sfepy.fem.simplex_cubature module

Generate simplex quadrature points. Code taken and adapted from pytools/hedge by Andreas Kloeckner.

sfepy.fem.simplex_cubature.factorial(n)

sfepy.fem.simplex_cubature.generate_decreasing_nonnegative_tuples_summing_to(n, length, min=0, max=None)

sfepy.fem.simplex_cubature.generate_permutations(original)

Generate all permutations of the list `original’.

Nicked from http://aspn.activestate.com/ASPN/Cookbook/Python/Recipe/252178

sfepy.fem.simplex_cubature.generate_unique_permutations(original)

Generate all unique permutations of the list `original’.

sfepy.fem.simplex_cubature.get_simplex_cubature(order, dimension)

Cubature on an M{n}-simplex.

cf. A. Grundmann and H.M. Moeller, Invariant integration formulas for the n-simplex by combinatorial methods, SIAM J. Numer. Anal. 15 (1978), 282–290.

This cubature rule has both negative and positive weights. It is exact for polynomials up to order

System Message: WARNING/2 (2s+1)

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.

, where

System Message: WARNING/2 (s)

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.

is given as order. The integration domain is the unit simplex

System Message: WARNING/2 (T_n := \{(x_1, \dots, x_n): x_i \ge -1, \sum_i x_i \le -1\})

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.

sfepy.fem.simplex_cubature.wandering_element(length, wanderer=1, landscape=0)