0 0]
B = [66 56 0; 11 33 55; -11 0 0]
C = A & B
D = and(B, A)
C == D

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

any

any of the elements of a matrix satisfy some condition.

Syntax

R = any(M)
R = any(M, dim)
R = any(M, 'all')

Input argument

M - a matrix.
dim - a integer value: dimension along it works.
'all' - tests over all elements of M.

Output argument

R - a logical matrix.

Description

any returns true if any of the elements of a matrix satisfy some condition.

Example

any([33, 22; 11, 0])
any([33, 22; 11, 0], 2)

History

Version	Description
1.0.0	initial version
1.6.0	manages input argument 'all'

Author

anyan CORNET

bitand

Bit-wise AND

Syntax

C = bitand(A, B)
C = bitand(A, B, assumedtype)

Input argument

A - a variable: double, logical, integer
B - a variable: double, logical, integer
assumedtype - 'int64', 'int32', 'int16', 'int8', 'uint64', 'uint32', 'uint16' or 'uint8'.

Output argument

C - Bit-wise AND result

Description

C = bitand(A, B) returns the bit-wise AND of A and B.

Example

A = uint16([0 1; 0 1]);
B = uint16([0 0; 1 1]);
R = bitand(A, B)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

bitor

Bit-wise OR

Syntax

C = bitor(A, B)
C = bitor(A, B, assumedtype)

Input argument

A - a variable: double, logical, integer
B - a variable: double, logical, integer
assumedtype - 'int64', 'int32', 'int16', 'int8', 'uint64', 'uint32', 'uint16' or 'uint8'.

Output argument

C - Bit-wise OR result

Description

C = bitor(A, B) returns the bit-wise OR of A and B.

Example

A = uint16([0 1; 0 1]);
B = uint16([0 0; 1 1]);
R = bitor(A, B)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

bitxor

Bit-wise XOR

Syntax

C = bitxor(A, B)
C = bitxor(A, B, assumedtype)

Input argument

A - a variable: double, logical, integer
B - a variable: double, logical, integer
assumedtype - 'int64', 'int32', 'int16', 'int8', 'uint64', 'uint32', 'uint16' or 'uint8'.

Output argument

C - Bit-wise XOR result

Description

C = bitxor(A, B) returns the bit-wise XOR of A and B.

Example

A = uint16([0 1; 0 1]);
B = uint16([0 0; 1 1]);
R = bitxor(A, B)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

cat

Concatenate arrays.

Syntax

R = cat(dim, A, B)
R = cat(dim, A1, A2, ..., An)

Input argument

dim - Dimension to operate along: positive integer scalar.
A - a variable: first input.
B - a variable: second input.
A1, A2, ..., An - List of inputs to concatenate

Output argument

R - concatenated array

Description

R = cat(dim, M1, M2, ... , MN) returns the concatenation of M1, M2, ... , MN along the dimension dim.

Example

A = eye(2, 2);
B = ones(2, 2);
C = cat(2, A, B)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

colon

colon operator ':'.

Syntax

R = colon(base, limit)
R = colon(base, increment, limit

Input argument

base - a variable
limit - a variable
increment - a variable (optional)

Output argument

C - result

Description

colon creates vectors. It is an usefull function for loop, extraction and insertion.

colon(base, limit) is equivalent to base:limit

colon(base, increment, limit) is equivalent to base:increment:limit

Examples

1:0.5:4

A = 1:6
B = 1:4:12
C = rand(3, 4)
C(:)
C(:, 3)
C(2, :)
C(:, 1, 1)
C(:) = rand(3, 4)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

ctranspose

Returns complex conjugate transpose: ' operator.

Syntax

C= ctranspose(A)
C = A'

Input argument

A - a variable

Output argument

C - result: complex conjugate transpose of A.

Description

C = ctranspose(A) returns the complex conjugate transpose of A.

Examples

A = 3
B = A'

A = -i
B = A'

A = sparse(eye(3, 4) * i)
B = A'

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

eq

equality, == operator.

Syntax

C = eq(A, B)
C = (A == B)

Input argument

A - a variable
B - a variable

Output argument

C - result of A == B

Description

C = eq(A, B) returns a logical array with elements set to logical true where arrays A and B are equals.

eq compares both real and imaginary parts of numeric arrays.

Examples

eye(2,2) == ones(2, 2)

0 == i

'Nelson' == 'Noslen'

"Nelson" == "Noslen"

'Nelson' == 'l'

eq(0.8-0.6-0.2, 0)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

ge

greater than or equal, >= operator.

Syntax

C = ge(A, B)
C = (A >= B)

Input argument

A - a variable
B - a variable

Output argument

C - result of A >= B

Description

C = ge(A, B) returns a logical array with elements set to logical true A is greater than or equal to B.

ge compares only the real part of numeric arrays.

Examples

eye(2,2) >= ones(2, 2)

0 >= i

'Nelson' >= 'Noslen'

'Nelson' >= 'l'

ge(0.8-0.6-0.2, 0)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

gt

greater than, > operator.

Syntax

C = gt(A, B)
C = (A > B)

Input argument

A - a variable
B - a variable

Output argument

C - result of A > B

Description

C = gt(A, B) returns a logical array with elements set to logical true A is greater than B.

gt compares only the real part of numeric arrays.

Examples

eye(2,2) > ones(2, 2)

0 > i

'Nelson' > 'Noslen'

'Nelson' > 'l'

gt(0.8 - 0.6 - 0.2, 0)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

horzcat

Horizontal concatenation.

Syntax

R = horzcat(M1, M2, ... , MN)
R = [M1, M2, ... , MN]

Input argument

M1 - a variable
M2 - a variable
MN - a variable

Output argument

R - result of [M1, M2, ... , MN]

Description

R = horzcat(M1, M2, ... , MN) returns the horizontal concatenation of M1, M2, ... , MN along the dimension 2.

Examples

A = eye(2, 2);
B = ones(2, 2);
C = horzcat(A, B)
D = [A, B]

A = 'nel';
B = 'son';
C = horzcat(A, B)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

ismember

Array elements that are members of another array.

Syntax

T = ismember(A, B)

Input argument

A - a variable
B - a variable

Output argument

T - result of ismember.

Description

T = ismember(A, B) returns an array of logical where the data in A is found in B.

Example

A = [50 30 40 20];
B = [20 40 40 40 60 80];
T = ismember(A, B)

T = ismember(["a","b","f"], ["b", "f", "c"])

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

ldivide

Left division, .\ operator.

Syntax

C = ldivide(A, B)
C = A .\ B

Input argument

A - a variable
B - a variable

Output argument

C - result of A .\ B

Description

C = ldivide(A, B) returns the element-by-element left division of A and B.

Examples

B = ones(3, 4)
A = B *2
A .\ B

B = 2
A = B *2
A .\ B

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

le

less than or equal, ≤ operator.

Syntax

C = le(A, B)

Input argument

A - a variable
B - a variable

Output argument

C - result of le(A, B)

Description

C = le(A, B) returns a logical array with elements set to logical true A is less than or equal to B.

le compares only the real part of numeric arrays.

Examples

eye(2,2) &#60;= ones(2, 2)

0 &#60;= i

'Nelson' &#60;= 'Noslen'

'Nelson' &#60;= 'l'

le(0.8 - 0.6 - 0.2, 0)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

lt

less than, < operator.

Syntax

C = lt(A, B)

Input argument

A - a variable
B - a variable

Output argument

C - result of lt(A, B)

Description

C = lt(A, B) returns a logical array with elements set to logical true A is less than B.

lt compares only the real part of numeric arrays.

Examples

eye(2,2) &#60; ones(2, 2)

0 &#60; i

'Nelson' &#60; 'Noslen'

'Nelson' &#60; 'l'

lt(0.8 - 0.6 - 0.2, 0)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

minus

Subtraction, - operator

Syntax

C = minus(A, B)
C = A - B

Input argument

A - a variable
B - a variable

Output argument

C - result of A - B

Description

C = minus(A, B) performs subtraction A - B variables.

Examples

minus(3, 4)
3 - 4

[1, 2] - 1
minus([1, 2], 1)

ones(0, 0) - 1

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

mldivide

Matrix left division, \ operator.

Syntax

C = mldivide(A, B)
C = A \ B

Input argument

A - a variable
B - a variable

Output argument

C - result of A \ B

Description

C = mldivide(A, B) returns the matrix left division of A and B.

Example

B = ones(3, 4)
A = B *2
A \ B

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

mpower

Matrix power, ^ operator

Syntax

C = mpower(A, B)
C = A ^ B

Input argument

A - a variable
B - a variable

Output argument

C - result of A^B

Description

C = mpower(A, B) performs matrix power operation: A^B

Example

mpower(3, 4)
3^4

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

mrdivide

Matrix right division, / operator.

Syntax

C = mrdivide(A, B)
C = A / B

Input argument

A - a variable
B - a variable

Output argument

C - result of A / B

Description

C = mrdivide(A, B) returns the matrix right division of A and B.

Example

B = ones(3, 4)
A = B *2
A / B

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

mtimes

Matrix multiplication, * operator

Syntax

C = mtimes(A, B)
C = A * B

Input argument

A - a variable
B - a variable

Output argument

C - result of A * B

Description

C = mtimes(A, B) performs matrix multiplication operation: A * B.

Examples

mtimes(3, 4)
3 * 4

M1 = [2 6 10; 4 8 70];
M2 = [-25 88 1; 23 29 41; 24 40 0];
M1 * M2

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

ne

Inequality, ~= operator

Syntax

C = ne(A, B)
C = A ~= B

Input argument

A - a variable
B - a variable

Output argument

C - result of A ~= B

Description

C = ne(A, B) performs inequality operation: A ~= B variables.

ne compares both real and imaginary parts of numeric arrays.

Example

ne(3, 4)
3 ~= 4

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

not

not logical, ~ operator

Syntax

C = not(A)
C = ~A

Input argument

A - a variable

Output argument

C - result of ~A

Description

C = not(A) performs not logical ~A.

Example

M = false(3, 3);
~M

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

or

logical 'OR' operator, |

Syntax

C = or(A, B)
C = A | B

Input argument

A - a variable
B - a variable

Output argument

C - result of A | B

Description

C = or(A, B) performs a logical OR operation.

Example

A = [6 8 0; 0 3 89; 15 0 0]
B = [66 56 0; 11 33 55; -11 0 0]
C = A | B
D = or(B, A)
C == D

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

plus

Addition, + operator

Syntax

C = plus(A, B)
C = A + B

Input argument

A - a variable
B - a variable

Output argument

C - result of A + B

Description

C = plus(A, B) performs addition A + B variables.

Examples

plus(3, 4)
3 + 4

[1, 2] + 1
plus([1, 2], 1)

ones(0, 0) + 1

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

power

Element wise power, .^ operator

Syntax

C = power(A, B)
C = A .^ B

Input argument

A - a variable
B - a variable

Output argument

C - result of A.^B

Description

C = power(A, B) performs an element wise power operation: A .^ B .

Example

power(3, 4)
3.^4

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

rdivide

Right division, ./ operator

Syntax

C = rdivide(A, B)
C = A ./ B

Input argument

A - a variable
B - a variable

Output argument

C - result of A ./ B

Description

C = rdivide(A, B) performs right division operation: A ./* B.

Examples

rdivide(3, 4)
3 ./ 4

M1 = [2];
M2 = [-25 88 1];
M1 ./ M2

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

shortcutand

Short circuit 'AND' operator, &&

Syntax

C = A && B

Input argument

A - a variable
B - a variable

Output argument

C - result of A && B

Description

C = A && B performs a logical AND operation, the second operand is evaluated only when the result is not fully determined by the first operand.

Example

A = [6 8 0; 0 3 89; 15 0 0]
B = [66 56 0; 11 33 55; -11 0 0]
C = A && B

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

shortcutor

Short circuit 'OR' operator, ||

Syntax

C = A || B

Input argument

A - a variable
B - a variable

Output argument

C - result of A || B

Description

C = A || B performs a logical OR operation, the second operand is evaluated only when the result is not fully determined by the first operand.

Example

A = [6 8 0; 0 3 89; 15 0 0]
B = [66 56 0; 11 33 55; -11 0 0]
C = A || B

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

subsasgn

Redefine subscripted assignment.

Syntax

B = subsasgn(A, S, B)

Input argument

A - Object used in indexing operation
S - Structure with two fields: 'type' and 'subs'.
B - The assigned value, located on the right side of the assignment statement.

Output argument

R - The outcome of the assignment statement is the object that has been modified, and this modified object is provided as the first argument.

Description

B = subsasgn(A, S, B) assigns a value to an element of a cell or matrix.

Example

Parentheses Indexing

R1 = {1, 'GoodBye', [1, 2;3, 4]};
S = substruct('{}', {1, 3});
R2 = subsasgn(R1, S, 'Hello')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

subsindex

Convert an object to an index vector.

Syntax

r = subsindex(O)

Input argument

O - a variable

Description

If O is an object then subsindex is the overloading method that allows to convert this object to a valid indexing vector.

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

subsref

Subscripted reference.

Syntax

B = subsref(A, S)

Input argument

A - Indexed object array
B - Indexing structure

Output argument

B - Result of indexing expression

Description

B = subsref(A, S) is invoked when using the syntax A(i), A{i}, or A.i with an object A.

Examples

Parentheses Indexing

A = magic(5);
S.type='()';
S.subs={1:2,':'};
R = subsref(A, S)

Brace Indexing

C = {"one", 2, 'three'};
S = [];
S.type = '{}';
S.subs = {[1 2]};
[R1, R2] = subsref(C, S);

Dot Indexing

A = struct('number', 10);
S = [];
S.type = '.';
S.subs = 'number';
R = subsref(A, S)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

mtimes

Element wise multiplication, .* operator

Syntax

C = times(A, B)
C = A .* B

Input argument

A - a variable
B - a variable

Output argument

C - result of A .* B

Description

C = times(A, B) performs element wise multiplication operation: A .* B.

Examples

times(3, 4)
3 .* 4

M1 = [2 6 10; 4 8 70];
M2 = [-25 88 1; 23 29 41];
M1 .* M2

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

transpose

Returns vector or matrix transpose: .' operator.

Syntax

C= transpose(A)
C = A .'

Input argument

A - a variable

Output argument

C - result: transpose of A.

Description

C = transpose(A) returns the transpose of A.

Examples

A = 3
B = A.'

A = -i
B = A.'

A = sparse(eye(3, 4) * i)
B = A.'

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

uminus

Unary minus, - operator

Syntax

C = uminus(A)
C = -A

Input argument

A - a variable

Output argument

C - result of -A

Description

C = uminus(A) performs unary minus ie -A.

Example

M = 3;
-M

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

uplus

Unary plus, + operator

Syntax

C = uplus(A)
C = +A

Input argument

A - a variable

Output argument

C - result of +A

Description

C = uplus(A) performs unary plus ie +A.

Example

M =-3;
+M

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

vertcat

Vertical concatenation.

Syntax

R = vertcat(M1, M2, ... , MN)
R = [M1; M2; ... ; MN]

Input argument

M1 - a variable
M2 - a variable
MN - a variable

Output argument

R - result of [M1; M2; ... ; MN]

Description

R = vertcat(M1, M2, ... , MN) returns the vertical concatenation of M1, M2, ... , MN along the dimension 1.

Examples

A = eye(2, 2);
B = ones(2, 2);
C = vertcat(A, B)
D = [A; B]

A = 'nel';
B = 'son';
C = vertcat(A, B)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

Elementary functions

Description

elementary functions

abs - Absolute value
allfinite - Check if all array elements are finite.
angle - Phase angle
base2dec - Convert number in a base to decimal.
bernsteinMatrix - Bernstein matrix
bin2dec - Convert number in base 2 to decimal.
bin2num - Convert two's complement binary string to number.
blkdiag - Block diagonal matrix
cast - Converts variable to a different data type
ceil - Round up
circshift - Circular shift
complex - Creates an complex number.
conj - Complex conjugate
deal - Distribute inputs to outputs.
dec2base - Convert decimal number to another base.
dec2bin - Convert decimal number to base 2.
dec2hex - Convert decimal number to base 16.
exp - Exponential
factorial - Factorial function
filter - 1-D digital filter
find - Find Non-zero Elements
fix - Round towards zero
flip - Flip order of elements
flipdim - Flip array along specified dimension
fliplr - Flip order of elements left to right
flipud - Flip order of elements up to dow
floor - Round down
hadamard - Hadamard matrix
hankel - Hankel matrix
hex2dec - Convert number in base 16 to decimal.
hilb - Hilbert matrix
hypot - Square root of sum of squares
imag - Imaginary part of an complex number.
ind2sub - Linear index to matrix subscript values
invhilb - Inverse of Hilbert matrix
ipermute - Inverse permute array dimensions.
isapprox - Return true if arguments are approximately equal, within the precision.
iscolumn - Determine whether input is column vector.
istriu - Checks if matrix is diagonal.
isequal - Return true if all arguments x1, x2, ... , xn are equal (same dimensions, same values).
isequaln - Return true if all arguments x1, x2, ... , xn are equal (same dimensions, same values or NaNs).
isequalto - Return true if all arguments x1, x2, ... , xn are equal (same type, same dimensions, same values or NaNs).
isfinite - Check for finite entries.
isinf - Check for Infinity entries.
ismatrix - determines whether input is matrix or not
isnan - Check for Not a Number entries.
isrow - Determine whether input is row vector.
isscalar - Check if the input is a scalar
istril - Checks if matrix is lower triangular.
istriu - Checks if matrix is upper triangular.
isvector - Checks input is vector.
length - Length of an object.
linspace - linearly spaced vector constructor.
log - Natural logarithm.
log10 - Common logarithm (base 10).
log1p - log(1 + x) accurately for small values of x.
log2 - dissect floating-point numbers into base 2 exponent and mantissa.
logspace - logarithmically spaced vector constructor.
magic - Magic square
meshgrid - Cartesian rectangular grid in 2-D or 3-D.
minus - Subtraction, - operator
mod - Modulus after division.
ndgrid - Rectangular grid in N-D space
ndims - Number of dimensions of an array.
nextpow2 - Exponent of next higher power of 2
norm - Matrix and vector norms
normest - 2-norm estimate
nthroot - The real 𝑛th root of real number.
num2bin - Convert number to binary representation.
numel - Number of elements.
permute - Permute array dimensions.
pinv - Moore-Penrose pseudoinverse
pow2 - Base 2 exponentiation and scaling of floating-point numbers.
real - Real part of an complex number.
rem - Remainder after division.
repmat - Replicate and tile an array.
reshape - Reshapes a vector or a matrix to a different size matrix.
rosser - Classic symmetric eigenvalue test problem.
rot90 - Rotate array 90 degrees.
round - Round to nearest integer
shiftdim - Shift array dimensions
sign - Find the sign function of a number.
size - Size of an object.
sqrt - Square root.
squeeze - Remove dimensions of length 1.
sub2ind - Matrix subscript values to linear index
substruct - Create structure argument for subsasgn or subsref
swapbytes - Swap byte ordering.
toeplitz - Toeplitz matrix
tril - Lower triangular part of matrix
triu - Upper triangular part of matrix
vander - Vandermonde matrix
wilkinson - Wilkinson's eigenvalue test matrix

abs

Absolute value

Syntax

R = abs(M)

Input argument

M - a variable

Output argument

R - result of abs: absolute value.

Description

abs computes the absolute value.

If input argument is a complex number, abs computes the complex magnitude.

Example

x = [1+i,-i;i,2i];
r = abs(x)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

allfinite

Check if all array elements are finite.

Syntax

tf = allfinite(M)

Input argument

M - a variable

Output argument

tf - logical: result of 'allfinite'.

Description

allfinite returns a logical scalar which is true where elements of M are all finite values.

Example

X = sparse([1 2 NaN 3 0 Inf 0 4]);
R = allfinite(X)
R2 = isfinite(X)

History

Version	Description
1.6.0	initial version

Author

Allan CORNET

angle

Phase angle

Syntax

R = angle(Z)

Input argument

Z - a variable (double, single, complex)

Output argument

R - result of angle function.

Description

angle computes the phase angle, equivalent to atan2(imag(Z), real(Z)).

Example

x = [1+i,-i;i,2i];
r = angle(x)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

base2dec

Convert number in a base to decimal.

Syntax

D = base2dec(TXT, B)

Input argument

TXT - a char array.
B - an integer value: [2, 36].

Output argument

D - result of base2dec: an integer value.

Description

base2dec converts number in a base to decimal.

Note:

- dec2base and base2dec are inverses of one another.

- values are cached to speed up next computation base2dec('', 2) to clear cache.

Example

base2dec('313', 3)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

bernsteinMatrix

Bernstein matrix

Syntax

B = bernsteinMatrix(n, t)

Input argument

n - nonnegative integer: Approximation order.
t - number or vector: Evaluation point.

Output argument

B - Bernstein Matrix: length(t) - by - n+1 matrix.

Description

B = bernsteinMatrix(n, t) constructs a Bernstein matrix B with dimensions length(t) - by - (n+1), where t is a vector.

The Bernstein matrix is also referred to as the Bezier matrix.

This function can be utilized to calculate the points of a Bezier curve.

Example

t = 0:1/100:1;
B = bernsteinMatrix(3, t);
P = [0 0 0; 1 2 1; 1 -2 3; 5 2 4];
bezierCurve = B * P;
plot3(bezierCurve(:,1), bezierCurve(:,2), bezierCurve(:,3))

History

Version	Description
1.5.0	initial version

Author

Allan CORNET

bin2dec

Convert number in base 2 to decimal.

Syntax

D = bin2dec(TXT)

Input argument

TXT - a char array.

Output argument

D - result of bin2dec: an integer value.

Description

bin2dec converts number in base 2 to decimal.

Note:

- bin2dec and dec2bin are inverses of one another.

Example

bin2dec('11')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

bin2num

Convert two's complement binary string to number.

Syntax

R = bin2num(M)

Input argument

M - a char array with.

Output argument

R - result of num2bin: logical, single or double.

Description

bin2num converts binary character arry to a numeric array.

Note:

- num2bin always returns the binary representations in a column

- bin2num and num2bin are inverses of one another.

Used function(s)

C++ std::bitset

Bibliography

http://www.oxfordmathcenter.com/drupal7/node/43

Example

X = [65535 128; 1 0]
Y = num2bin(X)
bin2num(Y)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

blkdiag

Block diagonal matrix

Syntax

R = blkdiag(M1, ... , MN)

Input argument

M1, ..., MN - a numeric 2D matrix

Output argument

R - a matrix.

Description

R = blkdiag(M1, ... , MN) build the block diagonal matrix created by aligning the input matrices M1, ... , MN along the diagonal of R.

Example

blkdiag(magic(2), magic(3), magic(4))

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

cast

Converts variable to a different data type

Syntax

R = cast(V, type_destination)
R = cast(V, 'like', W)

Input argument

V - a variable
type_destination - a string: name of destination data type.
W - a variable

Output argument

R - a variable with new data type.

Description

cast converts variable to a different data type.

R = cast(V, 'like', W) converts varible V to sparsity and same data type than W.

Example

r = cast([3.6 1.2 -2.4], 'like', int64(3))
r = cast([3.6 1.2 -2.4], 'int64')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

ceil

Round up

Syntax

C = ceil(A)

Input argument

A - a variable

Output argument

C - result of ceil.

Description

ceil returns an integer or complex matrix made of rounded up elements.

Example

ceil(pi)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

circshift

Circular shift

Syntax

R = circshift(M, N)
R = circshift(M, N, DIM)

Input argument

M - a variable
N - shift
DIM - dimension to operate

Output argument

R - result of 'circshift'.

Description

circshift computes circular shift.

Example

x = [10, 20, 30; 40, 50, 60; 70, 80, 90];
circshift (x, 1
circshift (x, -2))

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

complex

Creates an complex number.

Syntax

cpx = complex(a)
cpx = complex(a, b)

Input argument

a - a variable: real part
b - a variable: imaginary part

Output argument

cplx - result of a + b*i

Description

complex returns a complex value from real arguments.

With only one input argument, complex returns a complex value a + 0*i.

Example

z = complex(3, 2)
z2 = complex(Inf, Inf)
z3 = Inf + Inf * i

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

conj

Complex conjugate

Syntax

CZ = conj(M)

Input argument

M - a variable

Output argument

CZ - result of conj: complex conjugate.

Description

conj returns the complex conjugate.

Example

x = [1+i,-i;i,2i];
r = conj(x)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

deal

Distribute inputs to outputs.

Syntax

[R1, ... , Rn] = deal(A1, ... , An)
[R1, ... , Rn] = deal(A)

Input argument

A1, ... , An - variables

Output argument

R1, ... , Rn - variables

Description

deal replicates the input parameters to the corresponding output parameters.

If a singular input parameter is provided, its value will be duplicated across all outputs.

Examples

[A1, A2, A3] = deal(pi)

S = [];
S.A = [];
S(2).A = [];
S(3).A = [];
A1 = 200;
A2 = 'fifo';
A3 = 1:11;
[S.A] = deal(A1, A2, A3)

C = cell(1,3)
A1 = 200;
A2 = 'fifo';
A3 = 1:11;
[C{:}] = deal(A1, A2, A3)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

dec2base

Convert decimal number to another base.

Syntax

R = dec2base(D, B)
R = dec2base(D, B, N)

Input argument

D - a nonnegative integer smaller than the value returned by flintmax.
B - an integer value [2, 36].
N - an integer value. number of digits.

Output argument

R - result of dec2base: char array.

Description

dec2base converts decimal number to another base.

values are cached to speed up next computation dec2base([], 2) to clear cache.

Example

X = [65535 128; 1 0]
Y = dec2base(X, 2)
Y = dec2base(X, 2, 26)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

dec2bin

Convert decimal number to base 2.

Syntax

R = dec2bin(D)
R = dec2bin(D, N)

Input argument

D - a non negative integer smaller than the value returned by flintmax.
N - an integer value. number of digits.

Output argument

R - result of dec2bin: char array.

Description

dec2bin converts decimal number to base 2.

Example

Y = dec2bin(2)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

dec2hex

Convert decimal number to base 16.

Syntax

R = dec2hex(D)
R = dec2hex(D, N)

Input argument

D - a non negative integer smaller than the value returned by flintmax.
N - an integer value. number of digits.

Output argument

R - result of dec2hex: char array.

Description

dec2hex converts decimal number to base 16.

Example

Y = dec2hex(12)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

exp

Exponential

Syntax

R = exp(M)

Input argument

M - a variable

Output argument

R - result of exp: exponential.

Description

exp computes the exponential value.

If input argument is a complex number, exp computes exp(x) * (cos(y) + i * sin(y)) with z = x + i * y.

Example

x = [1+i,-i;i,2i];
r = exp(x)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

factorial

Factorial function

Syntax

R = factorial(M)

Input argument

M - a integer, real single or real double matrix.

Output argument

R - result of factorial function.

Description

factorial computes the factorial function: the product of all integers values: 1 * 2 * ... * M

Example

R = factorial([1:10])
R = factorial(int8(4))

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

filter

1-D digital filter

Syntax

y = filter(b, a, x)

Input argument

b - Numerator coefficients of rational transfer function: vector.
a - Denominator coefficients of rational transfer function: vector.
x - Input data: matrix.

Output argument

y - Filtered data: matrix.

Description

The function filter(b, a, x) applies a rational transfer function to filter the input data array x.

This transfer function is defined by the coefficients of the numerator (b) and denominator (a).

If the first coefficient of a (a(1)) is not equal to 1, the filter normalizes the coefficients by a(1). It is crucial for a(1) to be nonzero.

When x is a vector, the function returns a vector of the same size as x containing the filtered data.

Example

f = figure();
rng default
t = linspace(-pi,pi,100);
X = sin(t) + (0.33 * rand(size(t)));
windowSize = 7;
b = (1/windowSize)*ones(1,windowSize);
a = 1;
y = filter(b, a, X);
plot(t, X)
hold on
plot(t, y)
legend(_('Input Data'), _('Filtered Data'));

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

find

Find Non-zero Elements

Syntax

K = find(M)
[R, C] = find(M)
[R, C, V] = find(M)
K = find(M, N)
[R, C] = find(M, N)
[R, C, V] = find(M, N)
K = find(M, N, D)
[R, C] = find(M, N, D)
[R, C, V] = find(M, N, D)

Input argument

M - a scalar, vector, matrix, or multidimensional array.
N - positive integer scalar value: number of nonzeros to find.
D - direction: 'first' (default) or 'last'.

Output argument

K - indices to nonzero elements (vector).
R - row subscripts (vector).
C - column subscripts (vector).
V - nonzero elements of M (vector).

Description

K = find(M) returns a vector with the linear indices of each nonzero element of M.

Example

M = rand(4, 3, 5);
[R, C, V] = find(M > 0.9)
M(R(1),C(1),V(1))

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

fix

Round towards zero

Syntax

C = fix(A)

Input argument

A - a variable

Output argument

C - result of fix.

Description

fix returns an integer matrix made of nearest rounded integers toward zeros.

Example

fix(pi)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

flip

Flip order of elements

Syntax

B = flip(A, dim)

Input argument

A - an array
dim - an positive integer value

Output argument

B - flipped array.

Description

flip return an new array of A flipped about the dimension dim.

Example

x = eye(3, 2);
y = flip(x, 1)
y = flip(x, 2)
y = flip(x, 3)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

flipdim

Flip array along specified dimension

Syntax

B = flipdim(A, dim)

Input argument

A - an array
dim - an positive integer value

Output argument

B - flipped array.

Description

flipdim return an new array of A flipped about the dimension dim.

flipdim is similar to flip and available for compatibility with old existing scripts.

Example

x = eye(3, 2);
y = flipdim(x, 1)
y = flipdim(x, 2)
y = flipdim(x, 3)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

fliplr

Flip order of elements left to right

Syntax

B = fliplr(A)

Input argument

A - an array

Output argument

B - flipped array.

Description

fliplr return an new array of A flipped left to right.

Example

x = eye(3, 2);
y = fliplr(x)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

flipud

Flip order of elements up to dow

Syntax

B = flipud(A)

Input argument

A - an array

Output argument

B - flipped array.

Description

fliplr return an new array of A flipped up to down.

Example

x = eye(3, 2);
y = flipud(x)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

floor

Round down

Syntax

C = floor(A)

Input argument

A - a variable

Output argument

C - result of floor.

Description

floor returns an integer matrix made of nearest rounded down integers.

Example

floor(pi)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

hadamard

Hadamard matrix

Syntax

H = hadamard(n)
H = hadamard(n, classname)

Input argument

n - scalar integer value: order.
classname - row character vector or scalar string: class name desired ('double' by default).

Output argument

H - Hadamard Matrix.

Description

H = hadamard(n) returns the Hadamard Matrix of order n.

Bibliography

https://en.wikipedia.org/wiki/Hadamard_matrix , https://mathworld.wolfram.com/HadamardMatrix.html

Example

H = hadamard(4)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

hankel

Hankel matrix

Syntax

H = hankel(c)
H = hankel(c, r)

Input argument

c - First column of Hankel matrix: vector or scalar.
r - Last row of Hankel matrix: vector or scalar.

Output argument

H - Hankel Matrix.

Description

H = hankel(c) returns a square Hankel Matrix with c the first column of the matrix and the elements are zero below the main anti-diagonal.

H = hankel(c, r) returns a Hankel matrix with c as its first column and r as its last row.

If last element of c differs from the first element of r, then Hankel issues a warning and uses the last element of c for the anti-diagonal.

Example

c = [1 2 3 4 5];
hankel(c)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

hex2dec

Convert number in base 16 to decimal.

Syntax

D = hex2dec(TXT)

Input argument

TXT - a char array.

Output argument

D - result of hex2dec: an integer value.

Description

hex2dec converts number in base 16 to decimal.

Note:

- hex2dec and dec2hex are inverses of one another.

Example

bin2dec('11')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

hilb

Hilbert matrix

Syntax

h = invhilb(n)
h = invhilb(n, className)

Input argument

n - a scalar, nonnegative integer.
className - 'single' or 'double' (default).

Output argument

h - Hilbert matrix.

Description

hilb computes the exact inverse of the exact Hilbert matrix.

Bibliography

https://en.wikipedia.org/wiki/David_Hilbert, and Thanks to https://nhigham.com/2020/06/30/what-is-the-hilbert-matrix/

Example

h = invhilb(5)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

hypot

Square root of sum of squares

Syntax

C = hypot(A, B)

Input argument

A - a variable: scalars, vectors, matrices, multidimensional arrays single or double
B - a variable: scalars, vectors, matrices, multidimensional arrays single or double

Output argument

R - result of hypot: hypothenuse.

Description

hypot computes the hypothenuse.

If one or both inputs is NaN, then hypot returns NaN.

Example

R = hypot(1e308, 1e308)
R = hypot(1e309, 1e309)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

imag

Imaginary part of an complex number.

Syntax

im = imag(M)

Input argument

M - a variable

Output argument

R - imaginary part of the elements of the complex array M.

Description

R = imag(M) Return the imaginary part of M.

Example

cplx = 22+34*i;
r = imag(cplx)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

ind2sub

Linear index to matrix subscript values

Syntax

[row, col] = ind2sub(sz, ind)
[I1, I2, ..., In] = ind2sub(sz, ind)

Input argument

sz - size of array: vector of positive integers.
ind - linear indices.

Output argument

row - row subscripts.
col - column subscripts.
I1, I2, ..., In - multidimensional subscripts.

Description

ind2sub converts linear indices to subscript.

Example

ind = [4 5 6 7];
sz = [4 4];
[row,col] = ind2sub(sz,ind)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

invhilb

Inverse of Hilbert matrix

Syntax

h = hilb(n)
h = hilb(n, className)

Input argument

n - a scalar, nonnegative integer.
className - 'single' or 'double' (default).

Output argument

h - Hilbert matrix.

Description

hilb computes the Hilbert matrix.

Bibliography

https://en.wikipedia.org/wiki/David_Hilbert, and Thanks to https://nhigham.com/2020/06/30/what-is-the-hilbert-matrix/

Example

h = hilb(5)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

ipermute

Inverse permute array dimensions.

Syntax

R = ipermute(A, order)

Input argument

A - an array.
order - Dimension order: row vector

Output argument

R - result array rearranged with new dimension order.

Description

ipermute permutes the dimensions of an array (in inverse order of permute).

Example

x = [1 2 3; 4 5 6]
y = permute(x,[3 1 2])
x2 = ipermute(y,[3 1 2])

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

isapprox

Return true if arguments are approximately equal, within the precision.

Syntax

res = isapprox(x1, x2)
res = isapprox(x1, x2, precision)

Input argument

x1 - a matrix, a sparse matrix of doubles, or a multidimensional matrix.
x2 - a matrix, a sparse matrix of doubles, or a multidimensional matrix.
precision - a double value: 0. by default

Output argument

res - a logical value

Description

For matrices, the comparison is done using the Hilbert-Schmidt norm (aka Frobenius norm L2 norm).

isapprox manages complex numbers. In this case, the real parts of the input arguments are compared. If this fails, it returns false. If this succeeds, the imaginary parts are compared.

To compare values, NaN, Inf, -Inf and remaining values, are separated. As it is impossible to compare NaN values between them, we compare the indices where NaN value occurs. For infinity values, we also compare the indices where Inf values occurs.

Examples

A = pi
B = single(pi)
res = isapprox(A, B)

A = pi
B = single(pi)
res = isapprox(A, B, 1e-4)

A = [pi NaN]
res = isapprox(A, A)

A = [pi NaN]
B = [pi + 2*eps, NaN]
res = isapprox(A, B)
res = isapprox(A, B, eps)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

iscolumn

Determine whether input is column vector.

Syntax

tf = iscolumn(V)

Input argument

V - a variable

Output argument

tf - logical: result of 'iscolumn'.

Description

iscolumn(V) returns logical true if size(V) returns [n, 1] with a nonnegative integer value n, and logical false otherwise.

Example

iscolumn([1:4])
iscolumn([1:4]')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

istriu

Checks if matrix is diagonal.

Syntax

tf = isdiag(M)

Input argument

M - a numeric array

Output argument

tf - logical: result of 'isdiag'.

Description

isdiag returns an scalar logical if entry is diag.

Example

A = eye(3, 3);
R = isdiag(A)
R = isdiag(A(:,1))

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

isequal

Return true if all arguments x1, x2, ... , xn are equal (same dimensions, same values).

Syntax

res = isequal(x1, x2)
res = isequal(x1, x2, xn)

Input argument

x1 - a value
x2 - a value
xn - a value

Output argument

res - a logical value

Description

isequal returns true if x1 and x2 are the same size and their contents are of equal value; otherwise, it returns false. isequal compares real and imaginary parts of numeric arrays. NaN (Not a Number) values are considered to be unequal to other elements.

Examples

A = eye(3, 3);
res = isequal(A, A)

A = eye(3, 3);
B = single(A)
res = isequal(A, B)
res = isequalto(A, B)

res = isequal('nel', 'son')

res = isequalnNaN, NaN)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

isequaln

Return true if all arguments x1, x2, ... , xn are equal (same dimensions, same values or NaNs).

Syntax

res = isequaln(x1, x2)
res = isequaln(x1, x2, xn)

Input argument

x1 - a value
x2 - a value
xn - a value

Output argument

res - a logical value

Description

isequaln returns true if x1 and x2 are the same size and same values; otherwise, it returns false. isequaln compares real and imaginary parts of numeric arrays. NaN (Not a Number) values are considered to be equal to other elements.

Examples

A = eye(3, 3);
res = isequaln(A, A)

A = eye(3, 3);
B = single(A)
res = isequaln(A, B)
res = isequalto(A, B)

res = isequaln('nel', 'son')

res = isequaln(NaN, NaN)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

isequalto

Return true if all arguments x1, x2, ... , xn are equal (same type, same dimensions, same values or NaNs).

Syntax

res = isequalto(x1, x2)
res = isequalto(x1, x2, xn)

Input argument

x1 - a value
x2 - a value
xn - a value

Output argument

res - a logical value

Description

isequalto returns true if x1 and x2 are the same type, same size and same values; otherwise, it returns false.

Example

A = eye(3, 3);
res = isequal(A, single(A))
res = isequalto(A, single(A))

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

isfinite

Check for finite entries.

Syntax

tf = isfinite(M)

Input argument

M - a variable

Output argument

tf - logical: result of 'isfinite'.

Description

isfinite returns a logical array which is true where elements of M are finite values.

Example

isfinite(pi)
isfinite(Inf)
isfinite(-Inf)
isfinite(int32(3))
X = sparse([1 2 NaN 3 0 Inf 0 4]);
R = isfinite(X)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

isinf

Check for Infinity entries.

Syntax

tf = isinf(M)

Input argument

M - a variable

Output argument

tf - logical: result of 'isinf'.

Description

isnan returns a logical array which is true where elements of M are Infinity values.

Example

isnan(pi)
isinf(Inf)
isinf(-Inf)
isinf(int32(3))
X = sparse([1 2 NaN 3 0 Inf 0 4]);
R = isinf(X)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

ismatrix

determines whether input is matrix or not

Syntax

TF = ismatrix(A)

Input argument

A - input array as a scalar, vector, matrix, or multidimensional array.

Output argument

TF - a logical: true if it is a matrix.

Description

TF = ismatrix(A) returns true if A is a matrix.

A matrix is a two-dimensional array that has a size of m-by-n, where m and n are nonnegative integers.

Example

x = [1+i,-i;i,2i];
ismatrix(x)
ismatrix(ones(3,1,2))

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

isnan

Check for Not a Number entries.

Syntax

tf = isnan(M)

Input argument

M - a variable

Output argument

tf - logical: result of 'isnan'.

Description

isnan returns a logical array which is true where elements of M are "Not a Number" values.

Example

isnan(pi)
isnan(NaN)
isnan(int32(3))
X = sparse([1 2 NaN 3 0 NaN 0 4]);
R = isnan(X)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

isrow

Determine whether input is row vector.

Syntax

tf = isrow(V)

Input argument

V - a variable

Output argument

tf - logical: result of 'isrow'.

Description

isrow(V) returns logical true if size(V) returns [1, n] with a nonnegative integer value n, and logical false otherwise.

Example

isrow([1:4])
isrow([1:4]')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

isscalar

Check if the input is a scalar

Syntax

TF = iscalar(A)

Input argument

A - input array as a scalar, vector, matrix, or multidimensional array.

Output argument

TF - a logical: true if it is a scalar.

Description

TF = isscalar(A) returns logical true if A is a scalar, meaning it is a 1-by-1 two-dimensional array.

Otherwise, it returns logical false.

Example

x = [1+i, -i ; i, 2i];
isscalar(x)
isscalar(1)

History

Version	Description
1.10.0	initial version

Author

Allan CORNET

istril

Checks if matrix is lower triangular.

Syntax

tf = istril(M)

Input argument

M - a numeric array

Output argument

tf - logical: result of 'istril'.

Description

istril returns an scalar logical if entry is lower triangular.

Example

A = eye(3, 3);
R = istriu(A)
R = istriu(A(:,1))

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

istriu

Checks if matrix is upper triangular.

Syntax

tf = istriu(M)

Input argument

M - a numeric array

Output argument

tf - logical: result of 'istriu'.

Description

istriu returns an scalar logical if entry is upper triangular.

Example

A = eye(3, 3);
R = istriu(A)
R = istriu(A(:,1))

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

isvector

Checks input is vector.

Syntax

tf = isvector(M)

Input argument

M - a variable

Output argument

tf - logical: result of 'isvector'.

Description

isvector returns an scalar logical if entry is an vector.

Example

A = eye(3, 3);
R = isvector(A)
R = isvector(A(:,1))

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

length

Length of an object.

Syntax

l = length(M)

Input argument

M - a variable

Output argument

l - the length of the largest array dimension in M.

Description

For matrix or N-dimensional array, length returns the number of elements along the largest dimension. For empty object, length returns 0. For scalar, length returns 1. For a vector, length returns the number of elements.

Example

length(ones(3, 0))
length(3)
length([1 2 3 4 5])
length(ones(3, 4, 5))

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

linspace

linearly spaced vector constructor.

Syntax

V = linspace(s, e)
V = linspace(s, e, n)

Input argument

s - first value: a scalar, single or double.
e - last value: a scalar, single or double.
n - Number of points: a scalar, single or double (by default 100).

Output argument

V - result of linspace: an linearly spaced vector.

Description

linspace generates an linearly spaced vector.

Example

V = linspace(1+2i, 10+10i, 4)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

log

Natural logarithm.

Syntax

R = log(M)

Input argument

M - a variable

Output argument

R - result of log: Natural logarithm.

Description

log computes the natural logarithm.

If input argument is a complex number or negative, log(z) computes log(abs(z)) + angle(z) * i.

Example

x = [1+i,-i;i,2i];
r = log(x)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

log10

Common logarithm (base 10).

Syntax

R = log10(M)

Input argument

M - a variable

Output argument

R - result of log: base 10.

Description

log10 computes common logarithm (base 10).

For negative real and complex values of M, log10 function returns complex values.

Example

x = [1+i,-i;i,2i];
r = log10(x)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

log1p

log(1 + x) accurately for small values of x.

Syntax

R = log1p(M)

Input argument

M - a variable

Output argument

R - result of log(1 + x) accurately for small values of x.

Description

log1p computes log(1 + x) accurately for small values of x.

Example

x = [1+i,-i;i,2i];
r = log1p(x)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

log2

dissect floating-point numbers into base 2 exponent and mantissa.

Syntax

R = log2(M)
[F, E] = log2(M)

Input argument

M - a variable: a matrix

Output argument

R - result of log2: computes the base 2 logarithm of the elements of X.
F - Mantissa values that satisfy this equation: M= F.*2.^E
E - Exponent values that satisfy this equation: M= F.*2.^E

Description

log2 dissects several numbers into the exponent and mantissa.

[F, E] = log2(M), any zeros in M produce F = 0 and E = 0.

Input values of Inf, -Inf, or NaN are returned unchanged in F with a corresponding exponent of E = 0.

Used function(s)

std::frexp and std::logb C++ functions

Example

x = [1+i,-i;i,2i];
R = log2(x)
[F, E] = log2(x)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

logspace

logarithmically spaced vector constructor.

Syntax

V = logspace(s, e)
V = logspace(s, e, n)

Input argument

s - first value: a scalar, single or double.
e - last value: a scalar, single or double.
n - Number of points: a scalar, single or double (by default 100).

Output argument

V - result of logspace: an logarithmically spaced vector.

Description

logspace generates an logarithmically spaced vector.

Example

V = logspace(1+2i, 10+10i, 4)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

magic

Magic square

Syntax

M = magic(N)

Input argument

N - Matrix order, specified as a scalar integer.

Output argument

M - result of magic function.

Description

M = magic(N) computes an square matrix constructed as an arrangement of the 1:n^2 such that the row sums, column sums, and diagonal sums are all equal to the same value.

Example

M = magic(3)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

meshgrid

Cartesian rectangular grid in 2-D or 3-D.

Syntax

[X, Y] = meshgrid(x, y)
[X, Y] = meshgrid(x)
[X, Y, Z] = meshgrid(x, y, z)
[X, Y, Z] = meshgrid(x)

Input argument

x - x-coordinates of points: vector
y - y-coordinates of points: vector
z - z-coordinates of points: vector

Output argument

X - x-coordinates over grid: 2-D or 3-D array.
Y - y-coordinates over grid: 2-D or 3-D array.
Z - z-coordinates over grid: 3-D array.

Description

meshgrid creates Cartesian rectangular grid in 2-D or 3-D.

Example

x = -1:0.4:1;
y = -1:0.4:1;
[X, Y] = meshgrid(x, y)

x = 0:2:6;
y = 0:1:6;
z = 0:3:6;
[X,Y,Z] = meshgrid(x, y, z)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

minus

Subtraction, - operator

Syntax

C = minus(A, B)
C = A - B

Input argument

A - a variable
B - a variable

Output argument

C - result of A - B

Description

C = minus(A, B) performs subtraction A - B variables.

Examples

minus(3, 4)
3 - 4

[1, 2] - 1
minus([1, 2], 1)

ones(0, 0) - 1

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

mod

Modulus after division.

Syntax

C = mod(A, B)

Input argument

A - a variable: dividend
B - a variable: divisor

Output argument

C - result of mod(A, B)

Description

C = mod(A, B) computes the modulo of A and B, i.e : A - B .* floor (A ./ B).

This function manages also negative values.

Example

mod (-1, 3)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

ndgrid

Rectangular grid in N-D space

Syntax

[X1, X2, ..., Xn] = ndgrid(x1, x2, ... , xn)
[X1, X2, ..., Xn] = ndgrid(xg)

Input argument

x1, x2, … , xn - vector: grid vectors as separate arguments.
xg - vector: grid vector for all dimensions.

Output argument

X1, X2, … , Xn - array: full grid representation.

Description

[X1, X2, … , Xn] = ndgrid(x1, x2, … , xn) generates an n-dimensional full grid by replicating each grid vector.

