SLAGV2 (3)  Linux Manuals
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 2by2 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 2by2 matrix pencil (A,B) where B is upper triangular.
Purpose:

SLAGV2 computes the Generalized Schur factorization of a real 2by2 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 ``Apart'' of the generalized Schur form.
LDALDA is INTEGER THe leading dimension of the array A. LDA >= 2.
BB is REAL array, dimension (LDB, 2) On entry, the upper triangular 2 x 2 matrix B. On exit, B is overwritten by the ``Bpart'' of the generalized Schur form.
LDBLDB is INTEGER THe leading dimension of the array B. LDB >= 2.
ALPHARALPHAR is REAL array, dimension (2)
ALPHAIALPHAI is REAL array, dimension (2)
BETABETA 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.
CSLCSL is REAL The cosine of the left rotation matrix.
SNLSNL is REAL The sine of the left rotation matrix.
CSRCSR is REAL The cosine of the right rotation matrix.
SNRSNR 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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