claesy(l) [redhat man page]

CLAESY(l)								 )								 CLAESY(l)

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

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 eigenvec-
       tors 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.

LAPACK version 3.0						   15 June 2000 							 CLAESY(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 eigenvec-
       tors 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 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*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)