strsyl(3S)

NAME
     STRSYL - solve the real Sylvester matrix equation

SYNOPSIS
     SUBROUTINE STRSYL( TRANA, TRANB, ISGN, M, N, A, LDA, B, LDB, C, LDC,
                        SCALE, INFO )

         CHARACTER      TRANA, TRANB

         INTEGER        INFO, ISGN, LDA, LDB, LDC, M, N

         REAL           SCALE

         REAL           A( LDA, * ), B( LDB, * ), C( LDC, * )

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

PURPOSE
     STRSYL 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) CHARACTER*1
             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) CHARACTER*1
             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) INTEGER
             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) INTEGER
             The order of the matrix A, and the number of rows in the matrices
             X and C. M >= 0.

     N       (input) INTEGER
             The order of the matrix B, and the number of columns in the
             matrices X and C. N >= 0.

     A       (input) REAL array, dimension (LDA,M)
             The upper quasi-triangular matrix A, in Schur canonical form.

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

     B       (input) REAL array, dimension (LDB,N)
             The upper quasi-triangular matrix B, in Schur canonical form.

     LDB     (input) INTEGER
             The leading dimension of the array B. LDB >= max(1,N).

     C       (input/output) REAL array, dimension (LDC,N)
             On entry, the M-by-N right hand side matrix C.  On exit, C is
             overwritten by the solution matrix X.

     LDC     (input) INTEGER
             The leading dimension of the array C. LDC >= max(1,M)

     SCALE   (output) REAL
             The scale factor, scale, set <= 1 to avoid overflow in X.

     INFO    (output) INTEGER
             = 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).

SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)
     This man page is available only online.