[X1, X2, … , Xn] = ndgrid(xg) In this scenario, the single grid vector xg is used for all dimensions. The number of output arguments determines the dimensionality n of the resulting grid.

Examples

M = {'apple', 'banana', 'cherry'};
N = {'blue', 'green', 'red'};
ndgrid(M , N)

[X, Y] = ndgrid(1:2:19, 2:2:12)

History

Version	Description
1.6.0	initial version

Author

Allan CORNET

ndims

Number of dimensions of an array.

Syntax

n = ndims(M)

Input argument

M - a variable

Output argument

n - a integer value: Number of dimensions of M.

Description

n = ndims(M) return the number of dimension of the array M.

M is greater than or equal to 2.

Example

ndims(ones(3, 0))
ndims(3)
ndims([1 2 3 4 5])
ndims(ones(3, 4, 5))

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

nextpow2

Exponent of next higher power of 2

Syntax

R = nextpow2(M)

Input argument

M - a variable

Output argument

R - result of nextpow2: next higher power of 2.

Description

if M is a vector or a matrix nextpow2(M) applies element-wise.

If M is a scalar, nextpow2(M) returns the first p such that 2^p >= abs(M).

Example

R = nextpow2([10, Inf, 30, -Inf, 90, NaN])
M = uint32([1020 4000 32700]);
R = nextpow2(M)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

norm

Matrix and vector norms

Syntax

R = norm(V)
R = norm(V, p)
R = norm(V, 'fro')
R = norm(M)
R = norm(M, 1)
R = norm(M, 2)
R = norm(M, Inf)
R = norm(M, 'fro')

Input argument

M - a 2D matrix single or double
V - a vector single or double
p - a scalar (p-norm)

Output argument

R - result of norm: scalar.

Description

norm computes the norm of a vector or a matrix.

Frobenius norm of M is equal to sqrt (sum (diag (M' * M))) .

Examples

M = [1 2; 3 4];
norm(M)
norm(M, 1)
norm(M, 2)
norm(M, Inf)
norm(M, 'fro')
V = [1 2 3 4];
norm(V)
norm(V, 1)
norm(V, 2)
norm(V, Inf)
norm(V, 'fro')

x = ones(3000, 3000);
tic();R = norm(x);toc

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

normest

2-norm estimate

Syntax

nrm = normest(A)
[nrm, count] = normest(A)
nrm = normest(A, tolerance)
[nrm, count] = normest(A, tolerance)

Input argument

A - Input matrix
tolerance - Relative error tolerance

Output argument

nrm - Matrix norm: scalar.
count - Number of power iterations: scalar.

Description

nrm = normest(A) returns an estimate of the 2-norm of the matrix A.

Example

M = [    0    2.4495         0         0         0         0         0
    2.4495         0    3.1623         0         0         0         0
         0    3.1623         0    3.4641         0         0         0
         0         0    3.4641         0    3.4641         0         0
         0         0         0    3.4641         0    3.1623         0
         0         0         0         0    3.1623         0    2.4495
         0         0         0         0         0    2.4495         0];
[nrm, count] = normest(M)
norm(M)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

nthroot

The real 𝑛th root of real number.

Syntax

Y = nthroot(X, N)

Input argument

X - Input array: scalar, vector, matrix or multidimensional array.
N - Roots to calculate: scalar or array of same size as X.

Output argument

Y - result of 'nthroot'.

Description

𝑌 = nthroot(𝑋, 𝑁) returns the real 𝑛th root of the elements of 𝑋.

Both 𝑋 and 𝑁 must be real scalars or arrays of the same size. If an element in 𝑋 is negative, the corresponding element in 𝑁 must be an odd integer.

When computing roots where both real and complex roots exist, the power function efficiently computes only the complex roots.

To obtain the real root in such cases, use the nthroot function instead.

Example

X = [-2 -3 -2; 4 -2 -5]
N = [1 -1 3; 1/2 5 3]
Y = nthroot(X, N)

History

Version	Description
1.6.0	initial version

Author

Allan CORNET

num2bin

Convert number to binary representation.

Syntax

R = num2bin(M)

Input argument

M - a variable: logical, integer, single or double real full matrix.

Output argument

R - result of num2bin: char array.

Description

num2bin returns a char array giving the literal bit representation of a number.

Used function(s)

C++ std::bitset

Bibliography

http://www.oxfordmathcenter.com/drupal7/node/43

Example

X = [65535 128; 1 0]
Y = num2bin(X)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

numel

Number of elements.

Syntax

nbel = numel(M)

Input argument

M - a variable

Output argument

nbel - the number of elements.

Description

Return the number of elements in the object M.

Example

numel(ones(3, 0))
numel(ones(3,4))
numel(ones(3,4,5))

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

permute

Permute array dimensions.

Syntax

R = permute(A, order)

Input argument

A - an array.
order - Dimension order: row vector

Output argument

R - result array rearranged with new dimension order.

Description

permute permutes the dimensions of an array.

Example

x = [1 2 3; 4 5 6]
y = permute(x,[3 1 2])

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

pinv

Moore-Penrose pseudoinverse

Syntax

y = pinv(A)
y = pinv(A, tol)

Input argument

A - matrix: input matrix
tol - scalar: singular value tolerance

Output argument

y - Moore-Penrose Pseudoinverse of matrix A.

Description

pinv returns Moore-Penrose Pseudoinverse of matrix A.

Example

A = [1, 2, 3; 4, 5, 6];
R = pinv(A)
R = pinv(A, 2)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

pow2

Base 2 exponentiation and scaling of floating-point numbers.

Syntax

Y = pow2(E)
Y = pow2(X, E)

Input argument

E - Exponent values
X - Significand values

Output argument

Y - result of pow2.

Description

Y = pow2(E) computes 2 to the power of E.

Y = pow2(X, E) computes X times 2 to the power of E.

Example

R = pow2([1, 2, 3; 4, 5, 6], [6, 5, 4; 3, 2, 1])

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

real

Real part of an complex number.

Syntax

R = real(M)

Input argument

M - a variable

Output argument

R - real part of the elements of the complex array M.

Description

R = real(M) Return the real part of M.

Example

cplx = 22+34*i;
r = real(cplx)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

rem

Remainder after division.

Syntax

C = rem(A, B)

Input argument

A - a variable: dividend
B - a variable: divisor

Output argument

C - result of rem(A, B)

Description

C = rem(A, B) computes the remainder of A and B, i.e : A - fix(A ./ B) .* B.

This function manages also negative values.

mod(A, 0) = A , whereas rem(A, 0) = NaN.

mod(A, B) has the sign of B, while rem(A, B) has the sign of A.

mod and rem are equals if A and B have the same sign.

Example

rem (-1, 3)
mod(-1, 3)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

repmat

Replicate and tile an array.

Syntax

R = repmat(A, m)
R = repmat(A, m, n)
R = repmat(A, m, n, p …)
R = repmat(A, [m n])
R = repmat(A, [m n p …])

Input argument

A - an array.
m, n, p … - a value: integer

Output argument

R - result array form by tiling.

Description

repmat repeats matrix or N-D array.

Examples

repmat(1:5, 2)

repmat(1:5, [2 3])

repmat(1:5, [2 3 4])

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

reshape

Reshapes a vector or a matrix to a different size matrix.

Syntax

M2 = reshape(M1, s1, ... ,sN)
M2 = reshape(M1, ..., [], ...)
M2 = reshape(M1, size)

Input argument

M1 - a vector or an matrix
size - a size vector
s1, ... ,sN - a s1 - by - ... - by - sN array where s1, ..., sN indicates the size of each dimension.

Output argument

M2 - Matrix reshaped

Description

reshape performs a reshape to a different size matrix. If only one dimension is specified, reshape will determine complementary size automatically. [ ] is used to unspecify the dimension.

Example

M1 = ones(3, 4, 5);
M2 = reshape(M1, [5, 3, 4])
M2 = reshape(M1, 5, [], 4)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

rosser

Classic symmetric eigenvalue test problem.

Syntax

R = rosser()
R = rosser(classname)

Input argument

classname - row character vector or scalar string: class name desired ('double' by default).

Output argument

R - Rosser Matrix.

Description

R = rosser() returns the Rosser Matrix.

Bibliography

https://archive.org/details/jresv47n4p291

Example

R = rosser()

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

rot90

Rotate array 90 degrees.

Syntax

B = rot90(A)
B = rot90(A, k)

Input argument

A - an array
k - an positive integer value: Rotation constant.

Output argument

B - rotated array.

Description

B = rot90(A, k) rotates array A counter clockwise by k * 90 degrees, with k is an integer value.

Consider flip function to flip arrays in any dimension.

Example

x = eye(3, 2);
y = rot90(x, 0)
y = rot90(x, 1)
y = rot90(x, 2)
y = rot90(x, 3)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

round

Round to nearest integer

Syntax

C = round(A)

Input argument

A - a variable

Output argument

C - result of round.

Description

round rounds the elements to the nearest integers.

Example

round(pi)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

shiftdim

Shift array dimensions

Syntax

B = shiftdim(A, n)
B = shiftdim(A)
[B, m] = shiftdim(A)

Input argument

A - Input array: vector, matrix or multidimensional array.
n - Number of positions: integer value.

Output argument

B - vector, matrix, or multidimensional array.
m - Number of dimensions removed: non-negative integer.

Description

shiftdim(A, n) reorganizes the dimensions of an array A by n positions.

Specifically, when n is a positive integer, it shifts the dimensions to the left, and when n is a negative integer, it shifts the dimensions to the right.

Example

A = rand(2, 3, 4);
size(A)
% Shift the dimensions of array A by 2 positions to the left
B = shiftdim(A, 2)

History

Version	Description
1.3.0	initial version

Author

Allan CORNET

sign

Find the sign function of a number.

Syntax

R = sign(M)

Input argument

M - a variable

Output argument

R - result of sign.

Description

sign find the sign function of a number.

-1 if the corresponding element of M is less than 0.

0 if the corresponding element of M equals 0.

1 if the corresponding element of M is greater than 0.

If input argument is a complex number, sign computes M ./ abs(M).

Example

V = [-1 0 15 NaN Inf];
sign(V)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

size

Size of an object.

Syntax

s = size(X)
sdim = size(X, dim)
vec = size(X, dims)
[r, c] = size(X)
[s1, ... , sn] = size(X)

Input argument

X - a variable
dim - a variable: a positive integer to get the dimth dimension.
dims - a variable: a vector of positive integer to get the dimth dimensions.

Output argument

s - a row vector whose elements contain the length of the corresponding dimension of X.
sdim - the length of dimension dim.
vec - length of dimensions dims.
[r, c] - number of rows and columns.
[s1, ... , sn] - numbers with integer values.

Description

Examples

X = rand(3, 4, 5, 6);
size(X)
size(X, 3)
size(X, [2 4])
[r, c] =size(X)
[s1, s2, s3, s4] = size(X)

size(cell(4,3))

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

sqrt

Square root.

Syntax

R = sqrt(M)

Input argument

M - a variable

Output argument

R - result of sqrt: square root.

Description

sqrt computes the square root.

If input argument is a complex number or negative, sqrt(z) computes: sqrt(r) * (cos(phi/2) + sin(phi/2) * i) with

r = sqrt((real(z) * real(z)) + (imag(z) * imag(z))) and phi = atan2(imag(z), real(z))

Example

x = -3:3;
r = sqrt(x)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

squeeze

Remove dimensions of length 1.

Syntax

B = squeeze(A)

Input argument

A - input array: multidimensional array

Output argument

B - output array.

Description

B = squeeze(A) returns an array with the same elements as the input array A, but with dimensions of length 1 removed.

Example

A = zeros(1, 1, 3);
A(:, :, 1:3) = [1 20 3];
R = squeeze(A)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

sub2ind

Matrix subscript values to linear index

Syntax

ind = sub2ind(sz, row, col)
ind = sub2ind(sz, I1, I2, ..., In)

Input argument

sz - size of array: vector of positive integers.
row - row subscripts.
col - column subscripts.
I1, I2, ..., In - multidimensional subscripts.

Output argument

ind - linear indices.

Description

ind2sub converts subscripts to linear indices. .

Example

row = [2 3 4 2];
col = [2 2 2 3];
sz = [3 3];
ind = sub2ind(sz, row, col)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

substruct

Create structure argument for subsasgn or subsref

Syntax

S = substruct(type1, subs1, type2, subs2, ...)

Description

S = substruct(type1, subs1, type2, subs2, ...) generates a structure containing fields necessary for an overloaded subsref or subsasgn method.

Each type char vector is limited to '.', '()', or '{}'.

The associated subs argument should be a field name (for the '.' type) or a cell array containing index vectors (for the '()' or '{}' types).

Example

S = struct('field1', 10, 'field2', 'Hello', 'field3', [1, 2, 3]);
% Create a substruct for accessing the 'field2'
s = substruct('.', 'field2');
% Use subsref to get the value of 'field2'
value = subsref(S, s);

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

swapbytes

Swap byte ordering.

Syntax

R = swapbytes(M)

Input argument

M - a variable: integer, single or double real full matrix.

Output argument

R - result of swapbytes: reversed byte order of M.

Description

swapbytes Swap byte ordering.

endian (little - big) converter

Example

X = uint16([65535 128; 1 0])
Y = swapbytes(X)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

toeplitz

Toeplitz matrix

Syntax

T = toeplitz(c, r)
T = toeplitz(r)

Input argument

c - a scalar or vector: column of Toeplitz matrix.
r - a scalar or vector: row of Toeplitz matrix.

Output argument

T - Toeplitz matrix.

Description

T = toeplitz(c, r) returns the Toeplitz matrix whose first row is r and first column is c.

T = toeplitz(c) returns the symmetric Toeplitz matrix.

Bibliography

https://en.wikipedia.org/wiki/Toeplitz_matrix

Example

T = toeplitz(1:5, 1:2:7)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

tril

Lower triangular part of matrix

Syntax

T = tril(M)
T = tril(M, k)

Input argument

M - 2D input matrix
k - Diagonals to include: integer real value

Output argument

R - Lower Triangular Portions of Matrix

Description

tril computes Lower Triangular Portions of Matrix.

R = tril(M, k) returns the elements on and above the kth diagonal of M.

Example

x = [1+i,-i;i,2i];
r = tril(x)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

triu

Upper triangular part of matrix

Syntax

T = triu(M)
T = triu(M, k)

Input argument

M - 2D input matrix
k - Diagonals to include: integer real value

Output argument

R - Upper Triangular Portions of Matrix

Description

triu computes Upper Triangular Portions of Matrix.

R = triu(M, k) returns the elements on and above the kth diagonal of M.

Example

x = [1+i,-i;i,2i];
r = triu(x)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

vander

Vandermonde matrix

Syntax

A = vander(v)

Input argument

v - a numeric vector.

Output argument

A - Vandermonde Matrix.

Description

A = vander(v) returns the Vandermonde Matrix.

Bibliography

https://en.wikipedia.org/wiki/Vandermonde_matrix

Example

A = vander(1:.5:3)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

wilkinson

Wilkinson's eigenvalue test matrix

Syntax

W = wilkinson(n)
W = wilkinson(n, classname)

Input argument

n - scalar integer value: order.
classname - row character vector or scalar string: class name desired ('double' by default).

Output argument

W - Wilkinson's eigenvalue test matrix.

Description

W = wilkinson(n) returns the wilkinson Matrix of order n.

Bibliography

https://en.wikipedia.org/wiki/Wilkinson_matrix

Example

W = wilkinson(4)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

Data analysis

Description

data analysis

conv - Convolution and polynomial multiplication.
conv2 - 2-D convolution.
cumprod - Cumulative product of array elements.
cumsum - Cumulative sum of array elements.
ismissing - Check for missing values.
issorted - Determine if array is sorted.
max - Maximum elements of an array.
min - Minimum elements of an array.
prod - Product of array elements.
sort - Sort array elements by quick sort algorithm.
sum - Sum of array elements.
unique - Unique values.

conv

Convolution and polynomial multiplication.

Syntax

C = conv(u, v)
C = conv(u, v, shape)

Input argument

u - input vectors, specified as either row or column vectors.
v - input vectors, specified as either row or column vectors.
shape - subsection of convolution: 'full' (default: full 2-D convolution), 'same' (central part of the convolution) or 'valid' (parts of the convolution that are computed without zero-padded edges).

Output argument

C - convolution, returned as a vector or matrix.

Description

conv returns the convolution of vectors u and v.

Example

U = [-1 2 3 -2 0 1 2];
V = [2 4 -1 1];
R = conv(U, V, 'same')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

conv2

2-D convolution.

Syntax

C = conv2(A, B)
C = conv2(u, v, A)
C = conv2(A, B, shape)
C = conv2(u, v, A, shape)

Input argument

A - vector or matrix.
B - vector or matrix.
u - row or column vector.
v - row or column vector.
shape - subsection of convolution: 'full' (default: full 2-D convolution), 'same' (central part of the convolution) or 'valid' (parts of the convolution that are computed without zero-padded edges).

Output argument

C - 2-D convolution, returned as a vector or matrix.

Description

conv2 returns the two-dimensional convolution.

Example

A = magic(3);
B = magic(4);
R = conv2(A, B, 'same')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

cumprod

Cumulative product of array elements.

Syntax

R = cumprod(M)
R = cumprod(M, d)
R = cumprod(M, d, direction)
R = cumprod(M, d, direction, nanflag)

Input argument

M - an array of double, single, integers, ...
d - dimension to operate along: positive integer scalar.
direction - a string: 'reverse', 'forward' (default).
nanflag - a string: 'includenan' (default) or 'omitnan'.

Output argument

R - Cumulative Product of array elements.

Description

R = cumprod(M) returns the cumulative product of the array elements of M.

Example

M = uint8([10:30:70;20:30:80;30:30:90]);
R = cumprid(M)
R = cumprod(M, 'reverse')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

cumsum

Cumulative sum of array elements.

Syntax

R = cumsum(M)
R = cumsum(M, d)
R = cumsum(M, d, direction)
R = cumsum(M, d, direction, nanflag)

Input argument

M - an array of double, single, integers, ...
d - dimension to operate along: positive integer scalar.
direction - a string: 'reverse', 'forward' (default).
nanflag - a string: 'includenan' (default) or 'omitnan'.

Output argument

R - Cumulative Sum of array elements.

Description

R = cumsum(M) returns the cumulative sum of the array elements of M.

Example

M = uint8([10:30:70;20:30:80;30:30:90]);
R = cumsum(M)
R = cumsum(M, 'reverse')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

ismissing

Check for missing values.

Syntax

tf = ismissing(M)

Input argument

M - a variable

Output argument

tf - logical: result of 'ismissing'.

Description

ismissing returns a logical array which is true where elements of M are missing values.

missing data are defined as:

NaN for double or single

missing for string array

' ' for character array

'' for cell of character array

Example

A = ["Nel", NaN, "son"];
ismissing(A)
B = [1 2 NaN Inf];
ismissing(B)
C = 'Nel son'
ismissing(C)
D = {'Nel' '' 'son'}
ismissing(D)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

issorted

Determine if array is sorted.

Syntax

tf = issorted(A)
tf = issorted(A, dim)
tf = issorted(..., direction)
tf = issorted(A, 'rows')

Input argument

A - an nelson's variable (double, single, int8, int16, int32, int64, uint8, uint16, uint32, uint64, logical, char, string, cell).
dim - Dimension to operate along: positive integer scalar.
direction - Sorting direction: 'ascend' (default) or 'descend'.
'rows' - returns true when the elements of the first column of a matrix are sorted.

Output argument

tf - a logical: true if array is sorted.

Description

tf = issorted(A) returns true if the elements of A are sorted in ascending order, and false otherwise.

Example

x = [1 2 3 4];
issorted(x) % returns true
x = [1 3 2 4];
issorted(x) % returns false

% Check if a matrix is sorted by rows
A = [1 2 3; 4 5 6; 7 8 9];
issorted(A, 'rows') % returns true
A = [1 2 3; 7 8 9; 4 5 6];
issorted(A, 'rows') % returns false

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

max

Maximum elements of an array.

Syntax

M = max(A)
[M, I] = max(A)
M = max(A, [], dim)
[M, I] = max(A, [], dim)
M = max(A, [], dim, 'omitnan')
[M, I] = max(A, [], dim, 'includenan')
[M, I] = max(A, [], 'all')
[M, I] = max(A, [], 'all', 'omitnan')
[M, I] = max(A, [], 'all', 'includenan')
C = max(A, B)
C = max(A, B, 'omitnan')
C = max(A, B, 'includenan')

Input argument

A - a variable
dim - a positive integer scalar (Dimension to operate along)
'omitnan' - ignore all NaN values. default behaviour. max will return the first element, if all elements are NaN.
'includenan' - include the NaN values.
'all' - it finds the maximum over all elements.

Output argument

M - Maximum values of A.
I - Index to maximum values of A.
C - Maximum elements from A or B.

Description

max find maximum values in an array.

If A is a matrix then M = max(A) is a row vector containing the maximum value of each column.

If A is a vector then M = max(A) will return the maximum of A.

If A If A is complex number then M = max(A) will return founded complex number with the largest magnitude.

Example

A = [1 2 3; 4 5 6];
M = max(A)
M = max(A, [], 'all')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

min

Minimum elements of an array.

Syntax

M = min(A)
[M, I] = min(A)
M = min(A, [], dim)
[M, I] = min(A, [], dim)
M = min(A, [], dim, 'omitnan')
[M, I] = min(A, [], dim, 'includenan')
[M, I] = min(A, [], 'all')
[M, I] = min(A, [], 'all', 'omitnan')
[M, I] = min(A, [], 'all', 'includenan')
C = min(A, B)
C = min(A, B, 'omitnan')
C = min(A, B, 'includenan')

Input argument

A - a variable
dim - a positive integer scalar (Dimension to operate along)
'omitnan' - ignore all NaN values. default behaviour. min will return the first element, if all elements are NaN.
'includenan' - include the NaN values.
'all' - it finds the minimum over all elements.

Output argument

M - minimum values of A.
I - Index to minimum values of A.
C - minimum elements from A or B.

Description

min find minimum values in an array.

If A is a matrix then M = min(A) is a row vector containing the minimum value of each column.

If A is a vector then M = min(A) will return the minimum of A.

If A If A is complex number then M = min(A) will return founded complex number with the largest magnitude.

Example

A = [1 2 3; 4 5 6];
M = min(A)
M = min(A, [], 'all')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

prod

Product of array elements.

Syntax

R = prod(M)
R = prod(M, d)
R = prod(M, d)
R = prod(M, d, t)
R = prod(M, d, t, f)

Input argument

M - an array of double, single, integers, ...
d - dimension to operate along: positive integer scalar.
t - a string: 'default', 'double' or 'native'.
f - a string: 'includenan' or 'omitnan'.

Output argument

R - Product of array elements.

Description

R = prod(M) returns the product of the array elements of M.

Example

M = uint8([10:30:70;20:30:80;30:30:90]);
R = prod(M, 'native')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

sort

Sort array elements by quick sort algorithm.

Syntax

B = sort(A)
B = sort(A, dim)
B = sort(..., direction)
B = sort(..., name, value)
[B, I] = sort(...)

Input argument

A - an nelson's variable (double, single, int8, int16, int32, int64, uint8, uint16, uint32, uint64, logical, char, string, cell).
dim - Dimension to operate along: positive integer scalar.
direction - Sorting direction: 'ascend' (default) or 'descend'.
name, value - name-value pair arguments.

Output argument

B - sorted array.
I - sort index.

Description

sort implements quick sort algorithm.

name-value pair arguments:

'MissingPlacement' - Placement of missing values: 'auto' (default), 'first', 'last'.

'ComparisonMethod' - Element comparison method: 'auto' (default), 'real', 'abs'.

Used function(s)

qsort (stl)

Bibliography

Quick sort algorithm from Bentley and McIlroy's "Engineering a Sort Function". Software - Practice and Experience

Examples

ComparisonMethod

A = [10+20i 30+i 10i 0 -10i];
B = sort(A,'ComparisonMethod', 'auto')
B = sort(A, 'ComparisonMethod', 'real')
B = sort(A, 'ComparisonMethod', 'abs')

MissingPlacement

A = [NaN 3 6 0 NaN];
[B, I] = sort(A, 'MissingPlacement', 'auto')
[B, I] = sort(A, 'MissingPlacement', 'first')
[B, I] = sort(A, 'MissingPlacement', 'last')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

sum

Sum of array elements.

Syntax

R = sum(M)
R = sum(M, d)
R = sum(M, d)
R = sum(M, d, t)
R = sum(M, d, t, f)

Input argument

M - an array of double, single, integers, ...
d - dimension to operate along: positive integer scalar.
t - a string: 'default', 'double' or 'native'.
f - a string: 'includenan' or 'omitnan'.

Output argument

R - Sum of array elements.

Description

R = sum(M) returns the sum of the array elements of M.

Example

M = uint8([10:30:70;20:30:80;30:30:90]);
R = sum(M, 'native')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

unique

Unique values.

Syntax

C = unique(A)
C = unique(A, 'rows')
[C, ia, ic] = unique(...)

Input argument

A - an nelson's variable (double, single, int8, int16, int32, int64, uint8, uint16, uint32, uint64, logical, char, string, cell).

Output argument

C - Unique data of A.
ia - Index to A: column vector.
ic - Index to C: column vector.

Description

C = unique(A) returns the unique elements of array A in sorted order.

C = unique(A, 'rows') considers each row of A as a unique entity and returns the unique rows in sorted order.

Note that the 'rows' option does not support cell arrays.

[C, ia, ic] = unique(...) extends any of the previous syntaxes to also return index vectors ia and ic.

For a vector A, the relationships are C = A(ia) and A = C(ic).

For a matrix or array A, the relationships are C = A(ia) and A(:) = C(ic).

If the 'rows' option is used, the relationships are C = A(ia, :) and A = C(ic, :).

Used function(s)

std::sort, std::unique (stl)

Examples

A = [10+20i 30+i 10i 0 -10i];
[C, ia, ic] = unique(A)

A = {'hi', 'good'; 'good', 'tell'; 'hi', 'bye'}
[C, ia, ic] = unique(A)

History

Version	Description
1.6.0	initial version

Author

Allan CORNET

Trigonometric functions

Description

module about sine, cosine, and related functions.

acos - Computes the inverse cosine in radians for each element of x.
acosd - Inverse cosine in degrees.
acosh - Inverse hyperbolic cosine.
acot - Inverse cotangent of angle in radians
acotd - Inverse cotangent of angle in degrees
acoth - Inverse hyperbolic cotangent.
acsc - Inverse cosecant in radians.
acscd - Inverse cosecant in degrees.
acsch - Inverse hyperbolic cosecant.
asec - Inverse secant of angle in radians.
asecd - Inverse secant of argument in degrees.
asech - Inverse hyperbolic secant of angle in radians.
asin - Computes the inverse sine in radians for each element of x.
asind - Inverse sine in degrees.
asinh - Inverse hyperbolic sine function
atan - Computes the inverse tangent in radians for each element of x.
atan2 - Computes the four-quadrant inverse tangent.
atan2d - Four-quadrant inverse tangent in degrees.
atand - Inverse tangent in degrees.
atanh - Computes the inverse hyperbolic tangent.
cart2pol - Transforms Cartesian coordinates to polar or cylindrical.
cart2sph - Transforms Cartesian to spherical coordinates.
cos - Computes the cosine in radians for each element of x.
cosd - Computes the cosine in degree for each element of x.
cosh - Computes the hyperbolic cosine in radians for each element of x.
cosm - Computes the matrix cosine of a square matrix.
cospi - Computes cos(X * pi) accurately.
cot - Cotangent of angle in radians
cotd - Cotangent of argument in degrees
coth - Hyperbolic cotangent.
csc - Cosecant of input angle in radians.
cscd - Cosecant of argument in degrees.
csch - Hyperbolic cosecant.
deg2rad - Convert angle from degrees to radians.
pol2cart - Transforms polar or cylindrical coordinates to Cartesian.
rad2deg - Convert angle from radians to degrees.
sec - Secant of angle in radians.
secd - Secant of argument in degrees.
sech - Hyperbolic secant.
sin - Computes the sine in radians for each element of x.
sind - Computes the sine in degree for each element of x.
sinh - Computes the hyperbolic sine in radians for each element of x.
sinm - Computes the matrix sinus of a square matrix.
sinpi - Computes sin(X * pi) accurately.
sph2cart - Transform spherical coordinates to Cartesian.
tan - Computes the tangent in radians for each element of x.
tand - Computes the tangent in degree for each element of x.
tanh - Computes the hyperbolic tangent in radians for each element of x.
tanm - Computes the matrix tangent of a square matrix.

acos

Computes the inverse cosine in radians for each element of x.

Syntax

res = acos(x)

Input argument

x - a numeric value

Output argument

res - a numeric value

Description

acos computes the inverse cosine in radians for each element of x.

Example

A = eye(3, 3);
res = acos(A)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

acosd

Inverse cosine in degrees.

Syntax

res = acosd(x)

Input argument

x - a numeric value

Output argument

res - a numeric value

Description

atand computes the inverse cosine in degrees for each element of x.

Example

x = [1 -20 0 2 5];
y = acosd(x)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

acosh

Inverse hyperbolic cosine.

Syntax

res = acosh(x)

Input argument

x - a numeric value

Output argument

res - a numeric value

Description

acos computes the inverse hyperbolic cosine.

Example

A =  [1+2i, 2, -3];
res = acosh(A)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

acot

Inverse cotangent of angle in radians

Syntax

res = acot(x)

Input argument

x - a numeric value

Output argument

res - a numeric value

Description

acot computes the inverse cotangent of angle for each element of x.

Example

R = acot([-i pi+i*pi/2 -1+i*4])

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

acotd

Inverse cotangent of angle in degrees

Syntax

res = acotd(x)

Input argument

x - a numeric value

Output argument

res - a numeric value

Description

acotd computes the inverse cotangent of angle for each element of x in degrees.

Example

R = acotd([-i pi+i*pi/2 -1+i*4])

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

acoth

Inverse hyperbolic cotangent.

Syntax

res = acoth(x)

Input argument

x - a numeric value

Output argument

res - a numeric value

Description

acoth computes the inverse hyperbolic cotangent.

Example

A =  [1+2i, 2, -3];
res = acoth(A)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

acsc

Inverse cosecant in radians.

Syntax

res = acsc(x)

Input argument

x - a numeric value

Output argument

res - a numeric value

Description

acsc computes the inverse cosecant of argument in radians for each element of x.

Example

R = acsc(3)
R = acsc(0.5)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

acscd

Inverse cosecant in degrees.

Syntax

res = acsc(x)

Input argument

x - a numeric value

Output argument

res - a numeric value

Description

acscd computes the inverse cosecant of argument in degrees for each element of x.

Example

x = [0 1 20 10 Inf];
y = acscd(x)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

acsch

Inverse hyperbolic cosecant.

Syntax

res = acsch(x)

Input argument

x - a numeric value

Output argument

res - a numeric value

Description

acsch computes the inverse hyperbolic cosecant for each element of x.

Example

X = [3*pi, 2*pi, pi, 0];
R = acsch(X)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

asec

Inverse secant of angle in radians.

Syntax

res = asec(x)

Input argument

x - a numeric value

Output argument

res - a numeric value

Description

asec computes the inverse secant of argument in radians for each element of x.

Example

x = -pi:0.75:pi;
R = asec(x)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

asecd

Inverse secant of argument in degrees.

Syntax

res = asecd(x)

Input argument

x - a numeric value

Output argument

res - a numeric value

Description

asecd computes the inverse secant of argument in degrees for each element of x.

Example

R = asecd([1, 10+3i, 15+2i, 35+i])

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

asech

Inverse hyperbolic secant of angle in radians.

Syntax

res = asech(x)

Input argument

x - a numeric value

Output argument

res - a numeric value

Description

asech computes the inverse hyperbolic secant of argument in radians for each element of x.

Example

x = -pi:0.75:pi;
R = asech(x)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

asin

Computes the inverse sine in radians for each element of x.

Syntax

res = asin(x)

Input argument

x - a numeric value

Output argument

res - a numeric value

Description

asin computes the inverse sine in radians for each element of x.

Example

A = eye(3, 3);
res = asin(A)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

asind

Inverse sine in degrees.

Syntax

res = asind(x)

Input argument

x - a numeric value

Output argument

res - a numeric value

Description

asind computes the inverse sine in degrees for each element of x.

Example

x = [-50 -20 0 20 50];
y = asind(x)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

asinh

Inverse hyperbolic sine function

Syntax

res = asinh(x)

Input argument

x - a numeric value

Output argument

res - a numeric value

Description

cosh computes the inverse hyperbolic sine in radians for each element of x.

Example

A = eye(3, 3);
res = asinh(A)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

atan

Computes the inverse tangent in radians for each element of x.

Syntax

res = atan(x)

Input argument

x - a numeric value

Output argument

res - a numeric value

Description

atan computes the inverse tangent in radians for each element of x.

Example

A = eye(3, 3);
res = atan(A)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

atan2

Computes the four-quadrant inverse tangent.

Syntax

res = atan2(y, x)

Input argument

y - a numeric value (double or single real)
x - a numeric value (double or single real)

Output argument

res - a numeric value

Description

atan2 computes the four-quadrant inverse tangent.

Example

atan2(1, 0)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

atan2d

Four-quadrant inverse tangent in degrees.

Syntax

d = atan2d(y, x)

Input argument

y - a numeric value
x - a numeric value

Output argument

d - a numeric value

Description

d = atan2d(y, x) returns the four-quadrant inverse tangent (tan-1) of y and x, which must be real.

Example

x = [1 0 -1 0];
y = [0 1 0 -1];
d = atan2d(y, x)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

atand

Inverse tangent in degrees.

Syntax

res = atand(x)

Input argument

x - a numeric value

Output argument

res - a numeric value

Description

atand computes the inverse tangent in degrees for each element of x.

Example

x = [-50 -20 0 20 50];
y = atand(x)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

atanh

Computes the inverse hyperbolic tangent.

Syntax

res = atanh(x)

Input argument

x - a numeric value

Output argument

res - a numeric value

Description

acos computes the inverse hyperbolic tangent.

Example

A =  [1+2i, 2, -3];
res = atanh(A)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

cart2pol

Transforms Cartesian coordinates to polar or cylindrical.

Syntax

[theta, rho] = cart2pol(x, y)
[theta, rho, z] = cart2pol(x, y, z)

Input argument

x - a numeric value (double or single real): Cartesian coordinates
y - a numeric value (double or single real): Cartesian coordinates
z - a numeric value (double or single real): Cartesian coordinates

Output argument

theta - a numeric value: Angular coordinate.
rho - a numeric value: Radial coordinate.
z - a numeric value: Elevation coordinate.

Description

cart2pol transforms Cartesian coordinates to polar or cylindrical.

Examples

x = [5 3.5355 0 -10];
y = [0 3.5355 10 0];
[theta, rho] = cart2pol(x, y)

x = [1 2.1213 0 -5];
y = [0 2.1213 4 0];
z = [7 8 9 10];
[theta, rho, el] = cart2pol(x, y, z)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

cart2sph

Transforms Cartesian to spherical coordinates.

Syntax

[azimuth, elevation, r] = cart2sph(x, y, z)

Input argument

x - a numeric value (double or single real): Cartesian coordinates
y - a numeric value (double or single real): Cartesian coordinates
z - a numeric value (double or single real): Cartesian coordinates

Output argument

azimuth - a numeric value: Azimuth angle.
elevation - a numeric value: Elevation angle.
r - a numeric value: Radius.

Description

cart2sph transforms Cartesian to spherical coordinates.

Example

x = [1 1 1 1; -1 -1 -1 -1];
y = [1 1 -1 -1; 1 1 -1 -1];
z = [1 -1 1 -1; 1 -1 1 -1];
[az, el, r] = cart2sph(x, y, z)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

cos

Computes the cosine in radians for each element of x.

Syntax

res = cos(x)

Input argument

x - a numeric value

Output argument

res - a numeric value

Description

cos computes the cosine in radians for each element of x.

Example

A = eye(3, 3);
res = cos(A)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

cosd

Computes the cosine in degree for each element of x.

Syntax

res = cosd(x)

Input argument

x - a numeric value

Output argument

res - a numeric value

Description

cosd computes the cosine in degree for each element of x.

Example

A = [0 30 45 60 90 360];;
res = cosd(A)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

cosh

Computes the hyperbolic cosine in radians for each element of x.

Syntax

res = cosh(x)

Input argument

x - a numeric value

Output argument

res - a numeric value

Description

cosh computes the hyperbolic cosine in radians for each element of x.

Example

A = eye(3, 3);
res = cosh(A)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

cosm

Computes the matrix cosine of a square matrix.

Syntax

res = cosm(x)

Input argument

x - a numeric value: scalar or square matrix

Output argument

res - a numeric value: a square matrix

Description

cosm(x) computes the matrix cosine of x.

Example

A = eye(3, 3);
res = cosm(A)
A = [1, 2; 3, 4];
res = cosm(A)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

cospi

Computes cos(X * pi) accurately.

Syntax

res = cospi(x)

Input argument

x - a numeric value

Output argument

res - a numeric value

Description

res = cospi(x) computes cos(x * pi) accurately.

For integers, cospi(x) is +1 or -1.

For odd integers, cospi(x / 2) is exactly zero.

Example

x = [0, 1/2, 1, 3/2, 2];
r = cos(x * pi)
res = cospi(x)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

cot

Cotangent of angle in radians

Syntax

res = cot(x)

Input argument

x - a numeric value

Output argument

res - a numeric value

Description

acot computes the cotangent of angle for each element of x.

Example

R = cot([-i pi+i*pi/2 -1+i*4])

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

cotd

Cotangent of argument in degrees

Syntax

res = cotd(x)

Input argument

x - a numeric value

Output argument

res - a numeric value

Description

cotd computes the cotangent of argument in degrees for each element of x.

Example

R = cotd(35 + 5i)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

coth

Hyperbolic cotangent.

Syntax

res = coth(x)

Input argument

x - a numeric value

Output argument

res - a numeric value

Description

csch computes the hyperbolic cotangent for each element of x.

Example

X = [3*pi, 2*pi, pi, 0];
R = coth(X)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

csc

Cosecant of input angle in radians.

Syntax

res = csc(x)

Input argument

x - a numeric value

Output argument

res - a numeric value

Description

csc computes the cosecant of argument in radians for each element of x.

Example

R = csc(-pi+0.01:0.01:-0.01)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

cscd

Cosecant of argument in degrees.

Syntax

res = cscd(x)

Input argument

x - a numeric value

Output argument

res - a numeric value

Description

cscd computes the cosecant of argument in degrees for each element of x.

Example

R = cscd([35+i 15+2i 10+3i])

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

csch

Hyperbolic cosecant.

Syntax

res = csch(x)

Input argument

x - a numeric value

Output argument

res - a numeric value

Description

csch computes the hyperbolic cosecant for each element of x.

Example

X = [3*pi, 2*pi, pi, 0];
R = csch(X)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

deg2rad

Convert angle from degrees to radians.

Syntax

r = deg2rad(d)

Input argument

d - a numeric value (double or single)

Output argument

r - a numeric value

Description

d = deg2rad(r) converts angle units from degrees to radians for each element of r.

Example

D = 64.7;
R = deg2rad(D);
radEarth = 6371;
dist = radEarth * R

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

pol2cart

Transforms polar or cylindrical coordinates to Cartesian.

Syntax

[x, y] = pol2cart(theta, rho)
[x, y, z] = pol2cart(theta, rho, z)

Input argument

theta - a numeric value: Angular coordinate.
rho - a numeric value: Radial coordinate.
z - a numeric value: Elevation coordinate.

Output argument

x - a numeric value (double or single real): Cartesian coordinates
y - a numeric value (double or single real): Cartesian coordinates
z - a numeric value (double or single real): Cartesian coordinates

Description

pol2cart transforms polar or cylindrical coordinates to Cartesian.

Example

theta = [0 pi/4 pi/2 pi];
rho = [5 5 10 10];
[x, y] = pol2cart(theta, rho)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

rad2deg

Convert angle from radians to degrees.

Syntax

d = rad2deg(r)

Input argument

r - a numeric value (double or single)

Output argument

d - a numeric value

Description

d = rad2deg(r) converts angle units from radians to degrees for each element of r.

Example

dist = 7194;
radEarth = 6371;
D = rad2deg(dist / radEarth)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

sec

Secant of angle in radians.

Syntax

res = sec(x)

Input argument

x - a numeric value

Output argument

res - a numeric value

Description

sec computes the secant of argument in radians for each element of x.

Example

x = -pi:0.75:pi;
R = sec(x)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

secd

Secant of argument in degrees.

Syntax

res = secd(x)

Input argument

x - a numeric value

Output argument

res - a numeric value

Description

secd computes the secant of argument in degrees for each element of x.

Example

R = secd([1, 10+3i, 15+2i, 35+i])

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

sech

Hyperbolic secant.

Syntax

res = sech(x)

Input argument

x - a numeric value

Output argument

res - a numeric value

Description

sech computes the Hyperbolic secant for each element of x.

Example

X = [3*pi, 2*pi, pi, 0];
R = sech(X)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

sin

Computes the sine in radians for each element of x.

Syntax

res = sin(x)

Input argument

x - a numeric value

Output argument

res - a numeric value

Description

sin computes the sine in radians for each element of x.

Example

A = eye(3, 3);
res = sin(A)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

sind

Computes the sine in degree for each element of x.

Syntax

res = sind(x)

Input argument

x - a numeric value

Output argument

res - a numeric value

Description

sind computes the sine in degree for each element of x.

Example

A = [0 30 45 60 90 360];
sind(A)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

sinh

Computes the hyperbolic sine in radians for each element of x.

Syntax

res = sinh(x)

Input argument

x - a numeric value

Output argument

res - a numeric value

Description

sinh computes the hyperbolic sine in radians for each element of x.

Example

A = eye(3, 3);
res = sinh(A)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

sinm

Computes the matrix sinus of a square matrix.

Syntax

res = sinm(x)

Input argument

x - a numeric value: scalar or square matrix

Output argument

res - a numeric value: a square matrix

Description

sinm(x) computes the matrix sinus of x.

Example

A = eye(3, 3);
res = sinm(A)
A = [1, 2; 3, 4];
res = sinm(A)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

sinpi

Computes sin(X * pi) accurately.

Syntax

res = sinpi(x)

Input argument

x - a numeric value

Output argument

res - a numeric value

Description

res = sinpi(x) computes sin(x * pi) accurately.

For odd integers, sinpi(x / 2) is +1 or -1.

For integers, sinpi(x) is exactly zero.

Example

x = [0, 1/2, 1, 3/2, 2];
r = sin(x * pi)
res = sinpi(x)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

sph2cart

Transform spherical coordinates to Cartesian.

Syntax

[x, y, z] = sph2cart(azimuth, elevation, r)

Input argument

azimuth - a numeric value: Azimuth angle.
elevation - a numeric value: Elevation angle.
r - a numeric value: Radius.

Output argument

x - a numeric value (double or single real): Cartesian coordinates
y - a numeric value (double or single real): Cartesian coordinates
z - a numeric value (double or single real): Cartesian coordinates

Description

sph2cart transforms Cartesian to spherical coordinates.

Example

azimut = [0.7854, 0.7854, -0.7854, -0.7854; 2.3562, 2.3562, -2.3562, -2.3562];
elevation = [0.6155, -0.6155, 0.6155, -0.6155; 0.6155, -0.6155, 0.6155, -0.6155];
radius = 1.7321 * ones(2, 4);
[x, y, z] = sph2cart(azimut, elevation, radius)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

tan

Computes the tangent in radians for each element of x.

Syntax

res = tan(x)

Input argument

x - a numeric value

Output argument

res - a numeric value

Description

tan computes the tangent in radians for each element of x.

Example

A = eye(3, 3);
res = tan(A)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

tand

Computes the tangent in degree for each element of x.

Syntax

res = tand(x)

Input argument

x - a numeric value

Output argument

res - a numeric value

Description

tand computes the tangent in degree for each element of x.

Example

A = [0 30 45 60 90 360];
res = tand(A)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

tanh

Computes the hyperbolic tangent in radians for each element of x.

Syntax

res = tanh(x)

Input argument

x - a numeric value

Output argument

res - a numeric value

Description

tanhcomputes the hyperbolic tangent in radians for each element of x.

Example

A = eye(3, 3);
res = tanh(A)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

tanm

Computes the matrix tangent of a square matrix.

Syntax

res = tanm(x)

Input argument

x - a numeric value: scalar or square matrix

Output argument

res - a numeric value: a square matrix

Description

tanm(x) computes the matrix tangent of x.

Example

A = eye(3, 3);
res = tanm(A)
A = [1, 2; 3, 4];
res = tanm(A)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

Linear algebra

Description

linear algebra functions

balance - Diagonal scaling to improve eigenvalue accuracy.
bandwidth - Lower and upper matrix bandwidth.
chol - Cholesky factorization.
cond - Condition number for inversion.
condeig - Condition number with respect to eigenvalues.
det - Matrix determinant.
diff - Differences and approximate derivatives.
eig - Eigenvalues and eigenvectors.
expm - Computes the matrix exponential of a square matrix.
gradient - Numerical gradient.
inv - Matrix inverse.
isbanded - Determine if matrix is within specific bandwidth.
ishermitian - Computes if matrix is hermitian or skew-hermitian.
issymmetric - Computes if matrix is symmetric.
kron - Kronecker tensor product.
logm - Computes the matrix logarithm of a square matrix.
lu - LU matrix factorization.
orth - Range space of a matrix.
planerot - Givens plane rotation.
rank - Rank of matrix.
rcond - Inverse condition number.
rref - Gauss-Jordan elimination.
rsf2csf - Convert real Schur form to complex Schur form.
schur - Schur decomposition.
sqrtm - Computes the matrix square root of a square matrix.
subspace - Angle between two subspaces.
svd - Singular Value Decomposition.
trace - Matrix trace.
vecnorm - Vector-wise norm.

balance

Diagonal scaling to improve eigenvalue accuracy.

Syntax

B = balance(A)
B = balance(A,'noperm')
[T, B] = balance(A)
[S, P, B] = balance(A)

Input argument

A - a matrix: square, finite single or double.

Output argument

B - balanced matrix.
T - similarity transformation: Rearrange the elements of a diagonal matrix containing integer powers of two in order to minimize the impact of roundoff errors.
S - scaling vector
P - permutation vector

Description

B = balance(A) returns the balanced matrix B.

B = balance(A, 'noperm') scales A without permuting its rows and columns.

Used function(s)

LAPACKE_dgebal, LAPACKE_sgebal, LAPACKE_zgebal, LAPACKE_cgebal

Example

A = [10  1000  100000; .1  10  1000; .001  .1  10]
F = balance(A)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

bandwidth

Lower and upper matrix bandwidth.

