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dlagv2.f(3)				      LAPACK				      dlagv2.f(3)

NAME
       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, integerLDA, double precision,
       dimension( ldb, * )B, integerLDB, double precision, dimension( 2 )ALPHAR, double
       precision, dimension( 2 )ALPHAI, double precision, dimension( 2 )BETA, double
       precisionCSL, double precisionSNL, double precisionCSR, double precisionSNR)
       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

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   September 2012

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

       Definition at line 157 of file dlagv2.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			      dlagv2.f(3)
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