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RedHat 9 (Linux i386) - man page for zlaesy (redhat section l)

ZLAESY(l)					)					ZLAESY(l)

NAME
       ZLAESY - 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 ZLAESY( A, B, C, RT1, RT2, EVSCAL, CS1, SN1 )

	   COMPLEX*16	  A, B, C, CS1, EVSCAL, RT1, RT2, SN1

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 ]

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

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

       RT1     (output) COMPLEX*16
	       The eigenvalue of larger modulus.

       RT2     (output) COMPLEX*16
	       The eigenvalue of smaller modulus.

       EVSCAL  (output) COMPLEX*16
	       The complex value by which the eigenvector matrix was scaled to make it	orthonor-
	       mal.   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*16
	       SN1     (output) COMPLEX*16 If EVSCAL .NE. 0,  ( CS1, SN1  )  is  the  unit  right
	       eigenvector for RT1.

LAPACK version 3.0			   15 June 2000 				ZLAESY(l)


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