[Q_OUT, B_OUT, SCALE, WR, WI, INFO] = slicot_sb03od(DICO, FACT, TRANS, A, Q_IN, B_IN)
| Parameter | Description |
|---|---|
| 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. |
| Parameter | Description |
|---|---|
| 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. |
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.
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)| Version | Description |
|---|---|
| 1.0.0 | initial version |