SLAGV2(3S)SLAGV2(3S)NAMESLAGV2 - 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 )
IMPLEMENTATION
These routines are part of the SCSL Scientific Library and can be loaded
using either the -lscs or the -lscs_mp option. The -lscs_mp option
directs the linker to use the multi-processor version of the library.
When linking to SCSL with -lscs or -lscs_mp, the default integer size is
4 bytes (32 bits). Another version of SCSL is available in which integers
are 8 bytes (64 bits). This version allows the user access to larger
memory sizes and helps when porting legacy Cray codes. It can be loaded
by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
only one of the two versions; 4-byte integer and 8-byte integer library
calls cannot be mixed.
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.
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SLAGV2(3S)SLAGV2(3S)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
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 DETAILS
Based on contributions by
Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
SEE ALSOINTRO_LAPACK(3S), INTRO_SCSL(3S)
This man page is available only online.
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