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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

dlagv2(l)
DLAGV2

DLAGV2

NAME
SYNOPSIS
PURPOSE
ARGUMENTS
FURTHER DETAILS

NAME

DLAGV2 - compute the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular

SYNOPSIS

SUBROUTINE DLAGV2(

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

INTEGER

LDA, LDB

DOUBLE

PRECISION CSL, CSR, SNL, SNR

DOUBLE

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

PURPOSE

DLAGV2 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (2)

ALPHAI (output) DOUBLE PRECISION array, dimension (2) BETA (output) DOUBLE PRECISION 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) DOUBLE PRECISION

The cosine of the left rotation matrix.

SNL (output) DOUBLE PRECISION

The sine of the left rotation matrix.

CSR (output) DOUBLE PRECISION

The cosine of the right rotation matrix.

SNR (output) DOUBLE PRECISION

The sine of the right rotation matrix.

FURTHER DETAILS

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

dlagv2(l)