slanv2(3)

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 a complex conjugate pair, RT1I > 0.

CS (output) REAL

SN (output) REAL 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 possi

ble, that abs(RT1R) >= abs(RT2R).

LAPACK version 3.0 15 June 2000

SLANV2(3)