# slagv2.f - Man Page

SRC/slagv2.f

## Synopsis

### Functions/Subroutines

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.

## Function/Subroutine Documentation

### 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

NAG Ltd.

Contributors:

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

Definition at line 155 of file slagv2.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page slagv2(3) is an alias of slagv2.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK