---
name: "strsyl.f"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/strsyl.f"
---

# strsyl.f(3)

## NAME

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
!>          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 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

Univ. of Colorado Denver

NAG Ltd.

Definition at line **162** of file **strsyl.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.