
NAMEzlaesy.f SYNOPSISFunctions/Subroutinessubroutine zlaesy (A, B, C, RT1, RT2, EVSCAL, CS1, SN1) Function/Subroutine Documentationsubroutine 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 2by2 complex symmetric matrix. Purpose:ZLAESY computes the eigendecomposition of a 2by2 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 ] A
Author:
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 2by2 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 2by2 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*16SN1 SN1 is COMPLEX*16 If EVSCAL .NE. 0, ( CS1, SN1 ) is the unit right eigenvector for RT1. Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
September 2012
Definition at line 116 of file zlaesy.f.
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