NAME

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

SYNOPSIS

SUBROUTINE DLANV2(
A, B, C, D, RT1R, RT1I, RT2R, RT2I, CS, SN )

DOUBLE PRECISION A, B, C, CS, D, RT1I, RT1R, RT2I, RT2R, SN

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.
 

ARGUMENTS

A       (input/output) DOUBLE PRECISION
B       (input/output) DOUBLE PRECISION C       (input/output) DOUBLE PRECISION D       (input/output) DOUBLE PRECISION On entry, the elements of the input matrix. On exit, they are overwritten by the elements of the standardised Schur form.

RT1R    (output) DOUBLE PRECISION
RT1I    (output) DOUBLE PRECISION RT2R    (output) DOUBLE PRECISION RT2I    (output) DOUBLE PRECISION The real and imaginary parts of the eigenvalues. If the eigenvalues are both real, abs(RT1R) >= abs(RT2R); if the eigenvalues are a complex conjugate pair, RT1I > 0.

CS      (output) DOUBLE PRECISION
SN      (output) DOUBLE PRECISION Parameters of the rotation matrix.

  —  LAPACK version 2.0  —  08 October 1994