Syntax

[lower, upper] = bandwidth(A)
R = bandwidth(A, type)

Input argument

A - Input matrix
type - 'upper' or 'lower'

Output argument

lower, upper - lower bandwidth,
R - lower or upper bandwidth.

Description

[lower, upper] = bandwidth(A) returns lower and upper bandwidths of matrix A.

Example

M = [10 -20 40; -50 20 0; 10 0 30]
[lower, upper] = bandwidth(M)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

chol

Cholesky factorization.

Syntax

F = chol(A)

Input argument

A - a matrix: square and symmetric positive definite.

Output argument

F - Cholesky factor.

Description

F = chol(A) factorizes symmetric positive definite matrix A into an upper triangular F that satisfies A = F' * F.

Example

A = [10 0 10; 0 20 0; 10 0 30];
F = chol(A)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

cond

Condition number for inversion.

Syntax

c = rcond(A, p)

Input argument

A - a numeric value: square or rectangular (double or single)
p - norm type: Inf, 'fro', 1, 2 (default)

Output argument

c - a numeric value: a scalar.

Description

c = cond(A) returns the 2-norm condition number for inversion.

c = cond(A, p) returns the p-norm condition number, where p can be 1, 2, Inf, or 'fro'.

Example

X = rand(10, 10);
r = cond(X)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

condeig

Condition number with respect to eigenvalues.

Syntax

C = condeig(A)
[V, D, S] = condeig(A)

Input argument

A - Input matrix

Output argument

C - a vector of condition numbers for the eigenvalues of A.

Description

C = condeig(A) returns a vector of condition numbers for the eigenvalues of A.

Example

A = [10, 20; 30, 40];
S = condeig(A)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

det

Matrix determinant.

Syntax

res = det(x)

Input argument

x - a numeric value: scalar or square matrix (double or single)

Output argument

res - real or complex number (double or single), the determinant base 10.

Description

res = det(x) returns the determinant of square matrix x.

Example

A = [10 -20 40; -50 20 0; 10 0 30]
D = det(A)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

diff

Differences and approximate derivatives.

Syntax

Y = diff(X)
Y = diff(X, n)
Y = diff(X, n, dim)

Input argument

X - vector or matrix (real or single)
n - difference order: positive integer scalar or []
dim - dimension: positive integer scalar

Output argument

Y - difference array: vector or matrix.

Description

If X is a vector of length n, result of diff(X) is a vector of first differences X(2) - X(1), ..., X(n) - X(n-1).

If X is a matrix, result of diff(X) is a matrix of column differences along the first non-singleton dimension.

Example

h = .01; x = 0:h:pi;
X = sin(x.^2);
R = diff(X)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

eig

Eigenvalues and eigenvectors.

Syntax

e = eig(A)
[V, D] = eig(A)
e = eig(A, balanceOption)
[V, D] = eig(A, balanceOption)
e = eig(A, B)
[V, D] = eig(A, B)
e = eig(A, B, balanceOption)
[V, D] = eig(A, B, balanceOption)

Input argument

A - a numeric value: scalar or square matrix (double or single, complex or real)
B - a numeric value: scalar or square matrix (double or single, complex or real)
balanceOption - a string: 'nobalance' (disable preliminary balancing) or 'balance' (default).

Output argument

e - real or complex number (double or single), Eigenvalues (returned as column vector).
V - real or complex number (double or single), square right eigenvectors.
D - real or complex number (double or single), Eigenvalues (returned as diagonal matrix).

Description

eig(A) returns the Eigenvalues and eigenvectors.

eig(A, B) returns the generalized Eigenvalues and eigenvectors.

Bibliography

[1] Anderson, E., Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen, LAPACK User's Guide (http://www.netlib.org/lapack/lug/ lapack_lug.html), Third Edition, SIAM, Philadelphia, 1999.

Examples

A = [10 -20 40; -50 20 0; 10 0 30]
e = eig(A)
[V, D] = eig(A)

A = [1/sqrt(2) 0; 0 1];
B = [0 1; -1/sqrt(2) 0];
[V, D] = eig(A, B)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

expm

Computes the matrix exponential of a square matrix.

Syntax

res = expm(x)

Input argument

x - a numeric value: scalar or square matrix (double or single)

Output argument

res - a numeric value: a square matrix

Description

expm(x) computes the matrix exponential of x.

The computation is performed by first block-diagonalizing x and then applying a Pade approximation on each block.

Example

A = eye(3, 3);
res = expm(A)
res = expm(A+i)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

gradient

Numerical gradient.

Syntax

FX = gradient(F)
[FX, FY] = gradient(F)
[FX, FY, FZ, ..., FN] = gradient(F)
[...] = gradient(F, h)
[...] = gradient(F, hx, hy, ... , hN)

Input argument

F - Input array: vector, matrix or multidimensional array.
h - Uniform spacing between points: scalar or 1 (default).
hx, hy, ..., hN - Spacing between points: vector, scalar or 1 (default).

Output argument

FX, FY, FZ, ..., FN - Numerical gradients: array.

Description

gradient(F) calculates the one-dimensional numerical gradient of the vector or matrix F.

The output FX represents the differences in the x (horizontal) direction, corresponding to ∂F/∂x.

It assumes that the spacing between points is 1.

gradient(F, h) allows for specifying a uniform spacing h between points in each direction.

This uniform spacing can also be individually specified for each dimension of F using gradient(F, hx, hy, ..., hN).

Example

[X, Y] = meshgrid(-2:0.2:2);
Z = X .* exp(-X.^2 - Y.^2);
[U, V] = gradient(Z, 0.2, 0.2);

History

Version	Description
1.3.0	initial version

Author

Allan CORNET

inv

Matrix inverse.

Syntax

res = inv(x)

Input argument

x - a numeric value: scalar or square matrix (double or single)

Output argument

res - a numeric value: a square matrix

Description

inv(x) computes the matrix inverse of x.

Example

X = rand(10, 10);
Y = inv(X);
Y * X

History

Version	Description
1.0.0	initial version
1.4.0	warning about 'Matrix is singular to working precision'

Author

Allan CORNET

isbanded

Determine if matrix is within specific bandwidth.

Syntax

tf = isbanded(A, lower, upper)

Input argument

A - Input matrix
lower, upper - lower bandwidth,

Output argument

tf - logical

Description

tf = isbanded(A, lower, upper) returns true if matrix A is within the specified lower bandwidth, lower, and upper bandwidth, upper.

Example

M = [1 0 0 0 0; 2 1 0 0 0; 3 2 1 0 0]
TF = isbanded(M, 2, 0)
TF = isbanded(M, 2, 1)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

ishermitian

Computes if matrix is hermitian or skew-hermitian.

Syntax

res = ishermitian(x)
res = ishermitian(x, 'skew')
res = ishermitian(x, 'nonskew')

Input argument

x - a numeric value: scalar or matrix (double or single, integers, logical).

Output argument

res - a logical.

Description

ishermitian(x) computes if matrix is hermitian or skew-hermitian.

A matrix is skew-hermitian if the complex conjugate transpose of the matrix is equal to the negative of the original matrix.

Example

ishermitian([1 0 1i; 0 1 0; -1i 0 1])

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

issymmetric

Computes if matrix is symmetric.

Syntax

res = issymmetric(x)
res = issymmetric(x, 'skew')
res = issymmetric(x, 'nonskew')
res = issymmetric(x, tol)

Input argument

x - a numeric value: scalar or matrix (double or single, integers, logical).
tol - a numeric value: finite and >= 0.

Output argument

res - a logical.

Description

issymmetric(x) computes if matrix is symmetric.

With 'nonskew' argument, x square matrix, x is symmetric if it is equal to its nonconjugate transpose, x = x.'

With 'skew' argument, x square matrix, x is symmetric if it is equal to its nonconjugate transpose, x = -x.'

Example

issymmetric([1, 2; 2, 1])
issymmetric([1, 2.1; 2, 1.1], 0.2)
A = [0 1 -2 5; -1 0 3 -4; 2 -3 0 6; -5 4 -6 0];
issymmetric(A, 'skew')
issymmetric(A, 'nonskew')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

kron

Kronecker tensor product.

Syntax

K = kron(A, B)

Input argument

A - a matrix: scalars, vectors or matrices.
B - a matrix: scalars, vectors or matrices.

Output argument

K - result: Kronecker Tensor Product.

Description

K = kron(A, B) computes the Kronecker tensor product of matrices A and B.

Bibliography

https://en.wikipedia.org/wiki/Kronecker_product

Example

A = [1, 2; 3, 4];
B = [0, 5; 6, 7];
K = kron(A, B)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

logm

Computes the matrix logarithm of a square matrix.

Syntax

res = logm(x)

Input argument

x - a numeric value: scalar or square matrix (double or single)

Output argument

res - a numeric value: a square matrix

Description

expm(x) computes the matrix logarithm of x.

The computation is performed by first block-diagonalizing x and then applying a Pade approximation on each block.

Example

A = eye(3, 3);
res = logm(A)
res = logm(A+i)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

lu

LU matrix factorization.

Syntax

[L, U] = lu(A)
[L, U, P] = lu(A)

Input argument

A - a matrix: square, finite single or double.

Output argument

L - Lower triangular factor: matrix (same type A)
U - Upper triangular factor: matrix (same type A).
P - Row permutation: matrix (same type A).

Description

[L, U] = lu(A) function decomposes a full matrix A into two matrices: an upper triangular matrix U and a permuted lower triangular matrix L.

This factorization satisfies the equation A = L * U.

[L, U, P] = lu(A) function, when used with three output arguments, provides a permutation matrix P in addition to the unit lower triangular matrix L and the upper triangular matrix U.

This factorization is expressed as A = P'LU, where L is unit lower triangular, and U is upper triangular.

Used function(s)

LAPACKE_dgetrf, LAPACKE_sgetrf, LAPACKE_zgetrf, LAPACKE_cgetrf

Examples

A = magic(5)
[L, U] = lu(A)
L * U

A = magic(5)
[L, U, P] = lu(A);
subplot(1, 2, 1)
spy(L)
title(_('L factor'))
subplot(1, 2, 2)
spy(U)
title(_('U factor'))

History

Version	Description
1.1.0	initial version

Author

Allan CORNET

orth

Range space of a matrix.

Syntax

O = orth(A)
O = orth(A, tol)

Input argument

A - Input matrix
tol - a numeric value: scalar, singular value tolerance

Output argument

O - real or complex number (double or single).

Description

O = orth(A) returns an orthonormal basis for the range of A.

Example

M = [10 -20 40; -50 20 0; 10 0 30]
O = orth(M)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

planerot

Givens plane rotation.

Syntax

[G, Y] = planerot(X)

Input argument

X - two-element column vector.

Output argument

G - 2 by 2 orthogonal matrix.
Y - Y = G * X with Y(2) = 0.

Description

[G, Y] = planerot(X) computes the Givens rotation matrix for the two-element column vector X.

Example

X = [4; 5];
[G, X] = planerot(X)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

rank

Rank of matrix.

Syntax

r = rank(A)
r = rank(A, tol)

Input argument

A - matrix: double or single
tol - tolerance

Output argument

r - a numeric value: a scalar.

Description

rank(A) returns the number of linearly independent columns in a matrix (rank of the matrix).

Example

X = rand(10, 10);
r = rank(X)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

rcond

Inverse condition number.

Syntax

res = rcond(x)

Input argument

x - a numeric value: scalar or square matrix (double or single)

Output argument

res - a numeric value: a scalar.

Description

rcond(x) computes the reciprocal of the condition of x in the 1-norm.

Example

X = rand(10, 10);
r = rcond(X);

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

rref

Gauss-Jordan elimination.

Syntax

R = rref(A)
R = rref(A, tol)
[R, p] = rref(A)
[R, p] = rref(A, tol)

Input argument

A - input matrix (double or single)
tol - tolerance: scalar or max(rows, cols) _ eps(class(A)) _ norm(A, inf) (default)

Output argument

R - a matrix: reduced row echelon form of A.
p - a vector: nonzero pivot columns.

Description

R = rref(A) returns the reduced row echelon form of A.

[R, p] = rref(A) returns also the nonzero pivots p.

Bibliography

https://en.wikipedia.org/wiki/Gaussian_elimination

Example

A = [magic(4), eye(4)]
[R, p] = rref(A)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

rsf2csf

Convert real Schur form to complex Schur form.

Syntax

[Uc, Tc] = rsf2csf(U, T)

Input argument

U - unitary matrix (double or single, real or complex)
T - schur form (double or single, real or complex)

Output argument

Uc - transformed unitary matrix
Tc - transformed schur form

Description

[Uc, Tc] = rsf2csf(U, T) transforms the outputs of [U, T] = schur(X) for real matrices X from real Schur form to complex Schur form.

Example

X = [1,     1,     1,     3;
     1,     2,     1,     1;
     1,     1,     3,     1;
    -2,     1,     1,     4];
[U, T] = schur(X)
[Uc, Tc] = rsf2csf(U, T)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

schur

Schur decomposition.

Syntax

T = schur(M)
T = schur(M, 'real')
T = schur(M, 'complex')
[U, T] = schur(M)
[U, T] = schur(M, 'complex')
[U, T] = schur(M, 'real')

Input argument

M - a numeric value: scalar or square matrix (double or single)

Output argument

U - unitary matrix
T - upper triangular matrix

Description

schur(M) computes the schur decomposition.

With the flag 'complex', the complex schur form is upper triangular with the eigenvalues of M on the diagonal.

If A is real, the real schur form is returned.

With the flag 'real', the real schur form has the real eigenvalues on the diagonal and the complex eigenvalues in 2-by-2 blocks on the diagonal.

Example

X = [1 2; 3 4];
[U, T] = schur(X)
[U, T] = schur(X * i, 'complex')
[U, T] = schur(X * i, 'real')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

sqrtm

Computes the matrix square root of a square matrix.

Syntax

res = sqrtm(x)

Input argument

x - a numeric value: scalar or square matrix (double or single)

Output argument

res - a numeric value: a square matrix

Description

expm(x) computes the matrix square root of x.

Example

A = eye(3, 3);
res = sqrtm(A)
res = sqrtm(A+i)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

subspace

Angle between two subspaces.

Syntax

T = subspace(A, B)

Input argument

A - vector or matrix (real or single)
B - vector or matrix (real or single)

Output argument

T - scalar: angle.

Description

T = subspace(A, B) finds the angle between two subspaces specified by the columns of A and B.

Example

M = [1   1   1   1   1   1   1   1;
1  -1   1  -1   1  -1   1  -1;
1   1  -1  -1   1   1  -1  -1;
1  -1  -1   1   1  -1  -1   1;
1   1   1   1  -1  -1  -1  -1;
1  -1   1  -1  -1   1  -1   1;
1   1  -1  -1  -1  -1   1   1;
1  -1  -1   1  -1   1   1  -1];
A = M(:, 2:4);
B = M(:, 5:8);
R = subspace(A, B)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

svd

Singular Value Decomposition.

Syntax

s = svd(M)
[U, S, V] = svd(M)
[U, S, V] = svd(M, 0)
[U, S, V] = svd(M, 'econ')

Input argument

M - a numeric value: matrix (double or single)

Output argument

s - real vector (singular values) by descending order.
U - left singular values.
S - real diagonal matrix (singular values)
V - right singular values.

Description

[U, S, V] = svd(M) produces a diagonal matrix S of the same dimension as M and with nonnegative diagonal elements in decreasing order, and unitary matrices U and V so that X = U*S*V'.

[U, S, V] = svd(M, 0) produces the 'economy size' decomposition. If M is m-by-n with m > n then only the first n columns of U are computed and S is n-by-n.

[U, S, V] = svd(M,0) produces a different economy-size decomposition of m-by-n matrix M. If m > n then svd(M, 0) is equivalent to svd(M,'econ'). If m <= n then svd(M, 0) is equivalent to svd(M).

Example

X = eye(3, 3);
s = svd(X)
[U, S, V] = svd(X)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

trace

Matrix trace.

Syntax

res = trace(x)

Input argument

x - a numeric value: scalar or matrix (double or single)

Output argument

res - a numeric value: a scalar

Description

trace(x) computes the trace of x, the sum of the elements along the main diagonal.

Example

X = [1 0; 0 3];
Y = trace(X)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

vecnorm

Vector-wise norm.

Syntax

N = vecnorm(A)
N = vecnorm(A, p)
N = vecnorm(A, p, dim)

Input argument

A - vector, matrix or multidimensional array
p - Norm type: 2 (default), a positive scalar, or Inf.
dim - positive integer scalar

Output argument

n - norm: scalar or vector

Description

vecnorm computes the 2-norm or Euclidean norm of the input array A

If A is a vector, vecnorm returns the norm of the vector.

If A is a matrix, vecnorm returns the norm of each column.

For multidimensional arrays, vecnorm returns the norm along the first array dimension whose size does not equal 1.

To compute the generalized vector p-norm, you can use the syntax N = vecnorm(A, p).

To operate along a specific dimension dim, the function can be called as N = vecnorm(A, p, dim).

In this case, the size of the specified dimension reduces to 1, while the sizes of all other dimensions remain unchanged.

Example

A = [1, 2, 3; 4, 5, 6; 7, 8, 9];
n = vecnorm(A)
n = vecnorm(A, 2, 2)
n = vecnorm(A, 1)

History

Version	Description
1.3.0	initial version

Author

Allan CORNET

Statistics

Description

statistics functions

corrcoef - Correlation coefficients
cov - Covariance
mean - Mean of array elements.
normpdf - Normal probability density function
var - Variance

corrcoef

Correlation coefficients

Syntax

R = corrcoef(M)

Input argument

M - a vector or matrix

Output argument

R - Correlation coefficients of M.

Description

R = corrcoef(M) returns the matrix of correlation coefficients for M, where the columns of M represent random variables and the rows represent observations.

Example

M = [4 -7 3; 1 4 -2; 10 7 9];
R = corrcoef(M)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

cov

Covariance

Syntax

C = cov(M)

Input argument

M - a vector or matrix

Output argument

V - Covariance of M.

Description

C = cov(M) returns the covariance.

Example

M = [4 -7 3; 1 4 -2; 10 7 9];
C = cov(M)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

mean

Mean of array elements.

Syntax

R = mean(M)
R = mean(M, d)
R = mean(M, 'all')
R = mean(M, d, t)
R = mean(M, 'all', t)
R = mean(M, d, t, f)
R = mean(M, 'all', t, f)

Input argument

M - an array of double, single, integers, ...
d - dimension to operate along: positive integer scalar.
t - a string: 'default', 'double' or 'native'.
f - a string: 'includenan' or 'omitnan'.

Output argument

R - Mean of array elements.

Description

R = mean(M) returns the mean of the array elements of M.

Example

M = uint8([10:30:70;20:30:80;30:30:90]);
R = mean(M, 'native')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

normpdf

Normal probability density function

Syntax

y = normpdf(x)
y = normpdf(x, mu)
y = normpdf(x, mu, sigma)

Input argument

x - scalar value or array: Values at which to evaluate pdf.
mu - scalar value, 0 (default) or array: Mean.
sigma - positive scalar value, 1 (default) or array of positive values: Standard deviation.

Output argument

y - scalar value or array: pdf values.

Description

y = normpdf(x) calculates the probability density function (pdf) of the standard normal distribution at the given values in x.

y = normpdf(x, mu) computes the pdf of the normal distribution with a mean of mu and a standard deviation of 1, evaluated at the provided values in x.

y = normpdf(x, mu, sigma) determines the pdf of the normal distribution with a mean of mu and a standard deviation of sigma, evaluated at the specified values in x.

Bibliography

Evans, M., N. Hastings, and B. Peacock. Statistical Distributions. 2nd ed. Hoboken, NJ: John Wiley and Sons, Inc., 1993.

Example

x = [-0.2, -0.1, 0, 0.1, 0.2];
R = normpdf(x);

x = [-0.2, -0.1, 0, 0.1, 0.2];
R = normpdf(x, 2, 1);

R = normpdf(0, [-0.2, -0.1, 0, 0.1, 0.2], 1);

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

var

Variance

Syntax

V = var(M)

Input argument

M - a vector or matrix

Output argument

V - Variance of M.

Description

V = var(M) returns the variance of the elements of M along the first array dimension whose size does not equal 1.

Example

M = [4 -7 3; 1 4 -2; 10 7 9];
V = var(M)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

Polynomials

Description

Polynomial functions

deconv - Deconvolution and polynomial division.
poly - Polynomial with specified roots or characteristic polynomial.
polyder - Polynomial differentiation.
polyfit - Polynomial curve fitting.
polyint - Polynomial integration.
polyval - Polynomial evaluation.
polyvalm - Matrix polynomial evaluation.
roots - Find polynomial roots.

deconv

Deconvolution and polynomial division.

Syntax

[q, r] = deconv(b, a)

Input argument

a - row or column vectors
b - row or column vectors

Output argument

q - quotient: row or column vector
r - remainder: row or column vector

Description

[q, r] = deconv(b, a) performs deconvolution on vector b by vector a using long division.

It returns the quotient q and remainder r such that b = conv(a, q) + r.

In the context of polynomial coefficients, deconvolving vectors b and a is akin to dividing the polynomial represented by b by the polynomial represented by a.

Example

b = [1; 2; -1];  % Dividend (x^2 + 2x - 1)
a = [1; 1];      % Divisor (x + 1)

[q, r] = deconv(b, a)

History

Version	Description
1.3.0	initial version

Author

Allan CORNET

poly

Polynomial with specified roots or characteristic polynomial.

Syntax

p = poly(r)
p = poly(A)

Input argument

r - vector: polynomial roots
A - matrix: input matrix

Output argument

p - row vector: polynomial coefficients

Description

If A is a square matrix, p = poly(A) computes an n+1 element row vector. This result is composed the coefficients of the characteristic polynomial.

If r is a vector, p = poly(r) computes a row vector. This result is composed the coefficients of the polynomial roots of which are the elements of r.

Example

A = [1    2    3;
4    5    6;
7    8    1];
p = poly(A)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

polyder

Polynomial differentiation.

Syntax

k = polyder(p)
k = polyder(a, b)
[q, d] = polyder(a, b)

Input argument

p - vector: polynomial coefficients
a - row vector: polynomial coefficients
b - row vector: polynomial coefficients

Output argument

k - row vector: differentiated polynomial coefficients
q - row vector: numerator polynomial
d - row vector: denominator polynomial

Description

k = polyder(p) return the coefficients of the derivative of the polynomial whose coefficients are given by the vector p.

k = polyder(a, b) returns the derivative of the product of the polynomials a and b.

[q, d] = polyder(a, b) returns the derivative of the quotient of the polynomials a and b.

Example

p = [30 0 -20 0 10 50];
q = polyder(p)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

polyfit

Polynomial curve fitting.

Syntax

p = polyfit(x, y, n)

Input argument

x - vector: query points
y - vector: fitted values at query points
n - positive scalar: degree of polynomial fit

Output argument

p - vector: Least-squares fit polynomial coefficients

Description

p = polyfit(x, y, n) returns the coefficients for a polynomial p(x) of degree n that is a best fit for the data in y.

Example

x = linspace(0, 8 * pi, 15);
y = sin(x);
p = polyfit(x, y, 7)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

polyint

Polynomial integration.

Syntax

q = polyint(p, k)
q = polyint(p)

Input argument

p - vector: polynomial coefficients
k - numeric scalr: constant of integration

Output argument

q - row vector: integrated polynomial coefficients

Description

polyint returns the integral of the polynomial represented by the coefficients in p using a constant of integration k (0 by default).

Example

p = [10, 0, -10, 0, 0, 10];
v = [10, 0, 10];
k = 3;
q = polyint(conv(p,v),k)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

polyval

Polynomial evaluation.

Syntax

y = polyval(p, x)

Input argument

p - vector: polynomial coefficients
x - query points

Output argument

y - vector: Function values

Description

polyval evaluates polynomial at several points.

Example

p = [3 2 1];
x = [5 7 9];
R = polyval(p, x)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

polyvalm

Matrix polynomial evaluation.

Syntax

Y = polyvalm(p, X)

Input argument

p - vector: polynomial coefficients
X - square matrix: input matrix

Output argument

Y - row vector: Output polynomial coefficients

Description

polyvalm evaluates matrix polynomial.

Example

R = polyvalm ([1, 2, 3, 4], [3, -4, 1; -2, 0, 2; -1, 4, -3])

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

roots

Find polynomial roots.

Syntax

r = roots(p)

Input argument

p - vector: polynomial coefficients

Output argument

r - roots

Description

r = roots(c) finds the roots of the polynomial c. r is a column vector.

This function uses the companion matrix of the polynomial to find the roots.

Example

p = [1 0 0 0 -1];
r = roots(p)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

Signal Processing

Description

Functions to analyze sampled signals.

bartlett - Bartlett window.
blackman - Blackman window.
db2mag - Convert a gain in decibels (dB) to a magnitude.
db2pow - Convert a gain in decibels (dB) to power.
filter2 - 2-D digital filter.
hamming - Hamming window.
hann - Hann window.
mag2db - Convert a magnitude to decibels (dB).
pow2db - Convert power to decibel.
sinc - Sinc function.
xcorr2 - 2-D cross-correlation.
zp2tf - Zero-pole to transfer function conversion.

bartlett

Bartlett window.

Syntax

c = bartlett(m)

Input argument

m - positive integer: window length

Output argument

c - column vector

Description

c = bartlett(m) an L-point symmetric Bartlett window.

Example

c = bartlett(8)

Bibliography

Oppenheim, Alan V., Ronald W. Schafer, and John R. Buck. Discrete-Time Signal Processing. Upper Saddle River, NJ: Prentice Hall, 1999, pp. 468–471.

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

blackman

Blackman window.

Syntax

c = blackman(m)
c = blackman(m, opt)

Input argument

m - positive integer: window length
opt - string: 'symetric' (default) or 'periodic'

Output argument

c - column vector

Description

c = blackman(m) computes coefficients of a Blackman window of length m.

Example

c = blackman(8)
c = blackman(8, 'periodic')

Bibliography

Oppenheim, Alan V., Ronald W. Schafer, and John R. Buck. Discrete-Time Signal Processing. Upper Saddle River, NJ: Prentice Hall, 1999, pp. 468–471.

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

db2mag

Convert a gain in decibels (dB) to a magnitude.

Syntax

mag = db2mag(db)

Input argument

db - input array: scalar, vector or matrix.

Output argument

mag - corresponding magnitude

Description

mag = db2mag(db) returns corresponding magnitude.

Example

mag = db2mag([0, -20])

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

db2pow

Convert a gain in decibels (dB) to power.

Syntax

pow = db2pow(db)

Input argument

db - input array: scalar, vector or matrix.

Output argument

pow - corresponding power

Description

pow = db2pow(db) returns corresponding power.

Example

pow = db2pow([0, -20])

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

filter2

2-D digital filter.

Syntax

Y = filter2(H, X)
Y = filter2(H, X, shape)

Input argument

H - coefficients of rational transfer function.
X - input data.
shape - 'same' (default), 'valid' or 'full'.

Output argument

Y - result: 2-D digital filter.

Description

Y = filter2(H, X) applies a finite impulse response filter to a matrix of data X according to coefficients in a matrix H.

Example

A = zeros(10);
A(3:7, 3:7) = ones(5);
H = [1 2 1; 0 0 0; -1 -2 -1];
R = filter2(H, A, 'valid')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

hamming

Hamming window.

Syntax

c = hamming(m)
c = hamming(m, opt)

Input argument

m - positive integer: window length
opt - string: 'symetric' (default) or 'periodic'

Output argument

c - column vector

Description

c = hamming(m) computes coefficients of a Hamming window of length m.

Example

c = hamming(8)
c = hamming(8, 'periodic')

Bibliography

Oppenheim, Alan V., Ronald W. Schafer, and John R. Buck. Discrete-Time Signal Processing. Upper Saddle River, NJ: Prentice Hall, 1999.

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

hann

Hann window.

Syntax

c = hann(m)
c = hann(m, opt)

Input argument

m - positive integer: window length
opt - string: 'symetric' (default) or 'periodic'

Output argument

c - column vector

Description

c = hann(m) computes coefficients of a Hanning window of length m.

Example

c = hann(8)
c = hann(8, 'periodic')

Bibliography

Oppenheim, Alan V., Ronald W. Schafer, and John R. Buck. Discrete-Time Signal Processing. Upper Saddle River, NJ: Prentice Hall, 1999.

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

mag2db

Convert a magnitude to decibels (dB).

Syntax

db = mag2db(mag)

Input argument

mag - input array: scalar, vector or matrix.

Output argument

db - corresponding values in decibels

Description

db = mag2db(mag) returns corresponding values in decibels.

Example

DB = mag2db([1, 0.01])

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

pow2db

Convert power to decibel.

Syntax

db = pow2db(pow)

Input argument

pow - input array: scalar, vector or matrix.

Output argument

db - corresponding values in decibels

Description

db = pow2db(pow) returns corresponding values in decibels.

Example

DB = pow2db([1, 0.01])

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

sinc

Sinc function.

Syntax

c = sinc(m)

Input argument

m - input array: scalar, vector or matrix.

Output argument

c - sinc of input

Description

c = sinc(m) returns an array c whose elements are the sinc of the elements of the input: m.

Example

c = sinc(pi)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

xcorr2

2-D cross-correlation.

Syntax

C = xcorr2(A)
C = xcorr2(A, B)

Input argument

A - matrices
B - matrices

Output argument

C - 2-D cross-correlation or autocorrelation matrix

Description

xcorr2(A, B) calculates the cross-correlation between two matrices, A and B, in two dimensions, without any scaling applied.

Example

X = ones(2, 3);
H = [1 2; 3 4; 5 6];
C = xcorr2(H, X)

History

Version	Description
1.3.0	initial version

Author

Allan CORNET

zp2tf

Zero-pole to transfer function conversion.

Syntax

[NUM, DEN] = zp2tf(Z, P, K)

Input argument

Z - Locations of zeros, organized in columns for each system output.
P - Locations of poles, recorded as a column vector.
K - Gains.

Output argument

NUM - Coefficients in the numerator, organized by rows corresponding to each system output.
DEN - Coefficients in the denominator, arranged as a row vector.

Description

[NUM, DEN] = zp2tf(Z, P, K) returns polynomial transfer function representation from zeros and poles.

Example

p = [0.5;0.45+0.5i;0.45-0.5i];
z = [-1;i;-i];
k = 1;
[n, d] = zp2tf(z, p, k)

Bibliography

zpk2tf scipy implementation (MIT)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

Subroutine Library In COntrol Theory

Description

SLICOT provides numerical algorithms for computations in systems and control theory.

SLICOT License - About SLICOT license.
slicot_ab01od - Staircase form for multi-input systems using orthogonal state and input transformations.
slicot_ab04md - Discrete-time / continuous-time systems conversion by a bilinear transformation.
slicot_ab07nd - Inverse of a given linear system.
slicot_ab08nd - Construction of a regular pencil for a given system such that its generalized eigenvalues are invariant zeros of the system.
slicot_ag08bd - Zeros and Kronecker structure of a descriptor system pencil.
slicot_mb02md - Solution of Total Least-Squares problem using a SVD approach.
slicot_mb03od - Matrix rank determination by incremental condition estimation.
slicot_mb03pd - Matrix rank determination by incremental condition estimation (row pivoting).
slicot_mb03rd - Reduction of a real Schur form matrix to a block-diagonal form.
slicot_mb04gd - RQ factorization with row pivoting of a matrix.
slicot_mb04md - Balancing a general real matrix.
slicot_mb05od - Matrix exponential for a real matrix, with accuracy estimate.
slicot_mc01td - Checking stability of a given real polynomial.
slicot_sb01bd - Pole assignment for a given matrix pair (A,B).
slicot_sb02od - Solution of continuous- or discrete-time algebraic Riccati equations (generalized Schur vectors method).
slicot_sb03md - Solution of continuous- or discrete-time Lyapunov equations and separation estimation.
slicot_sb03od - Solution of stable continuous- or discrete-time Lyapunov equations (Cholesky factor).
slicot_sb04md - Solution of continuous-time Sylvester equations (Hessenberg-Schur method).
slicot_sb04qd - Solution of discrete-time Sylvester equations (Hessenberg-Schur method).
slicot_sb10jd - Converting a descriptor state-space system into regular state-space form.
slicot_sg02ad - Solution of continuous- or discrete-time algebraic Riccati equations for descriptor systems.
slicot_tb01id - Balancing a system matrix corresponding to a triplet (A, B, C).
slicot_tg01ad - Balancing the matrices of the system pencil corresponding to a descriptor triple (A-lambda E, B, C).

SLICOT License

About SLICOT license.

Description

Note that SLICOT is licensed under GPLv2 or higher, but the bindings to the library in this nelson's module, is licensed under LGPL v3.0.

This means that code using the SLICOT library via SLICOT bindings is subject to SLICOT's licensing terms.

If you distribute a derived or combined work, i.e. a program that links to and is distributed with the SLICOT library, then that distribution falls under the terms of the GPL.

if SLICOT library is available on platform, and user chooses to use it, distribution falls under the terms of the GPL.

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

slicot_ab01od

Staircase form for multi-input systems using orthogonal state and input transformations.

Syntax

[A_OUT, B_OUT, U_OUT, V, NCONT_OUT, INDCON_OUT, KSTAIR_OUT, INFO] = slicot_ab01od(STAGES, JOBU, JOBV, A_IN, B_IN, U_IN, NCONT_IN, INDCON_IN, KSTAIR_IN, TOL)

Input argument

STAGES - Specifies the reduction stage: 'F': Perform the forward stage only; 'B': Perform the backward stage only; 'A': Perform both (all) stages.
JOBU - Indicates whether the user wishes to accumulate in a matrix U the state-space transformations: 'N': Do not form U; 'I': U is internally initialized to the unit matrix
JOBV - Indicates whether the user wishes to accumulate in a matrix V the input-space transformations: 'N': Do not form V; I': V is initialized to the unit matrix and the orthogonal transformation matrix V is returned.
A_IN - the leading N-by-N part of this array must contain the state transition matrix A to be transformed
B_IN - the leading N-by-M part of this array must contain the input matrix B to be transformed.
U_IN - If STAGES ~= 'B' or JOBU = 'N', then U need not be set on entry. If STAGES = 'B' and JOBU = 'I', then, on entry, the leading N-by-N part of this array must contain the transformation matrix U that reduced the pair to the orthogonal canonical form.
NCONT_IN - The order of the controllable state-space representation. NCONT_IN is input only if STAGES = 'B'.
INDCON_IN - The number of stairs in the staircase form (also, the controllability index of the controllable part of the system representation).
TOL - The tolerance to be used in rank determination when transforming (A, B).

Output argument

A_OUT - On exit, the leading N-by-N part of this array contains the transformed state transition matrix U' _ A _ U. The leading NCONT-by-NCONT part contains the upper block Hessenberg state matrix Acont in Ac, given by U' _ A _ U, of a controllable realization for the original system. The elements below the first block-subdiagonal are set to zero. If STAGES ~='F', the subdiagonal blocks of A are triangularized by RQ factorization, and the annihilated elements are explicitly zeroed.
B_OUT - On exit with STAGES = 'F', the leading N-by-M part of this array contains the transformed input matrix U' _ B, with all elements but the first block set to zero. On exit with STAGES ~= 'F', the leading N-by-M part of this array contains the transformed input matrix U' _ B * V, with all elements but the first block set to zero and the first block in upper triangular form.
U_OUT - if JOBU = 'I', the leading N-by-N part of this array contains the transformation matrix U that performed the specified reduction. If JOBU = 'N', the array U is not referenced and can be supplied as a dummy array.
V - If JOBV = 'I', then the leading M-by-M part of this array contains the transformation matrix V.
NCONT_OUT - NCONT_OUT is input only if STAGES = 'B'.
INDCON_OUT - INDCON is input only if STAGES = 'B'.
KSTAIR_OUT - KSTAIR is input if STAGES = 'B', and output otherwise.
INFO - 0: successful exit; if INFO = -i, the i-th argument had an illegal value.

Description

To reduce the matrices A and B using (and optionally accumulating) state-space and input-space transformations U and V respectively, such that the pair of matrices

Ac = U' * A * U, Bc = U' * B * V

Used function(s)

AB01OD

Bibliography

http://slicot.org/objects/software/shared/doc/AB01OD.html

Example

N = 5;
M = 2;
TOL = 0.
STAGES = 'F';
JOBU = 'N';
JOBV = 'N';
A_IN = [17.0   24.0    1.0    8.0   15.0;
   23.0    5.0    7.0   14.0   16.0;
   4.0    6.0   13.0   20.0   22.0;
   10.0   12.0   19.0   21.0    3.0;
   11.0   18.0   25.0    2.0    9.0];

% SLICOT 5.0 have an error in the example.
A_IN = A_IN.';

B_IN = [   -1.0   -4.0;
    4.0    9.0;
   -9.0  -16.0;
   16.0   25.0;
  -25.0  -36.0];

U_IN = zeros(N, N);
INDCON_IN = N;
NCONT_IN = 1;
KSTAIR_IN = zeros(1,N);
[A_OUT, B_OUT, U_OUT, V, NCONT_OUT, INDCON_OUT, KSTAIR_OUT, INFO] = slicot_ab01od(STAGES, JOBU, JOBV, A_IN, B_IN, U_IN, NCONT_IN, INDCON_IN, KSTAIR_IN, TOL)

History

Version	Description
1.0.0	initial version

Author

SLICOT Documentation

slicot_ab04md

Discrete-time / continuous-time systems conversion by a bilinear transformation.

Syntax

[A_OUT, B_OUT, C_OUT, D_OUT, INFO] = slicot_ab04md(TYPE, ALPHA, BETA, A_IN, B_IN, C_IN, D_IN)

Input argument

TYPE - a character: 'D' discrete or 'C' continuous time
ALPHA, BETA - Parameters specifying the bilinear transformation. Recommended values for stable systems: ALPHA = 1, BETA = 1. ALPHA ~= 0, BETA ~= 0
A_IN - N-by-N part of this array must contain the state matrix A of the original system.
B_IN - N-by-M part of this array must contain the input matrix B of the original system.
C_IN - P-by-N part of this array must contain the output matrix C of the original system.
D_IN - P-by-M part of this array must contain the input/output matrix D for the original system.

Output argument

A_OUT - N-by-N part of this array contains the state matrix _A of the transformed system.
B_OUT - N-by-M part of this array contains the input matrix _B of the transformed system.
C_OUT - the leading P-by-N part of this array contains the output matrix _C of the transformed system.
D_OUT - P-by-M part of this array contains the input/output matrix _D of the transformed system.
INFO - Error Indicator: = 0: successful exit; less than 0: if INFO = -i, the i-th argument had an illegal value; = 1: if the matrix (ALPHAI + A) is exactly singular; = 2: if the matrix (BETAI - A) is exactly singular.

Description

To perform a transformation on the parameters (A, B, C, D) of a system, which is equivalent to a bilinear transformation of the corresponding transfer function matrix.

Used function(s)

AB04MD

Bibliography

http://slicot.org/objects/software/shared/doc/AB04MD.html

Example

N = 2;
M = 2;
P = 2;
TYPE= 'C';
ALPHA = 1;
BETA = 1;
A = [   1.0  0.5; 0.5  1.0];
B = [   0.0 -1.0; 1.0  0.0];
C = [  -1.0  0.0; 0.0  1.0];
D = [   1.0  0.0; 0.0 -1.0];
[A_OUT, B_OUT, C_OUT, D_OUT, INFO] = slicot_ab04md(TYPE, ALPHA, BETA, A, B, C, D)

History

Version	Description
1.0.0	initial version

Author

SLICOT Documentation

slicot_ab07nd

Inverse of a given linear system.

Syntax

[A_OUT, B_OUT, C_OUT, D_OUT, RCOND, INFO] = slicot_ab07nd(A_IN, B_IN, C_IN, D_IN)

Input argument

A_IN - The leading N-by-N part of this array must contain the state matrix A of the original system.
B_IN - The leading N-by-M part of this array must contain the input matrix B of the original system.
C_IN - The leading M-by-N part of this array must contain the output matrix C of the original system.
D_IN - The leading M-by-M part of this array must contain the feedthrough matrix D of the original system.

Output argument

A_OUT - The leading N-by-N part of this array contains the state matrix Ai of the inverse system.
B_OUT - The leading N-by-M part of this array contains the input matrix Bi of the inverse system.
C_OUT - The leading M-by-N part of this array contains the output matrix Ci of the inverse system.
D_OUT - The leading M-by-M part of this array contains the feedthrough matrix Di of the inverse system.
RCOND - The estimated reciprocal condition number of the feedthrough matrix D of the original system.
INFO - = 0: successful exit;

Description

To compute the inverse (Ai, Bi, Ci, Di) of a given system (A, B, C, D).

Used function(s)

AB07ND

Bibliography

http://slicot.org/objects/software/shared/doc/AB07ND.html

Example

A_IN = [1.0   2.0   0.0;
   4.0  -1.0   0.0;
   0.0   0.0   1.0];

B_IN = [1.0   0.0;
   0.0   1.0;
   1.0   0.0];

C_IN = [0.0   1.0  -1.0;
   0.0   0.0   1.0];

D_IN = [4.0   0.0;
   0.0   1.0];

[A_OUT, B_OUT, C_OUT, D_OUT, RCOND, INFO] = slicot_ab07nd(A_IN, B_IN, C_IN, D_IN)

History

Version	Description
1.0.0	initial version

Author

SLICOT Documentation

slicot_ab08nd

Construction of a regular pencil for a given system such that its generalized eigenvalues are invariant zeros of the system.

Syntax

[NU, RANK, DINFZ, NKROR, NKROL, INFZ, KRONR, KRONL, AF, BF, INFO] = slicot_ab08nd(EQUIL, N, M, P, A, B, C, D, TOL)

Input argument

EQUIL - 'S': Perform balancing (scaling) or 'N': Do not perform balancing.
N - The number of state variables, i.e., the order of the matrix A.
M - The number of system inputs.
P - The number of system outputs.
A - The leading N-by-N part of this array must contain the state dynamics matrix A of the system.
B - The leading N-by-M part of this array must contain the input/state matrix B of the system.
C - The leading P-by-N part of this array must contain the state/output matrix C of the system.
D - The leading P-by-M part of this array must contain the direct transmission matrix D of the system.
TOL - A tolerance used in rank decisions.

Output argument

NU - The number of (finite) invariant zeros.
RANK - The normal rank of the transfer function matrix.
DINFZ - The maximum degree of infinite elementary divisors.
NKROR - The number of right Kronecker indices.
NKROL - The number of left Kronecker indices.
INFZ - The leading DINFZ elements of INFZ contain information on the infinite elementary divisors as follows: the system has INFZ(i) infinite elementary divisors of degree i, where i = 1,2,...,DINFZ.
KRONR - The leading NKROR elements of this array contain the right Kronecker (column) indices.
KRONL - The leading NKROL elements of this array contain the left Kronecker (row) indices.
AF - The leading NU-by-NU part of this array contains the coefficient matrix A of the reduced pencil.
BF - The leading NU-by-NU part of this array contains the coefficient matrix B of the reduced pencil.
INFO - 0: successful exit; if INFO = -i, the i-th argument had an illegal value.

Description

To construct for a linear multivariable system described by a state-space model (A,B,C,D) a regular pencil (A - lambda*B ) which has the invariant zeros of the system as generalized eigenvalues.

The routine also computes the orders of the infinite zeros and the right and left Kronecker indices of the system (A,B,C,D).

Used function(s)

AB08ND

Bibliography

http://slicot.org/objects/software/shared/doc/AB08ND.html

Example

N = 6;
M = 2;
P = 3;
TOL = 0.0;
EQUIL = 'N';
%=============================================================================
A  = [1.0   0.0   0.0   0.0   0.0   0.0;
   0.0   1.0   0.0   0.0   0.0   0.0;
   0.0   0.0   3.0   0.0   0.0   0.0;
   0.0   0.0   0.0  -4.0   0.0   0.0;
   0.0   0.0   0.0   0.0  -1.0   0.0;
   0.0   0.0   0.0   0.0   0.0   3.0];
%=============================================================================
B = [0.0  -1.0;
  -1.0   0.0;
   1.0  -1.0;
   0.0   0.0;
   0.0   1.0;
  -1.0  -1.0];
%=============================================================================
C = [1.0   0.0   0.0   1.0   0.0   0.0;
   0.0   1.0   0.0   1.0   0.0   1.0;
   0.0   0.0   1.0   0.0   0.0   1.0];
D = [0.0   0.0;
   0.0   0.0;
   0.0   0.0];
%=============================================================================
% Check the observability and compute the ordered set of the observability indices (call the routine with M = 0).
[NU, RANK, DINFZ, NKROR, NKROL, INFZ, KRONR, KRONL, AF, BF, INFO] = slicot_ab08nd(EQUIL, N, 0, P, A, B, C, D, TOL)

% Check the controllability and compute the ordered set of the controllability indices (call the routine with P = 0)
[NU, RANK, DINFZ, NKROR, NKROL, INFZ, KRONR, KRONL, AF, BF, INFO] = slicot_ab08nd(EQUIL, N, M, 0, A, B, C, D, TOL)

% Compute the structural invariants of the given system.
[NU, RANK, DINFZ, NKROR, NKROL, INFZ, KRONR, KRONL, AF, BF, INFO] = slicot_ab08nd(EQUIL, N, M, P, A, B, C, D, TOL)

History

Version	Description
1.0.0	initial version

Author

SLICOT Documentation

slicot_ag08bd

Zeros and Kronecker structure of a descriptor system pencil.

Syntax

[A_OUT, E_OUT, NFZ, NRANK, NIZ, DINFZ, NKROR, NINFE, NKROL, INFZ, KRONR, INFE, KRONL, INFO] = slicot_ag08bd(EQUIL, M, P, A_IN, E_IN, B, C, D, TOL)

Input argument

EQUIL - = 'S': Perform balancing (scaling); = 'N': Do not perform balancing.
M - The number of columns of matrix B.
P - The number of rows of matrix C.
A_IN - The leading L-by-N part of this array must contain the state dynamics matrix A of the system.
E_IN - The leading L-by-N part of this array must contain the descriptor matrix E of the system.
B - The leading L-by-M part of this array must contain the input/state matrix B of the system.
C - The leading P-by-N part of this array must contain the state/output matrix C of the system.
D - The leading P-by-M part of this array must contain the direct transmission matrix D of the system.
TOL - A tolerance used in rank decisions to determine the effective rank, which is defined as the order of the largest leading (or trailing) triangular submatrix in the QR (or RQ) factorization with column (or row) pivoting whose estimated condition number is less than 1/TOL.

