NAME

lanv2 - lanv2: 2x2 Schur factor

SYNOPSIS

Functions

subroutine dlanv2 (a, b, c, d, rt1r, rt1i, rt2r, rt2i, cs, sn)
DLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form. subroutine slanv2 (a, b, c, d, rt1r, rt1i, rt2r, rt2i, cs, sn)
SLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form.

Detailed Description

Function Documentation

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.

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



          A is DOUBLE PRECISION



          B is DOUBLE PRECISION



          C is DOUBLE PRECISION



          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.

RT1R



          RT1R is DOUBLE PRECISION

RT1I



          RT1I is DOUBLE PRECISION

RT2R



          RT2R is DOUBLE PRECISION

RT2I



          RT2I is DOUBLE PRECISION


          The real and imaginary parts of the eigenvalues. If the


          eigenvalues are a complex conjugate pair, RT1I > 0.



          CS is DOUBLE PRECISION



          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).

Definition at line 126 of file dlanv2.f.

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.