slanv2 (l) - Linux Manuals

slanv2: computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form

Command to display slanv2 manual in Linux: $ man l slanv2

NAME

SLANV2 - computes 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 possible, that abs(RT1R) >= abs(RT2R).