SLAGV2 - Online Linux Manual PageSection : 1
Updated : November 2008
Source : LAPACK auxiliary routine (version 3.2)
Note : LAPACK auxiliary routine (version 3.2)
NAMESLAGV2 - computes the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular
SYNOPSISSUBROUTINE 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 )
PURPOSESLAGV2 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.
ARGUMENTSA (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 eigenvalues 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 DETAILSBased on contributions by
Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA 0
Johanes Gumabo
Data Size : 10,384 byte
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