slagv2(l) [redhat man page]
SLAGV2(l) ) SLAGV2(l) NAME
SLAGV2 - compute the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular SYNOPSIS
SUBROUTINE SLAGV2( A, LDA, B, LDB, ALPHAR, ALPHAI, BETA, CSL, SNL, CSR, SNR ) INTEGER LDA, LDB REAL CSL, CSR, SNL, SNR REAL A( LDA, * ), ALPHAI( 2 ), ALPHAR( 2 ), B( LDB, * ), BETA( 2 ) 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. ARGUMENTS
A (input/output) 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 (input) INTEGER THe leading dimension of the array A. LDA >= 2. B (input/output) 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 (input) INTEGER THe leading dimension of the array B. LDB >= 2. ALPHAR (output) REAL array, dimension (2) ALPHAI (output) REAL array, dimension (2) BETA (output) REAL array, dimension (2) (ALPHAR(k)+i*ALPHAI(k))/BETA(k) are the ei- genvalues of the pencil (A,B), k=1,2, i = sqrt(-1). Note that BETA(k) may be zero. CSL (output) REAL The cosine of the left rotation matrix. SNL (output) REAL The sine of the left rotation matrix. CSR (output) REAL The cosine of the right rotation matrix. SNR (output) REAL The sine of the right rotation matrix. FURTHER DETAILS
Based on contributions by Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA LAPACK version 3.0 15 June 2000 SLAGV2(l)
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dlagv2.f(3) LAPACK dlagv2.f(3) NAME
dlagv2.f - SYNOPSIS
Functions/Subroutines subroutine dlagv2 (A, LDA, B, LDB, ALPHAR, ALPHAI, BETA, CSL, SNL, CSR, SNR) DLAGV2 Function/Subroutine Documentation subroutine dlagv2 (double precision, dimension( lda, * )A, integerLDA, double precision, dimension( ldb, * )B, integerLDB, double precision, dimension( 2 )ALPHAR, double precision, dimension( 2 )ALPHAI, double precision, dimension( 2 )BETA, double precisionCSL, double precisionSNL, double precisionCSR, double precisionSNR) DLAGV2 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: November 2011 Contributors: Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA Definition at line 157 of file dlagv2.f. Author Generated automatically by Doxygen for LAPACK from the source code. Version 3.4.1 Sun May 26 2013 dlagv2.f(3)