NAME

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

SYNOPSIS

SUBROUTINE SLANV2(
A, B, C, D, RT1R, RT1I, RT2R, RT2I, CS, SN )

REAL A, B, C, CS, D, RT1I, RT1R, RT2I, RT2R, SN

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.
 

ARGUMENTS

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

RT1R    (output) REAL
RT1I    (output) REAL RT2R    (output) REAL RT2I    (output) REAL 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) REAL
SN      (output) REAL Parameters of the rotation matrix.

  —  LAPACK version 2.0  —  08 October 1994