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uni-m.cds-num-met/week1/ex2.py

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2020-02-12 12:26:58 +01:00
#!/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()