• NAME
• SYNOPSIS
• F95 INTERFACE
• C INTERFACE
• PURPOSE
• ARGUMENTS

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, double *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-diagonal 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).