(S|D|C|Z)TRSYL¶

Single, double, single complex, and double complex TRSYL.

Description¶

Solves one of the Sylvester equations:

$A \mult X + X \mult B = \alpha C$

$\herm{A} \mult X + X \mult B = \alpha C$

$A \mult X + X \mult \herm{B} = \alpha C$

$\herm{A} \mult X + X \mult \herm{B} = \alpha C$

$A \mult X - X \mult B = \alpha C$

$\herm{A} \mult X - X \mult B = \alpha C$

$A \mult X - X \mult \herm{B} = \alpha C$

$\herm{A} \mult X - X \mult \herm{B} = \alpha C$

Matrices A and B are upper triangular, A is M x M and B is N x N. Matrices C and X are M x N. The scale factor $\alpha$ is set less than one to avoid overflow in X.

LAPACK Interface¶

void strsyl(const char *TRANA, const char *TRANB, const qml_long *ISGN,
    const qml_long *M, const qml_long *N, float *A, const qml_long *LDA,
    float *B, const qml_long *LDB, float *C, const qml_long *LDC,
    float *SCALE, qml_long *INFO);

void dtrsyl(const char *TRANA, const char *TRANB, const qml_long *ISGN,
    const qml_long *M, const qml_long *N, double *A, const qml_long *LDA,
    double *B, const qml_long *LDB, double *C, const qml_long *LDC,
    double *SCALE, qml_long *INFO);

void ctrsyl(const char *TRANA, const char *TRANB, const qml_long *ISGN,
    const qml_long *M, const qml_long *N, qml_single_complex *A,
    const qml_long *LDA, qml_single_complex *B, const qml_long *LDB,
    qml_single_complex *C, const qml_long *LDC, float *SCALE,
    qml_long *INFO);

void ztrsyl(const char *TRANA, const char *TRANB, const qml_long *ISGN,
    const qml_long *M, const qml_long *N, qml_double_complex *A,
    const qml_long *LDA, qml_double_complex *B, const qml_long *LDB,
    qml_double_complex *C, const qml_long *LDC, double *SCALE,
    qml_long *INFO);

Arguments¶

TRANA	Specifies transform option for A, ‘N’ for none, ‘T’ for transpose, ‘C’ for conjugate transpose
TRANB	Specifies transform option for B, ‘N’ for none, ‘T’ for transpose, ‘C’ for conjugate transpose
ISGN	Solve $A\mult X + X \mult B = \alpha C$ (+1) or $A\mult X - X \mult B = \alpha C$ (-1)
M	Number of rows and columns of A
N	Number of rows and columns of B
A	Upper triangular matrix
LDA	Leading dimension of A
B	Upper triangular matrix
LDB	Leading dimension of B
C	Right hand side matrix, on exit overwritten by solution matrix X
LDC	Leading dimension of C
SCALE	Scale factor $\alpha$ to avoid overflow in X
INFO	0 on success, <0 on bad arguments, 1 if A and B have very close eigenvalues