LAPACK 3.11.0
LAPACK: Linear Algebra PACKage

◆ slanv2()

subroutine slanv2 ( real  A,
real  B,
real  C,
real  D,
real  RT1R,
real  RT1I,
real  RT2R,
real  RT2I,
real  CS,
real  SN 
)

SLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form.

Download SLANV2 + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 SLANV2 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 REAL
[in,out]B
          B is REAL
[in,out]C
          C is REAL
[in,out]D
          D is REAL
          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 REAL
[out]RT1I
          RT1I is REAL
[out]RT2R
          RT2R is REAL
[out]RT2I
          RT2I is REAL
          The real and imaginary parts of the eigenvalues. If the
          eigenvalues are a complex conjugate pair, RT1I > 0.
[out]CS
          CS is REAL
[out]SN
          SN is REAL
          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).