dtrsyl - solve the real Sylvester matrix equation
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);
Oracle Solaris Studio Performance Library dtrsyl(3P) NAME dtrsyl - 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); PURPOSE dtrsyl 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). 7 Nov 2015 dtrsyl(3P)