Output argument

A_OUT - The leading NFZ-by-NFZ part of this array contains the matrix Af of the reduced pencil.
E_OUT - The leading NFZ-by-NFZ part of this array contains the matrix Ef of the reduced pencil.
NFZ - The number of finite zeros.
NRANK - The normal rank of the system pencil.
NIZ - The number of infinite zeros.
DINFZ - The maximal multiplicity of infinite Smith zeros.
NKROR - The number of right Kronecker indices.
NINFE - The number of elementary infinite blocks.
NKROL - The number of left Kronecker indices.
INFZ - The leading DINFZ elements of INFZ contain information on the infinite elementary divisors
KRONR - The leading NKROR elements of this array contain the right Kronecker (column) indices.
KRONL - The leading NKROL elements of this array contain the left Kronecker (row) indices.
INFO - = 0: successful exit;

Description

To extract from the system pencil a regular pencil Af-lambda*Ef which has the finite Smith zeros of S(lambda) as generalized eigenvalues. The routine also computes the orders of the infinite Smith zeros and determines the singular and infinite Kronecker structure of system pencil, i.e., the right and left Kronecker indices, and the multiplicities of infinite eigenvalues.

Used function(s)

AG08BD

Bibliography

http://slicot.org/objects/software/shared/doc/AG08BD.html

Example

L = 9;
N = 9;
M = 3;
P = 3;
TOL= 1.e-7;
EQUIL='N';
A_IN = [1     0     0     0     0     0     0     0     0;
     0     1     0     0     0     0     0     0     0;
     0     0     1     0     0     0     0     0     0;
     0     0     0     1     0     0     0     0     0;
     0     0     0     0     1     0     0     0     0;
     0     0     0     0     0     1     0     0     0;
     0     0     0     0     0     0     1     0     0;
     0     0     0     0     0     0     0     1     0;
     0     0     0     0     0     0     0     0     1];

E_IN = [0     0     0     0     0     0     0     0     0;
     1     0     0     0     0     0     0     0     0;
     0     1     0     0     0     0     0     0     0;
     0     0     0     0     0     0     0     0     0;
     0     0     0     1     0     0     0     0     0;
     0     0     0     0     1     0     0     0     0;
     0     0     0     0     0     0     0     0     0;
     0     0     0     0     0     0     1     0     0;
     0     0     0     0     0     0     0     1     0];

B =[-1     0     0;
     0     0     0;
     0     0     0;
     0    -1     0;
     0     0     0;
     0     0     0;
     0     0    -1;
     0     0     0;
     0     0     0];

C = [ 0     1     1     0     3     4     0     0     2;
      0     1     0     0     4     0     0     2     0;
      0     0     1     0    -1     4     0    -2     2];

D = [ 1     2    -2;
      0    -1    -2;
      0     0     0];
%=============================================================================
% default call for the fortran routine
M = 3; P = 3;
[A_OUT, E_OUT, NFZ, NRANK, NIZ, DINFZ, NKROR, NINFE, NKROL, INFZ, KRONR, INFE, KRONL, INFO] = slicot_ag08bd(EQUIL, M, P, A_IN, E_IN, B, C, D, TOL)
%=============================================================================
% Compute poles (we need tp call fortran routine with M = 0, P = 0)
M = 0; P = 0;
[A_OUT, E_OUT, NFZ, NRANK, NIZ, DINFZ, NKROR, NINFE, NKROL, INFZ, KRONR, INFE, KRONL, INFO] = slicot_ag08bd(EQUIL, M, P, A_IN, E_IN, B, C, D, TOL)
%=============================================================================
%  Check the observability and compute the ordered set of the observability indices (call the routine with M = 0).
M = 0; P = 3;
[A_OUT, E_OUT, NFZ, NRANK, NIZ, DINFZ, NKROR, NINFE, NKROL, INFZ, KRONR, INFE, KRONL, INFO] = slicot_ag08bd(EQUIL, M, P, A_IN, E_IN, B, C, D, TOL)
%=============================================================================
% Check the controllability and compute the ordered set of the controllability indices (call the routine with P = 0)
M = 3; P = 0;
[A_OUT, E_OUT, NFZ, NRANK, NIZ, DINFZ, NKROR, NINFE, NKROL, INFZ, KRONR, INFE, KRONL, INFO] = slicot_ag08bd(EQUIL, M, P, A_IN, E_IN, B, C, D, TOL)
%=============================================================================

History

Version	Description
1.0.0	initial version

Author

SLICOT Documentation

slicot_mb02md

Solution of Total Least-Squares problem using a SVD approach.

Syntax

[RANK_OUT, C_OUT, S, X, IWARN, INFO] = slicot_mb02md(JOB, M, N, L, RANK_IN, C_IN, TOL)

Input argument

JOB - Determines whether the values of the parameters RANK and TOL are to be specified by the user or computed by the routine as follows: = 'R': Compute RANK only; = 'T': Compute TOL only; = 'B': Compute both RANK and TOL; = 'N': Compute neither RANK nor TOL.
M - The number of rows in the data matrix A and the observation matrix B.
N - The number of columns in the data matrix A.
L - The number of columns in the observation matrix B.
RANK_IN - if JOB = 'T' or JOB = 'N', then RANK must specify r, the rank of the TLS approximation [A + DA | B + DB].
C_IN - the leading M-by-(N+L) part of this array must contain the matrices A and B.
TOL - A tolerance used to determine the rank of the TLS approximation [A+DA|B+DB] and to check the multiplicity of the singular values of matrix C.

Output argument

RANK_OUT - if JOB = 'R' or JOB = 'B', and INFO = 0, then RANK contains the computed (effective) rank of the TLS approximation [A + DA | B + DB].
C_OUT - the leading (N+L)-by-(N+L) part of this array contains the (transformed) right singular vectors, including null space vectors, if any, of C = [A | B].
S - If INFO = 0, the singular values of matrix C
X - If INFO = 0, the leading N-by-L part of this array contains the solution X to the TLS problem specified by A and B.
IWARN - = 0: no warnings; = 1: if the rank of matrix C has been lowered because a singular value of multiplicity greater than 1 was found; = 2: if the rank of matrix C has been lowered because the upper triangular matrix F is (numerically) singular.
INFO - = 0: successful exit;

Description

To solve the Total Least Squares (TLS) problem using a Singular Value Decomposition (SVD) approach. The TLS problem assumes an overdetermined set of linear equations AX = B, where both the data matrix A as well as the observation matrix B are inaccurate. The routine also solves determined and underdetermined sets of equations by computing the minimum norm solution. It is assumed that all preprocessing measures (scaling, coordinate transformations, whitening, ... ) of the data have been performed in advance.

Used function(s)

MB02MD

Bibliography

http://slicot.org/objects/software/shared/doc/MB02MD.html

Example

M = 6;
N = 3;
L = 1;
JOB = 'B';
TOL = 0.0;
RANK_IN = 1;
C_IN = [0.80010  0.39985  0.60005  0.89999;
   0.29996  0.69990  0.39997  0.82997;
   0.49994  0.60003  0.20012  0.79011;
   0.90013  0.20016  0.79995  0.85002;
   0.39998  0.80006  0.49985  0.99016;
   0.20002  0.90007  0.70009  1.02994];
[RANK_OUT, C_OUT, S, X, IWARN, INFO] = slicot_mb02md(JOB, M, N, L, RANK_IN, C_IN, TOL)

History

Version	Description
1.0.0	initial version

Author

SLICOT Documentation

slicot_mb03od

Matrix rank determination by incremental condition estimation.

Syntax

[A_OUT, JPVT_OUT, TAU, RANK, SVAL, INFO] = slicot_mb03od(JOBQR, A_IN, JPVT_IN, RCOND, SVLMAX)

Input argument

JOBQR - = 'Q': Perform a QR factorization with column pivoting; = 'N': Do not perform the QR factorization (but assume that it has been done outside).
A_IN - with JOBQR = 'Q', the leading M by N part of this array must contain the given matrix A.
JPVT_IN - with JOBQR = 'Q', if JPVT(i) != 0, the i-th column of A is an initial column, otherwise it is a free column. Before the QR factorization of A, all initial columns are permuted to the leading positions; only the remaining free columns are moved as a result of column pivoting during the factorization. For rank determination it is preferable that all columns be free.
RCOND - RCOND is used to determine the effective rank of A, which is defined as the order of the largest leading triangular submatrix R11 in the QR factorization with pivoting of A, whose estimated condition number is less than 1/RCOND.
SVLMAX - If A is a submatrix of another matrix B, and the rank decision should be related to that matrix, then SVLMAX should be an estimate of the largest singular value of B

Output argument

A_OUT - with JOBQR = 'Q', the leading min(M,N) by N upper triangular part of A contains the triangular factor R, and the elements below the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of min(M,N) elementary reflectors.
JPVT_OUT - with JOBQR = 'Q', if JPVT(i) = k, then the i-th column of A*P was the k-th column of A.
TAU - with JOBQR = 'Q', the leading min(M,N) elements of TAU contain the scalar factors of the elementary reflectors.
RANK - The effective (estimated) rank of A, i.e. the order of the submatrix R11.
SVAL - The estimates of some of the singular values of the triangular factor R
INFO - = 0: successful exit

Description

To compute (optionally) a rank-revealing QR factorization of a real general M-by-N matrix A, which may be rank-deficient, and estimate its effective rank using incremental condition estimation.

Used function(s)

MB03OD

Bibliography

http://slicot.org/objects/software/shared/doc/MB03OD.html

Example

M = 6;
N = 5;
JOBQR = 'Q';
RCOND = 5.D-16;
SVLMAX = 0.0;
JPVT_IN = zeros(1, N);
A_IN = [1.    2.    6.    3.    5.;
  -2.   -1.   -1.    0.   -2.;
   5.    5.    1.    5.    1.;
  -2.   -1.   -1.    0.   -2.;
   4.    8.    4.   20.    4.;
  -2.   -1.   -1.    0.   -2.];

[A_OUT, JPVT_OUT, TAU, RANK, SVAL, INFO] = slicot_mb03od(JOBQR, A_IN, JPVT_IN, RCOND, SVLMAX)

History

Version	Description
1.0.0	initial version

Author

SLICOT Documentation

slicot_mb03pd

Matrix rank determination by incremental condition estimation (row pivoting).

Syntax

[A_OUT, JPVT_OUT, TAU, RANK, SVAL, INFO] = slicot_mb03pd(JOBRQ, A_IN, JPVT_IN, RCOND, SVLMAX)

Input argument

JOBRQ - = 'R': Perform an RQ factorization with row pivoting; = 'N': Do not perform the RQ factorization (but assume that it has been done outside).
A_IN - with JOBRQ = 'R', the leading M-by-N part of this array must contain the given matrix A.
JPVT_IN - with JOBRQ = 'R', if JPVT(i) != 0, the i-th row of A is a final row, otherwise it is a free row. Before the RQ factorization of A, all final rows are permuted to the trailing positions; only the remaining free rows are moved as a result of row pivoting during the factorization. For rank determination it is preferable that all rows be free.
RCOND - RCOND is used to determine the effective rank of A, which is defined as the order of the largest trailing triangular submatrix R22 in the RQ factorization with pivoting of A, whose estimated condition number is less than 1/RCOND.
SVLMAX - If A is a submatrix of another matrix B, and the rank decision should be related to that matrix, then SVLMAX should be an estimate of the largest singular value of B (for instance, the Frobenius norm of B). If this is not the case, the input value SVLMAX = 0 should work.

Output argument

A_OUT - with JOBRQ = 'R', if M less or equal than N, the upper triangle of the subarray A(1:M,N-M+1:N) contains the M-by-M upper triangular matrix R;
JPVT_OUT - with JOBRQ = 'R', if JPVT(i) = k, then the i-th row of P*A was the k-th row of A.
TAU - with JOBRQ = 'R', the leading min(M,N) elements of TAU contain the scalar factors of the elementary reflectors.
RANK - The effective (estimated) rank of A, i.e. the order of the submatrix R22.
SVAL - The estimates of some of the singular values of the triangular factor R.
INFO - = 0: successful exit

Description

To compute (optionally) a rank-revealing RQ factorization of a real general M-by-N matrix A, which may be rank-deficient, and estimate its effective rank using incremental condition estimation.

Used function(s)

MB03PD

Bibliography

http://slicot.org/objects/software/shared/doc/MB03PD.html

Example

M = 6;
N = 5;
JOBRQ = 'R';
RCOND = 5.D-16;
SVLMAX = 0.0;
JPVT_IN = zeros(1, M);
A_IN = [   1.    2.    6.    3.    5.;
  -2.   -1.   -1.    0.   -2.;
   5.    5.    1.    5.    1.;
  -2.   -1.   -1.    0.   -2.;
   4.    8.    4.   20.    4.;
  -2.   -1.   -1.    0.   -2.];
[A_OUT, JPVT_OUT, TAU, RANK, SVAL, INFO] = slicot_mb03pd(JOBRQ, A_IN, JPVT_IN, RCOND, SVLMAX)

History

Version	Description
1.0.0	initial version

Author

SLICOT Documentation

slicot_mb03rd

Reduction of a real Schur form matrix to a block-diagonal form.

Syntax

[A_OUT, X_OUT, NBLCKS, BLSIZE, WR, WI, INFO] = slicot_mb03rd(JOBX, SORT, PMAX, A_IN, X_IN, TOL)

Input argument

JOBX - Specifies whether or not the transformations are accumulated, as follows: = 'N': The transformations are not accumulated; = 'U': The transformations are accumulated in X (the given matrix X is updated)
SORT - Specifies whether or not the diagonal blocks of the real Schur form are reordered, as follows: = 'N': The diagonal blocks are not reordered; = 'S': The diagonal blocks are reordered before each step of reduction, so that clustered eigenvalues appear in the same block; = 'C': The diagonal blocks are not reordered, but the "closest-neighbour" strategy is used instead of the standard "closest to the mean" strategy. = 'B': The diagonal blocks are reordered before each step of reduction, and the "closest-neighbour" strategy is used.
PMAX - An upper bound for the infinity norm of elementary submatrices of the individual transformations used for reduction
A_IN - the leading N-by-N part of this array must contain the matrix A to be block-diagonalized, in real Schur form.
X_IN - if JOBX = 'U', the leading N-by-N part of this array must contain a given matrix X.
TOL - The tolerance to be used in the ordering of the diagonal blocks of the real Schur form matrix.

Output argument

A_OUT - the leading N-by-N part of this array contains the computed block-diagonal matrix, in real Schur canonical form. The non-diagonal blocks are set to zero.
X_OUT - if JOBX = 'U', the leading N-by-N part of this array contains the product of the given matrix X and the transformation matrix that reduced A to block-diagonal form. The transformation matrix is itself a product of non-orthogonal similarity transformations having elements with magnitude less than or equal to PMAX. If JOBX = 'N', this array is not referenced
NBLCKS - The number of diagonal blocks of the matrix A.
BLSIZE - The first NBLCKS elements of this array contain the orders of the resulting diagonal blocks of the matrix A.
WR - real parts of the eigenvalues of the matrix A.
WI - imaginary parts of the eigenvalues of the matrix A.
INFO - = 0: successful exit;

Description

To reduce a matrix A in real Schur form to a block-diagonal form using well-conditioned non-orthogonal similarity transformations. The condition numbers of the transformations used for reduction are roughly bounded by PMAX*PMAX, where PMAX is a given value. The transformations are optionally postmultiplied in a given matrix X. The real Schur form is optionally ordered, so that clustered eigenvalues are grouped in the same block.

Used function(s)

MB03RD

Bibliography

http://slicot.org/objects/software/shared/doc/MB03RD.html

Example

N = 8;
PMAX = 1.D03;
TOL = 1.D-2;
JOBX = 'U';
SORT = 'S';
A_IN = [1.   -1.    1.    2.    3.    1.    2.    3.;
   1.    1.    3.    4.    2.    3.    4.    2.;
   0.    0.    1.   -1.    1.    5.    4.    1.;
   0.    0.    0.    1.   -1.    3.    1.    2.;
   0.    0.    0.    1.    1.    2.    3.   -1.;
   0.    0.    0.    0.    0.    1.    5.    1.;
   0.    0.    0.    0.    0.    0.    0.99999999   -0.99999999;
   0.    0.    0.    0.    0.    0.    0.99999999    0.99999999];
X_IN = zeros(N, N);
[A_OUT, X_OUT, NBLCKS, BLSIZE, WR, WI, INFO] = slicot_mb03rd(JOBX, SORT, PMAX, A_IN, X_IN, TOL)

History

Version	Description
1.0.0	initial version

Author

SLICOT Documentation

slicot_mb04gd

RQ factorization with row pivoting of a matrix.

Syntax

[A_OUT, JPVT_OUT, TAU, INFO] = slicot_mb04gd(A_IN, JPVT_IN)

Input argument

A_IN - The m-by-n matrix A.
JPVT_IN - if JPVT(i) .ne. 0, the i-th row of A is permuted to the bottom of P*A (a trailing row); if JPVT(i) = 0, the i-th row of A is a free row.

Output argument

A_OUT - if m less or equal than n, the upper triangle of the subarray A(1:m,n-m+1:n) contains the m-by-m upper triangular matrix R; if m greater or equal than n, the elements on and above the (m-n)-th subdiagonal contain the m-by-n upper trapezoidal matrix R; the remaining elements, with the array TAU, represent the orthogonal matrix Q as a product of min(m,n) elementary reflectors
JPVT_OUT - if JPVT(i) = k, then the i-th row of P*A was the k-th row of A.
TAU - The scalar factors of the elementary reflectors.
INFO - = 0: successful exit.

Description

To compute an RQ factorization with row pivoting of a real m-by-n matrix A: P * A = R * Q.

Used function(s)

MB04GD

Bibliography

http://slicot.org/objects/software/shared/doc/MB04GD.html

Example

M = 6;
N = 5;
A_IN = [1.    2.    6.    3.    5.;
  -2.   -1.   -1.    0.   -2.;
   5.    5.    1.    5.    1.;
  -2.   -1.   -1.    0.   -2.;
   4.    8.    4.   20.    4.;
  -2.   -1.   -1.    0.   -2.];
JPVT_IN = zeros(1, M);
[A_OUT, JPVT_OUT, TAU, INFO] = slicot_mb04gd(A_IN, JPVT_IN)

History

Version	Description
1.0.0	initial version

Author

SLICOT Documentation

slicot_mb04md

Balancing a general real matrix.

Syntax

[MAXRED_OUT, A_OUT, SCALE, INFO] = slicot_mb04md(MAXRED_IN, A_IN)

Input argument

MAXRED_IN - The maximum allowed reduction in the 1-norm of A (in an iteration) if zero rows or columns are encountered. If MAXRED greater than 0.0, MAXRED must be larger than one (to enable the norm reduction). If MAXRED less or equal than 0.0, then the value 10.0 for MAXRED is used.
A_IN - The leading N-by-N part of this array must contain the input matrix A.

Output argument

MAXRED_OUT - If the 1-norm of the given matrix A is non-zero, the ratio between the 1-norm of the given matrix and the 1-norm of the balanced matrix. Usually, this ratio will be larger than one, but it can sometimes be one, or even less than one (for instance, for some companion matrices).
A_OUT - The leading N-by-N part of this array contains the balanced matrix.
SCALE - The scaling factors applied to A. If D(j) is the scaling factor applied to row and column j, then SCALE(j) = D(j), for j = 1,...,N.
INFO - = 0: successful exit.

Description

To reduce the 1-norm of a general real matrix A by balancing. This involves diagonal similarity transformations applied iteratively to A to make the rows and columns as close in norm as possible.

Used function(s)

MB04MD

Bibliography

http://slicot.org/objects/software/shared/doc/MB04MD.html

Example

MAXRED_IN  = 0.0;
A_IN = [1.0   0.0   0.0   0.0;
 300.0 400.0 500.0 600.0;
   1.0   2.0   0.0   0.0;
   1.0   1.0   1.0   1.0];
[MAXRED_OUT, A_OUT, SCALE, INFO] = slicot_mb04md(MAXRED_IN, A_IN)

History

Version	Description
1.0.0	initial version

Author

SLICOT Documentation

slicot_mb05od

Matrix exponential for a real matrix, with accuracy estimate.

Syntax

[A_OUT, MDIG, IDIG, IWARN, INFO] = slicot_mb05od(BALANC, NDIAG, DELTA, A_IN)

Input argument

BALANC - Specifies whether or not a balancing transformation (done by SLICOT Library routine MB04MD) is required, as follows: = 'N', do not use balancing; = 'S', use balancing (scaling).
NDIAG - The specified order of the diagonal Pade approximant. In the absence of further information NDIAG should be set to 9. NDIAG should not exceed 15. NDIAG greater or equal than 1.
DELTA - The scalar value delta of the problem.
A_IN - The leading N-by-N part of this array must contain the matrix A of the problem.

Output argument

A_OUT - if INFO = 0, the leading N-by-N part of this array contains the solution matrix exp(A * delta).
MDIG - The minimal number of accurate digits in the 1-norm of exp(A*delta).
IDIG - The number of accurate digits in the 1-norm of exp(A*delta) at 95% confidence level.
IWARN - = 0: no warning; = 1: if MDIG = 0 and IDIG greater than 0, warning for possible inaccuracy (the exponential has been computed); = 2: if MDIG = 0 and IDIG = 0, warning for severe inaccuracy (the exponential has been computed); = 3: if balancing has been requested, but it failed to reduce the matrix norm and was not actually used.
INFO - = 0: successful exit; = 1: if the norm of matrix A*delta (after a possible balancing) is too large to obtain an accurate result; = 2: if the coefficient matrix (the denominator of the Pade approximant) is exactly singular; try a different value of NDIAG; = 3: if the solution exponential would overflow, possibly due to a too large value DELTA; the calculations stopped prematurely. This error is not likely to appear.

Description

To compute exp(A*delta) where A is a real N-by-N matrix and delta is a scalar value. The routine also returns the minimal number of accurate digits in the 1-norm of exp(A*delta) and the number of accurate digits in the 1-norm of exp(A*delta) at 95% confidence level.

Used function(s)

MB05OD

Bibliography

http://slicot.org/objects/software/shared/doc/MB05OD.html

Example

N = 3;
NDIAG = 9;
DELTA = 1.0;
BALANC = 'S';
A_IN = [2.0   1.0   1.0;
   0.0   3.0   2.0;
   1.0   0.0   4.0];
[A_OUT, MDIG, IDIG, IWARN, INFO] = slicot_mb05od(BALANC, NDIAG, DELTA, A_IN)

History

Version	Description
1.0.0	initial version

Author

SLICOT Documentation

slicot_mc01td

Checking stability of a given real polynomial.

Syntax

[DP_OUT, STABLE, NZ, IWARN, INFO] = slicot_mc01td(DICO, DP_IN, P)

Input argument

DICO - Indicates whether the stability test to be applied to P(x) is in the continuous-time or discrete-time case as follows: = 'C': Continuous-time case; = 'D': Discrete-time case.
DP_IN - The degree of the polynomial P(x).
P - This array must contain the coefficients of P(x) in increasing powers of x.

Output argument

DP_OUT - if P(DP+1) = 0.0 on entry, then DP contains the index of the highest power of x for which P(DP+1) != 0.0.
STABLE - Contains the value int32(1) if P(x) is stable and the value int32(0) otherwise.
NZ - If INFO = 0, contains the number of unstable zeros - that is, the number of zeros of P(x) in the right half-plane if DICO = 'C' or the number of zeros of P(x) outside the unit circle if DICO = 'D'.
IWARN - = 0: no warning;
INFO - = 0: successful exit; = 1: if on entry, P(x) is the zero polynomial;= 2: if the polynomial P(x) is most probably unstable.

Description

To determine whether or not a given polynomial P(x) with real coefficients is stable, either in the continuous-time or discrete-time case.

A polynomial is said to be stable in the continuous-time case if all its zeros lie in the left half-plane, and stable in the discrete-time case if all its zeros lie inside the unit circle.

Used function(s)

MC01TD

Bibliography

http://slicot.org/objects/software/shared/doc/MC01TD.html

Example

DICO = 'C';
DP_IN = 4;
P = [2.0  0.0  1.0  -1.0  1.0];
[DP, STABLE, NZ, IWARN, INFO] = slicot_mc01td(DICO, DP_IN, P)

History

Version	Description
1.0.0	initial version

Author

SLICOT Documentation

slicot_sb01bd

Pole assignment for a given matrix pair (A,B).

Syntax

[A_OUT, WR_OUT, WI_OUT, NFP, NAP, NUP, F, Z, IWARN, INFO] = slicot_sb01bd(DICO, ALPHA, A_IN, B_IN, WR_IN, WI_IN, TOL)

Input argument

DICO - Specifies the type of the original system.'C': continuous-time system;'D': discrete-time system.
ALPHA - Specifies the maximum admissible value.
A_IN - the leading N-by-N part of this array must contain the state dynamics matrix A.
B_IN - The leading N-by-M part of this array must contain the input/state matrix.
WR_IN - contains the real parts of the desired eigenvalues of the closed-loop system state-matrix A+B*F.
WI_IN - contains the imaginary parts of the desired eigenvalues of the closed-loop system state-matrix A+B*F.
TOL - The absolute tolerance level below which the elements of A or B are considered zero (used for controllability tests).

Output argument

A_OUT - the leading N-by-N part of this array contains the matrix Z'(A+BF)*Z in a real Schur form.
WR_OUT - if INFO = 0, the leading NAP elements of these arrays contain the real parts of the assigned eigenvalues. The trailing NP-NAP elements contain the unassigned eigenvalues.
WI_OUT - if INFO = 0, the leading NAP elements of these arrays contain the imaginary parts of the assigned eigenvalues. The trailing NP-NAP elements contain the unassigned eigenvalues.
NFP - The number of eigenvalues of A having real parts less than ALPHA, if DICO = 'C', or moduli less than ALPHA, if DICO = 'D'. These eigenvalues are not modified by the eigenvalue assignment algorithm.
NAP - The number of assigned eigenvalues. If INFO = 0 on exit, then NAP = N-NFP-NUP.
NUP - The number of uncontrollable eigenvalues detected by the eigenvalue assignment algorithm.
F - The leading M-by-N part of this array contains the state feedback F, which assigns NAP closed-loop eigenvalues and keeps unaltered N-NAP open-loop eigenvalues.
Z - The leading N-by-N part of this array contains the orthogonal matrix Z which reduces the closed-loop system state matrix A + B*F to upper real Schur form.
IWARN - = 0: no warning; = K: K violations of the numerical stability condition.
INFO - = 0: successful exit;

Description

To determine the state feedback matrix F for a given system (A,B) such that the closed-loop state matrix A+B*F has specified eigenvalues.

Used function(s)

SB01BD

Bibliography

http://slicot.org/objects/software/shared/doc/SB01BD.html

Example

N = 4;
M = 2;
NP = 2;
ALPHA = -.4;
TOL = 1.E-8;
DICO = 'C';

A_IN = [  -6.8000   0.0000  -207.0000   0.0000;
   1.0000   0.0000     0.0000   0.0000;
  43.2000   0.0000     0.0000  -4.2000;
   0.0000   0.0000     1.0000   0.0000];

B_IN = [   5.6400   0.0000;
   0.0000   0.0000;
   0.0000   1.1800;
   0.0000   0.0000];

WR_IN = [-0.5000; -0.5000];
WI_IN = [ 0.1500; -0.1500];

[A_OUT, WR_OUT, WI_OUT, NFP, NAP, NUP, F, Z, IWARN, INFO] = slicot_sb01bd(DICO, ALPHA, A_IN, B_IN, WR_IN, WI_IN, TOL)

History

Version	Description
1.0.0	initial version

Author

SLICOT Documentation

slicot_sb02od

Solution of continuous- or discrete-time algebraic Riccati equations (generalized Schur vectors method).

Syntax

[RCOND, X, ALFAR, ALFAI, BETA, S, T, U, INFO] = slicot_sb02od(DICO, JOBB, FACT, UPLO, JOBL, SORT, P, A, B, Q, R, L, TOL)

Input argument

DICO - Specifies the type of Riccati equation to be solved as follows: = 'C': continuous-time case; 'D': discrete-time case.
JOBB - Specifies whether or not the matrix G is given, instead of the matrices B and R, as follows: = 'B': B and R are given; = 'G': G is given.
FACT - Specifies whether or not the matrices Q and/or R (if JOBB = 'B') are factored, as follows: = 'N': Not factored, Q and R are given; = 'C': C is given, and Q = C'C; = 'D': D is given, and R = D'D; = 'B': Both factors C and D are given, Q = C'C, R = D'D.
UPLO - If JOBB = 'G', or FACT = 'N', specifies which triangle of the matrices G and Q (if FACT = 'N'), or Q and R (if JOBB = 'B'), is stored, as follows: = 'U': Upper triangle is stored; = 'L': Lower triangle is stored.
JOBL - Specifies whether or not the matrix L is zero, as follows: = 'Z': L is zero; = 'N': L is nonzero. JOBL is not used if JOBB = 'G' and JOBL = 'Z' is assumed. SLICOT Library routine SB02MT should be called just before SB02OD, for obtaining the results when JOBB = 'G' and JOBL = 'N'.
SORT - Specifies which eigenvalues should be obtained in the top of the generalized Schur form, as follows: = 'S': Stable eigenvalues come first;= 'U': Unstable eigenvalues come first.
P - The number of system outputs. If FACT = 'C' or 'D' or 'B', P is the number of rows of the matrices C and/or D. P >= 0. Otherwise, P is not used.
A - The leading N-by-N part of this array must contain the state matrix A of the system.
B - If JOBB = 'B', the leading N-by-M part of this array must contain the input matrix B of the system.
Q - If FACT = 'N' or 'D', the leading N-by-N upper triangular part (if UPLO = 'U') or lower triangular part (if UPLO = 'L') of this array must contain the upper triangular part or lower triangular part, respectively, of the symmetric state weighting matrix Q. The stricly lower triangular part (if UPLO = 'U') or stricly upper triangular part (if UPLO = 'L') is not referenced.
R - If FACT = 'N' or 'C', the leading M-by-M upper triangular part (if UPLO = 'U') or lower triangular part (if UPLO = 'L') of this array must contain the upper triangular part or lower triangular part, respectively, of the symmetric input weighting matrix R. The stricly lower triangular part (if UPLO = 'U') or stricly upper triangular part (if UPLO = 'L') is not referenced.
L - If JOBL = 'N' (and JOBB = 'B'), the leading N-by-M part of this array must contain the cross weighting matrix L. This part is modified internally, but is restored on exit. If JOBL = 'Z' or JOBB = 'G', this array is not referenced.
TOL - The tolerance to be used to test for near singularity of the original matrix pencil, specifically of the triangular factor obtained during the reduction process.

Output argument

RCOND - An estimate of the reciprocal of the condition number (in the 1-norm) of the N-th order system of algebraic equations from which the solution matrix X is obtained.
X - The leading N-by-N part of this array contains the solution matrix X of the problem.
ALFAR, ALFAI, BETA - The generalized eigenvalues of the 2N-by-2N matrix pair, ordered as specified by SORT (if INFO = 0).
S - The leading 2N-by-2N part of this array contains the ordered real Schur form S of the first matrix in the reduced matrix pencil associated to the optimal problem, or of the corresponding Hamiltonian matrix, if DICO = 'C' and JOBB = 'G'.
T - If DICO = 'D' or JOBB = 'B', the leading 2N-by-2N part of this array contains the ordered upper triangular form T of the second matrix in the reduced matrix pencil associated to the optimal problem.
U - The leading 2N-by-2N part of this array contains the right transformation matrix U which reduces the 2N-by-2N matrix pencil to the ordered generalized real Schur form (S,T), or the Hamiltonian matrix to the ordered real Schur form S, if DICO = 'C' and JOBB = 'G'.
INFO - = 0: successful exit;

Description

Solution of continuous- or discrete-time algebraic Riccati equations (generalized Schur vectors method)

The routine uses the method of deflating subspaces, based on reordering the eigenvalues in a generalized Schur matrix pair.

A standard eigenproblem is solved in the continuous-time case if G is given.

Used function(s)

SB02OD

Bibliography

http://slicot.org/objects/software/shared/doc/SB02OD.html

Example

N = 2;
M = 1;
P = 3;
TOL = 0.0;
DICO = 'C';
JOBB = 'B';
FACT = 'B';
UPLO = 'U';
JOBL = 'Z';
SORT = 'S';
A = [0.0  1.0;
   0.0  0.0];
B = [0.0; 1.0];
Q = [1.0  0.0;
   0.0  1.0;
   0.0  0.0];
R = [0.0;
   0.0;
   1.0];
L = zeros(N, M);
[RCOND, X, ALFAR, ALFAI, BETA, S, T, U, INFO] = slicot_sb02od(DICO, JOBB, FACT, UPLO, JOBL, SORT, P, A, B, Q, R, L, TOL)

History

Version	Description
1.0.0	initial version

Author

SLICOT Documentation

slicot_sb03md

Solution of continuous- or discrete-time Lyapunov equations and separation estimation.

Syntax

[U_OUT, C_OUT, SCALE, SEP, FERR, WR, WI, INFO] = slicot_sb03md(DICO, JOB, FACT, TRANA, A, U_IN, C_IN)

Input argument

DICO - Specifies the type of Lyapunov equation to be solved as follows: = 'C': continuous-time case; 'D': discrete-time case.
JOB - Specifies the computation to be performed: 'X': Compute the solution only;= 'S': Compute the separation only; = 'B': Compute both the solution and the separation.
FACT - Specifies whether or not the real Schur factorization of the matrix A is supplied on entry. = 'F': On entry, A and Q contain the factors from the real Schur factorization of the matrix A; = 'N': The Schur factorization of A will be computed and the factors will be stored in A and Q.
TRANA - Specifies the form of op(A) to be used: = 'N': op(A) = A (No transpose); = 'T': op(A) = AT (Transpose); = 'C': op(A) = AT (Conjugate transpose = Transpose).
A - the leading N-by-N part of this array must contain the matrix A. If FACT = 'F', then A contains an upper quasi-triangular matrix in Schur canonical form; the elements below the upper Hessenberg part of the array A are not referenced.
U_IN - If FACT = 'N', zeros(N, N); If FACT = 'F', then U is an input argument and on entry the leading N-by-N part of this array must contain the orthogonal matrix U of the real Schur factorization of A.
C_IN - With JOB = 'X' or 'B', the leading N-by-N part of this array must contain the symmetric matrix C.

Output argument

U_OUT - if INFO = 0 or INFO = N+1, it contains the orthogonal N-by-N matrix from the real Schur factorization of A.
C_OUT - With JOB = 'X' or 'B', if INFO = 0 or INFO = N+1, the leading N-by-N part of C has been overwritten by the symmetric solution matrix X.
SCALE - The scale factor, scale, set less than or equal to 1 to prevent the solution overflowing.
SEP - If JOB = 'S' or JOB = 'B', and INFO = 0 or INFO = N+1, SEP contains the estimated separation of the matrices op(A) and -op(A)', if DICO = 'C' or of op(A) and op(A)', if DICO = 'D'.
FERR - If JOB = 'B', and INFO = 0 or INFO = N+1, FERR contains an estimated forward error bound for the solution X.
WR - If FACT = 'N', and INFO = 0 or INFO = N+1, WR contains the real parts of the eigenvalues of A.
WI - If FACT = 'N', and INFO = 0 or INFO = N+1, WI contains the imaginary parts of the eigenvalues of A.
INFO - = 0: successful exit;

Description

To solve for X either the real continuous-time Lyapunov equation

op(A)'*X + X*op(A) = scale*C

or the real discrete-time Lyapunov equation

op(A)'*X*op(A) - X = scale*C

and/or estimate an associated condition number, called separation, where op(A) = A or A' (A**T) and C is symmetric (C = C').

Used function(s)

SB03MD

Bibliography

http://slicot.org/objects/software/shared/doc/SB03MD.html

Example

N = 3;
DICO = 'D';
FACT = 'N';
JOB = 'X';
TRANA = 'N';

A = [3.0   1.0   1.0;
   1.0   3.0   0.0;
   0.0   0.0   3.0];

U_IN = zeros(N, N);

C_IN = [25.0  24.0  15.0;
  24.0  32.0   8.0;
  15.0   8.0  40.0];

[U_OUT, C_OUT, SCALE, SEP, FERR, WR, WI, INFO] = slicot_sb03md(DICO, JOB, FACT, TRANA, A, U_IN, C_IN)

History

Version	Description
1.0.0	initial version

Author

SLICOT Documentation

slicot_sb03od

Solution of stable continuous- or discrete-time Lyapunov equations (Cholesky factor).

Syntax

[Q_OUT, B_OUT, SCALE, WR, WI, INFO] = slicot_sb03od(DICO, FACT, TRANS, A, Q_IN, B_IN)

Input argument

DICO - Specifies the type of Lyapunov equation to be solved as follows: = 'C': continuous-time case; 'D': discrete-time case.
FACT - Specifies whether or not the real Schur factorization of the matrix A is supplied on entry. = 'F': On entry, A and Q contain the factors from the real Schur factorization of the matrix A; = 'N': The Schur factorization of A will be computed and the factors will be stored in A and Q.
TRANS - Specifies the form of op(K) to be used. = 'N': op(K) = K (No transpose); = 'T': op(K) = K**T (Transpose).
A - the leading N-by-N part of this array must contain the matrix A. If FACT = 'F', then A contains an upper quasi-triangular matrix S in Schur canonical form; the elements below the upper Hessenberg part of the array A are not referenced.
Q_IN - if FACT = 'F', then the leading N-by-N part of this array must contain the orthogonal matrix Q of the Schur factorization of A. Otherwise, Q need not be set on entry.
B_IN - if TRANS = 'N', and dimension (LDB,max(M,N)), if TRANS = 'T'. On entry, if TRANS = 'N', the leading M-by-N part of this array must contain the coefficient matrix B of the equation. On entry, if TRANS = 'T', the leading N-by-M part of this array must contain the coefficient matrix B of the equation.

Output argument

Q_OUT - the leading N-by-N part of this array contains the orthogonal matrix Q of the Schur factorization of A. The contents of array Q is not modified if FACT = 'F'.
B_OUT - the leading N-by-N part of this array contains the upper triangular Cholesky factor U of the solution matrix X of the problem, X = op(U)'*op(U). If M = 0 and N > 0, then U is set to zero.
SCALE - The scale factor, scale, set less than or equal to 1 to prevent the solution overflowing.
WR - If FACT = 'N', and INFO >= 0 and INFO less than 2, WR contains the real parts of the eigenvalues of A.
WI - If FACT = 'N', and INFO >= 0 and INFO less than 2, WI contains the imaginary parts of the eigenvalues of A.
INFO - = 0: successful exit.

Description

To solve for X = op(U)'*op(U) either the stable non-negative definite continuous-time Lyapunov equation or the convergent non-negative definite discrete-time Lyapunov equation.

Used function(s)

SB03OD

Bibliography

http://slicot.org/objects/software/shared/doc/SB03OD.html

Example

A = [-0.5000    0.5000         0;
         0         0         0;
   -0.5000         0    0.5000];
B_IN = [0.5000    1.5000    1.0000;
    1.0000    1.0000    1.0000;
    0.5000    1.0000    1.5000];
DICO = 'D';
FACT = 'N';
Q_IN = zeros(3, 3);
[Q_OUT, B_OUT, SCALE, WR, WI, INFO] = slicot_sb03od(DICO, FACT, TRANS, A, Q_IN, B_IN)

History

Version	Description
1.0.0	initial version

Author

SLICOT Documentation

slicot_sb04md

Solution of continuous-time Sylvester equations (Hessenberg-Schur method).

Syntax

[A_OUT, B_OUT, C_OUT, Z, INFO] = slicot_sb04md(A_IN, B_IN, C_IN)

Input argument

A_IN - The leading N-by-N part of this array must contain the coefficient matrix A of the equation.
B_IN - The leading M-by-M part of this array must contain the coefficient matrix B of the equation.
C_IN - The leading N-by-M part of this array must contain the coefficient matrix C of the equation.

Output argument

A_OUT - The leading N-by-N upper Hessenberg part of this array contains the matrix H, and the remainder of the leading N-by-N part, together with the elements 2,3,...,N of array DWORK, contain the orthogonal transformation matrix U (stored in factored form).
B_OUT - The leading M-by-M part of this array contains the quasi-triangular Schur factor S of the matrix B'.
C_OUT - The leading N-by-M part of this array contains the solution matrix X of the problem.
Z - The leading M-by-M part of this array contains the orthogonal matrix Z used to transform B' to real upper Schur form.
INFO - = 0: successful exit;

Description

To solve for X the continuous-time Sylvester equation AX + XB = C where A, B, C and X are general N-by-N, M-by-M, N-by-M and N-by-M matrices respectively.

Used function(s)

SB04MD

Bibliography

http://slicot.org/objects/software/shared/doc/SB04MD.html

Example

N = 3;
M = 2;
A_IN = [2.0   1.0   3.0;
   0.0   2.0   1.0;
   6.0   1.0   2.0];
B_IN = [2.0   1.0;
   1.0   6.0];
C_IN = [2.0   1.0;
   1.0   4.0;
   0.0   5.0];
[A_OUT, B_OUT, C_OUT, Z, INFO] = slicot_sb04md(A_IN, B_IN, C_IN)

History

Version	Description
1.0.0	initial version

Author

SLICOT Documentation

slicot_sb04qd

Solution of discrete-time Sylvester equations (Hessenberg-Schur method).

Syntax

[A_OUT, B_OUT, C_OUT, Z, INFO] = slicot_sb04qd(A_IN, B_IN, C_IN)

Input argument

A_IN - The leading N-by-N part of this array must contain the coefficient matrix A of the equation.
B_IN - The leading M-by-M part of this array must contain the coefficient matrix B of the equation.
C_IN - The leading N-by-M part of this array must contain the coefficient matrix C of the equation.

Output argument

A_OUT - The leading N-by-N upper Hessenberg part of this array contains the matrix H, and the remainder of the leading N-by-N part, together with the elements 2,3,...,N of array DWORK, contain the orthogonal transformation matrix U (stored in factored form).
B_OUT - The leading M-by-M part of this array contains the quasi-triangular Schur factor S of the matrix B'.
C_OUT - The leading N-by-M part of this array contains the solution matrix X of the problem.
Z - The leading M-by-M part of this array contains the orthogonal matrix Z used to transform B' to real upper Schur form.
INFO - = 0: successful exit;

Description

To solve for X the discrete-time Sylvester equation X + AXB = C, where A, B, C and X are general N-by-N, M-by-M, N-by-M and N-by-M matrices respectively. A Hessenberg-Schur method, which reduces A to upper Hessenberg form, H = U'AU, and B' to real Schur form, S = Z'B'Z (with U, Z orthogonal matrices), is used.

Used function(s)

SB04QD

Bibliography

http://slicot.org/objects/software/shared/doc/SB04QD.html

Example

N = 3;
M = 3;
A_IN = [1.0   2.0   3.0;
   6.0   7.0   8.0;
   9.0   2.0   3.0];
B_IN = [7.0   2.0   3.0;
   2.0   1.0   2.0;
   3.0   4.0   1.0];
C_IN = [271.0   135.0   147.0;
   923.0   494.0   482.0;
   578.0   383.0   287.0];

[A_OUT, B_OUT, C_OUT, Z, INFO] = slicot_sb04qd(A_IN, B_IN, C_IN)

History

Version	Description
1.0.0	initial version

Author

SLICOT Documentation

slicot_sb10jd

Converting a descriptor state-space system into regular state-space form.

Syntax

[A_OUT, B_OUT, C_OUT, D_OUT, E_OUT, NSYS, INFO] = slicot_sb10jd(A_IN, B_IN, C_IN, D_IN, E_IN)

Input argument

A_IN - the leading N-by-N part of this array must contain the state matrix A of the descriptor system.
B_IN - the leading N-by-M part of this array must contain the input matrix B of the descriptor system.
C_IN - the leading NP-by-N part of this array must contain the output matrix C of the descriptor system.
D_IN - the leading NP-by-M part of this array must contain the matrix D of the descriptor system.
E_IN - the leading N-by-N part of this array must contain the matrix E of the descriptor system.

Output argument

A_OUT - the leading NSYS-by-NSYS part of this array contains the state matrix Ad of the converted system.
B_OUT - the leading NSYS-by-M part of this array contains the input matrix Bd of the converted system.
C_OUT - the leading NP-by-NSYS part of this array contains the output matrix Cd of the converted system.
D_OUT - the leading NP-by-M part of this array contains the matrix Dd of the converted system.
E_OUT - this array contains no useful information.
NSYS - The order of the converted state-space system.
INFO - = 0: successful exit; = 1: the iteration for computing singular value decomposition did not converge.

Description

To convert the descriptor state-space system into regular state-space form.

Used function(s)

SB10JD

Bibliography

http://slicot.org/objects/software/shared/doc/SB10JD.html

Example

A_IN = [2 -4; 4 2];
B_IN = [0 -1; 0 0.5];
C_IN = [0 -0.5; 0 -2];
D_IN = [0 0; 0 -1];
E_IN = [1 0; -3 0.5];
[A_OUT, B_OUT, C_OUT, D_OUT, E_OUT, NSYS, INFO] = slicot_sb10jd(A_IN, B_IN, C_IN, D_IN, E_IN)

History

Version	Description
1.0.0	initial version

Author

SLICOT Documentation

slicot_sg02ad

Solution of continuous- or discrete-time algebraic Riccati equations for descriptor systems.

