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zlaesy.f

zlaesy.f(3)							      LAPACK							       zlaesy.f(3)

NAME

       zlaesy.f -

SYNOPSIS

   Functions/Subroutines
       subroutine zlaesy (A, B, C, RT1, RT2, EVSCAL, CS1, SN1)
	   ZLAESY computes the eigenvalues and eigenvectors of a 2-by-2 complex symmetric matrix.

Function/Subroutine Documentation
   subroutine zlaesy (complex*16A, complex*16B, complex*16C, complex*16RT1, complex*16RT2, complex*16EVSCAL, complex*16CS1, complex*16SN1)
       ZLAESY computes the eigenvalues and eigenvectors of a 2-by-2 complex symmetric matrix.

       Purpose:

	    ZLAESY 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 ]

       Parameters:
	   A

		     A is COMPLEX*16
		     The ( 1, 1 ) element of input matrix.

	   B

		     B is COMPLEX*16
		     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

		     C is COMPLEX*16
		     The ( 2, 2 ) element of input matrix.

	   RT1

		     RT1 is COMPLEX*16
		     The eigenvalue of larger modulus.

	   RT2

		     RT2 is COMPLEX*16
		     The eigenvalue of smaller modulus.

	   EVSCAL

		     EVSCAL is COMPLEX*16
		     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

		     CS1 is COMPLEX*16

	   SN1

		     SN1 is COMPLEX*16
		     If EVSCAL .NE. 0,	( CS1, SN1 ) is the unit right eigenvector
		     for RT1.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   September 2012

       Definition at line 116 of file zlaesy.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012						       zlaesy.f(3)