man slanv2 (Fonctions bibliothèques) - compute the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form
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 possible, that
abs(RT1R) >= abs(RT2R).