1SLAEV2(1)           LAPACK auxiliary routine (version 3.1)           SLAEV2(1)
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NAME

6       SLAEV2  -  the eigendecomposition of a 2-by-2 symmetric matrix  [ A B ]
7       [ 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
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21          [ CS1  SN1 ] [  A   B  ] [ CS1 -SN1 ]  =  [ RT1  0  ]
22          [-SN1  CS1 ] [  B   C  ] [ SN1  CS1 ]     [  0  RT2 ].
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ARGUMENTS

26       A       (input) REAL
27               The (1,1) element of the 2-by-2 matrix.
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29       B       (input) REAL
30               The (1,2) element and the conjugate of the (2,1) element of the
31               2-by-2 matrix.
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33       C       (input) REAL
34               The (2,2) element of the 2-by-2 matrix.
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36       RT1     (output) REAL
37               The eigenvalue of larger absolute value.
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39       RT2     (output) REAL
40               The eigenvalue of smaller absolute value.
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42       CS1     (output) REAL
43               SN1      (output)  REAL  The  vector (CS1, SN1) is a unit right
44               eigenvector for RT1.
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FURTHER DETAILS

47       RT1 is accurate to a few ulps barring over/underflow.
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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.
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54       CS1 and SN1 are accurate to a few ulps barring over/underflow.
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56       Overflow  is  possible only if RT1 is within a factor of 5 of overflow.
57       Underflow is harmless if the input data is 0 or exceeds
58          underflow_threshold / macheps.
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63 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006                       SLAEV2(1)
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