slagv2.f(3) LAPACK slagv2.f(3)NAMEslagv2.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
Generated automatically by Doxygen for LAPACK from the source code.
Version 3.4.2 Tue Sep 25 2012 slagv2.f(3)
