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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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