1SLANV2(1)             LAPACK driver routine (version 3.1)            SLANV2(1)
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NAME

6       SLANV2  -  the Schur factorization of a real 2-by-2 nonsymmetric matrix
7       in standard form
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SYNOPSIS

10       SUBROUTINE SLANV2( A, B, C, D, RT1R, RT1I, RT2R, RT2I, CS, SN )
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12           REAL           A, B, C, CS, D, RT1I, RT1R, RT2I, RT2R, SN
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PURPOSE

15       SLANV2 computes the Schur factorization of a real  2-by-2  nonsymmetric
16       matrix in standard form:
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18            [ A  B ] = [ CS -SN ] [ AA  BB ] [ CS  SN ]
19            [ C  D ]   [ SN  CS ] [ CC  DD ] [-SN  CS ]
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21       where either
22       1)  CC  = 0 so that AA and DD are real eigenvalues of the matrix, or 2)
23       AA = DD and BB*CC < 0, so that AA + or - sqrt(BB*CC) are complex conju‐
24       gate eigenvalues.
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ARGUMENTS

28       A       (input/output) REAL
29               B        (input/output)  REAL  C        (input/output)  REAL  D
30               (input/output) REAL On entry, the elements of the input matrix.
31               On  exit, they are overwritten by the elements of the standard‐
32               ised Schur form.
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34       RT1R    (output) REAL
35               RT1I    (output) REAL RT2R    (output)  REAL  RT2I     (output)
36               REAL  The  real  and imaginary parts of the eigenvalues. If the
37               eigenvalues are a complex conjugate pair, RT1I > 0.
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39       CS      (output) REAL
40               SN      (output) REAL Parameters of the rotation matrix.
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FURTHER DETAILS

43       Modified by V. Sima, Research  Institute  for  Informatics,  Bucharest,
44       Romania, to reduce the risk of cancellation errors,
45       when  computing  real  eigenvalues,  and  to  ensure, if possible, that
46       abs(RT1R) >= abs(RT2R).
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51 LAPACK driver routine (version 3.N1o)vember 2006                       SLANV2(1)
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