ctrsyl(3F)

NAME
     CTRSYL - solve the complex Sylvester matrix equation

SYNOPSIS
     SUBROUTINE CTRSYL( 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

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

PURPOSE
     CTRSYL 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) CHARACTER*1
             Specifies the option op(A):
             = 'N': op(A) = A    (No transpose)
             = 'C': op(A) = A**H (Conjugate transpose)

     TRANB   (input) CHARACTER*1
             Specifies the option op(B):
             = 'N': op(B) = B    (No transpose)
             = 'C': op(B) = B**H (Conjugate 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) COMPLEX array, dimension (LDA,M)
             The upper triangular matrix A.

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

     B       (input) COMPLEX array, dimension (LDB,N)
             The upper triangular matrix B.

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

     C       (input/output) COMPLEX 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).