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25 lines
906 B
Python
25 lines
906 B
Python
from functools import reduce
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from itertools import cycle
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from math import factorial
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import numpy as np
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import scipy.sparse as sp
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def difference(derivative, accuracy=1):
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# Central differences implemented based on the article here:
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# http://web.media.mit.edu/~crtaylor/calculator.html
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derivative += 1
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radius = accuracy + derivative // 2 - 1
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points = range(-radius, radius + 1)
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coefficients = np.linalg.inv(np.vander(points))
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return coefficients[-derivative] * factorial(derivative - 1), points
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def operator(shape, *differences):
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# Credit to Philip Zucker for figuring out
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# that kronsum's argument order is reversed.
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# Without that bit of wisdom I'd have lost it.
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differences = zip(shape, cycle(differences))
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factors = (sp.diags(*diff, shape=(dim,) * 2) for dim, diff in differences)
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return reduce(lambda a, f: sp.kronsum(f, a, format='csc'), factors) |