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""" |
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Class for approximating the solution to two-point boundary value problems using |
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either standard or orthogonal polynomials as basis functions. |
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@author: davidrpugh |
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""" |
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import numpy as np |
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from . import basis_functions |
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12
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class PolynomialBasis(basis_functions.BasisFunctionLike): |
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_valid_kinds = ['Polynomial', 'Chebyshev', 'Legendre', 'Laguerre', 'Hermite'] |
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@staticmethod |
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def _basis_monomial_coefs(degree): |
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"""Return coefficients for a monomial of a given degree.""" |
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return np.append(np.zeros(degree), 1) |
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@classmethod |
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def _basis_polynomial_factory(cls, kind): |
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"""Return a polynomial given some coefficients.""" |
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valid_kind = cls._validate(kind) |
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basis_polynomial = getattr(np.polynomial, valid_kind) |
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return basis_polynomial |
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@classmethod |
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def _validate(cls, kind): |
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"""Validate the kind argument.""" |
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if kind not in cls._valid_kinds: |
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mesg = "'kind' must be one of {}, {}, {}, or {}." |
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raise ValueError(mesg.format(*cls._valid_kinds)) |
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else: |
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return kind |
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@classmethod |
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def derivatives_factory(cls, coef, domain, kind, **kwargs): |
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""" |
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Given some coefficients, return a the derivative of a certain kind of |
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orthogonal polynomial defined over a specific domain. |
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""" |
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basis_polynomial = cls._basis_polynomial_factory(kind) |
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return basis_polynomial(coef, domain).deriv() |
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@classmethod |
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def fit(cls, ts, xs, degree, domain, kind): |
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basis_polynomial = cls._basis_polynomial_factory(kind) |
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return basis_polynomial.fit(ts, xs, degree, domain) |
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@classmethod |
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def functions_factory(cls, coef, domain, kind, **kwargs): |
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""" |
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Given some coefficients, return a certain kind of orthogonal polynomial |
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defined over a specific domain. |
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""" |
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basis_polynomial = cls._basis_polynomial_factory(kind) |
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return basis_polynomial(coef, domain) |
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@classmethod |
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def roots(cls, degree, domain, kind): |
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"""Return optimal collocation nodes for some orthogonal polynomial.""" |
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basis_coefs = cls._basis_monomial_coefs(degree) |
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basis_poly = cls.functions_factory(basis_coefs, domain, kind) |
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return basis_poly.roots() |
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davidrpugh /
pyCollocation
