# dtrsyl.f man page

dtrsyl.f —

## Synopsis

### Functions/Subroutines

subroutinedtrsyl(TRANA, TRANB, ISGN, M, N, A, LDA, B, LDB, C, LDC, SCALE, INFO)DTRSYL

## Function/Subroutine Documentation

### subroutine dtrsyl (characterTRANA, characterTRANB, integerISGN, integerM, integerN, double precision, dimension( lda, * )A, integerLDA, double precision, dimension( ldb, * )B, integerLDB, double precision, dimension( ldc, * )C, integerLDC, double precisionSCALE, integerINFO)

**DTRSYL**

**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.
```

**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
Specifies the sign in the equation:
= +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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 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*

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

*SCALE*

```
SCALE is DOUBLE PRECISION
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

Univ. of Colorado Denver

NAG Ltd.

**Date:**

November 2011

Definition at line 164 of file dtrsyl.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

dtrsyl(3) is an alias of dtrsyl.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK