# slagv2.f - Man Page

## 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

Univ. of Colorado Denver

NAG Ltd.

**Date:**December 2016

**Contributors:**Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

Definition at line 159 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 14 2017 Version 3.8.0 LAPACK