---
name: "dlagv2"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/dlagv2/3lapack"
---

# dlagv2(3lapack)

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

## NAME

DLAGV2 - 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.

## FURTHER DETAILS

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