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56 lines
1.8 KiB
Python
56 lines
1.8 KiB
Python
"""
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Python program to show how to interpolate and evaluate a polynomial
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using Neville's method.
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Neville’s method evaluates a polynomial that passes through a
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given set of x and y points for a particular x value (x0) using the
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Newton polynomial form.
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Reference:
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https://rpubs.com/aaronsc32/nevilles-method-polynomial-interpolation
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"""
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def neville_interpolate(x_points: list, y_points: list, x0: int) -> list:
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"""
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Interpolate and evaluate a polynomial using Neville's method.
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Arguments:
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x_points, y_points: Iterables of x and corresponding y points through
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which the polynomial passes.
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x0: The value of x to evaluate the polynomial for.
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Return Value: A list of the approximated value and the Neville iterations
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table respectively.
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>>> import pprint
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>>> neville_interpolate((1,2,3,4,6), (6,7,8,9,11), 5)[0]
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10.0
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>>> pprint.pprint(neville_interpolate((1,2,3,4,6), (6,7,8,9,11), 99)[1])
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[[0, 6, 0, 0, 0],
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[0, 7, 0, 0, 0],
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[0, 8, 104.0, 0, 0],
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[0, 9, 104.0, 104.0, 0],
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[0, 11, 104.0, 104.0, 104.0]]
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>>> neville_interpolate((1,2,3,4,6), (6,7,8,9,11), 99)[0]
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104.0
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>>> neville_interpolate((1,2,3,4,6), (6,7,8,9,11), '')
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Traceback (most recent call last):
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...
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TypeError: unsupported operand type(s) for -: 'str' and 'int'
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"""
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n = len(x_points)
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q = [[0] * n for i in range(n)]
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for i in range(n):
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q[i][1] = y_points[i]
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for i in range(2, n):
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for j in range(i, n):
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q[j][i] = (
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(x0 - x_points[j - i + 1]) * q[j][i - 1]
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- (x0 - x_points[j]) * q[j - 1][i - 1]
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) / (x_points[j] - x_points[j - i + 1])
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return [q[n - 1][n - 1], q]
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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