LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ 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).
!>