Provided by: liblapack-doc_3.3.1-1_all

#### NAME

```       LAPACK-3  -  computes  the  Generalized Schur factorization of a real 2-by-2 matrix pencil
(A,B) where B is upper triangular

```

#### SYNOPSIS

```       SUBROUTINE DLAGV2( A, LDA, B, LDB, ALPHAR, ALPHAI, BETA, CSL, SNL, CSR, SNR )

INTEGER        LDA, LDB

DOUBLE         PRECISION CSL, CSR, SNL, SNR

DOUBLE         PRECISION A( LDA, * ), ALPHAI( 2 ), ALPHAR( 2 ), B( LDB, * ), BETA( 2 )

```

#### 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.

```

#### ARGUMENTS

```        A       (input/output) 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     (input) INTEGER
THe leading dimension of the array A.  LDA >= 2.

B       (input/output) 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     (input) INTEGER
THe leading dimension of the array B.  LDB >= 2.

ALPHAR  (output) DOUBLE PRECISION array, dimension (2)
ALPHAI  (output) DOUBLE PRECISION array, dimension (2)
BETA    (output) 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     (output) DOUBLE PRECISION
The cosine of the left rotation matrix.

SNL     (output) DOUBLE PRECISION
The sine of the left rotation matrix.

CSR     (output) DOUBLE PRECISION
The cosine of the right rotation matrix.

SNR     (output) DOUBLE PRECISION
The sine of the right rotation matrix.

```

#### FURTHERDETAILS

```        Based on contributions by
Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

LAPACK auxiliary routine (version 3.2.2)   April 2011                            DLAGV2(3lapack)
```