1CLAEV2(1)           LAPACK auxiliary routine (version 3.2)           CLAEV2(1)
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NAME

6       CLAEV2  -  computes the eigendecomposition of a 2-by-2 Hermitian matrix
7       [ A B ]  [ CONJG(B) C ]
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SYNOPSIS

10       SUBROUTINE CLAEV2( A, B, C, RT1, RT2, CS1, SN1 )
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12           REAL           CS1, RT1, RT2
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14           COMPLEX        A, B, C, SN1
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PURPOSE

17       CLAEV2 computes the eigendecomposition of a 2-by-2 Hermitian matrix
18          [  A         B  ]
19          [  CONJG(B)  C  ].  On return, RT1 is the eigenvalue of larger abso‐
20       lute  value,  RT2  is  the  eigenvalue  of  smaller absolute value, and
21       (CS1,SN1) is the unit right eigenvector for RT1, giving the  decomposi‐
22       tion
23       [  CS1   CONJG(SN1)  ] [    A     B ] [ CS1 -CONJG(SN1) ] = [ RT1  0  ]
24       [-SN1     CS1     ] [ CONJG(B) C ] [ SN1     CS1     ]   [  0  RT2 ].
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ARGUMENTS

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

48       RT1 is accurate to a few ulps barring over/underflow.
49       RT2 may be inaccurate if there is massive cancellation in the  determi‐
50       nant  A*C-B*B; higher precision or correctly rounded or correctly trun‐
51       cated arithmetic would be needed  to  compute  RT2  accurately  in  all
52       cases.
53       CS1  and  SN1 are accurate to a few ulps barring over/underflow.  Over‐
54       flow is possible only if RT1 is within  a  factor  of  5  of  overflow.
55       Underflow is harmless if the input data is 0 or exceeds
56          underflow_threshold / macheps.
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60 LAPACK auxiliary routine (versionNo3v.e2m)ber 2008                       CLAEV2(1)
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