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

NAME

ztrsyl - solve the complex Sylvester matrix equation

SYNOPSIS

  SUBROUTINE ZTRSYL( TRANA, TRANB, ISGN, M, N, A, LDA, B, LDB, C, LDC, 
 *      SCALE, INFO)
  CHARACTER * 1 TRANA, TRANB
  DOUBLE COMPLEX A(LDA,*), B(LDB,*), C(LDC,*)
  INTEGER ISGN, M, N, LDA, LDB, LDC, INFO
  DOUBLE PRECISION SCALE

  SUBROUTINE ZTRSYL_64( TRANA, TRANB, ISGN, M, N, A, LDA, B, LDB, C, 
 *      LDC, SCALE, INFO)
  CHARACTER * 1 TRANA, TRANB
  DOUBLE COMPLEX A(LDA,*), B(LDB,*), C(LDC,*)
  INTEGER*8 ISGN, M, N, LDA, LDB, LDC, INFO
  DOUBLE PRECISION SCALE

F95 INTERFACE

  SUBROUTINE TRSYL( TRANA, TRANB, ISGN, [M], [N], A, [LDA], B, [LDB], 
 *       C, [LDC], SCALE, [INFO])
  CHARACTER(LEN=1) :: TRANA, TRANB
  COMPLEX(8), DIMENSION(:,:) :: A, B, C
  INTEGER :: ISGN, M, N, LDA, LDB, LDC, INFO
  REAL(8) :: SCALE

  SUBROUTINE TRSYL_64( TRANA, TRANB, ISGN, [M], [N], A, [LDA], B, [LDB], 
 *       C, [LDC], SCALE, [INFO])
  CHARACTER(LEN=1) :: TRANA, TRANB
  COMPLEX(8), DIMENSION(:,:) :: A, B, C
  INTEGER(8) :: ISGN, M, N, LDA, LDB, LDC, INFO
  REAL(8) :: SCALE

C INTERFACE

#include <sunperf.h>

void ztrsyl(char trana, char tranb, int isgn, int m, int n, doublecomplex *a, int lda, doublecomplex *b, int ldb, doublecomplex *c, int ldc, double *scale, int *info);

void ztrsyl_64(char trana, char tranb, long isgn, long m, long n, doublecomplex *a, long lda, doublecomplex *b, long ldb, doublecomplex *c, long ldc, double *scale, long *info);

PURPOSE

ztrsyl solves the complex 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**H, and A and B are both upper 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.

ARGUMENTS

• TRANA (input)
  Specifies the option op(A):

   = 'N': op(A)  = A    (No transpose)

   = 'C': op(A)  = A**H (Conjugate transpose)

• TRANB (input)
  Specifies the option op(B):

   = 'N': op(B)  = B    (No transpose)

   = 'C': op(B)  = B**H (Conjugate 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 triangular matrix A.

• LDA (input)
  The leading dimension of the array A. LDA > = max(1,M).

• B (input)
  The upper triangular matrix B.

• 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).