slagv2()

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.

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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

[in,out]	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. !>
[in]	LDA	!> LDA is INTEGER !> THe leading dimension of the array A. LDA >= 2. !>
[in,out]	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. !>
[in]	LDB	!> LDB is INTEGER !> THe leading dimension of the array B. LDB >= 2. !>
[out]	ALPHAR	!> ALPHAR is REAL array, dimension (2) !>
[out]	ALPHAI	!> ALPHAI is REAL array, dimension (2) !>
[out]	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. !>
[out]	CSL	!> CSL is REAL !> The cosine of the left rotation matrix. !>
[out]	SNL	!> SNL is REAL !> The sine of the left rotation matrix. !>
[out]	CSR	!> CSR is REAL !> The cosine of the right rotation matrix. !>
[out]	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.

Contributors:

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