dtrsyl(3P) Sun Performance Library dtrsyl(3P)NAMEdtrsyl - solve the real Sylvester matrix equation
SYNOPSIS
SUBROUTINE DTRSYL(TRANA, TRANB, ISGN, M, N, A, LDA, B, LDB, C, LDC,
SCALE, INFO)
CHARACTER * 1 TRANA, TRANB
INTEGER ISGN, M, N, LDA, LDB, LDC, INFO
DOUBLE PRECISION SCALE
DOUBLE PRECISION A(LDA,*), B(LDB,*), C(LDC,*)
SUBROUTINE DTRSYL_64(TRANA, TRANB, ISGN, M, N, A, LDA, B, LDB, C,
LDC, SCALE, INFO)
CHARACTER * 1 TRANA, TRANB
INTEGER*8 ISGN, M, N, LDA, LDB, LDC, INFO
DOUBLE PRECISION SCALE
DOUBLE PRECISION A(LDA,*), B(LDB,*), C(LDC,*)
F95 INTERFACE
SUBROUTINE TRSYL(TRANA, TRANB, ISGN, M, N, A, [LDA], B, [LDB], C,
[LDC], SCALE, [INFO])
CHARACTER(LEN=1) :: TRANA, TRANB
INTEGER :: ISGN, M, N, LDA, LDB, LDC, INFO
REAL(8) :: SCALE
REAL(8), DIMENSION(:,:) :: A, B, C
SUBROUTINE TRSYL_64(TRANA, TRANB, ISGN, M, N, A, [LDA], B, [LDB], C,
[LDC], SCALE, [INFO])
CHARACTER(LEN=1) :: TRANA, TRANB
INTEGER(8) :: ISGN, M, N, LDA, LDB, LDC, INFO
REAL(8) :: SCALE
REAL(8), DIMENSION(:,:) :: A, B, C
C INTERFACE
#include <sunperf.h>
void dtrsyl(char trana, char tranb, int isgn, int m, int n, double *a,
int lda, double *b, int ldb, double *c, int ldc, double
*scale, int *info);
void dtrsyl_64(char trana, char tranb, long isgn, long m, long n, dou‐
ble *a, long lda, double *b, long ldb, double *c, long ldc,
double *scale, long *info);
PURPOSEdtrsyl solves the real Sylvester matrix equation:
op(A)*X + X*op(B) = scale*C or
op(A)*X - X*op(B) = scale*C,
where op(A) = A or A**T, and A and B are both upper quasi- triangular.
A is M-by-M and B is N-by-N; the right hand side C and the solution X
are M-by-N; and scale is an output scale factor, set <= 1 to avoid
overflow in X.
A and B must be in Schur canonical form (as returned by SHSEQR), that
is, block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each
2-by-2 diagonal block has its diagonal elements equal and its off-diag‐
onal elements of opposite sign.
ARGUMENTS
TRANA (input)
Specifies the option op(A):
= 'N': op(A) = A (No transpose)
= 'T': op(A) = A**T (Transpose)
= 'C': op(A) = A**H (Conjugate transpose = Transpose)
TRANB (input)
Specifies the option op(B):
= 'N': op(B) = B (No transpose)
= 'T': op(B) = B**T (Transpose)
= 'C': op(B) = B**H (Conjugate transpose = Transpose)
ISGN (input)
Specifies the sign in the equation:
= +1: solve op(A)*X + X*op(B) = scale*C
= -1: solve op(A)*X - X*op(B) = scale*C
M (input) The order of the matrix A, and the number of rows in the
matrices X and C. M >= 0.
N (input) The order of the matrix B, and the number of columns in the
matrices X and C. N >= 0.
A (input) The upper quasi-triangular matrix A, in Schur canonical form.
LDA (input)
The leading dimension of the array A. LDA >= max(1,M).
B (input) The upper quasi-triangular matrix B, in Schur canonical form.
LDB (input)
The leading dimension of the array B. LDB >= max(1,N).
C (input/output)
On entry, the M-by-N right hand side matrix C. On exit, C is
overwritten by the solution matrix X.
LDC (input)
The leading dimension of the array C. LDC >= max(1,M)
SCALE (output)
The scale factor, scale, set <= 1 to avoid overflow in X.
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
= 1: A and B have common or very close eigenvalues; perturbed
values were used to solve the equation (but the matrices A
and B are unchanged).
6 Mar 2009 dtrsyl(3P)
