# slasy2.f - Man Page

SRC/slasy2.f

## Synopsis

### Functions/Subroutines

subroutine **slasy2** (ltranl, ltranr, isgn, n1, n2, tl, ldtl, tr, ldtr, b, ldb, scale, x, ldx, xnorm, info)**SLASY2** solves the Sylvester matrix equation where the matrices are of order 1 or 2.

## Function/Subroutine Documentation

### subroutine slasy2 (logical ltranl, logical ltranr, integer isgn, integer n1, integer n2, real, dimension( ldtl, * ) tl, integer ldtl, real, dimension( ldtr, * ) tr, integer ldtr, real, dimension( ldb, * ) b, integer ldb, real scale, real, dimension( ldx, * ) x, integer ldx, real xnorm, integer info)

**SLASY2** solves the Sylvester matrix equation where the matrices are of order 1 or 2.

**Purpose:**

SLASY2 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 REAL 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 REAL 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 REAL 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 REAL On exit, SCALE contains the scale factor. SCALE is chosen less than or equal to 1 to prevent the solution overflowing.

*X*X is REAL 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 REAL 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

Univ. of Colorado Denver

NAG Ltd.

Definition at line **172** of file **slasy2.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page slasy2(3) is an alias of slasy2.f(3).

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