# strsyl.f - Man Page

SRC/strsyl.f

## Synopsis

### Functions/Subroutines

subroutine strsyl (trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc, scale, info)
STRSYL

## Function/Subroutine Documentation

### subroutine strsyl (character trana, character tranb, integer isgn, integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, real, dimension( ldc, * ) c, integer ldc, real scale, integer info)

STRSYL

Purpose:

``` STRSYL 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 SHSEQR), 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.```
Parameters

TRANA

```          TRANA is 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

```          TRANB is 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

```          ISGN is INTEGER
= +1: solve op(A)*X + X*op(B) = scale*C
= -1: solve op(A)*X - X*op(B) = scale*C```

M

```          M is INTEGER
The order of the matrix A, and the number of rows in the
matrices X and C. M >= 0.```

N

```          N is INTEGER
The order of the matrix B, and the number of columns in the
matrices X and C. N >= 0.```

A

```          A is REAL array, dimension (LDA,M)
The upper quasi-triangular matrix A, in Schur canonical form.```

LDA

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

B

```          B is REAL array, dimension (LDB,N)
The upper quasi-triangular matrix B, in Schur canonical form.```

LDB

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

C

```          C is REAL 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

```          LDC is INTEGER
The leading dimension of the array C. LDC >= max(1,M)```

SCALE

```          SCALE is REAL
The scale factor, scale, set <= 1 to avoid overflow in X.```

INFO

```          INFO is 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).```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 162 of file strsyl.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page strsyl(3) is an alias of strsyl.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK