1DLAEV2(1)           LAPACK auxiliary routine (version 3.2)           DLAEV2(1)
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NAME

6       DLAEV2  -  computes the eigendecomposition of a 2-by-2 symmetric matrix
7       [ A B ]  [ B C ]
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SYNOPSIS

10       SUBROUTINE DLAEV2( A, B, C, RT1, RT2, CS1, SN1 )
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12           DOUBLE         PRECISION A, B, C, CS1, RT1, RT2, SN1
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PURPOSE

15       DLAEV2 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) DOUBLE PRECISION
25               The (1,1) element of the 2-by-2 matrix.
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27       B       (input) DOUBLE PRECISION
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) DOUBLE PRECISION
32               The (2,2) element of the 2-by-2 matrix.
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34       RT1     (output) DOUBLE PRECISION
35               The eigenvalue of larger absolute value.
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37       RT2     (output) DOUBLE PRECISION
38               The eigenvalue of smaller absolute value.
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40       CS1     (output) DOUBLE PRECISION
41               SN1      (output)  DOUBLE  PRECISION The vector (CS1, SN1) is a
42               unit right 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                       DLAEV2(1)
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