claesy.f(3) [debian man page]

claesy.f(3)							      LAPACK							       claesy.f(3)

NAME

       claesy.f -

SYNOPSIS

   Functions/Subroutines
       subroutine claesy (A, B, C, RT1, RT2, EVSCAL, CS1, SN1)
	   CLAESY

Function/Subroutine Documentation
   subroutine claesy (complexA, complexB, complexC, complexRT1, complexRT2, complexEVSCAL, complexCS1, complexSN1)
       CLAESY

       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 ]

       Parameters:
	   A

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

	   B

		     B is 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

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

	   RT1

		     RT1 is COMPLEX
		     The eigenvalue of larger modulus.

	   RT2

		     RT2 is COMPLEX
		     The eigenvalue of smaller modulus.

	   EVSCAL

		     EVSCAL is 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

		     CS1 is COMPLEX

	   SN1

		     SN1 is COMPLEX
		     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:
	   November 2011

       Definition at line 116 of file claesy.f.

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

Version 3.4.1							  Sun May 26 2013						       claesy.f(3)

Check Out this Related Man Page

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)

Linux and UNIX Man Pages

claesy.f(3) [debian man page]

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