# sfepy.discrete.simplex_cubature module

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

sfepy.discrete.simplex_cubature.factorial(n)

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

sfepy.discrete.simplex_cubature.generate_permutations(original)

  Generate all permutations of the list `original’.

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

sfepy.discrete.simplex_cubature.generate_unique_permutations(original)

  Generate all unique permutations of the list `original’.

sfepy.discrete.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 2s+1, where s is given as order. The integration domain is the unit simplex

  T_n := \{(x_1, \dots, x_n): x_i \ge -1, \sum_i x_i \le -1\}

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