Syntax

[RCONDU, X, ALFAR, ALFAI, BETA, S, T, U, IWARN, INFO] = slicot_sg02ad(DICO, JOBB, FACT, UPLO, JOBL, SCAL, SORT, ACC, P, A, E, B, Q, R, L, TOL)

Input argument

DICO - Specifies the type of Riccati equation to be solved as follows: = 'C': Equation (1), continuous-time case; = 'D': Equation (2), discrete-time case.
JOBB - Specifies whether or not the matrix G is given, instead of the matrices B and R, as follows: = 'B': B and R are given; = 'G': G is given.
FACT - Specifies whether or not the matrices Q and/or R (if JOBB = 'B') are factored, as follows: = 'N': Not factored, Q and R are given; = 'C': C is given, and Q = C'C; = 'D': D is given, and R = D'D; = 'B': Both factors C and D are given, Q = C'C, R = D'D.
UPLO - If JOBB = 'G', or FACT = 'N', specifies which triangle of the matrices G, or Q and R, is stored, as follows: = 'U': Upper triangle is stored; = 'L': Lower triangle is stored.
JOBL - Specifies whether or not the matrix L is zero, as follows: = 'Z': L is zero; = 'N': L is nonzero. JOBL is not used if JOBB = 'G' and JOBL = 'Z' is assumed. SLICOT Library routine SB02MT should be called just before SG02AD, for obtaining the results when JOBB = 'G' and JOBL = 'N'.
SCAL - If JOBB = 'B', specifies whether or not a scaling strategy should be used to scale Q, R, and L, as follows: = 'G': General scaling should be used; = 'N': No scaling should be used. SCAL is not used if JOBB = 'G'.
SORT - Specifies which eigenvalues should be obtained in the top of the generalized Schur form, as follows: = 'S': Stable eigenvalues come first; = 'U': Unstable eigenvalues come first.
ACC - Specifies whether or not iterative refinement should be used to solve the system of algebraic equations giving the solution matrix X, as follows: = 'R': Use iterative refinement; = 'N': Do not use iterative refinement.
P - The number of system outputs. If FACT = 'C' or 'D' or 'B', P is the number of rows of the matrices C and/or D.
A - The leading N-by-N part of this array must contain the state matrix A of the descriptor system.
E - The leading N-by-N part of this array must contain the matrix E of the descriptor system.
B - If JOBB = 'B', the leading N-by-M part of this array must contain the input matrix B of the system.
Q - If FACT = 'N' or 'D', the leading N-by-N upper triangular part (if UPLO = 'U') or lower triangular part (if UPLO = 'L') of this array must contain the upper triangular part or lower triangular part, respectively, of the symmetric state weighting matrix Q. The stricly lower triangular part (if UPLO = 'U') or stricly upper triangular part (if UPLO = 'L') is not referenced. If FACT = 'C' or 'B', the leading P-by-N part of this array must contain the output matrix C of the system. If JOBB = 'B' and SCAL = 'G', then Q is modified internally, but is restored on exit.
R - If FACT = 'N' or 'C', the leading M-by-M upper triangular part (if UPLO = 'U') or lower triangular part (if UPLO = 'L') of this array must contain the upper triangular part or lower triangular part, respectively, of the symmetric input weighting matrix R. The stricly lower triangular part (if UPLO = 'U') or stricly upper triangular part (if UPLO = 'L') is not referenced. If FACT = 'D' or 'B', the leading P-by-M part of this array must contain the direct transmission matrix D of the system. If JOBB = 'B' and SCAL = 'G', then R is modified internally, but is restored on exit.
L - If JOBL = 'N' and JOBB = 'B', the leading N-by-M part of this array must contain the cross weighting matrix L. If JOBB = 'B' and SCAL = 'G', then L is modified internally, but is restored on exit.
TOL - The tolerance to be used to test for near singularity of the original matrix pencil, specifically of the triangular M-by-M factor obtained during the reduction process.

Output argument

RCONDU - If N > 0 and INFO = 0 or INFO = 7, an estimate of the reciprocal of the condition number (in the 1-norm) of the N-th order system of algebraic equations from which the solution matrix X is obtained.
X - If INFO = 0, the leading N-by-N part of this array contains the solution matrix X of the problem.
ALFAR - The generalized eigenvalues of the 2N-by-2N matrix pair, ordered as specified by SORT (if INFO = 0, or INFO >= 5).
ALFAI - The generalized eigenvalues of the 2N-by-2N matrix pair, ordered as specified by SORT (if INFO = 0, or INFO >= 5).
BETA - The generalized eigenvalues of the 2N-by-2N matrix pair, ordered as specified by SORT (if INFO = 0, or INFO >= 5).
S - The leading 2N-by-2N part of this array contains the ordered real Schur form S of the first matrix in the reduced matrix pencil associated to the optimal problem, corresponding to the scaled Q, R, and L, if JOBB = 'B' and SCAL = 'G'.
T - The leading 2N-by-2N part of this array contains the ordered upper triangular form T of the second matrix in the reduced matrix pencil associated to the optimal problem, corresponding to the scaled Q, R, and L, if JOBB = 'B' and SCAL = 'G'.
U - The leading 2N-by-2N part of this array contains the right transformation matrix U which reduces the 2N-by-2N matrix pencil to the ordered generalized real Schur form (S,T).
IWARN - = 0: no warning; = 1: the computed solution may be inaccurate due to poor scaling or eigenvalues too close to the boundary of the stability domain (the imaginary axis, if DICO = 'C', or the unit circle, if DICO = 'D').
INFO - = 0: successful exit; = 1: if the computed extended matrix pencil is singular, possibly due to rounding errors; = 2: if the QZ algorithm failed; = 3: if reordering of the generalized eigenvalues failed; = 4: if after reordering, roundoff changed values of some complex eigenvalues so that leading eigenvalues in the generalized Schur form no longer satisfy the stability condition; this could also be caused due to scaling; = 5: if the computed dimension of the solution does not equal N; = 6: if the spectrum is too close to the boundary of the stability domain; = 7: if a singular matrix was encountered during the computation of the solution matrix X.

Description

To solve for X either the continuous-time algebraic Riccatiequation or the discrete-time algebraic Riccati equation

Used function(s)

SG02AD

Bibliography

http://slicot.org/objects/software/shared/doc/SG02AD.html

Example

N = 2;
M = 1;
P = 3;
TOL = 0.0;
DICO = 'C';
JOBB = 'B';
FACT = 'B';
UPLO = 'U';
JOBL = 'Z';
SCAL = 'N';
SORT = 'S';
ACC = 'N';
A = [0.0  1.0;
   0.0  0.0];
E = [1.0  0.0;
   0.0  1.0];
B = [0.0;
   1.0];
Q = [1.0  0.0;
   0.0  1.0;
   0.0  0.0];
R = [0.0;
   0.0;
   1.0];
L = zeros(N, N);
[RCONDU, X, ALFAR, ALFAI, BETA, S, T, U, IWARN, INFO] = slicot_sg02ad(DICO, JOBB, FACT, UPLO, JOBL, SCAL, SORT, ACC, P, A, E, B, Q, R, L, TOL)

History

Version	Description
1.0.0	initial version

Author

SLICOT Documentation

slicot_tb01id

Balancing a system matrix corresponding to a triplet (A, B, C).

Syntax

[MAXRED_OUT, A_OUT, B_OUT, C_OUT, SCALE, INFO] = slicot_tb01id(JOB, MAXRED_IN, A_IN, B_IN, C_IN)

Input argument

JOB - = 'A': All matrices are involved in balancing; = 'B': B and A matrices are involved in balancing; = 'C': C and A matrices are involved in balancing; = 'N': B and C matrices are not involved in balancing.
MAXRED_IN - the maximum allowed reduction in the 1-norm of S (in an iteration) if zero rows or columns are encountered.
A_IN - The leading N-by-N part of this array must contain the system state matrix A.
B_IN - The leading N-by-M part of this array must contain the system input matrix B.
C_IN - The leading P-by-N part of this array must contain the system output matrix C.

Output argument

MAXRED_OUT - if the 1-norm of the given matrix S is non-zero, the ratio between the 1-norm of the given matrix and the 1-norm of the balanced matrix.
A_OUT - The leading N-by-N part of this array contains the balanced matrix inv(D)AD.
B_OUT - The leading N-by-M part of this array contains the balanced matrix inv(D)*B.
C_OUT - The leading P-by-N part of this array contains the balanced matrix C*D.
SCALE - The scaling factors applied to S.
INFO - = 0: successful exit.

Description

To reduce the 1-norm of a system matrix corresponding to the triple (A,B,C), by balancing.

Used function(s)

TB01ID

Bibliography

http://slicot.org/objects/software/shared/doc/TB01ID.html

Example

N = 5;
M = 2;
P = 5;
JOB = 'A';
MAXRED_IN = 0.0;

A_IN = [0.0  1.0000e+000          0.0          0.0          0.0;
 -1.5800e+006 -1.2570e+003          0.0          0.0          0.0;
  3.5410e+014          0.0 -1.4340e+003          0.0 -5.3300e+011;
          0.0          0.0          0.0          0.0  1.0000e+000;
          0.0          0.0          0.0 -1.8630e+004 -1.4820e+000];

B_IN = [0.0          0.0;
  1.1030e+002          0.0;
          0.0          0.0;
          0.0          0.0;
          0.0  8.3330e-003];

C_IN = [1.0000e+000          0.0          0.0          0.0          0.0;
          0.0          0.0  1.0000e+000          0.0          0.0;
          0.0          0.0          0.0  1.0000e+000          0.0;
  6.6640e-001          0.0 -6.2000e-013          0.0          0.0;
          0.0          0.0 -1.0000e-003  1.8960e+006  1.5080e+002];
[MAXRED_OUT, A_OUT, B_OUT, C_OUT, SCALE, INFO] = slicot_tb01id(JOB, MAXRED_IN, A_IN, B_IN, C_IN)

History

Version	Description
1.0.0	initial version

Author

SLICOT Documentation

slicot_tg01ad

Balancing the matrices of the system pencil corresponding to a descriptor triple (A-lambda E, B, C).

Syntax

[A_OUT, E_OUT, B_OUT, C_OUT, LSCALE, RSCALE, INFO] = slicot_tg01ad(JOB, THRESH, A_IN, E_IN, B_IN, C_IN)

Input argument

JOB - = 'A': All matrices are involved in balancing; = 'B': B, A and E matrices are involved in balancing; = 'C': C, A and E matrices are involved in balancing; = 'N': B and C matrices are not involved in balancing.
THRESH - Threshold value for magnitude of elements: elements with magnitude less than or equal to THRESH are ignored for balancing.
A_IN - The leading L-by-N part of this array must contain the state dynamics matrix A.
E_IN - The leading L-by-N part of this array must contain the descriptor matrix E.
B_IN - The leading L-by-M part of this array must contain the input/state matrix B.
C_IN - The leading P-by-N part of this array must contain the state/output matrix C.

Output argument

A_OUT - The leading L-by-N part of this array contains the balanced matrix DlADr.
E_OUT - The leading L-by-N part of this array contains the balanced matrix DlEDr.
B_OUT - The leading L-by-M part of this array contains the balanced matrix Dl*B.
C_OUT - The leading P-by-N part of this array contains the balanced matrix C*Dr.
LSCALE - The scaling factors applied to S from left.
RSCALE - The scaling factors applied to S from right.
INFO - = 0: successful exit.

Description

To balance the matrices of the system pencil corresponding to the descriptor triple (A-lambda E,B,C), by balancing.

Used function(s)

TG01AD

Bibliography

http://slicot.org/objects/software/shared/doc/TG01AD.html

Example

L = 4;
N = 4;
M = 2;
P = 2;
JOB = 'A';
THRESH = 0;

A_IN = [ -1         0         0    0.003;
         0         0    0.1000    0.02;
       100        10         0    0.4;
         0         0         0    0.0];

E_IN = [1       0.2         0    0.0;
         0         1         0    0.01;
       300        90         6    0.3;
         0         0        20    0.0];

B_IN = [10         0;
         0         0;
         0      1000;
     10000     10000];

C_IN = [-0.1      0.0    0.001    0.0;
       0.0      0.01  -0.001    0.0001];

[A_OUT, E_OUT, B_OUT, C_OUT, LSCALE, RSCALE, INFO] = slicot_tg01ad(JOB, THRESH, A_IN, E_IN, B_IN, C_IN)

History

Version	Description
1.0.0	initial version

Author

SLICOT Documentation

Special functions

Description

special functions

betainc - Incomplete beta function
cross - Cross product.
dot - Dot product.
factor - Prime factors
gamma - Gamma special function
gammaln - Logarithm of gamma function
gcd - Greatest common divisor
interp1 - Linear 1-D data interpolation
peaks - Peaks function
primes - Prime numbers less than or equal to input value

betainc

Incomplete beta function

Syntax

R = betainc(X, Z, W)
R = betainc(X, Z, W, tail)

Input argument

X - a real single or real double matrix. It must be in the closed interval [0, 1].
Z - a real single or real double matrix. It must be nonnegative.
W - a real single or real double matrix. It must be nonnegative.
tail - a string 'upper' or 'lower' (default).

Output argument

R - result of betainc function.

Description

betainc computes the Incomplete beta function.

All arrays must be the same size or any of them can be scalar.

Example

R = betainc(0.5, 1:10, 3)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

cross

Cross product.

Syntax

R = cross(A, B)
R = cross(A, B, dim)

Input argument

A, B - numeric arrays.
dim - positive integer scalar: Dimension to operate along.

Output argument

R - Vector cross Product.

Description

R = cross(A, B) returns the cross product of A and B.

Bibliography

https://en.wikipedia.org/wiki/Cross_product

Example

A = [1 2 3;4 5 6;7 8 9];
B = [9 8 7;6 5 4;3 2 1];
R = cross(A, B)
R = cross(A, B, 2)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

dot

Dot product.

Syntax

R = dot(A, B)
R = dot(A, B, dim)

Input argument

A, B - numeric arrays.
dim - positive integer scalar: Dimension to operate along.

Output argument

R - Scalar Dot Product.

Description

R = dot(A, B) returns the scalar dot product of A and B.

Bibliography

https://en.wikipedia.org/wiki/Dot_product

Example

A = [1 2 3;4 5 6;7 8 9];
B = [9 8 7;6 5 4;3 2 1];
R = dot(A, B)
R = dot(A, B, 2)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

factor

Prime factors

Syntax

f = factor(n)

Input argument

n - real, nonnegative integer scalar

Output argument

p - vector with Prime factors.

Description

f = factor(n) returns a row vector with the prime factors of n.

Vector f is of the same data type as n.

Example

f = factor(204)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

gamma

Gamma special function

Syntax

R = gamma(M)

Input argument

M - a real single or real double matrix.

Output argument

R - result of gamma function.

Description

gamma computes the gamma function.

gamma is an extension of the factorial function.

Example

R = gamma([-pi:0.1:pi])

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

gammaln

Logarithm of gamma function

Syntax

R = gammaln(M)

Input argument

M - a real single or real double matrix.

Output argument

R - result of gammaln function.

Description

The function gammaln(A) computes the natural logarithm of the gamma function for a given input A, expressed as gammaln(A) = log(gamma(A)).

It's important to note that A must be a nonnegative real number.

Using gammaln helps prevent potential underflow and overflow issues that might arise if directly computing log(gamma(A)).

Example

R = gammaln([0:0.1:pi])

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

gcd

Greatest common divisor

Syntax

G = gcd(A, B)

Input argument

A - a scalar, vector, or matrix of real integer values.
B - a scalar, vector, or matrix of real integer values.

Output argument

G - result of gcd function (Greatest common divisor).

Description

G = gcd(A, B) computes the greatest common divisor using the Euclidian algorithm.

Bibliography

Knuth, D. “Algorithms A and X.” The Art of Computer Programming, Vol. 2, Section 4.5.2. Reading, MA: Addison-Wesley, 1973.

Example

A = [-5 7; 10 0];
B = [-15 3; 50 0];
G = gcd(A, B)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

interp1

Linear 1-D data interpolation

Syntax

vq = interp1(x, v, xq)
vq = interp1(x, v, xq, 'linear')
vq = interp1(v, xq)
vq = interp1(v, xq, 'linear')

Input argument

x - Sample points: vector.
v - Sample values: vector, matrix.
xq - Query points: scalar, vector, matrix.

Output argument

vq - Interpolated values: scalar, vector, matrix.

Description

vq = interp1(x, v, xq) returns interpolated values of a 1-D function at specific query points using linear interpolation.

Bibliography

de Boor, C., A Practical Guide to Splines, Springer-Verlag, 1978.

Example

f = figure();
v = [0  1.41  2  1.41  0  -1.41  -2  -1.41 0];
xq = 1.5:8.5;
vq = interp1(v,xq);
plot(1:9, v, 'o', xq, vq, '*');
legend('v','vq');

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

peaks

Peaks function

Syntax

Z = peaks()
Z = peaks(n)
Z = peaks(Xi, Yi)
[X, Y, Z] = peaks()
[X, Y, Z] = peaks(n)
[X, Y, Z] = peaks(Xi, Yi)

Input argument

n - Value representing 2-D grid: scalar or vector.
Xi - x-coordinates of points.
Yi - y-coordinates of points.

Output argument

X - x-coordinates of points.
Y - y-coordinates of points.
Z - z-coordinates of points.

Description

peaks function has the form:

f(x, y) = 3*(1-x)^2*exp(-x^2 - (y+1)^2) - 10*(x/5 - x^3 - y^5)*exp(-x^2-y^2) - 1/3*exp(-(x+1)^2 - y^2)

Example

x = -2:0.5:2;
y = 1:0.2:2;
[X, Y] = meshgrid(x, y);
Z = peaks(X, Y)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

primes

Prime numbers less than or equal to input value

Syntax

p = primes(n)

Input argument

n - scalar, real integer value

Output argument

p - vector with prime numbers.

Description

p = primes(n) returns a row vector containing all the prime numbers less than or equal to n.

The data type of p is the same as that of n.

Example

p = primes(15)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

FFTW

Description

Fastest Fourier Transform in the West

FFTW License - About FFTW license.
FFTWwrapper - load/free FFTW library dynamically.
fft - Fast Fourier transform.
fft2 - 2-D fast Fourier transform.
fftn - N-Dimensions fast Fourier transform.
fftshift - Shift the zero-frequency component to the center of the spectrum.
fftw - function for determining FFT algorithm.
ifft - Inverse Fast Fourier transform.
ifftn - Inverse multidimensional fast Fourier transform.
ifftshift - inverse of fftshift

FFTW License

About FFTW license.

Description

The FFTW library is no longer distributed as part of Nelson.

Note that FFTW is licensed under GPLv2 or higher (see http://www.fftw.org/doc/License-and-Copyright.html), but the bindings to the library in this nelson's module, is licensed under LGPL v3.0.

This means that code using the FFTW library via FFTW bindings is subject to FFTW's licensing terms.

Code using alternative implementations of the FFTW API, such as MKL's FFTW3 interface (https://software.intel.com/en-us/mkl-developer-reference-c-fftw3-interface-to-intel-math-kernel-library) are instead subject to the alternative's license.

If you distribute a derived or combined work, i.e. a program that links to and is distributed with the FFTW library, then that distribution falls under the terms of the GPL.

On Windows platforms, MKL FFTW implementation is used and distributed with Nelson.

On others plaforms, if FFTW library is available, and user chooses to use it, distribution falls under the terms of the GPL.

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

FFTWwrapper

load/free FFTW library dynamically.

Syntax

r = FFTWwrapper('load')
r = FFTWwrapper('load', fftwlibraryname, fftwflibraryname)
r = FFTWwrapper('free')

Input argument

'load' - load FFTW library.
'free' - free FFTW library.
fftwlibraryname - a string: fftw library name.
fftwflibraryname - a string: fftw float library name.

Output argument

r - a logical.

Description

FFTWwrapper is an internal builtin used to load FFTW library dynamically.

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

fft

Fast Fourier transform.

Syntax

Y = fft(X)
Y = fft(X, n)
Y = fft(X, n, dim)

Input argument

X - a vector, matrix or N-D array (double, single, integer, logical).
n - transform length: a non negative integer scalar or [] (default).
dim - dimension: a positive integer scalar.

Output argument

Y - a vector, matrix, N-D array: frequency domain representation.

Description

fft(X) computes the discrete Fourier transform of X using a Fast Fourier Transform (FFT) algorithm based on FFTW library.

Example

% Sampling frequency
Fs = 150;

% Time vector of 1 second
t = 0:1*inv(Fs):1;

% Creates a sine wave of f Hz.
f = 5;
x = sin(2 * pi * t * f);

% Length of FFT
nfft = 1024;
% Take fft, padding with zeros so that length(X) is equal to nfft
X = fft(x, nfft)
% FFT is symmetrix
X = X(1:nfft*inv(2))

% Frequency vector
f = (0:nfft *inv(2) -1)*Fs * inv(nfft);

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

fft2

2-D fast Fourier transform.

Syntax

Y = fft2(X)
Y = fft2(X, m, n)

Input argument

X - Input array.
m - Number of transform rows.
n - Number of transform columns.

Output argument

Y - a vector, matrix, N-D array: frequency domain representation.

Description

Y = fft2(X) returns the two-dimensional Fourier transform of X using a Fast Fourier Transform (FFT) algorithm.

Optional arguments m and n may be used specify the number of rows and columns of X to use.

If either of these is larger than the size of X, X is resized and padded with zeros.

If X is a multi-dimensional matrix, each two-dimensional sub-matrix of X is treated separately.

Example

R = fft2(eye(5, 5), 2, 3)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

fftn

N-Dimensions fast Fourier transform.

Syntax

Y = fftn(X)
Y = fftn(X, sz)

Input argument

X - a vector, matrix or N-D array (double, single, integer, logical).
sz - a multidimensional array

Output argument

Y - a vector, matrix, N-D array: frequency domain representation.

Description

Y = fftn(X, sz) pads X with zeros, or truncates X, to create a multidimensional array of size sz before performing the transform.

The size of the result Y is sz.

Y = fftn(X) performs the N-dimensional fast Fourier transform.

The result Y is the same size as X.

Example

f = zeros(5, 5);
f(1:5,4:5) = 1;
Y = ifftn(fftn(f));

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

fftshift

Shift the zero-frequency component to the center of the spectrum.

Syntax

Y = fftshift(X)
Y = fftshift(X, DIM)

Input argument

X - a vector, matrix or N-D array (double, single, integer).
DIM - axes over which to shift.

Output argument

Y - shifted array.

Description

fftshift(X) shift the zero-frequency component to the center of the spectrum.

Example

M = [ 0.,  10.,  20.; 30.,  40., -40.; -30., -20., -10.]
fftshift(M)
fftshift(M, 1)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

fftw

function for determining FFT algorithm.

Syntax

m = fftw('planner')
fftw('planner', m)
w = fftw('dwisdom')
fftw('dwisdom', w)
w = fftw('swisdom')
fftw('swisdom', w)

Input argument

m - method for setting transform parameters: 'estimate', 'measure', 'patient', 'exhaustive', or 'hybrid'.
w - a string: wisdom data.

Output argument

m - method: 'estimate', 'measure', 'patient', 'exhaustive', or 'hybrid'.
w - a string: wisdom data.

Description

The default method is 'estimate'.

Example

w = fftw('dwisdom')
M = rand(1000);
tic; fft(M); toc
fftw('dwisdom', w)
tic; fft(M); toc

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

ifft

Inverse Fast Fourier transform.

Syntax

Y = ifft(X)
Y = ifft(X, n)
Y = ifft(X, n, dim)

Input argument

X - a vector, matrix or N-D array (double, single, integer, logical).
n - transform length: a non negative integer scalar or [] (default).
dim - dimension: a positive integer scalar.

Output argument

Y - a vector, matrix, N-D array: frequency domain representation.

Description

ifft(X) computes the inverse discrete Fourier transform of X using a Fast Fourier Transform (FFT) algorithm based on FFTW library.

Example

A = [1:10]
Y = fft(A)
R = ifft(Y)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

ifftn

Inverse multidimensional fast Fourier transform.

Syntax

Y = ifftn(X)
Y = ifftn(X, sz)

Input argument

X - a vector, matrix or N-D array (double, single, integer, logical).
sz - a multidimensional array.

Output argument

Y - a vector, matrix, N-D array: frequency domain representation.

Description

Y = ifftn(X, sz) pads X with zeros, or truncates X, to create a multidimensional array of size sz before performing the transform.

The size of the result Y is sz.

Y = ifftn(X) performs the N-dimensional inverse fast Fourier transform.

The result Y is the same size as X.

Example

f = zeros(5, 5);
f(1:5,4:5) = 1;
Y = ifftn(fftn(f));

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

ifftshift

inverse of fftshift

Syntax

Y = ifftshift(X)
Y = ifftshift(X, DIM)

Input argument

X - a vector, matrix or N-D array (double, single, integer).
DIM - axes over which to shift.

Output argument

Y - shifted array.

Description

fftshift(X) computes the inverse fftshift.

Example

M = [ 0.,  10.,  20.; 30.,  40., -40.; -30., -20., -10.]
ifftshift(M)
ifftshift(M, 1)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

OS functions

Description

operating system functions

cmdsep - Command separator for current operating system.
computer - System information.
createGUID - Creates a GUID.
getenv - Get the value of an environment variable.
hostname - get host name of this computer.
ismac - Checks if version is for MacOS platform.
ispc - Checks if version is for Windows platform.
isunix - Checks if version is for GNU Linux or Unix platform.
searchenv - Searches for a file using environment paths.
setenv - Set the value of an environment variable.
system - Shell command execution.
username - get user name currently used.
winopen - Open file in appropriate application (Windows only).
winqueryreg - Read the Windows registry (Windows only).

cmdsep

Command separator for current operating system.

Syntax

sep = cmdsep()

Output argument

sep - a string: on windows "&&", on linux ";"

Description

cmdsep returns the command separator for current operating system.

This function is used by Nelson to build command lines for unix and dos operating systems.

Example

unix("cd c:/ " + cmdsep() + " nelson")

History

Version	Description
1.11.0	initial version

Author

Allan CORNET

computer

System information.

Syntax

c = computer()
[c, maxsize] = computer()
[c, maxsize, endian] = computer()
arch = computer('arch')

Input argument

'arch' - a string: returns the architecture of the computer.

Output argument

c - a string: computer type: 'PCWIN', 'PCWIN64', 'GLNXA64', 'GLNXA32', 'MACI32', 'MACI64'
maxsize - a integer value: maximum number of elements allowed in an array.
endian - a string: 'L' for little-endian, 'B' for big-endian.
arch - a string: architecture type: 'win64', 'win32', 'glnxa64', 'glnxa32', 'maci64', 'maci32'.

Description

computers identifies the type of computer that Nelson is running on.

Example

c = computer()
[c, maxsize] = computer()
[c, maxsize, endian] = computer()
arch = computer('arch')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

createGUID

Creates a GUID.

Syntax

s = createGUID()
c = createGUID(numbers_of_GUID)

Input argument

numbers_of_GUID - an integer value: numbers of GUID to create.

Output argument

s - a string
c - a cell of strings.

Description

createGUID creates a Globally Unique IDentifier (GUID), , a unique 128-bit integer used for CLSIDs and interface identifiers.

Example

createGUID()
createGUID(10)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

getenv

Get the value of an environment variable.

Syntax

s = getenv(env_name)

Input argument

env_name - string scalar, character vector, string array, cell array of character vectors: environment variable name.

Output argument

s - string scalar, character vector, string array, cell array of character vectors: the environment variable value.

Description

getenv returns the value of an environment variable if it exists.

If the environment variable does not exist, it will return ''.

If env_name is a nonscalar cell array of character vectors or string array, then val has the same dimensions and type as env_name.

If env_name is a string scalar, then s is a character vector.

Example

getenv('OS')
getenv('myenvvar')
getenv(["PATH"; "OS"])
getenv({'PATH'; 'OS'})

History

Version	Description
1.0.0	initial version
1.4.0	Retrieve the values of several environment variables.

Author

Allan CORNET

hostname

get host name of this computer.

Syntax

s = hostname()

Output argument

s - a char array: host name.

Description

hostname get host name of this computer.

Example

hostname()

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

ismac

Checks if version is for MacOS platform.

Syntax

s = ismac()

Output argument

s - a logical: true if it is a MacOS platform.

Description

ismac checks if it is a MacOs platform.

Example

if ismac
  disp('Your platform is MacOs')
else
  disp('Your platform is not MacOs')
end

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

ispc

Checks if version is for Windows platform.

Syntax

s = ispc()

Output argument

s - a logical: true if it is a Windows platform.

Description

ispc checks if it is a Windows platform.

Example

if ispc
  disp('Your platform is Windows')
else
  disp('Your platform is not Windows')
end

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

isunix

Checks if version is for GNU Linux or Unix platform.

Syntax

s = isunix()

Output argument

s - a logical: true if it is a GNU Linux or Unix platform.

Description

isunix checks if it is a GNU Linux or Unix platform.

MacOs platform is also detected as a GNU Linux or Unix platform.

Example

if isunix
  disp('Your platform is Unix or Linux')
else
  disp('Your platform is Unix or Linux')
end

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

searchenv

Searches for a file using environment paths.

Syntax

c = searchenv(filename, env_name)

Input argument

env_name - a string: environment variable name.
filename - a string: filename searched in environment variable.

Output argument

c - a cell of strings: full paths found in environment variable.

Description

searchenv Searches for a file using environment paths.

Example

[modules, paths] = getmodules();
env_value = '';
for p = paths
 env_value = [env_value, pathsep, p];
end

setenv('MY_PATH_ENV', env_value);
c = searchenv('loader.m', 'MY_PATH_ENV')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

setenv

Set the value of an environment variable.

Syntax

getenv(env_name, env_value)

Input argument

env_name - a string: environment variable name.
env_value - a string: environment variable value.

Description

setenv set the value of an environment variable.

Example

setenv('MY_ENV_VAR', 'funvalue')
getenv('MY_ENV_VAR')
setenv('MY_ENV_VAR', '')
getenv('MY_ENV_VAR')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

system

dos

unix

Shell command execution.

Syntax

status = system(command)
status = system(command, timeout)
status = dos(command)
status = unix(command)
status = unix(commands)
[status, output, duration] = system(command)
[status, output, duration] = dos(command)
[status, output, duration] = unix(command)
[status, output, duration] = system(command, '-echo')
[status, output, duration] = dos(command, '-echo')
[status, output, duration] = unix(command, '-echo')
[s, outputs, duration] = unix(commands)
[s, outputs, duration] = unix(commands, timeouts)

Input argument

command - a string: command to execute in command shell.
commands - a cell of string or a string array: commands to execute in command shell in parallel.
timeout - an integer value (scalar): kill process using timeout in seconds.
timeouts - an integer value (scalar: applied to all commands or vector: one by command): kill process using timeout in seconds.

Output argument

status - an integer value: exit code value of the command.
output - a string: output of the command.
duration - integer value: duration (milliseconds).
s - an matrix of integer value: exit code value of the commands (same dimensions than commands).
output - a string array: output of the commands.
duration - an matrix of integer value: duration of each execution (milliseconds).

Description

system sends a string to the operating system for execution. Standard output and standard errors of the shell command are written in the calling shell.

[status, output] = system(command, '-echo') forces the output to the Command Window, even though it is also being assigned into a variable.

Callback functions cannot be called until system command is not finished.

Nelson will convert characters to the encoding that your operating system shell accepts (ANSI on Windows by default, UTF-8 on others systems).

command can be interrupted with CTRL-C key, in this case status code returned will be 258 (WAIT_TIMEOUT) on Windows and 134 on others platforms (128 + SIGABRT)output contains 'ABORTED'.

if timeout value is 0. timeout disabled.

Examples

[s,w] = system('dir');
[s,w] = system('dir','-echo');

[s,w] = system(["echo hello", "dir", "echo world"])

tic();[s, w, d] = system(["PING -n 5 127.0.0.1>nul", "PING -n 7 127.0.0.1>nul", "PING -n 10 127.0.0.1>nul"]), toc()

tic();[s, w, d] = system(["PING -n 5 127.0.0.1>nul", "PING -n 7 127.0.0.1>nul", "PING -n 10 127.0.0.1>nul"], [1, 5, 3]), toc()

To detach an system command, include the trailing character, &, in the command argument.

[s,w] = system('notepad &');

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

username

get user name currently used.

Syntax

s = username()

Output argument

s - a char array: user name.

Description

username get user name currently used.

Example

username()

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

winopen

Open file in appropriate application (Windows only).

Syntax

winopen(filename)

Input argument

command - a string: command to execute in command shell.

Description

winopen(filename) opens filename in the appropriate Microsoft Windows application.

The winopen function uses the appropriate Windows shell command, and performs the same action as if you double-click the file in the Windows Explorer.

If filename is not in the current directory, specify the absolute path for filename.

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

winqueryreg

Read the Windows registry (Windows only).

Syntax

c = winqueryreg ('name', rootkey, subkey)
v = winqueryreg (rootkey, subkey, value_name)
v = winqueryreg (rootkey, subkey)

Input argument

rootkey - a string: root key.
subkey - a string: subkey path.
value_name - a string: name of value.

Output argument

c - a cell of strings.
v - a string or int32.

Description

c = winqueryreg ('name', rootkey, subkey) returns a cell of strings with key names in rootkey\subkey.

v = winqueryreg (rootkey, subkey, value_name) returns the value associated to value_name in rootkey\subkey.

If the value is a 32-bit integer, winqueryreg returns the value as int32. If this value is a string, it is a string.

v = winqueryreg (rootkey, subkey) returns value in rootkey\subkey that has no value name property.

Supported root keys:

'HKEY_CLASSES_ROOT', 'HKCR',

'HKEY_CURRENT_USER', 'HKCU',

'HKEY_LOCAL_MACHINE', 'HKLM',

'HKEY_USERS', 'HKU',

'HKEY_CURRENT_CONFIG', 'HKCC'

Example

winqueryreg('name', 'HKEY_LOCAL_MACHINE', 'HARDWARE\DESCRIPTION\System')
winqueryreg('HKLM', 'HARDWARE\DESCRIPTION\System\CentralProcessor\1\', 'ProcessorNameString')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

Files and folders functions

Description

files, folders and paths functions

cd - Changes Nelson current directory.
copyfile - Copy files or folder.
diff_file - diff two files or strings.
dir - Returns file list.
fileparts - Returns the path, filename and extension of a file path.
filesep - Return the file separator character for the current platform.
fullfile - Build full file name from parts.
fullpath - Returns canonical full path.
isdir - Returns true is the input argument is an directory.
isfile - Returns true is the input argument is a file.
isfolder - Returns true is the input argument is an directory.
ls - List folder contents.
mkdir - Creates a new directory.
pathsep - Return the search path separator character for the current platform.
pwd - Returns current directory.
relativepath - Returns the relative path from an actual path to the target path.
rmdir - Removes a directory.
rmfile - Removes a file.
tempdir - Returns the temporary directory path.
tempname - Returns an unique temporary filename.
userdir - Returns the current user's path.

cd

Changes Nelson current directory.

Syntax

cd(dirname)
cd dirname
previous_path = cd(dirname)
cd ..
cd

Input argument

dirname - a string: directory name to move.

Output argument

previous_path - a string: previous directory.

Description

Changes the current working directory to dirname.

a = cd() without input argument returns the current working directory.

cd() without input argument displays the current working directory.

Example

previous = cd(tempdir())
cd
cd ..

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

copyfile

Copy files or folder.

Syntax

copyfile(source, destination)
[status, msg] = copyfile(source, destination)
[status, msg] = copyfile(source, destination, 'f')

Input argument

source - a string: file or directory.
destination - a string: file or directory.
'f' or 'F' - force copy even destination is not writable.

Output argument

status - a logical true or false
msg - a string: error message

Description

copyfile(source , destination) copies the file or directory , source (and subdirectories) to the file or directory, destination.

If source is a directory, destination can not be a file.

copyfile replaces existing files without warning.

Example

copyfile([nelsonroot(), '/etc/startup.m'], [tempdir(), 'startup.m'])
[status, msg] = copyfile([nelsonroot(), '/etc/startup.m'], [tempdir(), 'startup.m'])

History

Version	Description
1.0.0	initial version
1.4.0	input arguments support scalar string array type

Author

Allan CORNET

diff_file

diff two files or strings.

Syntax

res = diff(filename_1, filename_2, with_eol)

Input argument

filename_1 - a string: a filename.
filename_2 - a string: a filename.
with_eol - a logical: with end of line considered or not (true by default).

Output argument

res - a string: '' if no diff detected.
msg - a string: error message

Description

diff_file compares two files and returns diff as unified format.

if compared files are equals, res is an empty string.

Example

res = diff_file([nelsonroot(), '/etc/startup.m'], [nelsonroot(), '/etc/startup.m'])
res = diff_file([nelsonroot(), '/etc/startup.m'], [nelsonroot(), '/etc/finish.m'])

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

dir

Returns file list.

Syntax

dir
dir(dirname)
dir(dirname, '-s')
res =dir()
res = dir(dirname)
res = dir(dirname, '-s')

Input argument

dirname - a string: file or directory name.
'-s' - a string: scan also subdirectories.

Output argument

res - a struct with fields: name, date, bytes, isdir, datenum.

Description

dir displays the list of files and folders in the current folder.

* (wildcard) is supported in filename and path name.

Example

res = dir(nelsonroot())
res = dir(nelsonroot(), '-s')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

fileparts

Returns the path, filename and extension of a file path.

Syntax

[p, f, e] = fileparts(fullpath)
p = fileparts(fullpath, 'path')
f = fileparts(fullpath, 'filename')
e = fileparts(fullpath, 'extension')

Input argument

fullpath - a string: file or directory name.

Output argument

p - a string: path of the directory fullpath.
f - a string: file name without extension of fullpath.
e - a string: extension name of fullpath.

Description

[p ,f, e] = fileparts(fullpath) splits in its three parts: path, filename, extension including the dot.

Example

[p, f, e] = fileparts([nelsonroot(), '/etc/finish.m'])
p = fileparts([nelsonroot(), '/etc/finish.m'], 'path')
f = fileparts([nelsonroot(), '/etc/finish.m'], 'filename')
e = fileparts([nelsonroot(), '/etc/finish.m'], 'extension')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

filesep

Return the file separator character for the current platform.

Syntax

res = filesep()

Output argument

res - a string: '/' or ''

Description

pathsep returns '' on Windows and '/' on others platforms.

Example

A = filesep

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

fullfile

Build full file name from parts.

Syntax

R = fullfile(part1, ... , partN)

Input argument

part1, ... , partN - a string or cell of string: filename to concat.

Output argument

R - a character array or string array or cell array of character vectors.

Description

R = fullfile(part1, ... , partN) build full file name from parts.

Example

fullfile([nelsonroot(), '/./toto'])

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

fullpath

Returns canonical full path.

Syntax

R = fullpath(path)

Input argument

path - a string or cell of string: filename to normalize.

Output argument

R - a string or cell of string: canonical paths.

Description

fullpath(path) returns full path from a relative path.

Example

fullpath([nelsonroot(), '/../toto'])

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

isdir

Returns true is the input argument is an directory.

Syntax

r = isdir(dirname)

Input argument

dirname - a string: directory name to check.

Output argument

r - a logical: true if it is an directory.

Description

isdir(dirname) returns true if dirname is a directory.

isdir and isfolder are same.

Example

isdir(nelsonroot())
isdir([nelsonroot(), '/not_exist_dir'])

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

isfile

Returns true is the input argument is a file.

Syntax

r = isfile(name)

Input argument

name - a string: filename to check.

Output argument

r - a logical: true if it is a file.

Description

isfile(name) returns true if name is a file.

Example

isfile(nelsonroot())
isfile([nelsonroot(), '/etc/finish.m'])

History

Version	Description
1.0.0	initial version
1.4.0	input arguments support scalar string array type

Author

Allan CORNET

isfolder

Returns true is the input argument is an directory.

Syntax

r = isfolder(dirname)

Input argument

dirname - a string: directory name to check.

Output argument

r - a logical: true if it is an directory.

Description

isfolder(dirname) returns true if dirname is a directory.

Example

isdir(nelsonroot())
isdir([nelsonroot(), '/not_exist_dir'])

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

ls

List folder contents.

Syntax

ls
ls(name)
res = ls()
res = ls(options)

Input argument

name - a string: file or directory name.
options - vary from system to system.

Output argument

res - On Windows, res is an m-by-n character array of names. m is the number of names and n is the number of characters in the longest name. On Unix plaftorms is a character vector of names separated by tab and space characters.

Description

ls is implemented by calling the native operating system's directory listing command—available options will vary from system to system.

Example

res = ls(nelsonroot())
if ~ispc()
  res = ls(nelsonroot(), '-l')
end

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

mkdir

Creates a new directory.

Syntax

mkdir(dirname)
mkdir(parentdir, dirname)
status = mkdir(dirname)
status = mkdir(parentdir, dirname)
[status, msg] = mkdir(dirname)
[status, msg] = mkdir(parentdir, dirname)

Input argument

dirname - a string: directory name to create
parentdir - a string: a directory in which the dirname directory will be created

Output argument

status - a logical true or false
msg - a string: error message

Description

Creates a directory named dirname in the directory parent.

If no parent directory is specified the present working directory is used.

If directory is created or already existing, status is true, otherwise it will be false.

Example

mkdir(tempdir(), 'subdir_example')
if isdir([tempdir(), 'subdir_example'])
	disp('OK')
else
	disp('NOT OK')
end

History

Version	Description
1.0.0	initial version
1.4.0	input arguments support scalar string array type

Author

Allan CORNET

pathsep

Return the search path separator character for the current platform.

Syntax

res = pathsep()

Output argument

res - a string: ';' or ':'

Description

pathsep returns ';' on Windows and ':' on others platforms.

Example

A = pathsep

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

pwd

Returns current directory.

Syntax

pwd()
r = pwd()

Output argument

r - a string: current directory.

Description

Returns the current working directory.

pwd() without input argument displays the current working directory.

Example

r = pwd()
pwd()

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

relativepath

Returns the relative path from an actual path to the target path.

Syntax

r = relativepath(path_1, path_2)

Input argument

path_1 - a string: file or directory.
path_2 - a string: file or directory.

Output argument

r - a string: relative path.

Description

Returns the relative path from an actual path to the target path.

Example

relativepath(nelsonroot(), [nelsonroot(), '/lgpl-3.0.md'])
relativepath(nelsonroot(), [nelsonroot(), '/etc/finish.m'])
relativepath([nelsonroot(),'/bin'], [nelsonroot(), '/lgpl-3.0.md'])
relativepath('.', '.')
relativepath('.', '..')
relativepath('..', '.')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

rmdir

Removes a directory.

Syntax

rmdir(dirname)
rmdir(dirname, 's')
res = rmdir(dirname)
res = rmdir(dirname, 's')
[res, msg] = rmdir(dirname)
[res, msg] = rmdir(dirname, 's')

Input argument

dirname - a string: file or directory name.
's' - a string: removes also subdirectories.

Output argument

res - a logical: true or false.
msg - a string: error message or ''.

Description

res = rmdir(dirname) removes the directory dirname.

If the directory is not empty, you must use the s argument.

Example

mkdir([tempdir(), 'test'])
rmdir([tempdir(), 'test'])

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

rmfile

Removes a file.

Syntax

rmfile(filename)
res = rmfile(filename)
[res, msg] = rmfile(filename)
[res, msg] = rmfile(filename)

Input argument

filename - a string: file name.

Output argument

res - a logical: true or false.
msg - a string: error message or ''.

Description

res = rmfile(filename) removes the file filename.

Example

fd = fopen([tempdir(), 'test_rmfile.txt'], 'wt')
fclose(fd)
isfile([tempdir(), 'test_rmfile.txt'])
rmfile([tempdir(), 'test_rmfile.txt'])
isfile([tempdir(), 'test_rmfile.txt'])

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

tempdir

Returns the temporary directory path.

Syntax

tempdir()
p = tempdir()

Output argument

p - a string: current temporary directory.

Description

Returns the name of the host system’s directory for temporary files.

Example

r = tempdir()

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

tempname

Returns an unique temporary filename.

Syntax

f = tempname()
f = tempname(path)

Input argument

path - a string: an existing directory used instead of tempdir().

Output argument

f - a string: an unique temporary filename.

Description

Returns the name of an unique temporary filename.

Example

r = tempname()

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

userdir

Returns the current user's path.

Syntax

userdir()
p = userdir()

Output argument

p - a string: current user directory.

Description

Returns the name of the user's directory.

Example

r = userdir()

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

Memory manager functions

Description

memory manager functions

acquirevar - Acquires variable value from a specified variables scope.
assignin - Assignin value to a variable in a specified variables scope.
clear - Remove variable from workspace.
global - Defines a global variable.
isglobal - Checks if a variable is global.
isvar - Check for the existence of an variable.
memory - Get memory information.
persistent - Persistent variable.
varislock - Checks if a variable is locked.
varlock - Locks a variable.
varunlock - Unlocks a variable.
who - List variables in memory or in .nh5 or in .mat file.
whos - List variables in memory or in .nh5 or in .mat file with sizes and types.

acquirevar

Acquires variable value from a specified variables scope.

Syntax

value = acquirevar(scope, variable_name)

Input argument

scope - a string: 'global', 'base', 'caller', 'local'.
variable_name - a string: the name of symbol to search.

Output argument

value - value of the variable searched.

Description

acquirevar search a symbol in a specific scope and copy the value in current scope.

Example

Y = 'variable in base scope';
function myfun()
  disp(acquirevar('base', 'Y')
end
myfun()

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

assignin

Assignin value to a variable in a specified variables scope.

Syntax

assignin(scope, variable_name, variable_value)

Input argument

scope - a string: 'global', 'base', 'caller', 'local'.
variable_name - a string: the name of variable destination.
variable_value - a variable to assign.

Description

assignin assign value to a variable in a specified variables scope.

Example

assignin('base', 'X', 33);
Y = acquirevar('base', 'X');

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

clear

Remove variable from workspace.

Syntax

clear
clear variable_name
clear global
clear all
clear mex
clear variables
clear functions
clear function_name
clear mexfunction_name
clear variable_name_1 ... variable_name_N
clear global variable_name

Input argument

variable_name - a string: variable name.
global - clears all global variables.
all - clears all variables in all scopes
mex - clears all mex functions in all scopes
variables - clears all variables in current scope.
functions - clears cache of macros functions and associated persistent variables.
function_name - clears persistent variables of a function.
mexfunction_name - clears mex function (see mexAtExit).

Description

clear is used to remove variable given by its name.

clear can also delete handle object if a function handle_TYPE_clear is defined.

Example

A = 3;
who
clear A
who
A

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

global

Defines a global variable.

Syntax

global variable_name
global(variable_name)
global variable_name1 ... variable_nameN

Input argument

variable_name - a string: valid variable name.

Description

global make variable in global assign value to a variable in a specified variables scope.

Example

function myfun()
global y;
y = 1;
end

myfun()
who
global y
who
disp(y)
who
clear global y
disp(y)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

isglobal

Checks if a variable is global.

Syntax

state = isglobal(variable_name)

Input argument

variable_name - a string: variable name.

Output argument

state - a logical: true if variable is global.

Description

isglobal returns true if variable_name has been declared as global variable and false otherwise.

Example

y = 3;
isglobal y
global b
b = 3
isglobal b
clear global b
isglobal b

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

isvar

Check for the existence of an variable.

Syntax

tf = isvar(varname)
tf = isvar(scope, varname)

Input argument

scope - a string: 'global', 'base', 'caller', 'local'.
varname - a string: variable name.

Output argument

tf - a logical: true if varname exists.

Description

isvar checks for the existence of an variable.

Example

isvar('A')
A = 3
isvar('A')
isvar('global','B')
global B
isvar('global','B')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

memory

Get memory information.

Syntax

memory
usermem = memory()
[usermem, systemmem] = memory()

Output argument

usermem - Get information about user memory (an struct).
systemmem - Get information about system memory (an struct)

Description

memory get memory information.

User Memory: returns Maximum Possible Array (MaxPossibleArrayBytes), Memory Available for All Arrays (MemAvailableAllArrays), Memory Used By Nelson (MemUsedNelson).

System Memory:

VirtualAddressSpace.Available: available swap file space

VirtualAddressSpace.Total: total swap file space

SystemMemory.Available: available system memory

PhysicalMemory.Available: available physical memory

PhysicalMemory.Total: total physical memory

Examples

memory()
A = ones(1000);
memory()

clear('A');
[u1, s1] = memory();
A = ones(1000);
[u2, s2] = memory();
disp(u2.MemUsedNelson - u1.MemUsedNelson);
clear('A');
[u3, s3] = memory();
disp(u3.MemUsedNelson - u2.MemUsedNelson);

[u1, s1] = memory()

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

persistent

Persistent variable.

