dtrsyl man page on Scientific

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```DTRSYL(1)		 LAPACK routine (version 3.2)		     DTRSYL(1)

NAME
DTRSYL - solves 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-diag‐
onal 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
= +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 matri‐
ces 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 canonical 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 canonical 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).

LAPACK routine (version 3.2)	 November 2008			     DTRSYL(1)
```
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