# dlagv2.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
Page Index

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, integer LDA, double precision, dimension( ldb, * ) B, integer LDB, double precision, dimension( 2 ) ALPHAR, double precision, dimension( 2 ) ALPHAI, double precision, dimension( 2 ) BETA, double precision CSL, double precision SNL, 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

NAG Ltd.

Date:

December 2016

Contributors:

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

Definition at line 159 of file dlagv2.f.

## Author

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