lagv2(3)

NAME
lagv2 - lagv2: 2x2 generalized Schur factor

SYNOPSIS

  Functions

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.
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.

Detailed Description

Function 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.

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

  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

Author

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