# dtrsyl3.f - Man Page

SRC/dtrsyl3.f

## Synopsis

### Functions/Subroutines

subroutine dtrsyl3 (trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc, scale, iwork, liwork, swork, ldswork, info)
DTRSYL3

## Function/Subroutine Documentation

### subroutine dtrsyl3 (character trana, character tranb, integer isgn, integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldb, * ) b, integer ldb, double precision, dimension( ldc, * ) c, integer ldc, double precision scale, integer, dimension( * ) iwork, integer liwork, double precision, dimension( ldswork, * ) swork, integer ldswork, integer info)

DTRSYL3

Purpose

```  DTRSYL3 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.

This is the block version of the algorithm.```
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 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.```

IWORK

```          IWORK is INTEGER array, dimension (MAX(1,LIWORK))
On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.```

LIWORK

```          IWORK is INTEGER
The dimension of the array IWORK. LIWORK >=  ((M + NB - 1) / NB + 1)
+ ((N + NB - 1) / NB + 1), where NB is the optimal block size.

If LIWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal dimension of the IWORK array,
returns this value as the first entry of the IWORK array, and
no error message related to LIWORK is issued by XERBLA.```

SWORK

```          SWORK is DOUBLE PRECISION array, dimension (MAX(2, ROWS),
MAX(1,COLS)).
On exit, if INFO = 0, SWORK(1) returns the optimal value ROWS
and SWORK(2) returns the optimal COLS.```

LDSWORK

```          LDSWORK is INTEGER
LDSWORK >= MAX(2,ROWS), where ROWS = ((M + NB - 1) / NB + 1)
and NB is the optimal block size.

If LDSWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal dimensions of the SWORK matrix,
returns these values as the first and second entry of the SWORK
matrix, and no error message related LWORK is issued by XERBLA.```

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).```

Definition at line 178 of file dtrsyl3.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page dtrsyl3(3) is an alias of dtrsyl3.f(3).

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