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/home/abuild/rpmbuild/BUILD/lapack-3.12.0/SRC/slagv2.f(3) Library Functions Manual /home/abuild/rpmbuild/BUILD/lapack-3.12.0/SRC/slagv2.f(3)

NAME

/home/abuild/rpmbuild/BUILD/lapack-3.12.0/SRC/slagv2.f

SYNOPSIS

Functions/Subroutines


subroutine SLAGV2 (a, lda, b, ldb, alphar, alphai, beta, csl, snl, csr, snr)
SLAGV2 computes the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular.

Function/Subroutine Documentation

subroutine SLAGV2 (real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, real, dimension( 2 ) alphar, real, dimension( 2 ) alphai, real, dimension( 2 ) beta, real csl, real snl, real csr, real snr)

SLAGV2 computes the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular.

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.

Contributors:

Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

Definition at line 155 of file slagv2.f.

Author

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Version 3.12.0 LAPACK