SRC/slanv2.f(3)

NAME
SRC/slanv2.f

SYNOPSIS

  Functions/Subroutines
subroutine slanv2 (a, b, c, d, rt1r, rt1i, rt2r, rt2i, cs, sn)
SLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form.

Function/Subroutine Documentation

  subroutine slanv2 (real a, real b, real c, real d, real rt1r, real rt1i, real rt2r, real rt2i, real cs, real sn)

SLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form.

Purpose:

    !>
    !> SLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric
    !> matrix in standard form:
    !>
    !>      [ A  B ] = [ CS -SN ] [ AA  BB ] [ CS  SN ]
    !>      [ C  D ]   [ SN  CS ] [ CC  DD ] [-SN  CS ]
    !>
    !> where either
    !> 1) CC = 0 so that AA and DD are real eigenvalues of the matrix, or
    !> 2) AA = DD and BB*CC < 0, so that AA + or - sqrt(BB*CC) are complex
    !> conjugate eigenvalues.
    !>

Parameters
    A

    !>          A is REAL
    !>

    B

    !>          B is REAL
    !>

    C

    !>          C is REAL
    !>

    D

    !>          D is REAL
    !>          On entry, the elements of the input matrix.
    !>          On exit, they are overwritten by the elements of the
    !>          standardised Schur form.
    !>

    RT1R

    !>          RT1R is REAL
    !>

    RT1I

    !>          RT1I is REAL
    !>

    RT2R

    !>          RT2R is REAL
    !>

    RT2I

    !>          RT2I is REAL
    !>          The real and imaginary parts of the eigenvalues. If the
    !>          eigenvalues are a complex conjugate pair, RT1I > 0.
    !>

    CS

    !>          CS is REAL
    !>

    SN

    !>          SN is REAL
    !>          Parameters of the rotation matrix.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

    !>
    !>  Modified by V. Sima, Research Institute for Informatics, Bucharest,
    !>  Romania, to reduce the risk of cancellation errors,
    !>  when computing real eigenvalues, and to ensure, if possible, that
    !>  abs(RT1R) >= abs(RT2R).
    !>

Definition at line 126 of file slanv2.f.

Author

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