Polynomial Interpolation

def evalPoly(a,xData,x):

    n = len(xData) - 1  # Degree of polynomial

    p = a[n]

    for k in range(1,n+1):

        p = a[n-k] + (x -xData[n-k])*p

    return p

def coeffts(xData,yData):

    m = len(xData)  # Number of data points

    a = yData.copy()

    for k in range(1,m):

        a[k:m] = (a[k:m] - a[k-1])/(xData[k:m] - xData[k-1])

        print('k = ',k,a)

    return a

import numpy as np

import matplotlib.pyplot as plt

xs = np.linspace(0,6,100)

x_set1 = np.array([0.0,1.0,3.0,4.0,6.0])

y_set1 = np.array([1.1,-2.1,3,7,-4])

ys = evalPoly(coeffts(x_set1,y_set1),x_set1,xs)

plt.plot(xs,ys)

plt.scatter(x_set1,y_set1)

from numpy import sin,pi

x_set2 = np.linspace(0,2*pi,7)

y_set2 = np.sin(x_set2)

xs2 = np.linspace(-0.5,2.25*pi,100)

ys2 = evalPoly(coeffts(x_set2,y_set2),x_set2,xs2)

plt.plot(xs2,ys2)

plt.scatter(x_set2,y_set2)

xs2a = np.linspace(-1,8,200)

ys2a = evalPoly(coeffts(x_set2,y_set2),x_set2,xs2a)

plt.plot(xs2a,ys2a)

plt.scatter(x_set2,y_set2)

x_set3 = np.array([-5,-4,-3,-2,-1,0,1,2,3,4,5],dtype=float)

y_set3 = np.array([0.0,0.0,0.05,0.25,0.70,1.0,0.65,0.25,0.05,0.0,0.0])

xs3 = np.linspace(-5.,5.,100)

ys3 = evalPoly(coeffts(x_set3,y_set3),x_set3,xs3)

plt.plot(xs3,ys3)

plt.scatter(x_set3,y_set3)

x_set4 = np.array([-6,-4,-3,-2,-1,0,1,2,3,4,5],dtype=float)

y_set4 = np.array([-0.1,0.0,0.0,0.05,0.25,0.70,1.0,0.65,0.25,0.05,0.0,0.0])

xs4 = np.linspace(-6.,5.,100)

ys4 = evalPoly(coeffts(x_set4,y_set4),x_set4,xs4)

plt.plot(xs4,ys4)

plt.scatter(x_set4,y_set4)

x_set5 = np.linspace(0.1,2,5)

y_set5 = np.log(x_set5)

xs5 = np.linspace(0,3,100)

ys5 = evalPoly(coeffts(x_set5,y_set5),x_set5,xs5)

ys5a = np.log(xs5)

plt.plot(xs5,ys5)

plt.scatter(x_set5,y_set5)

plt.plot(xs5,ys5a,'--')

x_set5