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);

Description

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)