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slagv2.f(3) LAPACK slagv2.f(3)

NAME

slagv2.f -

SYNOPSIS

Functions/Subroutines


subroutine slagv2 (A, LDA, B, LDB, ALPHAR, ALPHAI, BETA, CSL, SNL, CSR, SNR)
SLAGV2 computes the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular.

Function/Subroutine Documentation

subroutine slagv2 (real, dimension( lda, * )A, integerLDA, real, dimension( ldb, * )B, integerLDB, real, dimension( 2 )ALPHAR, real, dimension( 2 )ALPHAI, real, dimension( 2 )BETA, realCSL, realSNL, realCSR, realSNR)

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

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.

Parameters:

A


A is 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


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

B


B is 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


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

ALPHAR


ALPHAR is REAL array, dimension (2)

ALPHAI


ALPHAI is REAL array, dimension (2)

BETA


BETA is 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


CSL is REAL
The cosine of the left rotation matrix.

SNL


SNL is REAL
The sine of the left rotation matrix.

CSR


CSR is REAL
The cosine of the right rotation matrix.

SNR


SNR is REAL
The sine of the right rotation matrix.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

September 2012

Contributors:

Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

Definition at line 157 of file slagv2.f.

Author

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Tue Sep 25 2012 Version 3.4.2