101 lines
2.7 KiB
Python
101 lines
2.7 KiB
Python
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#!/usr/bin/env python3
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# Lagrange Polynomial Interpolation
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#----------------------------------
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import numpy as np
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def my_lagrange(data_x, data_y, x):
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"""
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Lagrange Interpolation
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param @data_x : array: x values to be interpolated
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param @data_y : array: y values to be interpolated
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param @x : array_like: x part of the interpolation set
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returns @p : array: y part of the interpolation set
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"""
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# make sure data_x is a numpy array with nd >= 1
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x = np.array(x, ndmin=1)
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p = np.zeros(np.size(x), dtype=np.float64)
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for i, x_i in enumerate( x ):
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p[i] = np.sum( data_y * my_lagrange_polynomials(data_x, x_i) )
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return p
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def my_lagrange_polynomials(data_x, x_i):
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"""
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Determine Lagrange Polynomials
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param @data_x : array_like : various data parts
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param @x_i : float : interpolating x value
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returns @L : array : lagrange polynomial terms for each x_i
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"""
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# make sure data_x is a numpy array with nd >= 1
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data_x = np.array(data_x, ndmin=1)
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L = np.zeros(np.size(data_x), dtype=np.float64)
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L_fixed = np.prod( x_i - data_x )
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for k, x_k in enumerate( data_x ):
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if x_k != x_i:
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L[k] = L_fixed / ( x_i - x_k )
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else:
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# Avoid dividing by zero if x_i and x_k are equal
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L[k] = np.prod( x_i - np.delete(data_x, k) )
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L[k] *= 1 / np.prod( x_k - np.delete(data_x,k) )
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return L
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def main(x_values = None, y_values = None, x = None, x_min = None, x_max = None, x_step = None, x_N = None):
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"""
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Example implementation of my_lagrange[_polynomials]()
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"""
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if x_values is None or y_values is None:
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x_values = [2,3,4,5,6]
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y_values = [2,5,5,5,6]
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if x is None:
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x_min = x_min if x_min is not None else min(x_values)
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x_max = x_max if x_max is not None else max(y_values)
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x_N = x_N if x_N is not None else (int(abs((x_max - x_min ) / x_step)) if x_step is not None else 1e3)
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x = np.linspace(x_min, x_max, x_N, endpoint=True)
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import matplotlib.pyplot as plt
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fig, ax = plt.subplots()
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ax.set_title("Lagrange Interpolations")
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ax.grid()
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ax.set_xlabel("x")
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ax.set_ylabel("y")
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# Plot my Lagrange Interpolation
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ax.plot(x, my_lagrange(x_values, y_values, x), '.', label="My Lagrange Interpolation")
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# Plot Scipy's Lagrange Interpolation
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from scipy.interpolate import lagrange as scipy_lagrange
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ax.plot(x, scipy_lagrange(x_values, y_values)(x), '--', label="Scipy Interpolation")
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# Plot the data
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ax.plot(x_values, y_values, 'gd', label="Data")
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ax.legend()
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plt.show()
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if __name__ == "__main__":
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main()
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