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近似多項式との誤差の極値を求める
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from scipy.signal import argrelmax | |
import numpy as np | |
def epsilon(f, coeffList): | |
a, b = -1, 1 # 区間 | |
dim = len(coeffList) | |
f = f | |
g = lambda x : sum([coeffList[n] * x**n for n in np.arange(dim)]) | |
ε = lambda f, g : f - g | |
# x 軸を細かく分割して、 | |
xList = np.linspace(a, b, 2**16+1) | |
# 各 x における誤差 ε を計算して、 | |
εList = ε(f(xList), g(xList)) | |
# 誤差 ε が極値となるところの x のインデックスを求めて、 | |
peaksIndex = argrelmax(np.abs(εList)) | |
# 区間の両端も含めて誤差 ε が極値となるところの x をリスト化する。 | |
x0List = np.concatenate(([a], xList[peaksIndex], [b])) | |
# 区間の両端も含めて誤差 ε の極値をリスト化する。 | |
εa = εList[0] | |
εb = εList[-1] | |
ε0List = np.concatenate(([εa], εList[peaksIndex], [εb])) | |
return x0List, ε0List | |
######## | |
# test # | |
######## | |
if __name__ == "__main__": | |
f = lambda x : np.sin(np.pi * x / 2) | |
# チェビシェフ補間で求めた近似多項式の係数が下のとおりであるとする。 | |
# この cList から、誤差 ε が極値を取るときの x とそのときの極値とを求める。 | |
cList = np.array([0.0, 1.57065736, -0.0, -0.64345777, 0.0, 0.07293465]) | |
x0List, ε0List = epsilon(f, cList) | |
print(x0List) | |
print(ε0List) | |
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