dlagv2.f - Online Linux Manual PageSection : 3
Updated : Tue Nov 14 2017
Source : Version 3.8.0
Note : LAPACK
NAMEdlagv2.f
SYNOPSIS
Functions/Subroutinessubroutine dlagv2 (A, LDA, B, LDB, ALPHAR, ALPHAI, BETA, CSL, SNL, CSR, SNR)
DLAGV2 computes the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular.
Function/Subroutine Documentation
subroutine dlagv2 (double precision, dimension( lda, * ) A, integer LDA, double precision, dimension( ldb, * ) B, integer LDB, double precision, dimension( 2 ) ALPHAR, double precision, dimension( 2 ) ALPHAI, double precision, dimension( 2 ) BETA, double precision CSL, double precision SNL, double precision CSR, double precision SNR)DLAGV2 computes the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular. 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.Parameters: A A is 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 LDA is INTEGER
THe leading dimension of the array A. LDA >= 2.
B B is 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 LDB is INTEGER
THe leading dimension of the array B. LDB >= 2.
ALPHAR ALPHAR is DOUBLE PRECISION array, dimension (2)
ALPHAI ALPHAI is DOUBLE PRECISION array, dimension (2)
BETA BETA is 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 CSL is DOUBLE PRECISION
The cosine of the left rotation matrix.
SNL SNL is DOUBLE PRECISION
The sine of the left rotation matrix.
CSR CSR is DOUBLE PRECISION
The cosine of the right rotation matrix.
SNR SNR is DOUBLE PRECISION
The sine of the right rotation matrix.Author: Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Date: December 2016 Contributors: Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA Definition at line 159 of file dlagv2.f.
AuthorGenerated automatically by Doxygen for LAPACK from the source code. 0
Johanes Gumabo
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