dlagv2.f man page

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

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

dlagv2(3) is an alias of dlagv2.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK