sfepy.linalg.eigen module

sfepy.linalg.eigen.arpack_eigs(mtx, nev=1, which='SM')

Calculate several eigenvalues and corresponding eigenvectors of a matrix using ARPACK from SciPy. The eigenvalues are sorted in ascending order.

sfepy.linalg.eigen.cg_eigs(mtx, rhs=None, precond=None, i_max=None, eps_r=1e-10, shift=None, select_indices=None, verbose=False, report_step=10)

Make several iterations of the conjugate gradients and estimate so the eigenvalues of a (sparse SPD) matrix (Lanczos algorithm).

Parameters:

mtx : spmatrix or array

The sparse matrix

System Message: WARNING/2 (A)

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precond : spmatrix or array, optional

The preconditioner matrix. Any object that can be multiplied by vector can be passed.

i_max : int

The maximum number of the Lanczos algorithm iterations.

eps_r : float

The relative stopping tolerance.

shift : float, optional

Eigenvalue shift for non-SPD matrices. If negative, the shift is computed as

System Message: WARNING/2 (|shift| ||A||_{\infty})

latex exited with error [stdout] This is pdfTeX, Version 3.1415926-2.5-1.40.14 (TeX Live 2013/TeX Live for SUSE Linux) restricted \write18 enabled. entering extended mode (./math.tex LaTeX2e <2011/06/27> Babel <3.9f> and hyphenation patterns for 78 languages loaded. (/usr/share/texmf/tex/latex/base/article.cls Document Class: article 2007/10/19 v1.4h Standard LaTeX document class (/usr/share/texmf/tex/latex/base/size12.clo)) (/usr/share/texmf/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def’ not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.131 \endinput ^^M No pages of output. Transcript written on math.log.

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select_indices : (min, max), optional

If given, computed only the eigenvalues with indices min <= i <= max.

verbose : bool

Verbosity control.

report_step : int

If verbose is True, report in every report_step-th step.

Returns:

vec : array

The approximate solution to the linear system.

n_it : int

The number of CG iterations used.

norm_rs : array

Convergence history of residual norms.

eigs : array

The approximate eigenvalues sorted in ascending order.

sfepy.linalg.eigen.sym_tri_eigen(diags, select_indices=None)

Compute eigenvalues of a symmetric tridiagonal matrix using scipy.linalg.eigvals_banded().