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dlagv2-f(3)

dlagv2.f –

Synopsis

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, integerLDA, double precision, dimension( ldb, * )B, integerLDB, double precision, dimension( 2 )ALPHAR, double precision, dimension( 2 )ALPHAI, double precision, dimension( 2 )BETA, double precisionCSL, double precisionSNL, double precisionCSR, double precisionSNR)

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:

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.

LDA

 LDA is INTEGER
 THe leading dimension of the array A. LDA >= 2.

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.

LDB

 LDB is INTEGER
 THe leading dimension of the array B. LDB >= 2.

ALPHAR

 ALPHAR is DOUBLE PRECISION array, dimension (2)

ALPHAI

 ALPHAI is DOUBLE PRECISION array, dimension (2)

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.

CSL

 CSL is DOUBLE PRECISION
 The cosine of the left rotation matrix.

SNL

 SNL is DOUBLE PRECISION
 The sine of the left rotation matrix.

CSR

 CSR is DOUBLE PRECISION
 The cosine of the right rotation matrix.

SNR

 SNR is DOUBLE PRECISION
 The sine of the right rotation matrix.

 

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

September 2012

Contributors:

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

Definition at line 157 of file dlagv2.f.

Author

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