# Author: Alex Gezerlis

# Numerical Methods in Physics with Python (CUP, 2020)

import matplotlib.pyplot as plt

def legendre(n,x):

if n==0:

val2 = 1.

dval2 = 0.

elif n==1:

val2 = x

dval2 = 1.

else:

val0 = 1.; val1 = x

for j in range(1,n):

val2 = ((2*j+1)*x*val1 - j*val0)/(j+1)

val0, val1 = val1, val2

dval2 = n*(val0-x*val1)/(1.-x**2)

return val2, dval2

def plotlegendre(der,nsteps):

plt.xlabel('$x$', fontsize=20)

dertostr = {0: "$P_n(x)$", 1: "$P_n'(x)$"}

plt.ylabel(dertostr[der], fontsize=20)

ntomarker = {1: 'k-', 2: 'r--', 3: 'b-.', 4: 'g:', 5: 'c^'}

xs = [i/nsteps for i in range (-nsteps+1,nsteps)]

for n,marker in ntomarker.items():

ys = [legendre(n,x)[der] for x in xs]

labstr = 'n={0}'.format(n)

plt.plot(xs, ys, marker, label=labstr, linewidth=3)

plt.ylim(-3*der-1, 3*der+1)

plt.legend(loc=4)

plt.show()

if __name__ == '__main__':

nsteps = 200

plotlegendre(0,nsteps)

plotlegendre(1,nsteps)