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Livre :
Expressions régulières,
Syntaxe et mise en oeuvre :

ISBN : 978-2-7460-9712-4
EAN : 9782746097124
(Editions ENI)

GNU/Linux

CentOS 4.8

 i386

slagv2(l)
SLAGV2

SLAGV2

NAME
SYNOPSIS
PURPOSE
ARGUMENTS
FURTHER DETAILS

NAME

SLAGV2 - compute the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular

SYNOPSIS

SUBROUTINE SLAGV2(

A, LDA, B, LDB, ALPHAR, ALPHAI, BETA, CSL, SNL, CSR, SNR )

INTEGER

LDA, LDB

REAL

CSL, CSR, SNL, SNR

REAL

A( LDA, * ), ALPHAI( 2 ), ALPHAR( 2 ), B( LDB, * ), BETA( 2 )

PURPOSE

SLAGV2 computes the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular. This routine computes orthogonal (rotation) matrices given by CSL, SNL and CSR, SNR such that

1) if the pencil (A,B) has two real eigenvalues (include 0/0 or 1/0
types), then

[ a11 a12 ] := [ CSL SNL ] [ a11 a12 ] [ CSR -SNR ]
[ 0 a22 ] [ -SNL CSL ] [ a21 a22 ] [ SNR CSR ]

[ b11 b12 ] := [ CSL SNL ] [ b11 b12 ] [ CSR -SNR ]
[ 0 b22 ] [ -SNL CSL ] [ 0 b22 ] [ SNR CSR ],

2) if the pencil (A,B) has a pair of complex conjugate eigenvalues,
then

[ a11 a12 ] := [ CSL SNL ] [ a11 a12 ] [ CSR -SNR ]
[ a21 a22 ] [ -SNL CSL ] [ a21 a22 ] [ SNR CSR ]

[ b11 0 ] := [ CSL SNL ] [ b11 b12 ] [ CSR -SNR ]
[ 0 b22 ] [ -SNL CSL ] [ 0 b22 ] [ SNR CSR ]

where b11 >= b22 > 0.

ARGUMENTS

A (input/output) REAL array, dimension (LDA, 2)

On entry, the 2 x 2 matrix A. On exit, A is overwritten by the ’’A-part’’ of the generalized Schur form.

LDA (input) INTEGER

THe leading dimension of the array A. LDA >= 2.

B (input/output) REAL array, dimension (LDB, 2)

On entry, the upper triangular 2 x 2 matrix B. On exit, B is overwritten by the ’’B-part’’ of the generalized Schur form.

LDB (input) INTEGER

THe leading dimension of the array B. LDB >= 2.

ALPHAR (output) REAL array, dimension (2)

ALPHAI (output) REAL array, dimension (2) BETA (output) REAL array, dimension (2) (ALPHAR(k)+i*ALPHAI(k))/BETA(k) are the eigenvalues of the pencil (A,B), k=1,2, i = sqrt(-1). Note that BETA(k) may be zero.

CSL (output) REAL

The cosine of the left rotation matrix.

SNL (output) REAL

The sine of the left rotation matrix.

CSR (output) REAL

The cosine of the right rotation matrix.

SNR (output) REAL

The sine of the right rotation matrix.

FURTHER DETAILS

Based on contributions by
Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

slagv2(l)