SRC/slanv2.f(3)            Library Functions Manual            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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LAPACK                          Version 3.12.0                 SRC/slanv2.f(3)