 LAPACK  3.4.2 LAPACK: Linear Algebra PACKage
dlagv2.f File Reference

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## Functions/Subroutines

subroutine dlagv2 (A, LDA, B, LDB, ALPHAR, ALPHAI, BETA, CSL, SNL, CSR, SNR)
DLAGV2 computes the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular.

## Function/Subroutine Documentation

 subroutine dlagv2 ( double precision, dimension( lda, * ) A, integer LDA, double precision, dimension( ldb, * ) B, integer LDB, double precision, dimension( 2 ) ALPHAR, double precision, dimension( 2 ) ALPHAI, double precision, dimension( 2 ) BETA, double precision CSL, double precision SNL, double precision CSR, double precision SNR )

DLAGV2 computes the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular.

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:
 [in,out] 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.``` [in] LDA ``` LDA is INTEGER THe leading dimension of the array A. LDA >= 2.``` [in,out] 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.``` [in] LDB ``` LDB is INTEGER THe leading dimension of the array B. LDB >= 2.``` [out] ALPHAR ` ALPHAR is DOUBLE PRECISION array, dimension (2)` [out] ALPHAI ` ALPHAI is DOUBLE PRECISION array, dimension (2)` [out] 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.``` [out] CSL ``` CSL is DOUBLE PRECISION The cosine of the left rotation matrix.``` [out] SNL ``` SNL is DOUBLE PRECISION The sine of the left rotation matrix.``` [out] CSR ``` CSR is DOUBLE PRECISION The cosine of the right rotation matrix.``` [out] SNR ``` SNR is DOUBLE PRECISION The sine of the right rotation matrix.```
Date:
September 2012
Contributors:
Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

Definition at line 157 of file dlagv2.f.

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