SRC/slagv2.f(3)            Library Functions Manual            SRC/slagv2.f(3)

NAME
       SRC/slagv2.f

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.

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

       Definition at line 155 of file slagv2.f.

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

LAPACK                          Version 3.12.0                 SRC/slagv2.f(3)