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, integer LDA, double precision,
       dimension( ldb, * ) B, integer LDB, double precision, dimension( 2 ) ALPHAR, double
       precision, dimension( 2 ) ALPHAI, double precision, dimension( 2 ) BETA, double precision
       CSL, double precision SNL, double precision CSR, double precision SNR)
       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

Author

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