dlanv2(3S)

NAME
     DLANV2 - compute the Schur factorization of a real 2-by-2 nonsymmetric
     matrix in standard form

SYNOPSIS
     SUBROUTINE DLANV2( A, B, C, D, RT1R, RT1I, RT2R, RT2I, CS, SN )

         DOUBLE         PRECISION A, B, C, CS, D, RT1I, RT1R, RT2I, RT2R, SN

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

PURPOSE
     DLANV2 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.


ARGUMENTS
     A       (input/output) DOUBLE PRECISION
             B       (input/output) DOUBLE PRECISION C       (input/output)
             DOUBLE PRECISION D       (input/output) DOUBLE PRECISION On
             entry, the elements of the input matrix.  On exit, they are
             overwritten by the elements of the standardised Schur form.

     RT1R    (output) DOUBLE PRECISION
             RT1I    (output) DOUBLE PRECISION RT2R    (output) DOUBLE
             PRECISION RT2I    (output) DOUBLE PRECISION The real and
             imaginary parts of the eigenvalues. If the eigenvalues are a
             complex conjugate pair, RT1I > 0.

     CS      (output) DOUBLE PRECISION
             SN      (output) DOUBLE PRECISION Parameters of the rotation
             matrix.
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).


SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

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