1ZLAESY(1)           LAPACK auxiliary routine (version 3.2)           ZLAESY(1)
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NAME

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

11       SUBROUTINE ZLAESY( A, B, C, RT1, RT2, EVSCAL, CS1, SN1 )
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13           COMPLEX*16     A, B, C, CS1, EVSCAL, RT1, RT2, SN1
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PURPOSE

16       ZLAESY 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.  RT1  is  the  eigenvalue  of
19       larger  absolute  value,  and  RT2  of  smaller absolute value.  If the
20       eigenvectors are computed, then on return ( CS1,  SN1  )  is  the  unit
21       eigenvector  for  RT1,  hence  [   CS1      SN1    ] . [ A  B ] . [ CS1
22       -SN1   ] = [ RT1  0  ] [ -SN1     CS1   ]   [ B  C ]    [  SN1      CS1
23       ]   [  0  RT2 ]
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ARGUMENTS

26       A       (input) COMPLEX*16
27               The ( 1, 1 ) element of input matrix.
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29       B       (input) COMPLEX*16
30               The  ( 1, 2 ) element of input matrix.  The ( 2, 1 ) element is
31               also given by B, since the 2-by-2 matrix is symmetric.
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33       C       (input) COMPLEX*16
34               The ( 2, 2 ) element of input matrix.
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36       RT1     (output) COMPLEX*16
37               The eigenvalue of larger modulus.
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39       RT2     (output) COMPLEX*16
40               The eigenvalue of smaller modulus.
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42       EVSCAL  (output) COMPLEX*16
43               The complex value by which the eigenvector matrix was scaled to
44               make  it orthonormal.  If EVSCAL is zero, the eigenvectors were
45               not computed.  This means one of two things:  the 2-by-2 matrix
46               could  not be diagonalized, or the norm of the matrix of eigen‐
47               vectors before scaling was  larger  than  the  threshold  value
48               THRESH (set below).
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50       CS1     (output) COMPLEX*16
51               SN1      (output) COMPLEX*16 If EVSCAL .NE. 0,  ( CS1, SN1 ) is
52               the unit right eigenvector for RT1.
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56 LAPACK auxiliary routine (versionNo3v.e2m)ber 2008                       ZLAESY(1)
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