# STRSYL (3) - Linux Man Pages

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 (characterTRANA, characterTRANB, integerISGN, integerM, integerN, real, dimension( lda, * )A, integerLDA, real, dimension( ldb, * )B, integerLDB, real, dimension( ldc, * )C, integerLDC, realSCALE, integerINFO)

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