ZTRSYL(3f)

NAME
ZTRSYL - the complex Sylvester matrix equation

SYNOPSIS

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

CHARACTER
    TRANA, TRANB

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

DOUBLE
    PRECISION SCALE

COMPLEX*16
    A( LDA, * ), B( LDB, * ), C( LDC, * )

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) 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*16 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*16 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*16 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) DOUBLE PRECISION
    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).