1SLAEV2(1)           LAPACK auxiliary routine (version 3.2)           SLAEV2(1)
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NAME

6       SLAEV2  -  computes the eigendecomposition of a 2-by-2 symmetric matrix
7       [ A B ]  [ B C ]
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SYNOPSIS

10       SUBROUTINE SLAEV2( A, B, C, RT1, RT2, CS1, SN1 )
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12           REAL           A, B, C, CS1, RT1, RT2, SN1
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PURPOSE

15       SLAEV2 computes the eigendecomposition of a 2-by-2 symmetric matrix
16          [  A   B  ]
17          [  B   C  ].  On return, RT1 is the eigenvalue  of  larger  absolute
18       value,  RT2  is the eigenvalue of smaller absolute value, and (CS1,SN1)
19       is the unit right eigenvector for RT1, giving the decomposition
20          [ CS1  SN1 ] [  A   B  ] [ CS1 -SN1 ]  =  [ RT1  0  ]
21          [-SN1  CS1 ] [  B   C  ] [ SN1  CS1 ]     [  0  RT2 ].
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ARGUMENTS

24       A       (input) REAL
25               The (1,1) element of the 2-by-2 matrix.
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27       B       (input) REAL
28               The (1,2) element and the conjugate of the (2,1) element of the
29               2-by-2 matrix.
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31       C       (input) REAL
32               The (2,2) element of the 2-by-2 matrix.
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34       RT1     (output) REAL
35               The eigenvalue of larger absolute value.
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37       RT2     (output) REAL
38               The eigenvalue of smaller absolute value.
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40       CS1     (output) REAL
41               SN1      (output)  REAL  The  vector (CS1, SN1) is a unit right
42               eigenvector for RT1.
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FURTHER DETAILS

45       RT1 is accurate to a few ulps barring over/underflow.
46       RT2 may be inaccurate if there is massive cancellation in the  determi‐
47       nant  A*C-B*B; higher precision or correctly rounded or correctly trun‐
48       cated arithmetic would be needed  to  compute  RT2  accurately  in  all
49       cases.
50       CS1  and  SN1 are accurate to a few ulps barring over/underflow.  Over‐
51       flow is possible only if RT1 is within  a  factor  of  5  of  overflow.
52       Underflow is harmless if the input data is 0 or exceeds
53          underflow_threshold / macheps.
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57 LAPACK auxiliary routine (versionNo3v.e2m)ber 2008                       SLAEV2(1)
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