50 lines
1.7 KiB
Python
50 lines
1.7 KiB
Python
# Python module for calculating the newton polynom from given points
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# _ _ _ _
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# __ ___ __(_) |_| |_ ___ _ __ | |__ _ _
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# \ \ /\ / / '__| | __| __/ _ \ '_ \ | '_ \| | | |
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# \ V V /| | | | |_| || __/ | | | | |_) | |_| |
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# \_/\_/ |_| |_|\__|\__\___|_| |_| |_.__/ \__, |
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# |___/
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# ____ __ __ _
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# / ___|_ _____ _ __ \ \ / /__ __ _ ___| |
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# \___ \ \ / / _ \ '_ \ \ \ / / _ \ / _` |/ _ \ |
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# ___) \ V / __/ | | | \ V / (_) | (_| | __/ |
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# |____/ \_/ \___|_| |_| \_/ \___/ \__, |\___|_|
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# |___/
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# Licensed under the GPLv2 License, Version 2.0 (the "License");
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# Copyright (c) Sven Vogel
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def combine_n(points):
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k = len(points)
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if k == 1:
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return points[0][1]
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elif k == 2:
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return (points[1][1] - points[0][1]) / (points[1][0] - points[0][0])
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else:
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return (combine_n(points[1:k]) - combine_n(points[0:(k - 1)])) / (points[k - 1][0] - points[0][0])
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# returns a polynom that will intersect all supplied points as long as
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# the number of points is bigger than 1
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def newton_polynom(points):
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polynom = ""
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for x in range(1, len(points)):
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if x == 1:
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polynom += '{r0:.2f} + '.format(r0=points[0][1])
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else:
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polynom += ' + '
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polynom += "{r:.2f}".format(r=combine_n(points[0:(x + 1)]))
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for y in range(x):
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polynom += " * (x - {value:.2f})".format(value=points[y][0])
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return polynom
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def test():
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points = [[-1, 5], [2, -1], [3, -1], [4, 5], [8, 9]]
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print("newton polynom: ", newton_polynom(points))
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