slagv2.f(3)

NAME
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, integerLDA, real, dimension( ldb, * )B, integerLDB, real, dimension( 2 )ALPHAR, real, dimension( 2 )ALPHAI, real, dimension( 2 )BETA, realCSL, realSNL, realCSR, realSNR)

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.

Date:
    September 2012

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

Definition at line 157 of file slagv2.f.

Author

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