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# Author: Daniele Bigoni
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=========================================
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=========================================
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Created on Mon Nov 19 09:45:24 2012
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@author: Daniele Bigoni (dabi@imm.dtu.dk)
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Implementation of Stroud equally weighted quadrature rules in N dimensions.
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Available quadrature rules:
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Some useful references used in while developing this toolbox are listed below
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.. [1] A.H. Stroud, "Remarks on the Disposition of Points in Numerical Integration Formulas", Mathematical Tables and Other Aids to Computation, Vol. 11, No. 60 (Oct. 1957), pp. 257-261
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.. [2] D. Xiu, "Numerical integration formulas of degree two", Applied Numerical Mathematics, Vol. 58, No. 10, pp. 1515-1520, 2008
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__revision__ = filter(str.isdigit, "$Revision: 84 $")
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__author__ = "Daniele Bigoni"
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AVAIL_WEIGHTS = [GAUSSIAN, BETA, GAMMA]
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""" Initialization of the Stroud integral points generator.
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This method generates an instance of the Stroud class, to be used in order to generate
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N-dimensional cubature rules with respect to the selected weight. Available weight types can be
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selected using their string name or by predefined attributes
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* 'Gaussian' or ``Stroud.GAUSSIAN``
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* 'Beta' or ``Stroud.BETA``
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* 'Gamma' or ``Stroud.GAMMA``
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Additional parameters are required for some weights.
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+--------------+--------------+
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| Weight | Parameters |
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+==============+==============+
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+--------------+--------------+
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| Beta | (alpha,beta) |
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+--------------+--------------+
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+--------------+--------------+
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See :cite:`Stroud1957` and :cite:`Xiu2008` for details.
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weight (Stroud.AVAIL_WEIGHTS): type of the multidimensional weight for the formula.
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params (object): The parameters needed by the selected weight
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def __init__(self, weight, params):
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Initialization of the Stroud integral points generator.
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``stroud = Stroud(weight, params)``
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* ``weight`` = (Stroud.AVAIL_WEIGHTS) type of the multidimensional weight for the formula.
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* ``params`` = The parameters needed by the selected weight
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This method generates an instance of the Stroud class, to be used in order to generate
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N-dimensional cubature rules with respect to the selected weight. Available weight types can be
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selected using their string name or by predefined attributes
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* 'Gaussian' or ``Stroud.GAUSSIAN``
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* 'Beta' or ``Stroud.BETA``
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* 'Gamma' or ``Stroud.GAMMA``
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Additional parameters are required for some weights.
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+--------------+--------------+
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| Weight | Parameters |
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+==============+==============+
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+--------------+--------------+
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| Beta | (alpha,beta) |
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+--------------+--------------+
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+--------------+--------------+
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if weight in AVAIL_WEIGHTS:
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if (weight == BETA):
added
removed
SpectralToolbox/Stroud.py
