dlagv2(l) [redhat man page]
DLAGV2(l) ) DLAGV2(l) NAME
DLAGV2 - compute the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular SYNOPSIS
SUBROUTINE DLAGV2( A, LDA, B, LDB, ALPHAR, ALPHAI, BETA, CSL, SNL, CSR, SNR ) INTEGER LDA, LDB DOUBLE PRECISION CSL, CSR, SNL, SNR DOUBLE PRECISION A( LDA, * ), ALPHAI( 2 ), ALPHAR( 2 ), B( LDB, * ), BETA( 2 ) 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. ARGUMENTS
A (input/output) 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 (input) INTEGER THe leading dimension of the array A. LDA >= 2. B (input/output) 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 (input) INTEGER THe leading dimension of the array B. LDB >= 2. ALPHAR (output) DOUBLE PRECISION array, dimension (2) ALPHAI (output) DOUBLE PRECISION array, dimension (2) BETA (output) 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 (output) DOUBLE PRECISION The cosine of the left rotation matrix. SNL (output) DOUBLE PRECISION The sine of the left rotation matrix. CSR (output) DOUBLE PRECISION The cosine of the right rotation matrix. SNR (output) DOUBLE PRECISION 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 DLAGV2(l)
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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 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 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: November 2011 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 3.4.1 Sun May 26 2013 slagv2.f(3)