1SLAEV2(1) LAPACK auxiliary routine (version 3.1) SLAEV2(1)
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6 SLAEV2 - the eigendecomposition of a 2-by-2 symmetric matrix [ A B ]
7 [ B C ]
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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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15 SLAEV2 computes the eigendecomposition of a 2-by-2 symmetric matrix
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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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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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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
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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)