DLANV2(3F)DLANV2(3F)NAME
DLANV2 - compute the Schur factorization of a real 2-by-2 nonsymmetric
matrix in standard form
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 both
real, abs(RT1R) >= abs(RT2R); if the eigenvalues are a complex
conjugate pair, RT1I > 0.
CS (output) DOUBLE PRECISION
SN (output) DOUBLE PRECISION Parameters of the rotation
matrix.
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