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# dtrsyl

```
NAME
DTRSYL - solve the real Sylvester matrix equation

SYNOPSIS
SUBROUTINE DTRSYL( 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

DOUBLE         PRECISION A( LDA, * ), B( LDB, * ), C(
LDC, * )

PURPOSE
DTRSYL 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
DHSEQR), 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 = Tran-
spose)

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 = Tran-
spose)

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) DOUBLE PRECISION array, dimension (LDA,M)
The upper quasi-triangular matrix A, in Schur canon-
ical form.

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

B       (input) DOUBLE PRECISION array, dimension (LDB,N)
The upper quasi-triangular matrix B, in Schur canon-
ical form.

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

C       (input/output) DOUBLE PRECISION 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).
```