1DLANV2(1)             LAPACK driver routine (version 3.1)            DLANV2(1)
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NAME

6       DLANV2  -  the Schur factorization of a real 2-by-2 nonsymmetric matrix
7       in standard form
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SYNOPSIS

10       SUBROUTINE DLANV2( A, B, C, D, RT1R, RT1I, RT2R, RT2I, CS, SN )
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12           DOUBLE         PRECISION A, B, C, CS, D, RT1I, RT1R, RT2I, RT2R, SN
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PURPOSE

15       DLANV2 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) DOUBLE PRECISION
29               B        (input/output) DOUBLE PRECISION C       (input/output)
30               DOUBLE PRECISION D        (input/output)  DOUBLE  PRECISION  On
31               entry,  the  elements  of  the input matrix.  On exit, they are
32               overwritten by the elements of the standardised Schur form.
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34       RT1R    (output) DOUBLE PRECISION
35               RT1I    (output) DOUBLE PRECISION RT2R    (output) DOUBLE  PRE‐
36               CISION RT2I    (output) DOUBLE PRECISION The real and imaginary
37               parts of the eigenvalues. If the eigenvalues are a complex con‐
38               jugate pair, RT1I > 0.
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40       CS      (output) DOUBLE PRECISION
41               SN       (output)  DOUBLE  PRECISION Parameters of the rotation
42               matrix.
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FURTHER DETAILS

45       Modified by V. Sima, Research  Institute  for  Informatics,  Bucharest,
46       Romania, to reduce the risk of cancellation errors,
47       when  computing  real  eigenvalues,  and  to  ensure, if possible, that
48       abs(RT1R) >= abs(RT2R).
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53 LAPACK driver routine (version 3.N1o)vember 2006                       DLANV2(1)
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