islocalmin

📝Syntax

TF = islocalmin(A)
TF = islocalmin(A, dim)
TF = islocalmin(..., Name, Value)
[TF, P] = islocalmin(...)

📥Input Arguments

Parameter	Description
A	input data: real numeric or logical vector, matrix, N-D array, table or timetable.
dim	dimension to operate along: positive integer scalar (default: first non-singleton dimension). Not supported for tables.
'MinProminence'	nonnegative scalar (default: 0): only the minima whose prominence is at least this value are returned.
'FlatSelection'	element marked in a flat minimum region: 'center' (default), 'first', 'last' or 'all'.
'MinSeparation'	nonnegative scalar (default: 0), in sample point units (a duration for datetime or duration sample points): a minimum closer than this value to a more prominent one is ignored.
'MaxNumExtrema'	positive integer: keep at most this number of the most prominent minima (default: no limit).
'ProminenceWindow'	positive scalar k or two-element vector [b f] of nonnegative values (a duration for datetime or duration sample points): the prominence of a minimum is computed with the data of the window [x-k/2, x+k/2) or [x-b, x+f] only.
'SamplePoints'	sorted vector of unique double, single, datetime or duration values: locations of the data (default: 1, 2, 3, ...). For a table, it can also be a table variable name. A timetable uses its row times.
'DataVariables'	table variables to operate on: names, indices, logical vector, function handle or vartype (default: all variables).
'OutputFormat'	'logical' (default): TF is a logical array; 'tabular': TF is a table with the DataVariables. Only for tables.

📤Output Arguments

Parameter	Description
TF	logical array of the size of A (or table), true at the local minima.
P	prominence of each local minimum (0 elsewhere), same size as A; unsigned integer class for integer data. For a table, P is a table with the DataVariables.

📄Description

islocalmin marks the elements of A that are smaller than their neighbors along the operating dimension. A run of equal values smaller than the values around it is one local minimum (see 'FlatSelection').

The first and last elements are never local minima. NaN values are ignored. -Inf values are always local minima, with an infinite prominence.

The prominence of a minimum measures how much it stands out: from the minimum, a horizontal line is drawn on each side up to the first strictly lower value or the end of the data; the basis is the lower of the two highest values found above these lines, and the prominence is the depth of the minimum below the basis. Every element of a flat minimum region carries its prominence.

islocalmin(A) gives the same result as islocalmax applied to the reversed data: the options behave the same way. The filters are applied in this order: 'MinProminence', 'MinSeparation' (a flat region counts as one minimum spanning its samples) and 'MaxNumExtrema' (on ties, the first minimum wins).

Without 'ProminenceWindow', the search runs in linear time: it is suitable for large signals.

💡Examples

Local minima and their prominence

A = [5 0 4 2 4 1 5];
[TF, P] = islocalmin(A)
islocalmin(A, 'MinProminence', 3)

Flat minima regions

x = 0:0.1:5;
A = max(-0.75, -sin(pi * x));
find(islocalmin(A, 'FlatSelection', 'first'))
find(islocalmin(A, 'FlatSelection', 'all'))

Most prominent minimum of each column

A = [3 4; 1 2; 2 4; 0 1; 3 4];
TF = islocalmin(A, 'MaxNumExtrema', 1)