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RedHat 9 (Linux i386) - man page for slagv2 (redhat section l)

SLAGV2(l)					)					SLAGV2(l)

NAME
       SLAGV2  - compute the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B)
       where B is upper triangular

SYNOPSIS
       SUBROUTINE SLAGV2( A, LDA, B, LDB, ALPHAR, ALPHAI, BETA, CSL, SNL, CSR, SNR )

	   INTEGER	  LDA, LDB

	   REAL 	  CSL, CSR, SNL, SNR

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

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.

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

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

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

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

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

       SNR     (output) REAL
	       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 				SLAGV2(l)


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