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[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) |
Specifies the reduction stage: 'F': Perform the forward stage only; 'B': Perform the backward stage only; 'A': Perform both (all) stages.
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
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.
the leading N-by-N part of this array must contain the state transition matrix A to be transformed
the leading N-by-M part of this array must contain the input matrix B to be transformed.
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.
The order of the controllable state-space representation. NCONT_IN is input only if STAGES = 'B'.
The number of stairs in the staircase form (also, the controllability index of the controllable part of the system representation).
The tolerance to be used in rank determination when transforming (A, B).
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.
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.
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.
If JOBV = 'I', then the leading M-by-M part of this array contains the transformation matrix V.
NCONT_OUT is input only if STAGES = 'B'.
INDCON is input only if STAGES = 'B'.
KSTAIR is input if STAGES = 'B', and output otherwise.
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 |
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