1DLANV2(1) LAPACK driver routine (version 3.2) DLANV2(1)
2
6 DLANV2 - computes the Schur factorization of a real 2-by-2 nonsymmetric
7 matrix in standard form
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10 SUBROUTINE DLANV2( A, B, C, D, RT1R, RT1I, RT2R, RT2I, CS, SN )
11 DOUBLE PRECISION A, B, C, CS, D, RT1I, RT1R, RT2I, RT2R, SN
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15 DLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric
16 matrix in standard form:
17 [ A B ] = [ CS -SN ] [ AA BB ] [ CS SN ]
18 [ C D ] [ SN CS ] [ CC DD ] [-SN CS ]
19 where either
20 1) CC = 0 so that AA and DD are real eigenvalues of the matrix, or 2)
21 AA = DD and BB*CC < 0, so that AA + or - sqrt(BB*CC) are complex conju‐
22 gate eigenvalues.
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25 A (input/output) DOUBLE PRECISION
26 B (input/output) DOUBLE PRECISION C (input/output)
27 DOUBLE PRECISION D (input/output) DOUBLE PRECISION On
28 entry, the elements of the input matrix. On exit, they are
29 overwritten by the elements of the standardised Schur form.
30 RT1R (output) DOUBLE PRECISION
32 RT1I (output) DOUBLE PRECISION RT2R (output) DOUBLE PRE‐
33 CISION RT2I (output) DOUBLE PRECISION The real and imaginary
34 parts of the eigenvalues. If the eigenvalues are a complex con‐
35 jugate pair, RT1I > 0.
36 CS (output) DOUBLE PRECISION
38 SN (output) DOUBLE PRECISION Parameters of the rotation
39 matrix.
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42 Modified by V. Sima, Research Institute for Informatics, Bucharest,
43 Romania, to reduce the risk of cancellation errors,
44 when computing real eigenvalues, and to ensure, if possible, that
45 abs(RT1R) >= abs(RT2R).
46 LAPACK driver routine (version 3.N2o)vember 2008 DLANV2(1)