Syntax

persistent variable_name
persistent('variable_name')
persistent variable_name1, ..., variable_nameN

Input argument

variable_name - a string: variable name.

Description

persistent defines a variable defined by his name variable_name as persistent in a function.

Before to use a persistent variable, it is necessary to initializ value.

Examples

function to define:

function r = test_persistent_function()
 persistent calls;
 if isempty(calls)
    calls = 0;
 end
 disp(['nb calls to test_persistent_function: ', int2str(calls)]);
 r= calls;
 calls = calls + 1;
end

calls test_persistent_function

for i = 1:30
  r = test_persistent_function();
end

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

varislock

Checks if a variable is locked.

Syntax

state = varislock(scope, variable_name)

Input argument

scope - a string: 'global', 'base', 'caller', 'local'.
variable_name - a string: variable name.

Description

varislock returns true if variable_name has been declared as locked variable and false otherwise.

Example

y = 3;
varislock('local', 'y')
varlock('local', 'y')
varislock('local', 'y')
y = 4
varunlock('local', 'y')
varislock('local', 'y')
y = 4

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

varlock

Locks a variable.

Syntax

varlock(scope, variable_name)

Input argument

scope - a string: 'global', 'base', 'caller', 'local'.
variable_name - a string: variable name.

Description

varlock locks a variable.

Locked variables cannot be killed.

ans variable cannot be locked.

Example

y = 3;
varislock('local', 'y')
varlock('local', 'y')
varislock('local', 'y')
y = 4
varunlock('local', 'y')
varislock('local', 'y')
y = 4
varlock('local', 'ans')
varislock('local', 'ans')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

varunlock

Unlocks a variable.

Syntax

varunlock(scope, variable_name)

Input argument

scope - a string: 'global', 'base', 'caller', 'local'.
variable_name - a string: variable name.

Description

varunlock unlocks a variable.

Example

y = 3;
varislock('local', 'y')
varlock('local', 'y')
varislock('local', 'y')
y = 4
varunlock('local', 'y')
varislock('local', 'y')
y = 4
varlock('local', 'ans')
varislock('local', 'ans')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

who

List variables in memory or in .nh5 or in .mat file.

Syntax

who
s = who()
who(scope)
s = who(scope)
who('-file', filename)
s = who('-file', filename)
who(... , var1, ..., varN)
s = who(... , var1, ..., varN)

Input argument

scope - a string: 'global', 'base', 'caller', 'local' or '-file'.
filename - string: an existing filename .nh5 or .mat file.
var1, ..., varN - string: variable name.

Output argument

s - a cell of strings: list of variable's name.

Description

who displays current variable names.

Example

clear
who
A = 3
b= 3
who
s = who()

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

whos

List variables in memory or in .nh5 or in .mat file with sizes and types.

Syntax

whos
s = whos()
whos(scope)
s = whos(scope)
whos('-file', filename)
s = whos('-file', filename)
whos(... , var1, ..., varN)
s = whos(... , var1, ..., varN)

Input argument

scope - a string: 'global', 'base', 'caller', 'local'.
var1, ..., varN - a string: variable name.
filename - string: an existing filename .nh5 or .mat file.

Output argument

st - stores information about the variables in the structure array s.

Description

whos displays current variable names in memory or in .nh5 or .mat file.

Example

clear
whos
A = 3
b= 3
whos
s = whos()
save([tempdir(), 'example_who.nh5'], 'A', 'b')
whos([tempdir(), 'example_who.nh5'])

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

Time functions

Description

time functions

addtodate - Modify date number by field.
calendar - Calendar.
clock - Return the current local date and time as a date vector.
cputime - Return the CPU time used by your Nelon session.
date - Return the Current date as character vector.
datenum - Return the date/time input as a serial day number.
datestr - Convert date and time to string format.
datevec - Convert a serial date number into a date vector.
eomday - Returns last day of month.
etime - Time elapsed between date vectors.
hour - Hours part of the input date and time.
leapyear - Determine leap year.
minute - Minutes part of the input date and time.
now - Returns current date under the form of a Unix hour.
second - Seconds part of the input date and time.
sleep - Suspend code execution.
tic - Starts a stopwatch timer.
time - Return the current time as the number of seconds or nanoseconds since the epoch.
timeit - Measure time required to run function.
toc - Read the stopwatch timer.
weekday - Return the day of week.

addtodate

Modify date number by field.

Syntax

r = addtodate(d, q, f)

Input argument

d - serial datenum.
q - quantile to add to date
f - 'year', 'month', 'day', 'hour', 'minute', 'second', or 'millisecond.

Output argument

r - date number.

Description

r = addtodate(d, q, f) adds quantity q to the indicated date field f of a scalar serial date number d, returning the updated date number r.

Example

t = datenum('07-Apr-2008 23:00:00');datevec(t)
t2 = addtodate(t, -2, 'hour');datevec(t2)
t3 = addtodate(t, 4, 'hour');datevec(t3)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

calendar

Calendar.

Syntax

calendar()
c = calendar()
c = calendar(d)
c = calendar(y, m)

Input argument

d - an integer value: a serial date number.
y - an integer value: 'year' desired [1400, 9999].
m - an integer value: 'month' desired [1, 12].

Output argument

c - a 6x7 matrix.

Description

calendar() returns the currently monthly calendar.

If no output arguments are specified,the calendar is displayed on the screen instead of returning a matrix 6x7.

Example

calendar()
c = calendar(1973, 8)
c = calendar(datenum(1973, 8, 4))

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

clock

Return the current local date and time as a date vector.

Syntax

v = clock()

Output argument

v - a vector: [year, month, day, hours, minutes, seconds].

Description

calendar() returns the currently monthly calendar.

The date vector contains the following fields:

year

months [1, 12]

days [1, 31]

hours [0, 23]

minutes [0, 59]

seconds [0, 61]

seconds: field has a fractional part after the decimal point for extended accuracy.

To time the duration of an event, use tic and toc functions instead of clock.

The clock function is based on the system time and thus might not be reliable for time comparison operations.

Example

c = clock()
fix(c)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

cputime

Return the CPU time used by your Nelon session.

Syntax

t = cputime()

Output argument

t - a double: time in seconds.

Description

cputime() returns the CPU time used by Nelson session.

To measure performance, it is better to use tic and toc functions.

Example

t1 = cputime;
sleep(10);
t2 = cputime;
t2 - t1

% versus tic toc
tic()
sleep(10);
toc()

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

date

Return the Current date as character vector.

Syntax

d = date()

Output argument

d - a string: date string using format dd-MMM-yyy. MMM: English abbreviation for the month name.

Description

d = date() returns the current date as a character vector in the format dd-MMM-yyyy.

Example

d = date()
fix(c)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

datenum

Return the date/time input as a serial day number.

Syntax

d = datetnum(datevec)
d = datenum(datestr)
d = datenum(datestr, format)
d = datenum(datestr, pivotYear)
d = datenum(DateString,format,pivotYear)
d = datetnum(Y, M, D)
d = datetnum(Y, M, D, H, MN, S)

Input argument

datevec - a vector: [Y, M, D, H, MN, S] or matrix N x 6.
format - a string specifying the date format, or leave it empty ('') for automatic format detection.
datestr - a string, cell of string or string array: text representing a date.
Y, M, D, H, MN, S - double: Year, Month, Day, Hours, Minutes, Secondes (scalar or vector).
pivotYear: Start year of 100-year date range - integer value or present minus 50 years (default).

Output argument

d - a double: serial date number (serial day 1 corresponds to 1-Jan-0000).

Description

d = datenum() returns the serial date number corresponding to current date.

d = datenum(datevec) converts date vector to serial date number.

d = datenum(datestr) and d = datenum(datestr, format) converts string to serial date number.

Supported format conversion:

dd-mmm-yyyy HH:MM:SS 10-Mar-2010 16:48:17

dd-mmm-yyyy 10-Mar-2010

mm/dd/yyyy 03/10/2010

mm/dd/yy 03/10/00

mm/dd 03/10

mmm.dd,yyyy HH:MM:SS Mar.10,2010 16:48:17

mmm.dd,yyyy Mar.10,2010

yyyy-mm-dd HH:MM:SS 2010-03-10 16:48:17

yyyy-mm-dd 2010-03-10

yyyy/mm/dd 2000/03/10

HH:MM:SS 16:48:17

HH:MM:SS PM 3:48:17 PM

HH:MM 16:48

HH:MM PM 3:35 PM

If format is not specified, the default format is dd-mmm-yyyy.

If format is specified and not using predefined format, the format must be specified as a character vector or string scalar composed of symbolic identifiers.

The format of the input text for representing dates and times, expressed as a character vector or string scalar composed of symbolic identifiers.

Symbolic Identifier	Description	Example
yyyy	Year in full	1995, 2012
yy	Year in two digits	89, 01
QQ	Quarter year using letter Q and one digit	Q1
mmmm	Month using full name	March, December
mmm	Month using first three letters	Mar, Dec
mm	Month in two digits	04, 12
m	Month using capitalized first letter	M, D
dddd	Day using full name	Monday, Tuesday
ddd	Day using first three letters	Mon, Tue
dd	Day in two digits	06, 21
d	Day using capitalized first letter	M, T
HH	Hour in two digits (no leading zeros when symbolic identifier AM or PM is used)	06, 6 AM
MM	Minute in two digits	11, 01
SS	Second in two digits	06, 59
FFF	Millisecond in three digits	056
AM or PM	AM or PM inserted in text representing time	5:46:02 PM

Example

d = datenum([1973,8,4,12,1,18])
datevec(d)
d = datenum('04–Aug-1973 12:01:18')
d = datenum(["04–Aug-1973 12:01:18"; "04–Aug-1974 11:01:18"])

History

Version	Description
1.0.0	initial version
1.8.0	date string parsing extended.
1.10.0	added: format '' means try to detect.

Author

Allan CORNET

datestr

Convert date and time to string format.

Syntax

dateAsString = datestr(dateVector)
dateAsString = datestr(dateNumber)
dateAsString = datestr(..., formatOut)
dateAsString = datestr(dateAsStringIn)
dateAsString = datestr(dateAsStringIn, formatOut, pivotYear)
dateAsString = datestr(..., 'local')

Input argument

dateVector - Date vectors or matrix.
dateNumber - Serial date numbers: An array of positive double-precision floating-point numbers.
formatOut - character vector, string scalar or integer value (-1 default): Output format for representing dates and times
dateAsStringIn - character vector, cell array or string array: text denoting dates and times to convert.
pivotYear - integer value: present minus 50 years (default).
'local' - returns the date in the language of the current locale.

Output argument

dateAsString - character vector or two-dimensional character array: text denoting dates and time.

Description

dateAsString = datestr(dateVector) converts date vectors into text that represents the corresponding dates and times. It returns a character array with m rows, where m is the number of date vectors in dateVector.

dateAsString = datestr(dateNumber) converts serial date numbers into text representing dates and times. The output is a character array with m rows, where m is the number of date numbers in dateNumber.

dateAsString = datestr(..., formatOut) allows you to specify the format of the output text using formatOut. You can apply this option with any of the previous input types.

dateAsString = datestr(dateAsStringIn) converts the input string dateAsStringIn into a text format of day-month-year hour:minute:second. All dates in dateAsStringIn must follow the same format.

dateAsString = datestr(dateAsStringIn, formatOut, pivotYear) converts dateAsStringIn into the format specified by formatOut, while using an optional pivotYear to interpret two-digit years.

dateAsString = datestr(..., 'local') returns the date in the language of the system's current locale. If 'local' is omitted, the default language is US English. The 'local' option can be used with any of the previous syntaxes, and must be the last argument in the sequence.

Supported format conversion:

dd-mmm-yyyy HH:MM:SS 10-Mar-2010 16:48:17

dd-mmm-yyyy 10-Mar-2010

mm/dd/yyyy 03/10/2010

mm/dd/yy 03/10/00

mm/dd 03/10

mmm.dd,yyyy HH:MM:SS Mar.10,2010 16:48:17

mmm.dd,yyyy Mar.10,2010

yyyy-mm-dd HH:MM:SS 2010-03-10 16:48:17

yyyy-mm-dd 2010-03-10

yyyy/mm/dd 2000/03/10

HH:MM:SS 16:48:17

HH:MM:SS PM 3:48:17 PM

HH:MM 16:48

HH:MM PM 3:35 PM

If format is not specified, the default format is dd-mmm-yyyy.

If format is specified and not using predefined format, the format must be specified as a character vector or string scalar composed of symbolic identifiers.

The format of the input text for representing dates and times, expressed as a character vector or string scalar composed of symbolic identifiers.

Symbolic Identifier	Description	Example
yyyy	Year in full	1995, 2012
yy	Year in two digits	89, 01
QQ	Quarter year using letter Q and one digit	Q1
mmmm	Month using full name	March, December
mmm	Month using first three letters	Mar, Dec
mm	Month in two digits	04, 12
m	Month using capitalized first letter	M, D
dddd	Day using full name	Monday, Tuesday
ddd	Day using first three letters	Mon, Tue
dd	Day in two digits	06, 21
d	Day using capitalized first letter	M, T
HH	Hour in two digits (no leading zeros when symbolic identifier AM or PM is used)	06, 6 AM
MM	Minute in two digits	11, 01
SS	Second in two digits	06, 59
FFF	Millisecond in three digits	056
AM or PM	AM or PM inserted in text representing time	5:46:02 PM

Examples

dateVector = [2019, 4, 2, 9, 7, 18];
datestr(dateVector)

dateVector = [2019, 4, 2, 9, 7, 18];
formatOut = 'mm/dd/yy';
datestr(dateVector, formatOut)

datestr(now, 'mmmm dd, yyyy HH:MM:SS.FFF AM')

datestr('06:33 PM','HH:MM')

datestr('06:33','HH:MM PM')

formatOut = 'dd mmm yyyy';
datestr(datenum('18-05-45','dd-mm-yy',1900),formatOut)

datestr(datenum({'09/17/2017';'06/14/1906';'10/29/2014'}, 'mm/dd/yyyy')))

dateStringIn = '5/17/56';
formatOut = 1;
pivotYear = 1900;
datestr(dateStringIn, formatOut, pivotYear)
pivotYear = 2000;
datestr(dateStringIn,formatOut, pivotYear)

History

Version	Description
1.8.0	initial version

Author

Allan CORNET

datevec

Convert a serial date number into a date vector.

Syntax

[Y, M, D, H, MN, S] = datevec(dv)
V = datevec(dv)

Input argument

dv - a scalar, vector, or multidimensional array e: a serial date number.

Output argument

Y, M, D, H, MN, S - double: Year, Month, Day, Hour, Minutes, Seconds.
V - a vector of double: [Year, Month, Day, Hour, Minutes, Seconds].

Description

datevec converts a serial date number into a date vector.

To measure performance, it is better to use tic and toc functions.

Example

datevec(now())
datevec(720840)
V = datevec([720840, now()])
[Y, M, D, H, MN, S] = datevec([720840, now()])

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

eomday

Returns last day of month.

Syntax

E = eomday(Y, M)

Input argument

Y - year: real.
M - month: real.

Output argument

E - last day of month: real.

Description

E = eomday(Y, M) returns the last day of the month M for the year Y.

Example

eomday(1900, 1:12)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

etime

Time elapsed between date vectors.

Syntax

e = etime(t2, t1)

Input argument

t2 - Date vectors: 1-by-6 vector or m-by-6 matrix.
t1 - Date vectors: 1-by-6 vector or m-by-6 matrix.

Output argument

e - a scalar or a vector: time elapsed (seconds).

Description

e = etime(t2, t1) returns the number of seconds between two date vectors or matrices of date vectors, t1 and t2.

Example

t1 = clock()
sleep(6)
t2 = clock()
etime(t2, t1)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

hour

Hours part of the input date and time.

Syntax

h = hour(t)
h = hour(t, formatIn)

Input argument

t - serial date number or text inputs
formatIn - valid date format

Output argument

h - a double: integer value.

Description

h = hour(t) extracts the hour component from each date and time specified in t.

The output h is a double array containing integer values ranging from 0 to 23.

Example

h = hour(738427.656845093)
h = hour("2021/09/28 15:45:51", 'YYYY/M/DD HH:MM:SS')

History

Version	Description
1.10.0	initial version

Author

Allan CORNET

leapyear

Determine leap year.

Syntax

tf = leapyear(year)

Input argument

year - year: scalar or array numeric value.

Output argument

tf - Leap year determination result: scalar or array logical value.

Description

leapyear determines leap years.

Leap years is done by Gregorian calendar rules.

Example

tf = leapyear([2020 2021 2022])

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

minute

Minutes part of the input date and time.

Syntax

m = minute(t)
m = minute(t, formatIn)

Input argument

t - serial date number or text inputs
formatIn - valid date format

Output argument

m - a double: integer value.

Description

m = minute(t) extracts the minute component from each date and time specified in t.

The output m is a double array containing integer values ranging from 0 to 59.

Example

m = minute(738427.656845093)
m = minute("2021/09/28 15:45:51", 'YYYY/M/DD HH:MM:SS')

History

Version	Description
1.10.0	initial version

Author

Allan CORNET

now

Returns current date under the form of a Unix hour.

Syntax

n = now()

Output argument

n - a double.

Description

now() returns the current date and time as a serial date number.

Example

datevec(now())

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

second

Seconds part of the input date and time.

Syntax

s = second(t)
s = second(t, formatIn)

Input argument

t - serial date number or text inputs
formatIn - valid date format

Output argument

s - a double: integer value.

Description

s = second(t) extracts the second component from each date and time specified in t.

The output s is a double array containing integer values ranging from 0 to 59.

Example

s = second(738427.656845093)
s = second("2021/09/28 15:45:51", 'YYYY/M/DD HH:MM:SS')

History

Version	Description
1.10.0	initial version

Author

Allan CORNET

sleep

Suspend code execution.

Syntax

sleep(sec)

Input argument

n - a double: duration of the sleep in seconds (decimal number).

Description

sleep stops Nelson processing any instruction for a speficied number of seconds.

CTRL-C interruption stops sleep.

Example

tic();sleep(1);toc()
tic();sleep(0.1);toc()
tic();sleep(0.01);toc()

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

tic

Starts a stopwatch timer.

Syntax

tic()
t = tic()

Output argument

t - a unsigned integer 64 bit: value of internal timer of the tic function.

Description

The sequence of commands tic(); commands ; t = toc() returns the number of seconds required for the commands.

Consecutive tic commands overwrite the tic timer.

Example

tic()
sleep(10)
toc()

tic()
sleep(10)
t = toc()

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

time

Return the current time as the number of seconds or nanoseconds since the epoch.

Syntax

t_s = time()
t_s = time('s')
t_ns = time('ns')

Output argument

t_s - a double: value of current time as the number of seconds since the epoch.
t_ns - a unsigned integer 64 bit: value of current time as the number of nanoseconds since the epoch.

Description

time returns the current time as the number of seconds or nanoseconds since the epoch.

The epoch is referenced to 00:00:00 UTC (Coordinated Universal Time) 1 Jan 1970.

Example

t1=time()
sleep(10)
t2 = time()
t2 - t1

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

timeit

Measure time required to run function.

Syntax

t = timeit(f)
t = timeit(f, nLhs)
t = timeit(f, nLhs, x1, ..., xm)

Input argument

f - Function handle: Function to run.
nLhs - integer value: number of output arguments. (1: default)
x1, ..., xm - Input arguments, specified as a comma-separated list of variables or expressions.

Output argument

t - time (in seconds).

Description

t = timeit(f) measures the time elapsed required to run the function specified by the function handle f.

To perform a robust measurement, timeit calls function multiple times and returns the median of the measurements.

If the function runs fast, timeit might call the function many times.

Examples

f = str2func('@()sleep(6)');
tic();t = timeit(f), toc()

X = rand(100);
f = str2func('@(X) svd(X);');
tic(), t1 = timeit(f, 1, X), toc()
tic(), t2 = timeit(f, 3, X), toc()

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

weekday

Return the day of week.

Syntax

number = weekday(D)
[number, name] = weekday(D)
[number, name] = weekday(D, form)
[number, name] = weekday(D, language)
[number, name] = weekday(D, form, language)

Input argument

D - Serial date numbers or text representing dates and times (vector, matrix, character vector, cell array of character vectors, string array or character array).
form - a string: 'short' (default) or 'long'.
language - a string: 'en_US' (default) or 'local'.

Output argument

number - array of integers values in the range [1, 7].
name - character array. if 'local' output uses current local if day name is available as translation.

Description

dayweek returns the day of the week as a number in number and as a string in name.

Example

[DayNumber, DayName] = weekday(datenum('12-21-2012'), 'long', 'en_US')
[DayNumber, DayName] = weekday(datenum('12-21-2012'), 'long', 'local')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

Random

Description

random functions

rand - Random Number.
randn - Normally distributed random number.
randperm - Random permutation of integers values.
rng - Random Number Generator.

rand

Random Number.

Syntax

M = rand
M = rand(n)
M = rand(x1, x2, ... , xN)
M = rand(sz)
M = rand(x1, x2, ... , xN, classname)
M = rand(x1, x2, ... , xN, 'like', var)

Input argument

n - a variable: n-by-n matrix will be generated.
x1, x2, ... , xN - x1-by-...-by-xN values
classname - a string: 'single' or 'double'
var - a variable: single or double

Output argument

M - a matrix of random numbers.

Description

rand returns a matrix with random elements uniformly distributed on the interval [0, 1].

seed can be modified using rng.

The Mersenne Twister designers consider 5489 as default seed. Nelson uses it as default seed (0).

Bibliography

M. Matsumoto and T. Nishimura, Mersenne Twister: A 623-dimensionally equidistributed uniform pseudorandom number generator, ACM Trans. on Modeling and Computer Simulation Vol. 8, No. 1, pp. 3–30, January 1998

Examples

rng('default');
rand
rng('default');
rand

rng('default');
rand(6)

rng('default');
rand(3, 2, 3)

rng('default');
rand(3, 2, 'single')

rng('default');
v = single([3, 3]);
rand(3, 2, 'like', v)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

randn

Normally distributed random number.

Syntax

M = randn
M = randn(n)
M = randn(x1, x2, ... , xN)
M = randn(sz)
M = randn(x1, x2, ... , xN, classname)
M = randn(x1, x2, ... , xN, 'like', var)

Input argument

n - a variable: n-by-n matrix will be generated.
x1, x2, ... , xN - x1-by-...-by-xN values
classname - a string: 'single' or 'double'
var - a variable: single or double

Output argument

M - a matrix of random numbers.

Description

randn returns a matrix with normally distributed random elements having zero mean and variance one.

By default, randn uses the ziggurat algorithm implemented by Boost.

seed can be modified using rng.

Examples

rng('default');
randn
rng('default');
randn

rng('default');
randn(6)

rng('default');
randn(3, 2, 3)

rng('default');
randn(3, 2, 'single')

rng('default');
v = single([3, 3]);
randn(3, 2, 'like', v)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

randperm

Random permutation of integers values.

Syntax

p = randperm(n)

Input argument

n - Number of integers in sample interval (positive integer).

Output argument

p - a row vector.

Description

p = randperm(n) returns a row vector containing a random permutation of 1:n.

Example

randperm(7)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

rng

Random Number Generator.

Syntax

lst = rng('enginelist')
rng('default')
s = rng('default')
rng('shuffle')
s = rng('shuffle')
rng(seed)
s = rng(seed)
rng(seed, generator)
s = rng(seed, generator)
rng('shuffle', generator)
s = rng('shuffle', generator)
s = rng
rng(s)

Input argument

seed - an integer value: new seed for random generator
generator - a string: 'twister', 'twister64', 'laggedfibonacci607'
s - a struct

Output argument

lst - a cell of strings.
s - a struct

Description

lst = rng('enginelist') returns the list of available random number generator.

rng('default') puts the settings of the random number generator to default values.

s = rng('default') puts the settings of the random number generator to default values.

rng('shuffle') puts the settings of the random number generator to default values and returns previous generator as an struct.

s = rng('shuffle') seeds the random number generator based on the current time.

rng(seed) seeds the random number generator using the nonnegative integer.

s = rng(seed) seeds the random number generator using the nonnegative integer and returns previous generator as an struct.

rng(seed, generator) seeds the random number generator using the nonnegative integer and specify also the type of generator used.

s = rng(seed, generator) seeds the random number generator using the nonnegative integer and specify also the type of generator used and returns previous generator as an struct.

rng('shuffle', generator) seeds the random number generator based on the current time and specify also the type of generator used.

s = rng('shuffle', generator) seeds the random number generator based on the current time,specify also the type of generator used and returns previous generator as an struct.

s = rng returns current generator as an struct.

rng(s) restores the settings of the random number generator using a previous struct returned by s = rng.

Example

rng('default');
r = rng()
lst = rng('enginelist')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

Message Passing Interface

Description

In the world of parallel computing the Message Passing Interface (MPI) is the de facto standard for implementing programs on multiple processors.

MPI_Allreduce - Combines values from all processes and distributes the result back to all processes.
MPI_Barrier - Blocks until all processes in the communicator have reached this routine.
MPI_Bcast - Broadcasts a message from the process with rank "root" to all other processes of the communicator
MPI_Comm_delete - Removes MPI_Comm object.
MPI_Comm_get_name - Return the print name from the communicator.
MPI_Comm_object - Creates MPI_Comm object.
MPI_Comm_rank - Determines the rank of the calling process in the communicator.
MPI_Comm_size - Determines the size of the group associated with a communicator.
MPI_Comm_split - Partitions the group that is associated with the specified communicator into a specified number of disjoint subgroups.
MPI_Comm_used - Returns list of current used MPI_Comm handle.
MPI_Finalize - Terminate the MPI execution environment.
MPI_Get_library_version - Return the version number of MPI library.
MPI_Get_processor_name - Gets the name of the processor.
MPI_Get_version - Return the version number of MPI.
MPI_Init - Initialize the MPI execution environment.
MPI_Initialized - Indicates whether MPI_Init has been called.
MPI_Iprobe - Nonblocking test for a message.
MPI_Probe - Blocking test for a message.
MPI_Recv - Blocking receive for a message.
MPI_Reduce - Reduces values on all processes to a single value.
MPI_Send - Performs a blocking send.
MPI examples - Some Nelson MPI examples.
MPI overview - Access to MPI features from Nelson.
mpiexec - Run an MPI script.

MPI_Allreduce

Combines values from all processes and distributes the result back to all processes.

Syntax

r = MPI_Allreduce(Value, Operation, Comm)

Input argument

Value - value to send: numeric or logical array (sparse not supported).
Operation - a string: MPI_SUM, MPI_MAX, MPI_MIN, MPI_SUM, MPI_PROD, MPI_LAND, MPI_LOR, MPI_BAND, MPI_BOR, MPI_LXOR or MPI_BXOR
Comm - a MPI_Comm object.

Output argument

r - received value

Description

Combines values from all processes and distributes the result back to all processes.

Nelson does not check to ensure that the reduction operation are all the same size across the various processes in the group.

Please be sure that each process passes the same sized array to the MPI_Allreduce operation.

Example

mpiexec([modulepath('mpi'), '/examples/help_examples/MPI_Allreduce.m'], 4)

if ~MPI_Initialized()
  MPI_Init();
end
comm = MPI_Comm_object();
my_rank = MPI_Comm_rank ();
num_ranks = MPI_Comm_size();

A = [1 + my_rank:3 + my_rank]
B = MPI_Allreduce(A, 'MPI_PROD', comm);
if (my_rank == 0)
  disp('Result:')
  disp(B);
end
if MPI_Initialized()
  MPI_Finalize();
end

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

MPI_Barrier

Blocks until all processes in the communicator have reached this routine.

Syntax

r = MPI_Barrier(Comm)

Input argument

Comm - a MPI_Comm object.

Output argument

r - integer value: MPI_SUCCESS (0) or MPI_ERR_COMM (5).

Description

This function is used as a synchronization point for all processes in a group. All processes are blocked until every process calls MPI_Barrier.

Example

mpiexec([modulepath('mpi'), '/examples/help_examples/MPI_Barrier.m'], 4)

if ~MPI_Initialized()
  MPI_Init();
end
my_rank = MPI_Comm_rank ();
num_ranks = MPI_Comm_size();
comm = MPI_Comm_object('MPI_COMM_WORLD');
sleep(my_rank);
MPI_Barrier(comm);
disp(['I am ', int2str(my_rank), ' of ', int2str(num_ranks)]);
if MPI_Initialized()
  MPI_Finalize();
end

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

MPI_Bcast

Broadcasts a message from the process with rank "root" to all other processes of the communicator

Syntax

A = MPI_Bcast(A, Root)
A = MPI_Bcast(A, Root, Comm)

Input argument

A - a nelson variable.
Root - a integer value: rank of broadcast root.
Comm - a MPI_Comm object.

Output argument

A - broadcasted array.

Description

This function is used to broadcast an array to all group members.

Example

mpiexec([modulepath('mpi'), '/examples/help_examples/MPI_Bcast.m'], 4)

if ~MPI_Initialized()
  MPI_Init();
end
my_rank = MPI_Comm_rank();
num_ranks = MPI_Comm_size();
root = 0;
if (my_rank == 0)
  buff = 777;
else
  buff = 0;
end
disp(['rank: ', int2str(my_rank), ': before Bcast, buff is ', int2str(buff)])
buff = MPI_Bcast(buff, root);
disp(['rank: ', int2str(my_rank), ': after Bcast, buff is ', int2str(buff)])
if MPI_Initialized()
  MPI_Finalize();
end

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

MPI_Comm_delete

Removes MPI_Comm object.

Syntax

MPI_Comm_delete(h)
delete(h)

Input argument

h - a handle: a MPI_Comm object.

Description

delete(h) deletes MPI_Comm object itself.

Do not forget to clear variable afterward.

Example

CLI required

if ~MPI_Initialized()
  MPI_Init();
end
comm = MPI_Comm_object();
MPI_Comm_used
delete(COM_used())
MPI_Comm_used
if MPI_Initialized()
  MPI_Finalize();
end

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

MPI_Comm_get_name

Return the print name from the communicator.

Syntax

MPI_Comm_get_name(comm)

Input argument

comm - a handle: a MPI_Comm object.

Description

MPI_Comm_get_name(comm) returns the print name from the communicator.

Example

CLI required

if ~MPI_Initialized()
  MPI_Init();
end
comm = MPI_Comm_object();
MPI_Comm_get_name(comm)
delete(comm)
if MPI_Initialized()
  MPI_Finalize();
end

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

MPI_Comm_object

Creates MPI_Comm object.

Syntax

comm = MPI_Comm_object()
comm = MPI_Comm_object(str)

Input argument

str - a string: MPI_COMM_SELF, or MPI_COMM_WORLD.

Description

MPI_Comm_object(h) creates an MPI_Comm object.

Example

CLI required

if ~MPI_Initialized()
  MPI_Init();
end
comm = MPI_Comm_object();
MPI_Comm_used
delete(MPI_Comm_used())
MPI_Comm_used
if MPI_Initialized()
  MPI_Finalize();
end

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

MPI_Comm_rank

Determines the rank of the calling process in the communicator.

Syntax

r = MPI_Comm_rank(Comm)

Input argument

Comm - a MPI_Comm object.

Output argument

r - an integer value: rank of the calling process in the group of Comm.

Description

Return the rank of the calling process in the specified communicator.

Example

mpiexec([modulepath('mpi'), '/examples/MPI_helloworld.m'], 4)

if ~MPI_Initialized()
  MPI_Init();
end
comm = MPI_Comm_object()
my_rank = MPI_Comm_rank (comm)
num_ranks = MPI_Comm_size(comm)

TAG= 1;
if (my_rank != 0)
  rankvect = 0;
  MPI_Send(rand(3,3) + my_rank, rankvect, TAG, comm);
else
  disp('MPI master receive:')
  for source = 1:num_ranks - 1
    disp(['From slave ', int2str(source)])
    message = MPI_Recv (source, TAG, comm);
    disp(message)
  end
end

if MPI_Initialized()
  MPI_Finalize();
end

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

MPI_Comm_size

Determines the size of the group associated with a communicator.

Syntax

r = MPI_Comm_size(Comm)

Input argument

Comm - a MPI_Comm object.

Output argument

r - an integer value: number of processes in the group of Comm.

Description

Determines the size of the group associated with a communicator.

Example

mpiexec([modulepath('mpi'), '/examples/MPI_helloworld.m'], 4)

if ~MPI_Initialized()
  MPI_Init();
end
comm = MPI_Comm_object()
my_rank = MPI_Comm_rank (comm)
num_ranks = MPI_Comm_size(comm)

TAG= 1;
if (my_rank != 0)
  rankvect = 0;
  MPI_Send(rand(3,3) + my_rank, rankvect, TAG, comm);
else
  disp('MPI master receive:')
  for source = 1:num_ranks - 1
    disp(['From slave ', int2str(source)])
    message = MPI_Recv (source, TAG, comm);
    disp(message)
  end
end

if MPI_Initialized()
  MPI_Finalize();
end

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

MPI_Comm_split

Partitions the group that is associated with the specified communicator into a specified number of disjoint subgroups.

Syntax

newcomm = MPI_Comm_split(comm, color, key)

Input argument

comm - a MPI_Comm object.
color - an integer value: The new communicator that the calling process is to be assigned to. The value of color must be non-negative.
key - an integer value: The relative rank of the calling process in the group of the new communicator.

Output argument

newcomm - MPI_Comm object: handle to a new communicator.

Description

Partitions the group that is associated with the specified communicator into a specified number of disjoint subgroups.

Example

mpiexec([modulepath('mpi'), '/examples/help_examples/MPI_Comm_split.m'], 10)

if ~MPI_Initialized()
  MPI_Init();
end
comm = MPI_Comm_object();
world_rank = MPI_Comm_rank();
world_size = MPI_Comm_size();

color = world_rank * inv(4);

% Split the communicator based on the color and use the
% original rank for ordering
row_comm = MPI_Comm_split(comm, color, world_rank);

row_rank = MPI_Comm_rank();
row_size = MPI_Comm_size();

disp(['WORLD RANK/SIZE: ',int2str(world_rank), '/', int2str(world_size), ' ROW RANK/SIZE: ', int2str(row_rank), '/', int2str(row_size)]);
if MPI_Initialized()
  MPI_Finalize();
end

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

MPI_Comm_used

Returns list of current used MPI_Comm handle.

Syntax

r = MPI_Comm_used()

Output argument

h - a vector of MPI_Comm handle.

Description

Returns list of current used MPI_Comm handle.

Example

CLI required

if ~MPI_Initialized()
  MPI_Init();
end
comm = MPI_Comm_object();
MPI_Comm_used
delete(comm)
MPI_Comm_used
if MPI_Initialized()
  MPI_Finalize();
end

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

MPI_Finalize

Terminate the MPI execution environment.

Syntax

MPI_Finalize()
r = MPI_Finalize()

Output argument

r - a logical.

Description

Terminate the MPI execution environment.

MPI process are launched in CLI mode (no gui, no plot).

Example

if ~MPI_Initialized()
  MPI_Init();
end
if MPI_Initialized()
  MPI_Finalize();
end

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

MPI_Get_library_version

Return the version number of MPI library.

Syntax

name = MPI_Get_library_version()

Output argument

name - a string: Version of MPI.

Description

This function returns the version number of MPI library.

Example

if ~MPI_Initialized()
  MPI_Init();
end
name = MPI_Get_library_version()
if MPI_Initialized()
  MPI_Finalize();
end

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

MPI_Get_processor_name

Gets the name of the processor.

Syntax

[name, namelen, info] = MPI_Get_processor_name()

Output argument

name - a string: name of the processor that is using MPI.
namelen - an integer value: Length (in characters) of the name.
info - an integer value: 0 MPI_SUCCESS, 16 MPI_ERR_OTHER.

Description

This function get the name of the processor that is using MPI.

Example

if ~MPI_Initialized()
  MPI_Init();
end
[name, len, info] = MPI_Get_processor_name()
if MPI_Initialized()
  MPI_Finalize();
end

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

MPI_Get_version

Return the version number of MPI.

Syntax

[major, minor] = MPI_Get_version()

Output argument

major - an integer value.
minor - an integer value.

Description

Return the version number of MPI.

Example

if ~MPI_Initialized()
  MPI_Init();
end
[major, minor] = MPI_Get_version()
if MPI_Initialized()
  MPI_Finalize();
end

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

MPI_Init

Initialize the MPI execution environment.

Syntax

MPI_Init()
r = MPI_Init()

Output argument

r - a logical.

Description

Initialize the MPI execution environment.

MPI process are launched in CLI mode (no gui, no plot).

Example

if ~MPI_Initialized()
  MPI_Init();
end
if MPI_Initialized()
  MPI_Finalize();
end

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

MPI_Initialized

Indicates whether MPI_Init has been called.

Syntax

r = MPI_Initialized()

Output argument

r - a logical.

Description

Indicates whether MPI_Init has been called.

Example

if ~MPI_Initialized()
  MPI_Init();
end
if MPI_Initialized()
  MPI_Finalize();
end

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

MPI_Iprobe

Nonblocking test for a message.

Syntax

[flag, stat, info] = MPI_Iprobe(rank, tag)
[flag, stat, info] = MPI_Iprobe(rank, tag, comm)

Input argument

rank - an integer value: source rank.
tag - an integer value: message tag.
comm - a MPI_Comm object.

Output argument

flag - an integer value: 1 if the message is ready to be received, 0 if it is not.
stat - a struct: source rank, message tag, error, count, cancelled for the accepted message.
info - an integer value: 0 (MPI_SUCCESS) other value is an error.

Description

Nonblocking test for a message.

Example

mpiexec([modulepath('mpi'), '/examples/help_examples/MPI_Iprobe.m'], 4)

if ~MPI_Initialized()
  MPI_Init();
end
comm = MPI_Comm_object();
world_rank = MPI_Comm_rank();
world_size = MPI_Comm_size();

[FLAG, STAT, INFO] = MPI_Iprobe(world_rank,1, comm)

if MPI_Initialized()
  MPI_Finalize();
end

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

MPI_Probe

Blocking test for a message.

Syntax

[flag, stat, info] = MPI_Probe(rank, tag)
[flag, stat, info] = MPI_Probe(rank, tag, comm)

Input argument

rank - an integer value: source rank.
tag - an integer value: message tag.
comm - a MPI_Comm object.

Output argument

flag - an integer value: 1 if the message is ready to be received, 0 if it is not.
stat - a struct: source rank, message tag, error, count, cancelled for the accepted message.
info - an integer value: 0 (MPI_SUCCESS) other value is an error.

Description

Blocking test for a message.

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

MPI_Recv

Blocking receive for a message.

Syntax

r = MPI_Recv(Source, Tag)
[r, mpi_source, mpi_tag] = MPI_Reduce(Source, Tag, Comm)

Input argument

Source - an integer value: rank of source.
Tag - an integer value: message tag.
Comm - a MPI_Comm object.

Output argument

r - received value

Description

This function receives an array from a source node on a given communicator with the specified tag.

Throws an exception if there is an error.

Receive arrays of arbitrary complexity, including cell arrays, structures, strings, sparse, etc ...

Example

mpiexec([modulepath('mpi'), '/examples/MPI_helloworld.m'], 4)

if ~MPI_Initialized()
  MPI_Init();
end
comm = MPI_Comm_object()
my_rank = MPI_Comm_rank (comm)
num_ranks = MPI_Comm_size(comm)

TAG= 1;
if (my_rank != 0)
  rankvect = 0;
  MPI_Send(rand(3,3) + my_rank, rankvect, TAG, comm);
else
  disp('MPI master receive:')
  for source = 1:num_ranks - 1
    disp(['From slave ', int2str(source)])
    message = MPI_Recv (source, TAG, comm);
    disp(message)
  end
end

if MPI_Initialized()
  MPI_Finalize();
end

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

MPI_Reduce

Reduces values on all processes to a single value.

Syntax

r = MPI_Reduce(Value, Operation, Root)
r = MPI_Reduce(Value, Operation, Root, Comm)

Input argument

Value - value to send: numeric or logical array (sparse not supported).
Operation - a string: MPI_SUM, MPI_MAX, MPI_MIN, MPI_SUM, MPI_PROD, MPI_LAND, MPI_LOR, MPI_BAND, MPI_BOR, MPI_LXOR or MPI_BXOR
Root - a integer value: rank of root process.
Comm - a MPI_Comm object.

Output argument

r - received value

Description

Reduces values on all processes to a single value.

Nelson does not check to ensure that the reduction operation are all the same size across the various processes in the group.

Please be sure that each process passes the same sized array to the MPI_Allreduce operation.

Example

mpiexec([modulepath('mpi'), '/examples/help_examples/MPI_Reduce.m'], 4)

if ~MPI_Initialized()
  MPI_Init();
end
my_rank = MPI_Comm_rank ();
num_ranks = MPI_Comm_size();

A = [1 + my_rank:3 + my_rank]
B = MPI_Reduce(A, 'MPI_SUM', 0);
if (my_rank == 0)
  disp('Result:')
  B
end
if MPI_Initialized()
  MPI_Finalize();
end

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

MPI_Send

Performs a blocking send.

Syntax

MPI_Send(A, destination, tag)
MPI_Send(A, destination, tag, comm)

Input argument

A - an nelson array to send.
destination - an integer value: rank of source.
tag - an integer value: message tag.
comm - a MPI_Comm object.

Description

This function sends an array to a destination node on a given communicator with a specific message tag.

Note that there has to be a matching receive issued by the destination node.

Throws an exception if there is an error.

Example

mpiexec([modulepath('mpi'), '/examples/MPI_helloworld.m'], 4)

if ~MPI_Initialized()
  MPI_Init();
end
comm = MPI_Comm_object()
my_rank = MPI_Comm_rank (comm)
num_ranks = MPI_Comm_size(comm)

TAG= 1;
if (my_rank != 0)
  rankvect = 0;
  MPI_Send(rand(3,3) + my_rank, rankvect, TAG, comm);
else
  disp('MPI master receive:')
  for source = 1:num_ranks - 1
    disp(['From slave ', int2str(source)])
    message = MPI_Recv (source, TAG, comm);
    disp(message)
  end
end

if MPI_Initialized()
  MPI_Finalize();
end

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

MPI examples

Some Nelson MPI examples.

Description

See below for some basic examples about MPI interfaces available in Nelson.

Examples

mpiexec([modulepath('mpi'), '/examples/MPI_helloworld.m'], 4)

edit([modulepath('mpi'), '/examples/MPI_helloworld.m'])

mpiexec([modulepath('mpi'), '/examples/MPI_simpledemo.m'], 4)

edit([modulepath('mpi'), '/examples/MPI_simpledemo.m'])

mpiexec([modulepath('mpi'), '/examples/MPI_parallel_sum.m'], 40)

edit([modulepath('mpi'), '/examples/MPI_parallel_sum.m'])

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

MPI overview

Access to MPI features from Nelson.

Description

As many others MPI applications, MPI/Nelson as be started through the mpiexec/mpirun command.

MPI features are only avaible in CLI mode. But you can call in others mode with mpiexec builtin.

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

mpiexec

Run an MPI script.

Syntax

mpiexec(script)
mpiexec(script, nb_process)
r = mpiexec(script, nb_process)
[r, msg] = mpiexec(script, nb_process)

Input argument

script - an filename with .m extension.
nb_process - an integer value: number of process.

Output argument

r - an integer value: maximum of the exit status values of all of the processes created by mpiexec.

Description

Run an MPI script in nelson.

MPI process are launched in CLI mode (no gui, no plot).

Example

mpiexec([modulepath('mpi'), '/examples/help_examples/MPI_Allreduce.m'], 4)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

Parallel

Description

parallel functions

afterAll - Run function after all functions finish running in the background.
afterEach - Run function after each function finish running in the background.
backgroundPool - Environment for running nelson's code in the background.
cancel - Stop function running in the background.
cancelAll - Stop all functions running in the background.
fetchNext - Retrieve next unread outputs from FevalFuture array.
fetchOutputs - Retrieve results from function running in the background pool.
parfeval - Run function in background.
wait - Wait for futures to be completed.

afterAll

Run function after all functions finish running in the background.

Syntax

B = afterAll(F, fcn, n)

Input argument

F - Input Future object (scalar or array).
fcn - Function handle: Function to run after all input futures.
n - Number of output arguments.

Output argument

B - AfterAllFuture object.

Description

B = afterAll(F, fcn, n) returns a AfterAllFuture object B.

Function fcn is automatically runned after all elements in the Future array F were finished.

If any of the elements in F encounters an error, the Error property of B contains an error.

Example

pool = backgroundPool()
fptrRand = str2func('rand')
fptrMax = str2func('@(r) max(r)')
fptrMin = str2func('@(r) min(r)')
for idx= 1:10
    f(idx) = parfeval(pool, fptrRand, 1, 1000, 1);
end
maxFuture = afterEach(f, fptrMax, 1);
minFuture = afterAll(maxFuture, fptrMin, 1);
fetchOutputs(minFuture)
fetchOutputs(maxFuture)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

afterEach

Run function after each function finish running in the background.

Syntax

B = afterEach(F, fcn, n)

Input argument

F - Input Future object (scalar or array).
fcn - Function handle: Function to run after all input futures.
n - Number of output arguments.

Output argument

B - AfterEachFuture object.

Description

B = afterEach(F, fcn, n) returns a AfterEachFuture object B.

Function fcn is automatically runned after each element in the Future array F was finished.

If any of the elements in F encounters an error, the Error property of B contains an error.

Example

pool = backgroundPool()
fptrRand = str2func('rand')
fptrMax = str2func('@(r) max(r)')
fptrMin = str2func('@(r) min(r)')
for idx= 1:10
    f(idx) = parfeval(pool, fptrRand, 1, 1000, 1);
end
maxFuture = afterEach(f, fptrMax, 1);
minFuture = afterAll(maxFuture, fptrMin, 1);
fetchOutputs(minFuture)
fetchOutputs(maxFuture)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

backgroundPool

Environment for running nelson's code in the background.

Syntax

pool = backgroundPool()

Output argument

pool - backgroundPool object.

Description

pool = backgroundPool() returns the background pool.

This allows to run other code in your Nelson's session at the same time.

Properties of backgroundPool object:

'FevalQueue': Queue of FevalFuture objects to run on the background pool (read only).

'NumWorkers': Number of workers (read only).

'Busy': Flag that indicates whether the background pool is busy, logical (read only).

Example

b = backgroundPool()
fptr = str2func('magic');
f = parfeval(b, fptr, 1, 9);

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

cancel

Stop function running in the background.

Syntax

cancel(f)

Input argument

f - FevalFuture object: scalar or array.

Description

cancel(f) will stop each running or queued element of the Future array f.

Future cancelled Findicates an error as property.

Some functions cannot be interrupted by pressing Ctrl+C or cancel, such as save function.

