redhat man page for dlagv2

DLAGV2(l)								 )								 DLAGV2(l)

NAME
       DLAGV2 - compute 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

LAPACK version 3.0						   15 June 2000 							 DLAGV2(l)