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dlagv2.f(3) LAPACK dlagv2.f(3)

NAME

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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Tue Sep 25 2012 Version 3.4.2