Example

fptr = str2func('pause');
for i = 1:100
 f(i) = parfeval(backgroundPool, fptr, 0, 5);
end
f(70)
cancel(f(70))
f(70)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

cancelAll

Stop all functions running in the background.

Syntax

cancel(fevalQueue)

Input argument

fevalQueue - FevalQueue object: scalar.

Description

cancelAll(fevalQueue) stops all running or queued elements of the background pool.

Example

fptr = str2func('pause');
pool = backgroundPool;
pool.FevalQueue
f = parfeval(pool, fptr, 0, Inf);
f
pool.FevalQueue
cancelAll(pool.FevalQueue)
pool.FevalQueue
f

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

fetchNext

Retrieve next unread outputs from FevalFuture array.

Syntax

[idx, y1, ... , ym] = fetchNext(f)
[idx, y1, ... , ym] = fetchNext(f, timeout)

Input argument

f - FevalFuture object
timeout - timeout seconds: waits for a maximum of timeout seconds for a result in f to become available.

Output argument

idx - Index of the FevalFuture array, returned as an integer scalar.
y1, ... , ym - outputs

Description

[idx, y1, ... , ym] = fetchNext(f) retrieves index idx of the new readable FevalFuture object in the array f that is finished, and m results from that FevalFuture as Y1, ... , Ym.

Example

tic()
N = 100;
for idx = N:-1:1
    F(idx) = parfeval(backgroundPool,str2func('rank'),1,magic(idx));
end
results = zeros(1,N);
for idx = 1:N
    [finishedIdx, result] = fetchNext(F);
    results(finishedIdx) = result;
    disp(sprintf('Result: %d', result));
end
toc()

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

fetchOutputs

Retrieve results from function running in the background pool.

Syntax

[y1, ... , ym] = fetchOutputs(f)

Input argument

f - FevalFuture object

Output argument

y1, ... , ym - outputs

Description

[y1, ... , ym] = fetchOutputs(f) retrieves m results from a Future array f.

fetchOutputs waits for the function associated to f to finish before retrieving results.

If fetchOutputs is called, Read property of each element in f is set to true.

Examples

Sequential version

tic()
R1 = magic(5000);
R2 = magic(5000);
toc()
size(R1)

Parallel version

b = backgroundPool()
tic()
fptr = str2func('magic');
f1 = parfeval(b, fptr, 1, 5000);
f2 = parfeval(b, fptr, 1, 5000);
b
r1 = fetchOutputs(f1);
r2 = fetchOutputs(f2);
toc()
size(r1)
f1
f2

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

parfeval

Run function in background.

Syntax

f = parfeval(bPool, fptr, n, x1, ..., xm)

Input argument

bPool - backgroundPool object returned by backgroundPool().
fptr - Function handle: Function to run.
n - Number of output arguments.
x1, ..., xm - Input arguments, specified as a comma-separated list of variables or expressions.

Output argument

f - FevalFuture object.

Description

f = parfeval(bPool, fptr, n, x1, ..., xm) starts the function fptr to run in the background.

backgroundPool has NumWorkers available. If there are more functions scheduled, functions wait than one entry is available in pool.

parfeval runs the function fptr on a background worker.

Example

b = backgroundPool()
fptr = str2func('cos');
f = parfeval(b, fptr, 1, 5);
r = fetchOutputs(f)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

wait

Wait for futures to be completed.

Syntax

wait(f)
wait(f, state)
TF = wait(f, state, timeout)

Input argument

f - FevalFuture object: scalar or array.
state - state to wait: 'finished' (default) or 'running'
timeout - seconds to wait: real numeric scalar.

Output argument

TF - logical: If each element of the Future array f finishes before timeout seconds elapse, TF is true. Otherwise, TF is false.

Description

wait(f) pauses execution until each element of the Future array f is finished.

wait(f, state) pauses execution until each element of the Future array f has its 'State' property set to state.

tf = wait(f, state, timeout) pauses execution for a maximum of timeout seconds.

Example

fptr = str2func('pause');
for i = 1:15
 f(i) = parfeval(backgroundPool, fptr, 0, 5);
end
tic()
R = wait(f, 'finished');
toc()

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

Help tools functions

Description

help tools

buildhelp - Build help of Nelson's modules.
buildhelpmd - Build help of Nelson's modules for GitBook.
buildhelpweb - Build help of Nelson's modules for website.
docroot - Retrieve or update the root directory for Nelson Help system.
headcomments - Display Nelson function header comments.
htmltopdf - Convers html page to pdf.
markdown - Converts markdown to html.
xmldocbuild - Internal function to convert xml document files to html.
xmldocchecker - Checks a xml documentation file.
xmldoctohelp - Converts xml Nelson help files to Nelson format.
xmldoctohtml - Converts xml Nelson help files to html.
xmldoctomd - Converts xml Nelson help files to markdown format.

buildhelp

Build help of Nelson's modules.

Syntax

buildhelp()
buildhelp(module_name)

Input argument

module_name - a string: module name (module must be loaded).

Description

buildhelp generates help files.

Example

buildhelp();
buildhelp('core');

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

buildhelpmd

Build help of Nelson's modules for GitBook.

Syntax

buildhelpmd(dirdest)
buildhelpmd(dirdest, module_name)

Input argument

dirdest - a string: a path destination.
module_name - a string: module name (module must be loaded).

Description

buildhelpmd generates help files for GitBook (markdown).

Example

buildhelpmd(tempdir());
buildhelpmd(tempdir(), 'core');

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

buildhelpweb

Build help of Nelson's modules for website.

Syntax

buildhelpweb(destination_dir)
buildhelpweb(destination_dir, language)

Input argument

destination_dir - a string: destination directory.
language - a string: language. if it is missing, current default language used.

Description

buildhelpweb generates help files for website.

internal function

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

docroot

Retrieve or update the root directory for Nelson Help system.

Syntax

r = docroot()
r = docroot(new_docroot)

Input argument

new_docroot - a string: '', '.', or a URL.

Description

docroot retrieves or updates the root directory for Nelson Help.

When called without an argument, docroot returns the current root directory for Nelson Help. By default, it returns the URL of the help website used by Nelson.

When called with an argument, docroot updates the root directory for Nelson Help.

docroot('') resets the root directory for Nelson Help to the default value.

docroot('.') uses local help files and the local browser (restores behavior before v1.11.0).

Example

docroot()
doc rand
docroot('.')
doc rand
docroot('')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

headcomments

Display Nelson function header comments.

Syntax

headcomments(function_name)
ce = headcomments(function_name)

Input argument

function_name - a string: function name or a .m filename.

Output argument

ce - a cell of strings

Description

head_comments displays the function header comments.

Comments are read from the associated .m file.

Nelson predefined functions have no header comments.

Example

comments = headcomments('cellstr'); md = markdown(comments);inserthtml(md)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

htmltopdf

Convers html page to pdf.

Syntax

htmltopdf(html_filename, pdf_filename)

Input argument

html_filename - a string: html filename.
pdf_filename - a string: pdf filename (destination).

Description

htmltopdf converts html page to pdf.

Example

txt = {'## Example of Markdown text';
'>Nelson html to pdf conversion example'};

html = markdown(txt);
f = fopen([tempdir(), 'htmltopdf_example.html'], 'wt');
fwrite(f, html);
fclose(f);

htmltopdf([tempdir(), 'htmltopdf_example.html'], [tempdir(), 'htmltopdf_example.pdf'])
if ispc()
  winopen([tempdir(), 'htmltopdf_example.pdf']);
end

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

markdown

Converts markdown to html.

Syntax

html_txt = markdown(md_txt)
status = markdown(md_filename, html_filename)

Input argument

md_txt - a string: markdown text to convert.
md_filename - a string: markdown filename to convert (source).
html_filename - a string: html filename (destination).

Output argument

status - a logical: html file generated or not.

Description

markdown converts Markdown text-to-HTML.

Example

txt = {'## Example of Markdown text';
'>Nelson supports markdown ...'};
html = markdown(txt);
filewrite([tempdir(), 'markdown_example.html'], html)

if ispc()
  winopen([tempdir(), 'markdown_example.html']);
end

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

xmldocbuild

Internal function to convert xml document files to html.

Syntax

status = xmldocbuild(source_dirs, destination_dir, main_title, export_format, overwrite)

Input argument

source_dirs - a cell of string: list of xml filenames.
destination_dir - a string: directory destination.
main_title - a string: title of main index.
export_format - a string: 'qt' or 'html'.
overwrite - a logical: force overwrite if file destination already exists

Output argument

status - a logical: files generated or not.

Description

xmldocbuild convert xml document files to html.

internal function

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

xmldocchecker

Checks a xml documentation file.

Syntax

xmldocchecker(xmldocfilename)
[errors_detected, warnings_detected] = xmldocchecker(xmldocfilename)

Input argument

xmldocfilename - a string: xml document.

Output argument

errors_detected - a cell of strings: errors detected.
warnings_detected - a cell of strings: warnings detected.

Description

xmldocchecker is a tool to check that a xml document is valid.

Example

xmldocchecker([nelsonroot(),'/module_skeleton/help/en_US/xml/nelson_sum.xml'])

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

xmldoctohelp

Converts xml Nelson help files to Nelson format.

Syntax

status = xmldoctohelp(source_dirs, destination_dir, main_title, overwrite)

Input argument

source_dirs - a cell of string: list of xml filenames.
destination_dir - a string: directory destination.
main_title - a string: title of main index.
overwrite - a logical: force overwrite if file destination already exists

Output argument

status - a logical: files generated or not.

Description

xmldoctohelp converts xml Nelson help files to Nelson format.

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

xmldoctohtml

Converts xml Nelson help files to html.

Syntax

status = xmldoctohtml(source_dirs, destination_dir, main_title, overwrite)

Input argument

source_dirs - a cell of string: list of xml filenames.
destination_dir - a string: directory destination.
main_title - a string: title of main index.
overwrite - a logical: force overwrite if file destination already exists

Output argument

status - a logical: files generated or not.

Description

xmldoctohelp converts xml Nelson help files to html.

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

xmldoctomd

Converts xml Nelson help files to markdown format.

Syntax

status = xmldoctomd(source_dirs, destination_dir, main_title, overwrite)

Input argument

source_dirs - a cell of string: list of xml filenames.
destination_dir - a string: directory destination.
main_title - a string: title of main index.
overwrite - a logical: force overwrite if file destination already exists

Output argument

status - a logical: files generated or not.

Description

xmldoctomd converts xml Nelson help files to markdown format.

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

History manager

Description

history functions

history - history manager.

history

history manager.

Syntax

history()
c = history()
s = history('size')
f = history('filename')
l = history('enable_save')
c = history('get')
history('display')
history('save')
history('load')
history('clear')
history('duplicated')
history('saveafter')
history('removeexit')
history('size', new_size)
history('enable_save', true_false)
history('delete', lines)
history('append', str)
history('filename', name)
history('load', filename_history)
history('save', filename_history)
history('duplicated', true_false)
history('removeexit', true_false)
history('get', lines)
history('saveafter', nb_commands)

Input argument

new_size - a integer value: new size max of history.
true_false - a logical.
lines - a integer value or a vector of size 1x2.
str - a string.
name - a string: new default history filename
filename_history - a string: filename
nb_commands - a integer value: number of commands.

Output argument

c - a cell of strings.
l - a logical.
s - a integer value.
f - a string.

Description

history() displays the current Nelson history.

c = history() returns the current Nelson history in a cell of strings.

s = history('size') returns history size max.

f = history('filename') returns the history filename.

l = history('enable_save') returns the history manager state.

c = history('get') returns the current Nelson history in a cell of strings.

history('display') displays the current Nelson history.

history('save') saves current history file.

history('load') load current history file.

history('clear') clears history.

history('duplicated') get state about save of consecutive duplicated commands.

history('saveafter') get state about save the history after nth commands.

history('removeexit') get state about do not save exit in history file.

history('size', new_size) set history size max with new_size.

history('enable_save', true_false) set the history manager state: false for 'off', true for 'on'.

history('delete', lines) deletes lines by index: a scalar value or a vector 1x2.

history('append', str) append command to history.

history('filename', name) set the history filename.

history('load', filename_history) load history file.

history('save', filename_history) save history file

history('duplicated', true_false) set state about consecutive duplicated commands. true remove duplicated.

history('removeexit', true_false) set state about do not save exit in history file.

history('get', lines)returns the current Nelson history in a cell of strings by index: a scalar value or a vector 1x2.

history('saveafter', nb_commands) saves the history file after nb_commands statements are added to the file.

Tips: You can easily share your history file in the cloud by adding few lines code in your user startup file.

If nelson launched with '--nouserstartup' option, history file will be not loaded at startup and not saved at exit.

Examples

Example to share your history file in OneDrive cloud

OneDrivePath = getenv('OneDrive');
if (strcmp(OneDrivePath, '') == false)
  NelsonOneDrivePath = [OneDrivePath, '/Nelson'];
  mkdir(NelsonOneDrivePath);
  NelsonOneDrivePathFilename = [NelsonOneDrivePath, '/', 'Nelson.history'];
 history('filename', NelsonOneDrivePathFilename);
  history('load', NelsonOneDrivePathFilename);
end

history()
c = history()

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

Console

Description

Console

clc - Clear Command Window.
input - Display prompt and wait for user input.
terminal_size - Query the size of the terminal window.

clc

Clear Command Window.

Syntax

clc()

Description

clc() clears the console and move the cursor to the upper left corner.

Example

disp('Hello');
clc()

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

input

Display prompt and wait for user input.

Syntax

r = input(prompt_str)
r = input(prompt_str, 's')

Input argument

prompt_str - a string: temp. prompt displayed

Output argument

r - a string

Description

Display prompt and wait for user input. input returns a string which is the expression entered at keyboard.

Example

res = input('Please input a value ', 's');
r = execstr(['A = ', res, ';'], 'errcatch');
if (r)
  disp('It was a value.');
  disp(A)
else
 disp('It was NOT a value.');
end

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

terminal_size

Query the size of the terminal window.

Syntax

[r, c] = terminal_size()

Output argument

[r, c] - a vector: rows and columns

Description

terminal_size() returns a vector with size of the terminal window in characters (rows and columns).

Example

terminal_size()

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

Gui module

Description

functions about gui

commandhistory - Command History
errordlg - Creates a error dialog box.
filebrowser - Current Folder Browser
helpdlg - Creates a help dialog box.
inserthtml - Insert html in GUI console.
lookandfeel - default current application look and feel.
msgbox - Creates a message dialog box.
qt_verbose - show/hide Qt debug message.
questdlg - Creates a question dialog box.
uigetdir - Opens dialog box to select a directory.
helpdlg - Creates a warning dialog box.
workspace - Workspace Browser

commandhistory

Command History

Syntax

commandhistory

Description

The Command History window presents a record of statements executed in both the current and past Nelson sessions.

Each session is timestamped with the short date format of your operating system, followed by the corresponding statements.

Entries within the Command History window can be selected for various actions and operations.

History

Version	Description
1.1.0	initial version

Author

Allan CORNET

errordlg

Creates a error dialog box.

Syntax

h = errordlg()
h = errordlg(text_error)
h = errordlg(text_error, title)
h = errordlg(text_error, title, mode)

Input argument

text_error - a string or a cell of string: the error message.
title - a string: the title of the dialog box.
mode - a string: 'mode', 'non-modal', 'replace'.

Output argument

h - a QObject handle.

Description

errordlg creates an error dialog box.

h = errordlg(text_error, title, 'replace') specifies whether to replace an existing dialog box having the same title.

Examples

h = errordlg()

h = errordlg('error string')

h = errordlg('error string', 'dialog title')

h = errordlg('error string', 'dialog title')
h = errordlg('error string', 'dialog title', 'on')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

filebrowser

Current Folder Browser

Syntax

filebrowser

Description

The Current Folder browser in Nelson facilitates interactive file and folder management. Utilize it to navigate, create, access, relocate, and rename files and folders within the current directory.

History

Version	Description
1.1.0	initial version

Author

Allan CORNET

helpdlg

Creates a help dialog box.

Syntax

h = helpdlg()
h = helpdlg(text_help)
h = helpdlg(text_help, title)
h = helpdlg(text_help, title, 'on')

Input argument

text_help - a string or a cell of string: the help message.
title - a string: the title of the dialog box.

Output argument

h - a QObject handle.

Description

errordlg creates an help dialog box.

h = helpdlg(text_help, title, 'on') specifies whether to replace an existing dialog box having the same name.

Examples

h = helpdlg()

h = helpdlg('help string')

h = helpdlg('help string', 'dialog title')

h = helpdlg('help string', 'dialog title')
h = helpdlg('help string', 'dialog title', 'on')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

inserthtml

Insert html in GUI console.

Syntax

inserthtml(html_txt)

Input argument

html_txt - a string: html text

Description

inserthtml inserts html code in GUI console.

Example

inserthtml(markdown(fileread([nelsonroot(),'/CHANGELOG.md'])))

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

lookandfeel

default current application look and feel.

Syntax

r = lookandfeel()
ce = lookandfeel('available')
p = lookandfeel(lf)
ss = lookandfeel('stylesheet')
pp = lookandfeel('stylesheet', ss)

Input argument

lf - a string: look and feel to apply.
ss - a string: style sheet to apply.

Output argument

r - a string: current look and feel.
ce - a cell of strings: list of look and feel available.
ss - a string: current style sheet applied.
p - a string: previous look and feel applied.
pp - a string: previous style sheet applied.

Description

lookandfeel manages look and feel Nelson application.

Examples

currentlf = lookandfeel();
lfs = lookandfeel('available')
for lf = lfs'
  lookandfeel(lf{1})
  sleep(10);
end
lookandfeel(currentlf)

currentstylesheet = lookandfeel('stylesheet')
stylefilename = [modulepath('gui'), '/resources/darkstyle.qss'];
edit(stylefilename)
newstyle = fileread(stylefilename);
previousstylesheet = lookandfeel('stylesheet', newstyle)
sleep(10);
lookandfeel('stylesheet', previousstylesheet)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

msgbox

Creates a message dialog box.

Syntax

h = msgbox(message)
h = msgbox(message, mode)
h = msgbox(message, title)
h = msgbox(message, title, mode)
h = msgbox(message, title, icon)
h = msgbox(message, title, icon, mode)

Input argument

message - a string or a cell of string: the message to display.
title - a string: the title of the dialog box.
icon - a string: 'none', 'error', 'help', 'warn' or 'question'.
mode - a string: 'modal', 'on' or 'nonmodal'.

Output argument

h - a QObject handle.

Description

msgbox creates an message dialog box.

h = msgbox(message, title, 'on') specifies whether to replace an existing dialog box having the same name.

Examples

h = msgbox('help string')

h = msgbox('help string', 'dialog title')

h = msgbox('help string', 'dialog title')
h = msgbox('help string', 'dialog title', 'on')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

qt_verbose

show/hide Qt debug message.

Syntax

r = qt_verbose()
p = qt_verbose(logical)

Input argument

logical - a logical: true to show messages, false to hide.

Output argument

r - logical: current value
p - logical: previous value

Description

qt_verbose how/hide Qt debug message.

This function is usefull to debug Qt and Qml.

Example

h = qt_verbose()

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

questdlg

Creates a question dialog box.

Syntax

buttonname = questdlg(question)
buttonname = questdlg(question, title)
buttonname = questdlg(question, title, default)
buttonname = questdlg(question, title, text1, default)
buttonname = questdlg(question, title, text1, text2, default)
buttonname = questdlg(question, title, text1, text2, text3, default)

Input argument

question - a string or a cell of string: the question.
title - a string: the title of the dialog box.
text1 - a string: text of button 1.
text2 - a string: text of button 2.
text3 - a string: text of button 3.
default - a string: text of selected button by default.

Output argument

buttonname - a string: text of the clicked button or ''.

Description

questdlg displays a string using a question dialog box and return the caption of the activated button.

The dialog has three default buttons: 'Yes', 'No', 'Cancel' with 'Yes' as default.

Examples

res = questdlg('What is the answer to the ultimate question of life, the universe and everything ?', 'A question for geeks', '41', '42', '43', '42')

res = questdlg ('Easy ?', 'Jeff', 'No', 'Okay', 'Okay')

res = questdlg('How are you ?', 'Health', 'Fine', 'Good', 'sick', 'Fine')

res = questdlg({'Is', 'this', 'a', 'multi line', 'test ?'}, 'Test :)')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

uigetdir

Opens dialog box to select a directory.

Syntax

dir_ans = uigetdir()
dir_ans = uigetdir(path)
dir_ans = uigetdir(path, title)

Input argument

path - a string: initial path
title - a string: title of the dialog box

Output argument

dir_ans - a string (returned path) or 0 if dialogbox is canceled

Description

uigetdir opens a dialog box for selecting a directory.

If path is wrong or not given, the current working directory will be used.

Example

A = uigetdir();

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

helpdlg

Creates a warning dialog box.

Syntax

h = warndlg()
h = warndlg(text_warning)
h = warndlg(text_warning, title)
h = warndlg(text_warning, title, 'on')

Input argument

text_warning - a string or a cell of string: the warning message.
title - a string: the title of the dialog box.

Output argument

h - a QObject handle.

Description

errordlg creates an warning dialog box.

h = warndlg(text_warning, title, 'on') specifies whether to replace an existing dialog box having the same name.

Examples

h = warndlg()

h = warndlg('help string')

h = warndlg('help string', 'dialog title')

h = warndlg('help string', 'dialog title')
h = warndlg('help string', 'dialog title', 'on')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

workspace

Workspace Browser

Syntax

workspace

Description

The Workspace browser allows you to observe and actively oversee the contents of the workspace within Nelson, providing access and control over each variable or object present.

History

Version	Description
1.1.0	initial version

Author

Allan CORNET

QML engine

Description

The QML engine enables nelson programs to display and manipulate graphical content using Qt's QML framework.

QObject_classname - Returns class name of an QObject handle.
QObject_findchildren - Returns all children of this object with the given name.
QObject_get - Retrieve a property value from an QObject handle.
QObject_iswidgettype - Returns true if the QObject is a widget.
QObject_iswindowtype - Returns true if the QObject is a window.
QObject_methodsignature - Returns the signature of a method of a QObject handle.
QObject_root - QObject root object.
QObject_set - Set a property value of an QObject handle (set).
QObject_undefine - Undefine a dynamic property of a QObject handle.
QObject_used - Returns list of current used QObject handle.
nelsonObject - nelson object callable from QML.
qml_addimportpath - Adds path as directory where the qml engine searches for installed modules.
qml_addpluginpath - Adds path as directory where the qml engine searches for native plugins.
qml_clearcomponentcache - Clears the engine's internal component cache..
qml_collectgarbage - Runs the Qml garbage collector.
qml_createqquickview - Load a QML file and creates a window.
qml_demos - QML demos.
qml_evaluatefile - Evaluates a js file.
qml_evaluatestring - Evaluates a js string.
qml_importpathlist - Returns the list of directories where the engine searches for installed modules in a URL-based directory structure.
qml_loadfile - Load a QML file.
qml_loadstring - Load a QML string.
qml_offlinestoragepath - Get the Property contains the directory to store offline user data.
qml_pluginpathlist - Returns the list of directories where the engine searches for native plugins for imported modules.
qml_setofflinestoragepath - Set the Property contains the directory to store offline user data.
qt_constant - Returns Qt constant value.
qt_version - Returns Qt version used.

QObject_classname

Returns class name of an QObject handle.

Syntax

s = QObject_classname(h)

Input argument

h - an QObject handle.

Output argument

s - a string: class name.

Description

Returns class name of an QObject handle.

Example

h1 = QObject_root()
h1.className
QObject_classname(h1)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

QObject_findchildren

Returns all children of this object with the given name.

Syntax

hr = QObject_findchildren(h, objectName, recursive)

Input argument

h - an QObject handle.
objectName - a string.
recursive - a logical: true (The search is performed recursively).

Output argument

hr - a vector of QObject handle.

Description

Returns all children of this object with the given name.

Example

h1 = errordlg()
h2 = errordlg()
hr = QObject_findchildren(QObject_root(), 'errordlg', true)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

QObject_get

Retrieve a property value from an QObject handle.

Syntax

R = get(h, property_name)

Input argument

h - an QObject handle.
property_name - a string: property name.

Output argument

R - The data type of the return value depends on the invoked method.

Description

R = get(h, property_name) returns the value of property asked.

Example

h = errordlg();
h.visible % or get(h, 'visible')
h.windowTitle % or get(h, 'windowTitle')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

QObject_iswidgettype

Returns true if the QObject is a widget.

Syntax

R = QObject_iswidgettype(h)

Input argument

h - an QObject handle.

Output argument

R - a logical.

Description

Returns true if the QObject is a widget; otherwise returns false.

Example

h = errordlg()
r = QObject_iswidgettype(h)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

QObject_iswindowtype

Returns true if the QObject is a window.

Syntax

R = QObject_iswindowtype(h)

Input argument

h - an QObject handle.

Output argument

R - a logical.

Description

Returns true if the QObject is a window; otherwise returns false.

Example

h = errordlg()
r = QObject_iswindowtype(h)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

QObject_methodsignature

Returns the signature of a method of a QObject handle.

Syntax

res = QObject_methodsignature(h, method_name)

Input argument

h - an QObject handle.
method_name - a string : method name.

Output argument

R - a string: method signature.

Description

Returns the signature of a method of a QObject handle.

Example

h = errordlg()
QObject_methodsignature(h, 'setVisible')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

QObject_root

QObject root object.

Syntax

r = QObject_root()

Output argument

h - QObject handle of Nelson gui.

Description

Returns QObject handle of Nelson gui.

Example

h1 = QObject_root()
h1.windowTitle
h1.windowTitle = 'Your title'

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

QObject_set

Set a property value of an QObject handle (set).

Syntax

R = set(h, property_name, value)

Input argument

h - an QObject handle.
property_name - a string: property name.
value - a variable.

Output argument

R - user-settable properties and possible values for the object identified by h.

Description

This routine can be used to modify the value of a specified property from an QObject object.

Example

h = errordlg()
h.visible = false; % or set(h, 'visible', false)
h.windowTitle = 'new title' % or set(h, 'windowTitle', 'new title')
h.visible = true;

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

QObject_undefine

Undefine a dynamic property of a QObject handle.

Syntax

QObject_undefine(h, property_name)

Input argument

h - an QObject handle.
property_name - a string : dynamic property name.

Output argument

R - a string: method signature.

Description

Undefine a dynamic property of a QObject handle.

Example

h = errordlg()
set(h, 'myProp', 33)
h
get(h, 'myProp')
QObject_undefine(h, 'myProp')
get(h, 'myProp')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

QObject_used

Returns list of current used QObject handle.

Syntax

r = QObject_used()

Output argument

h - a vector of QObject handle.

Description

Returns list of current used QObject handle.

Example

h1 = errordlg()
h2 = errordlg()
h3 = errordlg()
used = QObject_used()delete(used)
used = QObject_used()
delete(used)
used = QObject_used()

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

nelsonObject

nelson object callable from QML.

Syntax

nelson.disp(msg)
nelson.evaluate(cmd)
nelson.processevent()
nelson.call(function_name)
nelson.call(function_name, arg1, ..., arg5)

Input argument

msg - a string.
cmd - a string.
function_name - a string: nelson function name to call
arg1, ..., arg5 - javascript variables

Description

nelson object contains some methods used as callback to call nelson from QML

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

qml_addimportpath

Adds path as directory where the qml engine searches for installed modules.

Syntax

qml_addimportpath(path)

Input argument

path - a string : valid path.

Description

qml_addimportpath adds path as a directory where the engine searches for installed modules in a URL-based directory structure.

The newly added path will be first in qml_importpathlist.

Example

qml_importpathlist()
qml_addimportpath(tempdir)
qml_importpathlist()

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

qml_addpluginpath

Adds path as directory where the qml engine searches for native plugins.

Syntax

qml_addpluginpath(path)

Input argument

path - a string : valid path.

Description

qml_addpluginpath adds path as a directory where the engine searches for native plugins.

By default, the list contains only .. The newly added path will be first in the qml_pluginpathlist.

Example

qml_pluginpathlist()
qml_addpluginpath(tempdir)
qml_pluginpathlist()

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

qml_clearcomponentcache

Clears the engine's internal component cache..

Syntax

qml_clearcomponentcache

Description

This function causes the property metadata of all components previously loaded by the engine to be destroyed.

All previously loaded components and the property bindings for all extant objects created from those components will cease to function.

Example

qml_clearcomponentcache()

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

qml_collectgarbage

Runs the Qml garbage collector.

Syntax

qml_collectgarbage

Description

The garbage collector will attempt to reclaim memory by locating and disposing of objects that are no longer reachable in the script environment.

Example

qml_collectgarbage()

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

qml_createqquickview

Load a QML file and creates a window.

Syntax

h = qml_createqquickview(filename)

Input argument

filename - a string: a QML filename.

Output argument

h - a QObject handle.

Description

Load a QML file

It creates a QML component, a window, and load .qml file.

Example

% see examples in [nelsonroot(), '/modules/qml_engine/examples']

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

qml_demos

QML demos.

Syntax

qml_demos()

Description

qml_demos shows QML -- Nelson demos.

Example

qml_demos()

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

qml_evaluatefile

Evaluates a js file.

Syntax

r = qml_evaluatefile(filename)

Input argument

filename - a string: a js filename.

Output argument

r - a double, logical, int or string.

Description

Evaluates a js file.

If returned value cannot be converted to a basic type, it will converted to string.

Example

test_file = [tempdir() , '/example_qml_evaluatefile.js'];
f = fopen(test_file, 'wt');
fwrite(f, 'a = 2 + 4');
fclose(f);
qml_evaluatefile(test_file)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

qml_evaluatestring

Evaluates a js string.

Syntax

r = qml_evaluatestring(string_to_eval)

Input argument

string_to_eval - a string: a js code.

Output argument

r - a double, logical, int or string.

Description

Evaluates a js string.

If returned value cannot be converted to a basic type, it will converted to string.

Example

qml_evaluatestring('a = 2 + 4')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

qml_importpathlist

Returns the list of directories where the engine searches for installed modules in a URL-based directory structure.

Syntax

p = qml_importpathlist()

Output argument

p - a cell of strings: paths.

Description

Returns the list of directories where the engine searches for installed modules in a URL-based directory structure.

Example

qml_importpathlist()

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

qml_loadfile

Load a QML file.

Syntax

h = qml_loadfile(filename)

Input argument

filename - a string: a QML filename.

Output argument

h - a QObject handle.

Description

Load a QML file

It creates a QML component and load .qml file.

Example

% see examples in [nelsonroot(), '/modules/qml_engine/examples']

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

qml_loadstring

Load a QML string.

Syntax

h = qml_loadstring(str_to_eval)

Input argument

str_to_eval - a string.

Output argument

h - a QObject handle.

Description

Load a QML string

It creates a QML component and load .qml file.

Example

% see examples in [nelsonroot(), '/modules/qml_engine/examples']

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

qml_offlinestoragepath

Get the Property contains the directory to store offline user data.

Syntax

p = qml_offlinestoragepath()

Input argument

path_data - a string

Output argument

p - a string: path.

Description

Get the Property contains the directory to store offline user data.

Example

qml_offlinestoragepath()
qml_setofflinestoragepath(tmpdir())
qml_offlinestoragepath()

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

qml_pluginpathlist

Returns the list of directories where the engine searches for native plugins for imported modules.

Syntax

p = qml_pluginpathlist()

Output argument

p - a string: path.

Description

Returns the list of directories where the engine searches for native plugins for imported modules.

Example

qml_pluginpathlist()

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

qml_setofflinestoragepath

Set the Property contains the directory to store offline user data.

Syntax

qml_setofflinestoragepath(path_data)

Input argument

path_data - a string

Description

Set the Property contains the directory to store offline user data.

Example

qml_setofflinestoragepath(tmpdir())

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

qt_constant

Returns Qt constant value.

Syntax

v = qt_constant(constant_name)
ce = qt_constant()

Input argument

constant_name - a string: desired Qt constant.

Output argument

v - a scalar integer value (Qt constant value).
ce - a cell with all constant name available.

Description

v = qt_version(constant_name) returns Qt constant value.

Qt 5 family allows to get constant easily with qml_evaluatestring(constant_name), but it is no more available with Qt 6

Example

qt_constant('Qt.WindowModal')
c = qt_constant()

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

qt_version

Returns Qt version used.

Syntax

v = qt_version()

Output argument

v - a string : valid path.

Description

v = qt_version() returns the version number of Qt at run-time as a string (for example, "5.15.2").

Example

semver(qt_version(), '>5.15')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

Graphics functions

Description

graphics functions

abyss - Abyss colormap array.
ancestor - Ancestor of graphics object.
autumn - Autumn colormap array.
axes - Create cartesian axes.
axis - Set axis limits and aspect ratios.
bar - Bar graph.
bone - Bone colormap array.
cla - Clear axes.
clf - Clear figure.
clim - Set colormap limits.
close - Close one or more figures
colorbar - Colorbar showing color scale.
colormap - View and set current colormap.
colstyle - Parse color and style from string.
contour - Contour plot of matrix
contour3 - Contour 3D plot of matrix
cool - Cool colormap array.
copper - Copper colormap array.
copygraphics - Copy plot to clipboard.
cylinder - Create cylinder.
drawnow - Update figures and process callbacks
figure - Creates an figure window.
fill - Create filled 2-D patches.
gca - get current axes graphics object.
gcf - get current figure graphics object.
Managing Callback Interruptions in Nelson
gray - Gray colormap array.
grid - Display or hide axes grid lines.
groot - graphic root object.
hggroup - Create group object.
hist - Histogram plot.
hold - Retain current plot when adding new plots.
hot - Hot colormap array.
im2double - Convert image to double precision.
image - Display image from array.
imagesc - Display image from array with scaled colors.
imread - Read image from graphics file.
imshow - Display image.
imwrite - Write image to graphics file.
is2D - Checks if ax is a 2-D Polar or Cartesian axes.
isValidGraphicsProperty - Check property name is valid.
isgraphics - Check for graphics object.
ishold - Get current hold state.
jet - Jet colormap array.
legend - Add legend to axes.
line - Create primitive line.
loglog - Log-log scale plot.
mesh - Mesh surface plot.
meshz - Mesh surface plot with curtain.
newplot - Prepare to produce a new plot.
pan - Enable pan mode.
parula - Parula colormap array.
patch - Create patches of colored polygons
pcolor - Pseudocolor plot.
pie - Legacy pie chart.
pink - Pink colormap array.
plot - Linear 2-D plot.
plot3 - 3-D line plot.
quiver - Vector plot.
refresh - Redraw current figure.
rgbplot - Plot colormap.
ribbon - Ribbon plot.
rotate3d - Enable rotate mode.
saveas - Save figure to specific file format.
scatter - Scatter plot.
semilogx - Semilog plot (x-axis has log scale).
semilogy - Semilog plot (y-axis has log scale).
sky - Sky colormap array.
sphere - Create sphere.
spring - Spring colormap array.
spy - Visualize sparsity pattern of matrix.
stairs - Stairstep graph.
stem - Plot discrete sequence data.
subplot - Create axes in tiled positions.
summer - Summer colormap array.
surf - surface plot.
surface - Primitive surface plot.
text - creates text descriptions to data points.
title - Add title.
turbo - Turbo colormap array.
uicontrol - Create user interface component.
validatecolor - Validate color values.
view - Camera line of sigh.
viridis - Viridis colormap array.
waitfor - Wait for condition.
waitforbuttonpress - Wait for click or key press.
waterfall - waterfall plot.
white - white colormap array.
winter - Winter colormap array.
xlabel - Label x-axis.
xlim - set or get x-axis limits.
ylabel - Label y-axis.
ylim - set or get y-axis limits.
zlabel - Label z-axis.
zlim - set or get z-axis limits.
zoom - Enable zoom mode.

abyss

Abyss colormap array.

Syntax

c = abyss
c = abyss(m)

Input argument

m - a scalar integer value: Number of colors (256 as default value).

Output argument

c - Abyss colormap array.

Description

abyss returns the colormap with abyss colors.

Example

f = figure();
surf(peaks);
colormap('abyss');

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

ancestor

Ancestor of graphics object.

Syntax

p = ancestor(h, type)
p = ancestor(h, type, 'toplevel')

Input argument

h - graphics object
type - a row vector character or cell of strings:
'toplevel' - a row vector character: return the highest parent in the object hierarchy that matches the condition.

Output argument

p - a graphics object or []

Description

ancestor returns the handle of the specified object's ancestor of a given type.

Example

f = figure();
ax = gca();
s = surf(peaks);
AX = ancestor(s, 'axes')
F = ancestor(s, 'figure')
R = ancestor(s, 'root')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

autumn

Autumn colormap array.

Syntax

c = autumn
c = autumn(m)

Input argument

m - a scalar integer value: Number of colors (256 as default value).

Output argument

c - Autumn colormap array.

Description

autumn returns the colormap with autumn colors.

Example

f = figure();
surf(peaks);
colormap('autumn');

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

axes

Create cartesian axes.

Syntax

ax = axes()
ax = axes(parent)
ax = axes(propertyName, propertyValue)
ax = axes(parent, propertyName, propertyValue)
axes(cax)

Input argument

parent - a scalar graphics object value: parent container, specified as a figure.
cax - axes to make current.
propertyName - a scalar string or row vector character.
propertyValue - a value.

Output argument

ax - a graphics object: axes type.

Description

axes creates axes in the current figure and set it as the current axes.

axes(cax) set current axes.

Clicking on an axis automatically sets it as the current axes object.

Properties:

ALim Alpha limits: two-element vector of the form [amin, amax].

ALimMode Selection mode for ALim: 'manual' or 'auto' (default).

AmbientLightColor Background light color: RGB triplet or string color.

Box Box: 'on' or 'off'.

CLim Color limits: two-element vector of the form [cmin, cmax] or [0 1] (default).

CLimMode Selection mode for CLim: 'manual' or 'auto' (default).

CameraPosition Camera location: vector [x, y, z].

CameraPositionMode Selection mode for CameraPosition: 'manual' or 'auto' (default).

CameraTarget Camera target point: vector [x, y, z].

CameraTargetMode Selection mode for CameraTarget: 'manual' or 'auto' (default).

CameraUpVector Vector defining upwards direction: vector [x, y, z].

CameraUpVectorMode Selection mode for CameraUpVector: 'manual' or 'auto' (default).

CameraViewAngle Field of view: 0 (default) | scalar angle in range [0,180]

CameraViewAngleMode Selection mode for CameraViewAngle: 'manual' or 'auto' (default).

Children Array of graphics objects: A vector containing graphics objects to children of the current axis.

Clipping Clipping of objects to axes limits: 'on' (default) or 'off'.

Color Background color for the axes: RGB triplet, string color or hexadecimal color code.

ColorOrder Color order: three-column matrix of RGB triplets.

ColorOrderIndexColor order index: positive integer value, specifies the next color used.

DataAspectRatio Relative length of data units: vector [x, y, z].

DataAspectRatioMode Data aspect ratio mode: 'manual' or 'auto' (default).

FontAngle Character slant: 'italic' or 'normal' (default).

FontName Font name

FontSize Font size: scalar numeric value

FontUnits Font size units: 'inches', 'centimeters', 'normalized', 'pixels' or 'points' (default).

FontWeight Character thickness: 'bold' or 'normal' (default).

GridAlpha Grid-line transparency (0.15 (default) or value in the range [0, 1]).

GridColor Color of grid lines ([0.15, 0.15, 0.15] (default) or RGB triplet).

GridLineStyle Line style for grid lines: '--' , ':', '-.', 'none' or '-' (default).

HandleVisibility Visibility of object handle: 'on' (default) or 'off'.

HitTest Response to captured mouse clicks: 'on' (default) or 'off'.

BeingDeleted Flag indicating that the object is being deleted.

Interruptible Callback interruption:

Layer Placement of grid lines and tick marks: 'top' or 'bottom' (default).

LineStyleOrder Line style order: character vector, cell array of character vectors, string array or '-' solid line (default).

LineStyleOrderIndexColor order index: positive integer value, property specifies the next line style used.

LineWidth Line width: positive numeric value.

MinorGridLineStyle Line style for minor grid lines: '-', '--', '-.', 'none' or ':' (default).

NextPlot Properties to reset: 'add', 'replacechildren', 'replaceall' or 'replace' (default).

OuterPosition Size and location, including labels and margin: four-element vector.

Parent Parent container: Figure graphics object.

PlotBoxAspectRatio Relative length of each axis: vector [x, y, z].

PlotBoxAspectRatioMode Selection mode for PlotBoxAspectRatio: 'manual' or 'auto' (default).

Position Size and location, excluding margin for labels: four-element vector

PositionMode: 'manual' or 'auto' (default).

Projection Type of projection onto 2-D screen: 'perspective' or 'orthographic' (default).

Selected Selection state: 'on' or 'off' (default).

SelectionHighlight Display of selection graphics objects: 'on' (default) or 'off'.

Tag Object identifier: character vector, string scalar or '' (default).

TickDir Tick mark direction: 'out', 'both', 'none' or 'in' (default).

TickDirMode Selection mode for TickDir: 'manual' or 'auto' (default).

TickLength Tick mark length: two-element vector.

TightInset Margins for text labels: four-element vector [left bottom right top].

Title Text object for title: text object

Type Type of graphics object: 'axes'.

Units Position units: 'inches', 'centimeters', 'points', 'pixels', 'characters' or 'normalized' (default).

UserData User data: array or []

View Azimuth and elevation of view (default: [0 90])

Visible State of visibility: 'on' (default) or 'off'.

XAxisLocation x-axis location: 'top', 'origin' or 'bottom' (default).

XColorColor of axis line, tick values, and labels: RGB triplet.

XDir x-axis direction: 'reverse' or 'normal' (default).

XGrid Grid lines: 'on' or 'off' (default).

XLabel Text object for axis label: text object

XLim Minimum and maximum axis limits: two element vector [min max].

XLimMode Selection mode for axis limits: 'manual' or 'auto' (default).

XMinorGrid Minor grid lines: 'on' or 'off' (default).

XScale Scale of values along axis: 'log' or 'linear' (default).

XTick Tick values: vector of increasing values or [] (default).

XTickLabel Tick labels: cell array of character vectors or '' (default).

XTickLabelMode Selection mode for tick labels: 'manual' or 'auto' (default).

XTickMode Selection mode for tick values: 'manual' or 'auto' (default).

YAxisLocation y-axis location: 'top', 'origin' or 'bottom' (default).

YColorColor of axis line, tick values, and labels: RGB triplet.

YDir y-axis direction: 'reverse' or 'normal' (default).

YGrid Grid lines: 'on' or 'off' (default).

YLabel Text object for axis label : text object

YLim Minimum and maximum axis limits: two element vector [min max].

YLimMode Selection mode for axis limits: 'manual' or 'auto' (default).

YMinorGrid Minor grid lines: 'on' or 'off' (default).

YScale Scale of values along axis: 'log' or 'linear' (default).

YTick Tick values: vector of increasing values or [] (default).

YTickLabel Tick labels: cell array of character vectors or '' (default).

YTickLabelMode Selection mode for tick labels: 'manual' or 'auto' (default).

YTickModeSelection mode for tick values: 'manual' or 'auto' (default).

ZColorColor of axis line, tick values, and labels: RGB triplet.

ZDir z-axis direction: 'reverse' or 'normal' (default).

ZGrid Grid lines: 'on' or 'off' (default).

ZLabel Text object for axis label : text object

ZLim Minimum and maximum axis limits: two element vector [min max].

ZLimMode Selection mode for axis limits: 'manual' or 'auto' (default).

ZMinorGrid Minor grid lines: 'on' or 'off' (default).

ZScale Scale of values along axis: 'log' or 'linear' (default).

ZTick Tick values: vector of increasing values or [] (default).

ZTickLabel Tick labels: cell array of character vectors or '' (default).

ZTickLabelMode Selection mode for tick labels: 'manual' or 'auto' (default).

ZTickModeSelection mode for tick values: 'manual' or 'auto' (default).

CreateFcnCallback (function handle, string or cell) called when object is created. Set this property on an existing component has no effect.

DeleteFcnCallback (function handle, string or cell) called when object is deleted.

Some properties are available only for compatibility and have currently no effect on the axes.

Example

f = figure();
ax1 = axes('Position', [0.1 0.1 0.7 0.7]);
ax2 = axes('Position', [0.65 0.65 0.28 0.28]);
x = linspace(0,10);
y1 = sin(x);
y2 = cos(x);
plot(ax1, x, y1);
plot(ax2, x, y2);

History

Version	Description
1.0.0	initial version
1.2.0	Clicking on an axis automatically sets it as the current axes object.
--	GridAlpha, GridColor propertiew for Axes.
1.7.0	CreateFcn, DeleteFcn callback added.
--	BeingDeleted property added.

Author

Allan CORNET

axis

Set axis limits and aspect ratios.

Syntax

axis([xmin, xmax, ymin, ymax, zmin, zmax, cmin, cmax])
axis([xmin, xmax, ymin, ymax, zmin, zmax])
axis([xmin, xmax, ymin, ymax])
axis(style)
axis(mode)
axis(visibility)
lim = axis()
axis(ax, ...)

Input argument

[xmin, xmax, ymin, ymax, zmin, zmax, cmin, cmax] - sets the limits in the X, Y, Z and color axes.
[xmin, xmax, ymin, ymax, zmin, zmax] - sets only the limits in the X, Y, Z.
[xmin, xmax, ymin, ymax] - sets only the limits in the X, Y.
style - 'tight', 'equal', 'image', 'square', 'fill', 'vis3d' or 'normal' (default).
cax - axes.
visibility - 'off' or 'on' (default).
mode - 'manual' (turns off automatic scaling of the axis based on the children of the current axis object) or 'auto' (choose automatically all axis limits) .

Output argument

lim - For 2D: [xmin, xmax, ymin, ymax] or for 3D: [xmin, xmax, ymin, ymax, zmin, zmax]

Description

axes set axis limits and appearance.

Example

f = figure();
t = 0:0.01:2*pi;
x = cos(t);
subplot(2, 2, 1);
plot(t, x);
title ('normal plot');

subplot(2, 2, 2);
plot (t, x);
title('axis square');
axis('square');

subplot(2, 2, 3);
plot (t, x);
title('axis equal');
axis('equal');

subplot(2, 2, 4);
plot (t, x);
title('normal plot again');
axis('normal');

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

bar

Bar graph.

Syntax

bar(Y)
bar(X, Y)
bar(..., width)
bar(..., color)
bar(..., propertyName, propertyValue)
bar(ax, ...)
b = bar(...)

Input argument

X - x-coordinates: scalar, vector or string array.
Y - y-coordinates: vector.
width - scalar, 0.8 (default).
color - a scalar string or row vector character: short name color.
propertyName - a scalar string or row vector character.
propertyValue - a value.
ax - Axes object.

Output argument

b - patch graphics object.

