# dlasy2.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
Page Index

dlasy2.f

## SYNOPSIS

### Functions/Subroutines

subroutine dlasy2 (LTRANL, LTRANR, ISGN, N1, N2, TL, LDTL, TR, LDTR, B, LDB, SCALE, X, LDX, XNORM, INFO)
DLASY2 solves the Sylvester matrix equation where the matrices are of order 1 or 2.

## Function/Subroutine Documentation

### subroutine dlasy2 (logical LTRANL, logical LTRANR, integer ISGN, integer N1, integer N2, double precision, dimension( ldtl, * ) TL, integer LDTL, double precision, dimension( ldtr, * ) TR, integer LDTR, double precision, dimension( ldb, * ) B, integer LDB, double precision SCALE, double precision, dimension( ldx, * ) X, integer LDX, double precision XNORM, integer INFO)

DLASY2 solves the Sylvester matrix equation where the matrices are of order 1 or 2.

Purpose:

``` DLASY2 solves for the N1 by N2 matrix X, 1 <= N1,N2 <= 2, in

op(TL)*X + ISGN*X*op(TR) = SCALE*B,

where TL is N1 by N1, TR is N2 by N2, B is N1 by N2, and ISGN = 1 or
-1.  op(T) = T or T**T, where T**T denotes the transpose of T.
```

Parameters:

LTRANL

```          LTRANL is LOGICAL
On entry, LTRANL specifies the op(TL):
= .FALSE., op(TL) = TL,
= .TRUE., op(TL) = TL**T.
```

LTRANR

```          LTRANR is LOGICAL
On entry, LTRANR specifies the op(TR):
= .FALSE., op(TR) = TR,
= .TRUE., op(TR) = TR**T.
```

ISGN

```          ISGN is INTEGER
On entry, ISGN specifies the sign of the equation
as described before. ISGN may only be 1 or -1.
```

N1

```          N1 is INTEGER
On entry, N1 specifies the order of matrix TL.
N1 may only be 0, 1 or 2.
```

N2

```          N2 is INTEGER
On entry, N2 specifies the order of matrix TR.
N2 may only be 0, 1 or 2.
```

TL

```          TL is DOUBLE PRECISION array, dimension (LDTL,2)
On entry, TL contains an N1 by N1 matrix.
```

LDTL

```          LDTL is INTEGER
The leading dimension of the matrix TL. LDTL >= max(1,N1).
```

TR

```          TR is DOUBLE PRECISION array, dimension (LDTR,2)
On entry, TR contains an N2 by N2 matrix.
```

LDTR

```          LDTR is INTEGER
The leading dimension of the matrix TR. LDTR >= max(1,N2).
```

B

```          B is DOUBLE PRECISION array, dimension (LDB,2)
On entry, the N1 by N2 matrix B contains the right-hand
side of the equation.
```

LDB

```          LDB is INTEGER
The leading dimension of the matrix B. LDB >= max(1,N1).
```

SCALE

```          SCALE is DOUBLE PRECISION
On exit, SCALE contains the scale factor. SCALE is chosen
less than or equal to 1 to prevent the solution overflowing.
```

X

```          X is DOUBLE PRECISION array, dimension (LDX,2)
On exit, X contains the N1 by N2 solution.
```

LDX

```          LDX is INTEGER
The leading dimension of the matrix X. LDX >= max(1,N1).
```

XNORM

```          XNORM is DOUBLE PRECISION
On exit, XNORM is the infinity-norm of the solution.
```

INFO

```          INFO is INTEGER
On exit, INFO is set to
0: successful exit.
1: TL and TR have too close eigenvalues, so TL or
TR is perturbed to get a nonsingular equation.
NOTE: In the interests of speed, this routine does not
check the inputs for errors.
```

Author:

Univ. of Tennessee

Univ. of California Berkeley