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ctrsyl

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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 triangu-
lar. 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 fac-
tor, 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
= +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).
```