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