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 a complex conjugate pair, RT1I > 0.

CS (output) DOUBLE PRECISION

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

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).