Description

bar(X, Y) creates a bar graph using two sets of X-Y data vectors.

When only one argument is provided (Y), it is interpreted as a vector containing Y values, and the X coordinates are generated as a sequence from 1 to the number of elements in the Y vector.

You can optionally specify the width of the bars.

A value of 1.0 will make each bar exactly touch its neighboring bars, while the default width is set to 0.8.

Examples

f = figure();
y = [ 91 75 123.5 105 150 131 203 179 249 226 281.5];
bar(y);

f = figure();
y = [ 91 75 123.5 105 150 131 203 179 249 226 281.5];
bar(y, 0.5);

f = figure();
x = 1900:10:2000;
y = [75 91 105 123.5 131 150 179 203 226 249 281.5];
bar(x, y, 'r');

f = figure();
x = [ "Summer", "Spring", "Winter", "Autumn"];
y = [ 2 1 4 3];
bar(x, y);

f = figure();
y = [91 75 123.5 105 150 131 203 179 249 226 281.5];
bar(y, 'FaceColor', [0 .5 .5], 'EdgeColor', [0 .9 .9], 'LineWidth', 1.5)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

bone

Bone colormap array.

Syntax

c = bone
c = bone(m)

Input argument

m - a scalar integer value: Number of colors (256 as default value).

Output argument

c - Bone colormap array.

Description

bone returns the colormap with bone colors.

Example

f = figure();
surf(peaks);
colormap('bone');

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

cla

Clear axes.

Syntax

cla
cla(ax)
ca = cla(...)

Input argument

ax - a scalar graphics object on an existing axes.

Output argument

ca - a graphics object: used axes graphics object.

Description

cla clears the current axes.

Example

f = figure();
x = linspace(0, 2*pi);
y = sin(3 * x);
plot(x, y)
sleep(5)
cla

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

clf

Clear figure.

Syntax

clf
clf(f)
F = clf(...)

Input argument

f - a scalar graphics object on an existing figure.

Output argument

F - a graphics object: used figure graphics object.

Description

clf clears the current figure.

Example

f = figure();
x = linspace(0, 2*pi);
y = sin(3 * x);
plot(x, y)
sleep(5)
clf

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

clim

Set colormap limits.

Syntax

clim(limits)
clim('auto')
clim('manual')
clim(ax, ...)
lims = clim()

Input argument

limits - New limits: [cmin cmax].
'auto' - enables automatic limit updates when values in the colormap indexing array change.
'manual' - disables automatic limit update.
ax - Target object: axes graphics object.

Output argument

lims - [cmin cmax]

Description

clim set or get colormap limits.

Examples

f = figure();
[X,Y] = meshgrid(-5:.5:5);
Z = X .^ 2 + Y .^ 2;
surf(Z);
limits = clim()

f = figure();
[X,Y] = meshgrid(-5:.5:5);
Z = X.^2 + Y.^2;
surf(Z);
clim([25 75])
limits = clim()

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

close

Close one or more figures

Syntax

close()
close('all')
close(name)
close(ID)
close(GO)
tf = close(...)

Input argument

ID - a scalar integer value: figure ID.
GO - a scalar graphics object on an existing figure.
GO - a scalar graphics object on an existing figure.

Output argument

tf - a scalar logical: true if figure was closed.

Description

close closes the current figure.

close(ID) closes the figure specified by figure ID.

close(GO) closes the figure specified by figure graphics object.

close('all') closes all figures.

Example

f = figure(1)
close();
h = figure(3)
close(h)
f1 = figure()
f2 = figure()
close('all')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

colorbar

Colorbar showing color scale.

Syntax

colorbar()
colorbar('off')
colorbar(..., propertyName, propertyValue)
colorbar(target, ...)
colorbar(target, 'off')
c = colorbar(...)

Input argument

propertyName - a scalar string or row vector character.
propertyValue - a value.
target - Target: axes.
'off' - deletes colorbar associated with the current axes.

Output argument

c - graphics object: axes on color bar.

Description

colorbaradds a color bar into a plot.

Examples

f = figure();
surf(peaks);
colormap('summer');
colorbar()

f = figure();
surf(peaks);
colormap('gray');
cb = colorbar(gca);

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

colormap

View and set current colormap.

Syntax

colormap(map)
colormap(target ,map)
cmap = colormap()
cmap = colormap(target)

Input argument

map - colormap name, 'default' or RGB triplets (matrix).
target - Target: figure or axes.

Output argument

cmap - Colormap values: RGB triplets (matrix).

Description

colormapallows to view and set the colormap used into a plot.

Examples

f = figure()
x = linspace(-1, 1, 1024)' * ones(1, 1024);
y = x';
Z = exp(-(x .^ 2 + y .^ 2) / 0.4);
imagesc(Z);
colormap('summer')

f = figure()
x = linspace(-1, 1, 1024)' * ones(1, 1024);
y = x';
Z = exp(-(x .^ 2 + y .^ 2) / 0.4);
imagesc(Z);
colormap('gray')

f = figure()
x = linspace(-1, 1, 1024)' * ones(1, 1024);
y = x';
Z = exp(-(x .^ 2 + y .^ 2) / 0.4);
imagesc(Z);

map = [0 0 0.3;
    0 0 0.4;
    0 0 0.5;
    0 0 0.6;
    0 0 0.8;
    0 0 1.0];
colormap(map)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

colstyle

Parse color and style from string.

Syntax

[linespec, colorspec, markerspec, msg] = colstyle (str)
[linespec, colorspec, markerspec, msg] = colstyle (str, 'plot')

Input argument

str - a row vector of character or scalar string: line specification.
'plot' - linespec returns 'none' and not '' with this option.

Output argument

linespec - a string: line type.
colorspec - a string: color part.
markerspec - a string: marker part.
msg - a string: contain the error message string.

Description

colstyle parses color and style from string.

Example

[l, c, m, msg] = colstyle('r:x')
[l, c, m, msg] = colstyle('*')
[l, c, m, msg] = colstyle('*', 'plot')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

contour

Contour plot of matrix

Syntax

contour(Z)
contour(X, Y, Z)
contour(..., levels)
contour(..., LineSpec)
contour(ax, ...)
M = contour(...)
[M, h] = contour(...)

Input argument

X - x-coordinates: vector or matrix.
Y - y-coordinates: vector or matrix.
Z - z-coordinates: vector or matrix.
levels - Contour levels: scalar or vector.
LineSpec - Line style and color
ax - a scalar graphics object value: parent container, specified as a axes.

Output argument

M - Contour matrix.
h - a graphics object: contour type.

Description

contour(Z) generates a contour plot representing isolines of the matrix Z. Each isoline corresponds to a specific height value on the x-y plane.

Nelson automatically selects the contour lines to display based on the values in Z. The column and row indices of Z serve as the x and y coordinates in the plane, respectively.

contour(X, Y, Z) allows the user to specify the x and y coordinates corresponding to the values in matrix Z. This enables more precise control over the positioning of the contour plot on the x-y plane.

The matrices X and Y provide the coordinates, while Z contains the height values for generating the contour plot.

Property Name-Value Pairs:

LevelList: The contour levels, specified as a vector of z values, determine the height levels at which the contour lines are drawn. By default, when not explicitly provided, the contour function automatically selects these values to cover the range of values present in the ZData property, ensuring comprehensive coverage of the data range. Default: empty matrix.

LevelListMode: Selection mode for LevelList: 'manual' or 'auto' (default).

LevelStep: Spacing between contour lines: scalar numeric value or 0 (default).

LevelStepMode:Selection mode for LevelStep: 'manual' or 'auto' (default).

EdgeColor: Color of contour lines: rgb color or 'flat' (default).

EdgeAlpha: Contour line transparency: scalar in range [0, 1] or 1 (default).

LineStyle: Line style: '--', ':', '-.' or '-' (default).

LineWidth: Line Width: positive value or 0.5 (default).

ContourMatrix: contour matrix.

XData: x values: vector or matrix or [] (default).

YData: y values: vector or matrix or [] (default).

ZData: z values: vector or matrix or [] (default).

XDataMode: Selection mode for XData: 'manual' or 'auto' (default).

YDataMode: Selection mode for YData: 'manual' or 'auto' (default).

DisplayName: Legend label: character vector, string scalar or '' (default).

Visible: State of visibility: on/off logical value, 'on' (default).

Parent: Parent: Axes object or Group object.

Children: Children.

HandleVisibility: Visibility of handle 'on', 'off'.

Type: Type of graphics object 'contour'.

Tag: Object identifier: character vector, string scalar or '' (default).

UserData: User data: array or [] (default).

CreateFcnCallback (function handle, string or cell) called when object is created. Set this property on an existing component has no effect.

DeleteFcnCallback (function handle, string or cell) called when object is deleted.

BeingDeleted Flag indicating that the object is being deleted.

Examples

f = figure();
subplot(2, 3, 1)
x = linspace(-2 * pi, 2 * pi);
y = linspace(0, 4 * pi);
[X, Y] = meshgrid(x, y);
Z = sin(X) + cos(Y);
contour(X, Y, Z);

subplot(2, 3, 2)
[X, Y, Z] = peaks;
contour(X, Y, Z, 20)

subplot(2, 3, 3)
[X, Y, Z] = peaks;
v = [1,1];
contour(X, Y, Z, v)

subplot(2, 3, 4)
[X, Y, Z] = peaks;
contour(X, Y, Z, '-.')

subplot(2, 3, 5)
Z = peaks;
[M, c] = contour(Z);
c.LineWidth = 3;

subplot(2, 3, 6)
[theta, r] = meshgrid (linspace (0,2*pi,64), linspace (0,1,64));
[X, Y] = pol2cart (theta, r);
Z = sin (2*theta) .* (1-r);
contour (X, Y, abs (Z), 10);

rng('default');
f = figure();
N = 50;
contour(1:N, 1:N, rand(N), 5)

f = figure();
Z = peaks;
Z(:,26) = NaN;
contour(Z)

History

Version	Description
1.3.0	initial version
1.7.0	CreateFcn, DeleteFcn callback added.
--	BeingDeleted property added.

Author

Allan CORNET

contour3

Contour 3D plot of matrix

Syntax

contour3(Z)
contour3(X, Y, Z)
contour3(..., levels)
contour3(..., LineSpec)
contour3(ax, ...)
M = contour3(...)
[M, h] = contour3(...)

Input argument

X - x-coordinates: vector or matrix.
Y - y-coordinates: vector or matrix.
Z - z-coordinates: vector or matrix.
levels - Contour levels: scalar or vector.
LineSpec - Line style and color
ax - a scalar graphics object value: parent container, specified as a axes.

Output argument

M - Contour matrix.
h - a graphics object: contour type.

Description

contour3(Z) generates a 3-D contour plot illustrating the isolines of the matrix Z, where Z represents heights on the x-y plane.

The x and y coordinates in the plane correspond to the column and row indices of Z, respectively.

To specify the x and y coordinates for Z values, use contour3(X,Y,Z).

Example

f = figure();
[X,Y,Z] = sphere(50);
[M, C ]= contour3(X,Y,Z);
C.LineWidth = 3;

History

Version	Description
1.3.0	initial version

Author

Allan CORNET

cool

Cool colormap array.

Syntax

c = cool
c = cool(m)

Input argument

m - a scalar integer value: Number of colors (256 as default value).

Output argument

c - Cool colormap array.

Description

cool returns the colormap with cool colors.

Example

f = figure();
surf(peaks);
colormap('cool');

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

copper

Copper colormap array.

Syntax

c = copper
c = copper(m)

Input argument

m - a scalar integer value: Number of colors (256 as default value).

Output argument

c - Copper colormap array.

Description

copper returns the colormap with copper colors.

Example

f = figure();
surf(peaks);
colormap('copper');

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

copygraphics

Copy plot to clipboard.

Syntax

copygraphics(fig)

Input argument

fig - figure object.

Description

copygraphics copy figure to clipboard.

Example

x = -2:0.25:2;
y = x;
[X,Y] = meshgrid(x);
F = X.*exp(-X.^2-Y.^2);
surf(X,Y,F);
copygraphics(gcf());

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

cylinder

Create cylinder.

Syntax

[X, Y, Z] = cylinder()
[X, Y, Z] = cylinder(r)
[X, Y, Z] = cylinder(r, n)
cylinder()
cylinder(r)
cylinder(r, n)
cylinder(ax, ...)

Input argument

r - Profile curve: vector.
n - Number of points: positive whole number.
ax - Target axes: 'axes' object.

Output argument

X, Y, Z - x-, y-, and z- coordinates of a cylinder without drawing it.

Description

cylinder creates cylinder and plots it.

Examples

f1 = figure();
colormap(spring)
cylinder()

f2 = figure();
colormap(summer)
r = 4;
cylinder(r);

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

drawnow

Update figures and process callbacks

Syntax

drawnow()

Description

drawnow flushes the event queue and updates the figure window.

Example

x = -pi:pi/20:pi;
plot(x, cos(x))
drawnow
title('Title Here ...')
grid on

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

figure

Creates an figure window.

Syntax

f = figure()
f = figure(ID)
f = figure(H)
f = figure(propertyName, propertyValue)
f = figure(ID, propertyName, propertyValue)
f = figure(H, propertyName, propertyValue)

Input argument

ID - a scalar integer value: find or creates with ID.
H - a scalar graphics object on an existing figure.
propertyName - a scalar string or row vector character.
propertyValue - a value.

Output argument

f - a graphics object: figure handle.

Description

figure creates figure.

Clicking on an figure automatically sets it as the current figure object.

Properties:

AlphaMap: Transparency map for Axes content.

Children: Children of figure: empty array (default) or 1-D array of objects.

Color: Background color [R, G, B] or string (example: 'blue') or hexadecimal color code ('#FFAA00').

Colormap: Color map for axes content of figure: m-by-3 array of RGB triplets, parula (default).

CurrentAxes: Target axes in current figure: Axes object.

Name: Name (default '').

GraphicsSmoothing: GraphicsSmoothing (default 'on').

MenuBar: Figure menu bar display: 'none' or 'figure' (default).

NextPlot: Directive on how to add next plot: 'new', 'replace', 'replacechildren' or 'add' (default).

Number: Figure Number.

NumberTitle: Use number title: 'off' or 'on' (default).

Parent: Figure parent: root graphics object.

Position: Location and size of drawable area: [left, bottom, width, height]

'width' and 'height' define the size of the window. 'left' and 'bottom' define the position of the first addressable pixel in the lower left corner of the window

Resize: Resize figure: 'on' or 'off' (default).

Tag: Object identifier: string scalar, character vector, '' (default).

ToolBar: Figure toolbar display: 'none', 'auto' (default), 'figure'.

Type: Type 'figure'.

UserData: User data: array or [] (default).

Visible: State of visibility: 'off' or 'on' (default).

DrawLater: is used to delay a huge succession of graphics commands (implying several drawings or redrawings): 'on' or 'off' (default).

CloseRequestFcn: Close request callback: function handle, cell array, character vector with 'closereq' (default).

CreateFcn Callback (function handle, string or cell) called when object is created. Set this property on an existing component has no effect.

DeleteFcn Callback (function handle, string or cell) called when object is deleted.

KeyPressFcn Callback (function handle, string or cell) called when a key is pressed while the figure has the focus.

KeyReleaseFcn Callback (function handle, string or cell) called when a key is released while the figure has the focus.

ButtonDownFcn Callback (function handle, string or cell) called when a mouse button is pressed while the figure has the focus.

BeingDeleted Flag indicating that the object is being deleted.

Example

f = figure(1)
g = figure(2)
h = figure(3)
figure(g)
gcf()
figure('Name', 'Hello')

History

Version	Description
1.0.0	initial version
1.2.0	Clicking on an figure automatically sets it as the current figure object.
1.7.0	CreateFcn, DeleteFcn, CloseRequestFcn, KeyPressFcn, KeyReleaseFcn, ButtonDownFcn callback added.
--	BeingDeleted property added.
1.8.0	Resize property added.

Author

Allan CORNET

fill

Create filled 2-D patches.

Syntax

fill(X, Y, C)
fill(..., propertyName, propertyValue)
fill(ax, ...)
go = fill(...)

Input argument

X - x-coordinates: vector or matrix.
Y - y-coordinates: vector or matrix.
C - Color array: scalar, vector, m-by-n-by-3 array of RGB triplets.
ax - a scalar graphics object value: parent container, specified as a axes.
propertyName - a scalar string or row vector character.
propertyValue - a value.

Output argument

go - a graphics object: patch type.

Description

fill(X, Y, C) creates a 2D polygonal shape with vertices defined by X and Y coordinates, and fills the shape with color C.

fill(..., PropertyName, PropertyValue, ...) sets optional properties for the fill/patch object using name-value pairs.

go = fill(...) returns the handle go to the created patch object.

Property Name-Value Pairs:

'FaceColor': color of the filled shape. FaceColor can be a character vector or a 3-element RGB vector. Default: 'flat'.

'EdgeColor': color of the edges of the polygonal shape. EdgeColor can be a character vector or a 3-element RGB vector. Default: 'none'.

'LineWidth': width of the edges of the polygonal shape. Default: 0.5.

'LineStyle': style of the edges of the polygonal shape. LineStyle can be a character vector or a line style code. Default: '-'.

'FaceAlpha': transparency of the filled shape. FaceAlpha can be a scalar between 0 and 1. Default: 1.

'EdgeAlpha': transparency of the edges of the polygonal shape. EdgeAlpha can be a scalar between 0 and 1. Default: 1.

'Parent': handle of the parent object for the patch. Default: gca().

'Vertices': matrix of vertex coordinates. The matrix must have size N-by-2 or N-by-3, where N is the number of vertices. Default: the vertex coordinates are specified by the X, Y, and Z input arguments.

Examples

f = figure();
outerX = [0, 0.3, 1, 0.7, 1, 0.3, 0, -0.3, -1, -0.7, -1, -0.3, 0];
outerY = [1, 0.3, 0.3, 0, -0.3, -1, -0.3, -1, -0.3, 0, 0.3, 0.3, 1];
innerX = [0, 0.2, 0.5, 0.35, 0.5, 0.2, 0, -0.2, -0.5, -0.35, -0.5, -0.2, 0];
innerY = [0.6, 0.3, 0.3, 0, -0.3, -0.6, -0.3, -0.6, -0.3, 0, 0.3, 0.3, 0.6];
fill(outerX, outerY, 'y');
fill(innerX, innerY, 'r');

% Define the vertices of a colorful geometric pattern
x1 = [0, 1, 1, 0];
y1 = [0, 0, 1, 1];
x2 = [0.5, 1.5, 1.5, 0.5];
y2 = [0.5, 0.5, 1.5, 1.5];
x3 = [1, 2, 2, 1];
y3 = [1, 1, 2, 2];

% Define colors for the polygons
colors = ['r', 'g', 'b'];

% Create a figure with a white background
figure('Color', 'w');

% Fill the polygons with different colors
fill(x1, y1, colors(1));
hold on;
fill(x2, y2, colors(2));
fill(x3, y3, colors(3));

% Add labels to distinguish the regions
text(0.5, 0.5, 'Polygon 1', 'Color', 'w', 'HorizontalAlignment', 'center', 'FontWeight', 'bold');
text(1.25, 1.25, 'Polygon 2', 'Color', 'w', 'HorizontalAlignment', 'center', 'FontWeight', 'bold');
text(1.5, 0.5, 'Polygon 3', 'Color', 'w', 'HorizontalAlignment', 'center', 'FontWeight', 'bold');

axis equal;
title('Colorful Geometric Pattern');

Alpha channel

f = figure();
x = [10 30 40 30 10 0];
y = [0 0 20 40 40 20];
hold on
fill(x, y, 'cyan', 'FaceAlpha', 0.3);
fill(x + 2, y, 'magenta', 'FaceAlpha', 0.3);
fill(x + 1, y + 2, 'yellow', 'FaceAlpha', 0.3);

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

gca

get current axes graphics object.

Syntax

ca = gca()

Output argument

ca - a graphics object: axes graphics object.

Description

ca = gca() returns the current axes graphics object.

If there are no axes, gca() creates an axes and returns its graphics object.

Example

ca = gca()
isgraphics(ax, 'axes')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

gcf

get current figure graphics object.

Syntax

cf = gcf()

Output argument

cf - a graphics object: figure graphics object.

Description

cf = gcf() returns the current figure graphics object.

If a figure does not exist, gcf() creates a figure and returns its graphics object.

Example

cf = gcf();
root = groot();
isequal(root.CurrentFigure, cf)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

Managing Callback Interruptions in Nelson

Description

You can assign a callback function to a callback property using one of the following methods:

Function handle: Use this approach when your callback does not need extra input arguments.

Cell array: Ideal for situations where your callback requires additional input arguments. The cell array should include the function handle as the first element, followed by the input arguments.

Anonymous function: This method is suitable for simple callback code or when you want to reuse a function that isn't exclusively used as a callback.

Characters vector or scalar string containing commands.

Nelson provides control over whether a callback function can be interrupted during its execution. In some cases, allowing interruptions might be desirable, such as enabling users to stop an animation loop through an interrupting callback. However, in scenarios where the execution order of callbacks is crucial, it might be necessary to prevent interruptions to maintain the intended behavior, such as ensuring smooth responsiveness in applications that respond to pointer movements.

Callback Interruption Behavior:

Callbacks are executed in the order they are queued. When a callback is running and another user action triggers a second callback, this second callback attempts to interrupt the first one. The first callback is referred to as the "running callback," while the second is the "interrupting callback."

In some cases, specific commands within the running callback prompt Nelson to process any pending callbacks in the queue.

When Nelson encounters one of these commands such as drawnow, figure, waitfor, or pause it evaluates whether an interruption should occur.

No Interruption: If the running callback does not include any of these commands, Nelson will complete the running callback before executing the interrupting callback.

Interruption Conditions: If the running callback includes any of these commands, the behavior depends on the Interruptible property of the object that owns the running callback:

If Interruptible is set to 'on', Nelson allows the interruption. The running callback is paused, the interrupting callback is executed, and once it is finished, Nelson resumes the execution of the running callback.

If Interruptible is set to 'off', the interruption is blocked. The BusyAction property of the interrupting callback then dictates the next step:

If BusyAction is 'queue', the interrupting callback will be executed after the running callback completes.

If BusyAction is 'cancel', the interrupting callback is discarded and not executed.

By default, the Interruptible property is 'on', and BusyAction is 'queue'.

Notably, certain callbacks specifically DeleteFcn, CloseRequestFcn, and SizeChangedFcn will interrupt the running callback regardless of the Interruptible property's value.

Example

uicontrol demo Interruptible

addpath([modulepath('graphics','root'), '/examples/uicontrol'])
edit uicontrol_demo_interruptible
uicontrol_demo_interruptible

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

gray

Gray colormap array.

Syntax

c = gray
c = gray(m)

Input argument

m - a scalar integer value: Number of colors (256 as default value).

Output argument

c - Gray colormap array.

Description

gray returns the colormap with gray colors.

Example

f = figure();
surf(peaks);
colormap('gray');

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

grid

Display or hide axes grid lines.

Syntax

grid
grid('on')
grid('off')
grid('minor')
grid(ax, ...)

Input argument

'on' - displays the major grid line.
'off' - removes all grid lines.
'minor' - toggles the visibility of the minor grid lines.
ax - Target object: axes.

Description

grid() toggles the visibility of the major grid lines.

Example

f = figure();
x = linspace(0, 20);
y = cos(x);
plot(x, y)
grid on

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

groot

graphic root object.

Syntax

g = groot()

Output argument

g - a graphics object: root object.

Description

groot returns graphic root object.

Properties:

Children: Array of available figure objects.

CurrentFigure: Current figure graphics object.

Parent: empty array (No parent)

PointerLocation: Current location of pointer.

ScreenDepth: Number of bits that define each pixel color.

ScreenSize: Size of primary display (vector).

Tag: Object identifier: string scalar, character vector, '' (default).

Type: Type 'root'.

Units: 'pixels'.

UserData: User data: array or [] (default).

Example

g = groot()
g.ScreenDepth

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

hggroup

Create group object.

Syntax

h = hggroup()
h = hggroup(..., propertyName, propertyValue, ...)
h = hggroup(ax, ...)

Input argument

ax - graphics object: axes or hggroup.
propertyName - a scalar string or row vector character.
propertyValue - a value.

Output argument

p - a graphics object of type: hggroup

Description

hggroup creates a hggroup object as a child of the current axes and returns its handle, h.

The hggroup object is used to group graphics objects, such as lines, patches, and text, so that they can be manipulated together.

Example

figure();
ax = gca();
g = hggroup();
h = text(0.1, 0.1, 'tttt', 'Parent', g);
h.Parent
h.Visible
h.Visible = 'off';

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

hist

Histogram plot.

Syntax

hist(x)
hist(x, nbins)
hist(ax, ...)
counts = hist(...)
[counts, centers] = hist(...)

Input argument

x - vector or matrix
nbins - vector.
ax - Axes object.

Output argument

counts - Counts of the number of elements in each bin: row vector.
centers - Bin centers: vector.

Description

A histogram is a graphical representation that illustrates the distribution of data values.

When you use the hist function, it organizes the elements in the vector Y into 10 equally spaced containers and provides the count of elements in each container as a row vector.

hist(Y, x) with a vector x, the function will return the distribution of values in Y among bins determined by the length of x, with centers specified by the values in x.

For instance, if x is a 5-element vector, hist will categorize the elements of Y into five bins, each centered on the x-axis at the values specified in x.

When you use hist(...) without specifying any output arguments, it generates a histogram plot. The bins are distributed along the x-axis between the minimum and maximum values found in the input vector Y.

Example

f = figure();
for i = 1:4
  subplot(2, 2, i)
  hist(randn(1000, 1), 50)
end

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

hold

Retain current plot when adding new plots.

Syntax

hold('on')
hold('off')
hold('all')
hold()
hold(ax, ...)

Input argument

'on' - turn hold on.
'off' - turn hold off.
'all' - same as hold on.
ax - Target axes: axes.

Output argument

ax - a graphics object: axes type.

Description

hold allows to construct a plot sequence incrementally.

Example

f = figure();
x = linspace(-pi, pi);
y1 = cos(x);
plot(x, y1)
hold on
y2 = sin(x);
plot(x, y2)
hold off

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

hot

Hot colormap array.

Syntax

c = hot
c = hot(m)

Input argument

m - a scalar integer value: Number of colors (256 as default value).

Output argument

c - Hot colormap array.

Description

hot returns the colormap with hot colors.

Example

f = figure();
surf(peaks);
colormap('hot');

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

im2double

Convert image to double precision.

Syntax

IM = im2double(I)
IM = im2double(I,'indexed')

Input argument

I - Input image: scalar, vector, matrix or multidimensional array with type single, double, int16, uint8, uint16 or logical.

Output argument

IM - The converted image is returned as a numeric array with the same dimensions as the input image I with type double.

Description

IM = im2double(I) converts the input image I to double precision format. The input image IM can be a grayscale, truecolor, or binary image. When converting, im2double rescales the pixel values from their original integer format to a floating-point range of [0, 1].

For an indexed image, IM = im2double(I, 'indexed') converts the image I to double precision as well, but with an added offset of 1 to the pixel values during the conversion from integer types.

Example

I = reshape(uint8(linspace(1,255,25)),[5 5]);
IM1 = im2double(I)
IM2 = im2double(I, 'indexed')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

image

Display image from array.

Syntax

image()
image(C)
image(X, Y, C)
image('CData', C)
image('XData', X, 'YData', Y,'CData', C)
image(..., propertyName, propertyValue)
image(parent, ...)
go = image(...)

Input argument

X - x-coordinates: vector or matrix.
Y - y-coordinates: vector or matrix.
C - Color array: m-by-n-by-3 array of RGB triplets.
parent - a scalar graphics object value: parent container, specified as a axes.
propertyName - a scalar string or row vector character.
propertyValue - a value.

Output argument

go - a graphics object: image type.

Description

image displays C data as an image.

Properties:

AlphaData Transparency data: scalar, array the same size as CData, or 1 (default).

AlphaDataMapping

CData Image color data: vector or matrix, 3-D array of RGB triplets.

CDataMapping Color data mapping method: 'scaled' or 'direct' (default).

Children [].

Parent Parent: axes object.

Tag Object identifier: string scalar, character vector, '' (default).

Type Type of graphics object: 'surface'.

UserData: User data: array or [] (default).

Visible State of visibility: 'off' or 'on' (default).

XData Placement along x-axis: two-element vector, scalar, [1 size(CData, 1)] (default).

YData Placement along y-axis: two-element vector, scalar, [1 size(CData, 2)] (default).

CreateFcnCallback (function handle, string or cell) called when object is created. Set this property on an existing component has no effect.

DeleteFcnCallback (function handle, string or cell) called when object is deleted.

BeingDeleted Flag indicating that the object is being deleted.

Example

f = figure();
L = linspace(0, 1);
R = L' * L;
G = L' * (L .^ 2);
B = L' * (0 *L + 1);
C(:, :, 1) = G;
C(:, :, 2) = G;
C(:, :, 3) = B;
im = image(C)
figure();
image();

History

Version	Description
1.0.0	initial version
1.7.0	CreateFcn, DeleteFcn callback added.
--	BeingDeleted property added.

Author

Allan CORNET

imagesc

Display image from array with scaled colors.

Syntax

imagesc()
imagesc(C)
image(X, Y, C)
imagesc('CData', C)
imagesc('XData', X, 'YData', Y,'CData', C)
imagesc(..., propertyName, propertyValue)
imagesc(parent, ...)
go = imagesc(...)

Input argument

X - x-coordinates: vector or matrix.
Y - y-coordinates: vector or matrix.
C - Color array: m-by-n-by-3 array of RGB triplets.
parent - a scalar graphics object value: parent container, specified as a axes.
propertyName - a scalar string or row vector character.
propertyValue - a value.

Output argument

go - a graphics object: image type.

Description

imagessc displays C data as an image. This image is colormapped using the colormap for the current figure.

Properties:

AlphaData Transparency data: scalar, array the same size as CData, or 1 (default).

AlphaDataMapping

CData Image color data: vector or matrix, 3-D array of RGB triplets.

CDataMapping Color data mapping method: 'direct' or 'scaled' (default).

Children [].

Parent Parent: axes object.

Tag Object identifier: string scalar, character vector, '' (default).

Type Type of graphics object: 'surface'.

UserData: User data: array or [] (default).

Visible State of visibility: 'off' or 'on' (default).

XData Placement along x-axis: two-element vector, scalar, [1 size(CData, 1)] (default).

YData Placement along y-axis: two-element vector, scalar, [1 size(CData, 2)] (default).

CreateFcnCallback (function handle, string or cell) called when object is created. Set this property on an existing component has no effect.

DeleteFcnCallback (function handle, string or cell) called when object is deleted.

BeingDeleted Flag indicating that the object is being deleted.

Examples

f1 = figure();
C = [0 2 4 6; 8 10 12 14; 16 18 20 22];
imagesc(C)

f2 = figure();
C = [0 2 4 6; 8 10 12 14; 16 18 20 22];
imagesc(C)
colormap(gray)

History

Version	Description
1.0.0	initial version
1.7.0	CreateFcn, DeleteFcn callback added.
--	BeingDeleted property added.

Author

Allan CORNET

imread

Read image from graphics file.

Syntax

A = imread(filename)
[A, map] = imread(filename)
[A, map, transparency] = imread(filename)

Input argument

filename - a row vector characters or scalar string: name of graphics file.

Output argument

A - Image data: array.
map - Colormap: m-by-3 matrix.
transparency - Transparency information: matrix.

Description

imread reads the image data from the given file into a matrix.

Format	Description
BMP	Windows Bitmap
GIF	Graphic Interchange Format (optional)
JPG	Joint Photographic Experts Group
JPEG	Joint Photographic Experts Group
PNG	Portable Network Graphics
PBM	Portable Bitmap
PGM	Portable Graymap
PPM	Portable Pixmap
XBM	X11 Bitmap
XPM	X11 Pixmap

Example

f = figure();
filename = [tempdir, 'ngc6543a.gif'];
websave(filename, 'https://solarviews.com/raw/ds/ngc6543a.gif');
img = imread(filename);
imagesc(img);

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

imshow

Display image.

Syntax

imshow(filename)
imshow(img)
imshow(RGB)
imshow(img, [low high])
imshow(img, [])
imshow(img, map)
imshow(..., propertyName, propertyValue)
go = imshow(...)

Input argument

filename - row vector character: file name of the image to display.
img - grayscale image: matrix.
RGB - truecolor image: m-by-n-by-3 array.
[low high] - grayscale image display range.
map - colormap: c-by-3 matrix.
propertyName - a scalar string or row vector character (for compatibility).
propertyValue - a value (for compatibility).

Output argument

go - a graphics object: image type.

Description

imshow(img) displays the image im.

Example

f = figure();
filename = [tempdir, 'apollo_8_earthrise_1968_as08-14-2383.jpg'];
websave(filename, 'https://www.nasa.gov/sites/default/files/thumbnails/image/apollo_8_earthrise_1968_as08-14-2383.jpg');
h = imshow(filename)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

imwrite

Write image to graphics file.

Syntax

imwrite(A, filename)
imwrite(A, map, filename)
imwrite(..., fmt)
imwrite(..., , propertyName, propertyValue)

Input argument

A - matrix: 3D for color and 2D for gray or indexed image.
map - Colormap of indexed image:m-by-3 array.
fmt - Format of output file: 'bmp', 'png', 'jpg', ...
filename - a row vector characters or scalar string: name of graphics file.
propertyName - a scalar string or row vector character.
propertyValue - a value.

Description

imwrite(A, filename) writes image data A to the file specified by filename

Property name:

Quality: quality of output file: scalar in the range [0, 100] (75 as default).

Alpha: matrix of values in the range [0, 1]: Transparency of each pixel.

Comment: character vector, string scalar, cell array of character vectors or string array: Comment added to image.

Author: character vector or string scalar: Author information.

Example

f = figure();
A = rand(69, 69);
A(:,:,2) = rand(69,69);
A(:,:,3) = rand(69,69);
imshow(A);
imwrite(A, [tempdir, '69x69-RGB.png']);

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

is2D

Checks if ax is a 2-D Polar or Cartesian axes.

Syntax

tf = is2D(ax)

Input argument

ax - a scalar graphic object: axe.

Output argument

tf - a logical scalar.

Description

is2D returns Checks if ax is a 2-D Polar or Cartesian axes.

Example

f = figure();
ax = gca();
plot(ax, 1:10, sin(1:10));
assert_istrue(is2D(ax));

f = figure();
surf(peaks);
ax = gca();
assert_isfalse(is2D(ax));

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

isValidGraphicsProperty

Check property name is valid.

Syntax

tf = isValidGraphicsProperty(typename, propertyname)

Input argument

typename - a character vector or scalar string: 'axes', 'line', 'image', 'root', 'text', 'figure'.
propertyname - a character vector or scalar string: property name to check.

Output argument

tf - a scalar logical.

Description

isValidGraphicsProperty checks is property name is existing for graphical object class.

This function is an helper to check input parameters graphical functions.

Example

tf = isValidGraphicsProperty('figure', 'Type')
tf = isValidGraphicsProperty('figure', 'TypeType')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

isgraphics

Check for graphics object.

Syntax

tf = isgraphics(GO)
tf = isgraphics(GO, type)

Input argument

GO - variable or graphics object.
type - a character vector or scalar string: 'axes', 'line', 'image', 'root', 'text', 'figure'.

Output argument

tf - a scalar logical.

Description

isgraphics checks is variable is an graphics object.

Example

f = figure()
tf = isgraphics(f)
tf = isgraphics(f, 'figure')
tf = isgraphics(f, 'text')
f = 3
tf = isgraphics(f)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

ishold

Get current hold state.

Syntax

tf = ishold()
tf = ishold(ax)

Input argument

ax - scalar graphics object: axes.

Output argument

tf - a scalar logical: true if it is hold on.

Description

tf = ishold(ax) returns the hold state of the specified axes object.

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

jet

Jet colormap array.

Syntax

c = jet
c = jet(m)

Input argument

m - a scalar integer value: Number of colors (256 as default value).

Output argument

c - Jet colormap array.

Description

jet returns the colormap with jet colors.

Example

f = figure();
surf(peaks);
colormap('jet');

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

legend

Add legend to axes.

Syntax

legend()
legend(label1, ..., labelN)
legend(labels)
legend('off')
legend('hide')
legend('show')
legend('toggle')
legend('boxon')
legend('boxoff')
legend(ax, ...)
legend(..., 'Location', lcn)
legend(..., propertyName, propertyValue)
L = legend(...)

Input argument

label1, ..., labelN - sets the legend labels: row vector characters.
labels - cell array of character vectors or string array.
'off' - delete the legend.
'toggle' - toggle legend visibility.
'hide' - hide legend.
'show' - show legend.
'boxon' - display box around legend.
'boxoff' - hide box around legend.
ax - axes to make current.
lcn - Legend location: a string ('NE' default).
propertyName - a scalar string or row vector character.
propertyValue - a value.

Output argument

L - a graphics object: axes type.

Description

legend creates a legend in the current figure.

Location for legend on the plot:

'northeast' or 'NE': Top right (default).

'north' or 'N': Top center.

'south' or 'S': Bottom center.

'east' or 'E': Middle right.

'west' or 'W': Middle left.

'northwest' or 'NW': Top left.

'southeast' or 'SE': Bottom right.

'southwest' or 'SW': Bottom left.

Example

f = figure();
x = linspace(0,10);
y1 = sin(x);
y2 = cos(x);
ax = gca();
plot(ax, x, y1);
plot(ax, x, y2);
legend('sin(x)', 'cos(x)', 'Location', 'N')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

line

Create primitive line.

Syntax

go = line()
po = line(x, y)
go = line(x, y, z)
go = line(ax, x, y, z)
go = line(ax, x, y, z, propertyName, propertyValue)

Input argument

x, y , z - a scalar graphics object value: parent container, specified as a figure.
ax - Target axes: axes object.
propertyName - a scalar string or row vector character.
propertyValue - a value.

Output argument

go - a graphics object: line type.

Description

line(x, y) creates a line in the current axes with vectors x and y.

line(x, y, z) creates a line in three-dimensional coordinates.

Properties:

Children [] (currently not used).

Color Line color: RGB triplet, [0, 0, 0] or hexadecimal color code.

DisplayName Legend label: character vector or string scalar, '' (default).

LineStyle Line style: '--', ':', '-.', 'none' or '-' (default).

LineWidth Line width: scalar positive value.

MarkerMarker symbol: 'o' (circle), '+' (Plus sign), '*' (asterik), '.' (point), 'x' (cross), '_' (horizontal line) , '|' (vertical line), 'square', 'diamond', '^' (Upward-pointing triangle), 'v' (Downward-pointing triangle), '>' (Right-pointing triangle), '<' (Left-pointing triangle), 'pentagram', 'hexagram', 'none'(default).

MarkerEdgeColor Marker outline color: RGB triplet.

MarkerFaceColor Marker fill color: RGB triplet.

MarkerSize Marker size: scalar positive value.

Parent Parent: axes graphics object.

Tag Object identifier: string scalar, character vector, '' (default).

Type Type of graphics object: 'line'

UserData User data: array, [] (default).

Visible State of visibility: 'off' or 'on' (default).

XData x values: vector, [0 1] (default).

YData y values: vector, [0 1] (default).

ZData z values: vector, [] (default).

CreateFcnCallback (function handle, string or cell) called when object is created. Set this property on an existing component has no effect.

DeleteFcnCallback (function handle, string or cell) called when object is deleted.

BeingDeleted Flag indicating that the object is being deleted.

Examples

f = figure();
x = linspace(0,10)';
y1 = sin(x);
y2 = cos(x);
line(x, y1, 'Color', [0 1 0])
line(x, y2, 'Color', [1 0 0])

f = figure();
x = [1 9];
y = [2 12];
line(x,y,'Color','red','LineStyle','--')

f = figure();
t = linspace(0,10*pi,400);
x = sin(t);
y = cos(t);
z = t;
line(x,y,z)
view(3)

History

Version	Description
1.0.0	initial version
1.7.0	CreateFcn, DeleteFcn callback added.
--	BeingDeleted property added.

Author

Allan CORNET

loglog

Log-log scale plot.

Syntax

loglog(X, Y)
loglog(X, Y, LineSpec)
loglog(Y)
loglog(Y, LineSpec)
loglog(ax, ...)
loglog(..., propertyName, propertyValue)
go = loglog(...)

Input argument

X - Log scale coordinates: scalar, vector or matrix.
Y - Log scale coordinates: scalar, vector or matrix.
LineSpec - Line style, marker, and/or color: character vector or scalar string.
ax - a scalar graphics object value: parent container, specified as a axes.
propertyName - a scalar string or row vector character. see help of 'line' for property list.
propertyValue - a value.

Output argument

go - a graphics object: line type.

Description

loglog(X, Y) plots data using a base 10 logarithmic scale for the x-axis and the y-axis.

loglog has the exact same syntax as the plot command.

Examples

f = figure();
x = logspace(-1,2);
y = 2 .^ x;
loglog(x,y)
grid on

f = figure();
x = logspace(-1,2,20);
y = 10 .^ x;
loglog(x,y,'s','MarkerFaceColor',[0 0.447 0.741])
grid on

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

mesh

Mesh surface plot.

Syntax

mesh(X, Y, Z)
mesh(Z)
mesh(Z, C)
mesh(X, Y, Z, C)
mesh(parent, ...)
mesh(..., propertyName, propertyValue)
go = mesh(...)

Input argument

X - x-coordinates: vector or matrix.
Y - y-coordinates: vector or matrix.
Z - z-coordinates: vector or matrix.
C - Color array: m-by-n-by-3 array of RGB triplets.
parent - a scalar graphics object value: parent container, specified as a axes.
propertyName - a scalar string or row vector character.
propertyValue - a value.

Output argument

go - a graphics object: surface type.

Description

mesh creates a 3-D wireframe mesh.

You can customize the appearance of the plot using various options such as color, lighting, and shading.

Examples

f = figure();
[X, Y] = meshgrid(-8:.5:8);
R = sqrt(X.^2 + Y.^2) + eps;
Z = sin(R) ./ R;
mesh(X, Y, Z)
axis square

f = figure();
F = str2func('@(z) z .^ 3 - 1');
x = linspace(-2, 2, 100);
y = linspace(-2, 2, 100);
[X, Y] = meshgrid(x, y);
Z = X + 1i*Y;
W = F(Z);
mesh(real(W), imag(W), abs(W))
xlabel('Real')
ylabel('Imaginary')
zlabel('Magnitude')

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

meshz

Mesh surface plot with curtain.

Syntax

meshz(X, Y, Z)
meshz(Z)
meshz(Z, C)
meshz(X, Y, Z, C)
meshz(parent, ...)
meshz(..., propertyName, propertyValue)
go = meshz(...)

Input argument

X - x-coordinates: vector or matrix.
Y - y-coordinates: vector or matrix.
Z - z-coordinates: vector or matrix.
C - Color array: m-by-n-by-3 array of RGB triplets.
parent - a scalar graphics object value: parent container, specified as a axes.
propertyName - a scalar string or row vector character.
propertyValue - a value.

Output argument

go - a graphics object: surface type.

Description

meshz creates a 3-D surface plot with a wireframe plot on top.

The function takes the same input arguments as the mesh function.

Example

f = figure();
[X,Y] = meshgrid(-5:.5:5);
Z = Y.*sin(X) - X.*cos(Y);
s = meshz(X,Y,Z)

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

newplot

Prepare to produce a new plot.

Syntax

go = newplot()
go = newplot(ax)

Input argument

ax - specified figure or axes rather than the current figure and axes.

Output argument

go - a graphics object: axes type.

Description

newplot prepares a figure and axes for graphics commands.

Example

h = newplot()

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

pan

Enable pan mode.

Syntax

pan
pan option
pan(fig, ...)
pan(ax, ...)

Input argument

option - string: 'on', 'off', 'out', 'xon', 'yon' or 'toggle'.
fig - Figure object: Target figure
ax - a scalar graphics object value: parent container, specified as a axes.

Description

Utilize the pan mode to dynamically adjust axis limits for interactive data exploration.

Enable or disable the pan mode and configure additional basic settings using the pan function.

Pan mode is compatible with various charts like line, bar, histogram, and surface charts. These charts typically feature pan icon on the toolbar to facilitate pan functionality.

pan option configures the pan mode for all axes within the current figure.

Once pan mode is active, you can adjust the view of axes using the cursor, or keyboard:

Cursor: Click and drag the cursor in the axes.

Keyboard: To pan horizontally, press the left arrow (←) or the right arrow (→) key. To pan vertically, press the up arrow (↑) or the down arrow (↓) key.

The pan mode option can be specified using one of the following values:

'toggle': Toggles the pan mode. If pan mode is disabled, 'toggle' reverts to the most recently used pan option of 'on', 'xon', or 'yon'. This option behaves the same as calling pan without any arguments.

'xon': Enables pan mode for the x-dimension exclusively.

'yon': Activates pan mode for the y-dimension exclusively.

'on': Activates pan mode.

'off': Deactivates pan mode. Note that certain default interactions may persist regardless of the interaction mode.

Example

surf(peaks)
pan on

History

Version	Description
1.2.0	initial version

Author

Allan CORNET

parula

Parula colormap array.

Syntax

c = parula
c = parula(m)

Input argument

m - a scalar integer value: Number of colors (256 as default value).

Output argument

c - Parula colormap array.

Description

parula returns the colormap with parula colors.

parula is the default colormap.

Example

f = figure();
surf(peaks);
colormap('parula');

History

Version	Description
1.0.0	initial version

Author

Allan CORNET

patch

Create patches of colored polygons

Syntax

patch(X, Y, C)
patch(X, Y, Z, C)
patch('XData', X, 'YData', Y)
patch('XData', X, 'YData', Y, 'ZData', Z)
patch('Faces', F, 'Vertices', V)
patch(S)
patch(..., propertyName, propertyValue)
patch(ax, ...)
go = patch(...)

Input argument

X - x-coordinates: vector or matrix.
Y - y-coordinates: vector or matrix.
Z - z-coordinates: vector or matrix.
C - Color array: scalar, vector, m-by-n-by-3 array of RGB triplets.
ax - a scalar graphics object value: parent container, specified as a axes.
propertyName - a scalar string or row vector character.
propertyValue - a value.
S - a structure with fields that correspond patch property names and field values.

Output argument

go - a graphics object: patch type.

Description

patch(X, Y, C) creates a 2D polygonal shape with vertices defined by X and Y coordinates, and fills the shape with color C.

patch(X, Y, Z, C) creates a 3D polygonal shape with vertices defined by X, Y, and Z coordinates, and fills the shape with color C.

patch(..., PropertyName, PropertyValue, ...) sets optional properties for the patch object using name-value pairs.

patch('Faces', F, 'Vertices', V) creates one or more polygons .

go = patch(...) returns the handle go to the created patch object.