claesy-f(3)

claesy.f –

Synopsis

Functions/Subroutines

subroutine claesy (A, B, C, RT1, RT2, EVSCAL, CS1, SN1)
CLAESY computes the eigenvalues and eigenvectors of a 2-by-2 complex symmetric matrix.

Function/Subroutine Documentation

subroutine claesy (complexA, complexB, complexC, complexRT1, complexRT2, complexEVSCAL, complexCS1, complexSN1)

CLAESY computes the eigenvalues and eigenvectors of a 2-by-2 complex symmetric matrix.

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

 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 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:

September 2012

Definition at line 116 of file claesy.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.