[A_OUT, X_OUT, NBLCKS, BLSIZE, WR, WI, INFO] = slicot_mb03rd(JOBX, SORT, PMAX, A_IN, X_IN, TOL)
| Parameter | Description |
|---|---|
| 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. |
| Parameter | Description |
|---|---|
| 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; |
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.
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)| Version | Description |
|---|---|
| 1.0.0 | initial version |