1CLAESY(1)           LAPACK auxiliary routine (version 3.1)           CLAESY(1)
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NAME

6       CLAESY  - the eigendecomposition of a 2-by-2 symmetric matrix  ( ( A, B
7       );( B, C ) ) provided the norm of the matrix of eigenvectors is  larger
8       than some threshold value
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SYNOPSIS

11       SUBROUTINE CLAESY( A, B, C, RT1, RT2, EVSCAL, CS1, SN1 )
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13           COMPLEX        A, B, C, CS1, EVSCAL, RT1, RT2, SN1
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PURPOSE

16       CLAESY computes the eigendecomposition of a 2-by-2 symmetric matrix
17          (  (  A, B );( B, C ) ) provided the norm of the matrix of eigenvec‐
18       tors is larger than some threshold value.
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20       RT1 is the eigenvalue of larger absolute  value,  and  RT2  of  smaller
21       absolute  value.   If  the  eigenvectors are computed, then on return (
22       CS1, SN1 ) is the unit eigenvector for RT1, hence
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24       [  CS1     SN1   ] . [ A  B ] . [ CS1    -SN1   ] = [ RT1  0  ] [  -SN1
25       CS1   ]   [ B  C ]   [ SN1     CS1   ]   [  0  RT2 ]
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ARGUMENTS

29       A       (input) COMPLEX
30               The ( 1, 1 ) element of input matrix.
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32       B       (input) COMPLEX
33               The  ( 1, 2 ) element of input matrix.  The ( 2, 1 ) element is
34               also given by B, since the 2-by-2 matrix is symmetric.
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36       C       (input) COMPLEX
37               The ( 2, 2 ) element of input matrix.
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39       RT1     (output) COMPLEX
40               The eigenvalue of larger modulus.
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42       RT2     (output) COMPLEX
43               The eigenvalue of smaller modulus.
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45       EVSCAL  (output) COMPLEX
46               The complex value by which the eigenvector matrix was scaled to
47               make  it orthonormal.  If EVSCAL is zero, the eigenvectors were
48               not computed.  This means one of two things:  the 2-by-2 matrix
49               could  not be diagonalized, or the norm of the matrix of eigen‐
50               vectors before scaling was  larger  than  the  threshold  value
51               THRESH (set below).
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53       CS1     (output) COMPLEX
54               SN1     (output) COMPLEX If EVSCAL .NE. 0,  ( CS1, SN1 ) is the
55               unit right eigenvector for RT1.
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59 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006                       CLAESY(1)
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