Man page - lagv2(3)

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Manual

lagv2

NAME
SYNOPSIS
Functions
Detailed Description
Function 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, doubleprecision, dimension( 2 ) beta, double precision csl, double precisionsnl, double precision csr, double precision snr)
subroutine slagv2 (real, dimension( lda, * ) a, integer lda, real,dimension( ldb, * ) b, integer ldb, real, dimension( 2 ) alphar, real,dimension( 2 ) alphai, real, dimension( 2 ) beta, real csl, real snl,real csr, real snr)
Author

NAME

lagv2 - lagv2: 2x2 generalized Schur factor

SYNOPSIS

Functions

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.
subroutine slagv2 (a, lda, b, ldb, alphar, alphai, beta, csl, snl, csr, snr)
SLAGV2 computes the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular.

Detailed Description

Function 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, doubleprecision, dimension( 2 ) beta, double precision csl, double precisionsnl, 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

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.

Contributors:

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

subroutine slagv2 (real, dimension( lda, * ) a, integer lda, real,dimension( ldb, * ) b, integer ldb, real, dimension( 2 ) alphar, real,dimension( 2 ) alphai, real, dimension( 2 ) beta, real csl, real snl,real csr, real snr)

SLAGV2 computes the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular.

Purpose:

SLAGV2 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 REAL 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 REAL 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 REAL array, dimension (2)

ALPHAI

ALPHAI is REAL array, dimension (2)

BETA

BETA is REAL 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 REAL
The cosine of the left rotation matrix.

SNL

SNL is REAL
The sine of the left rotation matrix.

CSR

CSR is REAL
The cosine of the right rotation matrix.

SNR

SNR is REAL
The sine of the right rotation matrix.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

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

Author

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