[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)
| Parameter | Description |
|---|---|
| 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). |
| Parameter | Description |
|---|---|
| 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. |
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
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)| Version | Description |
|---|---|
| 1.0.0 | initial version |