claesy(3S)

NAME
     CLAESY - compute the eigendecomposition of a 2-by-2 symmetric matrix ( (
     A, B );( B, C ) ) provided the norm of the matrix of eigenvectors is
     larger than some threshold value

SYNOPSIS
     SUBROUTINE CLAESY( A, B, C, RT1, RT2, EVSCAL, CS1, SN1 )

         COMPLEX        A, B, C, CS1, EVSCAL, RT1, RT2, SN1

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
     CLAESY computes the eigendecomposition of a 2-by-2 symmetric matrix ( (
     A, B );( B, C ) ) provided the norm of the matrix of eigenvectors is
     larger than some threshold value. RT1 is the eigenvalue of larger
     absolute value, and RT2 of smaller absolute value.  If the eigenvectors
     are computed, then on return ( CS1, SN1 ) is the unit eigenvector for
     RT1, hence

     [  CS1     SN1   ] . [ A  B ] . [ CS1    -SN1   ] = [ RT1  0  ] [ -SN1
     CS1   ]   [ B  C ]   [ SN1     CS1   ]   [  0  RT2 ]


ARGUMENTS
     A       (input) COMPLEX
             The ( 1, 1 ) element of input matrix.

     B       (input) COMPLEX
             The ( 1, 2 ) element of input matrix.  The ( 2, 1 ) element is
             also given by B, since the 2-by-2 matrix is symmetric.

     C       (input) COMPLEX
             The ( 2, 2 ) element of input matrix.

     RT1     (output) COMPLEX
             The eigenvalue of larger modulus.

     RT2     (output) COMPLEX
             The eigenvalue of smaller modulus.
     EVSCAL  (output) COMPLEX
             The complex value by which the eigenvector matrix was scaled to
             make it orthonormal.  If EVSCAL is zero, the eigenvectors were
             not computed.  This means one of two things:  the 2-by-2 matrix
             could not be diagonalized, or the norm of the matrix of
             eigenvectors before scaling was larger than the threshold value
             THRESH (set below).

     CS1     (output) COMPLEX
             SN1     (output) COMPLEX If EVSCAL .NE. 0,  ( CS1, SN1 ) is the
             unit right eigenvector for RT1.

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

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