Loading...
Searching...
No Matches

## dlanv2()

subroutine dlanv2 | ( | double precision | a,
|  | double precision | b,
|  | double precision | c,
|  | double precision | d,
|  | double precision | rt1r,
|  | double precision | rt1i,
|  | double precision | rt2r,
|  | double precision | rt2i,
|  | double precision | cs,
|  | double precision | sn )

DLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form.

Download DLANV2 + dependencies [TGZ] [ZIP] [TXT]

Purpose:

      !>
      !> DLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric
      !> matrix in standard form:
      !>
      !>      [ A  B ] = [ CS -SN ] [ AA  BB ] [ CS  SN ]
      !>      [ C  D ]   [ SN  CS ] [ CC  DD ] [-SN  CS ]
      !>
      !> where either
      !> 1) CC = 0 so that AA and DD are real eigenvalues of the matrix, or
      !> 2) AA = DD and BB*CC < 0, so that AA + or - sqrt(BB*CC) are complex
      !> conjugate eigenvalues.
      !>

Parameters

  [in,out]

  A

      !>          A is DOUBLE PRECISION
      !>

  [in,out]

  B

      !>          B is DOUBLE PRECISION
      !>

  [in,out]

  C

      !>          C is DOUBLE PRECISION
      !>

  [in,out]

  D

      !>          D is DOUBLE PRECISION
      !>          On entry, the elements of the input matrix.
      !>          On exit, they are overwritten by the elements of the
      !>          standardised Schur form.
      !>

  [out]

  RT1R

      !>          RT1R is DOUBLE PRECISION
      !>

  [out]

  RT1I

      !>          RT1I is DOUBLE PRECISION
      !>

  [out]

  RT2R

      !>          RT2R is DOUBLE PRECISION
      !>

  [out]

  RT2I

      !>          RT2I is DOUBLE PRECISION
      !>          The real and imaginary parts of the eigenvalues. If the
      !>          eigenvalues are a complex conjugate pair, RT1I > 0.
      !>

  [out]

  CS

      !>          CS is DOUBLE PRECISION
      !>

  [out]

  SN

      !>          SN is DOUBLE PRECISION
      !>          Parameters of the rotation matrix.
      !>

Author
  Univ. of Tennessee
  Univ. of California Berkeley
  Univ. of Colorado Denver
  NAG Ltd.

Further Details:

      !>
      !>  Modified by V. Sima, Research Institute for Informatics, Bucharest,
      !>  Romania, to reduce the risk of cancellation errors,
      !>  when computing real eigenvalues, and to ensure, if possible, that
      !>  abs(RT1R) >= abs(RT2R).
      !>