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# poly.m - simple set of polynomial basis functions
# TODO: rename this as taylor.m
# RMM, 10 Nov 2012
#
# This class implements a set of simple basis functions consisting of powers
# of t: 1, t, t^2, ...
#
# Copyright (c) 2012 by California Institute of Technology
# All rights reserved.
#
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions
# are met:
#
# 1. Redistributions of source code must retain the above copyright
# notice, this list of conditions and the following disclaimer.
#
# 2. Redistributions in binary form must reproduce the above copyright
# notice, this list of conditions and the following disclaimer in the
# documentation and/or other materials provided with the distribution.
#
# 3. Neither the name of the California Institute of Technology nor
# the names of its contributors may be used to endorse or promote
# products derived from this software without specific prior
# written permission.
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
# "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
# LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
# FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL CALTECH
# OR THE CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
# SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
# LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF
# USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
# ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
# OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
# OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
# SUCH DAMAGE.
import numpy as np
from scipy.special import factorial
from .basis import BasisFamily
class PolyFamily(BasisFamily):
r"""Polynomial basis functions.
This class represents the family of polynomials of the form
.. math::
\phi_i(t) = t^i
"""
def __init__(self, N):
"""Create a polynomial basis of order N."""
super(PolyFamily, self).__init__(N)
# Compute the kth derivative of the ith basis function at time t
def eval_deriv(self, i, k, t):
"""Evaluate the kth derivative of the ith basis function at time t."""
if (i < k): return 0; # higher derivative than power
return factorial(i)/factorial(i-k) * np.power(t, i-k)