Man page - lasy2(3)

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Manual

lasy2

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine dlasy2 (logical ltranl, logical ltranr, integer isgn, integern1, integer n2, double precision, dimension( ldtl, * ) tl, integerldtl, double precision, dimension( ldtr, * ) tr, integer ldtr, doubleprecision, dimension( ldb, * ) b, integer ldb, double precision scale,double precision, dimension( ldx, * ) x, integer ldx, double precisionxnorm, integer info)
subroutine slasy2 (logical ltranl, logical ltranr, integer isgn, integern1, 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, realxnorm, integer info)
Author

NAME

lasy2 - lasy2: Sylvester equation

SYNOPSIS

Functions

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.
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.

Detailed Description

Function Documentation

subroutine dlasy2 (logical ltranl, logical ltranr, integer isgn, integern1, integer n2, double precision, dimension( ldtl, * ) tl, integerldtl, double precision, dimension( ldtr, * ) tr, integer ldtr, doubleprecision, dimension( ldb, * ) b, integer ldb, double precision scale,double precision, dimension( ldx, * ) x, integer ldx, double precisionxnorm, 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

Univ. of Colorado Denver

NAG Ltd.

subroutine slasy2 (logical ltranl, logical ltranr, integer isgn, integern1, 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, realxnorm, 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.

Author

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