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# This file is unit04_elliptic_integrand.py. It draws a graph
# of a function described in the in-class material: the integrand of a
# complete elliptic integral of the second kind. This integral gives
# the perimeter of an ellipse with semi-major, minor axes a and b.

# George Gollin, University of Illinois, May 26, 2016

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# import libraries

import numpy as np
import matplotlib
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D 

# semimajor and minor axes:

axis_a = 2.
axis_b = 1.5

# squares:

axis_asq = axis_a**2
axis_bsq = axis_b**2

# integral will go from 0 to pi/2. and I want to plot its integrand. define
# an array holding theta values.

theta_min = 0.
theta_max = np.pi / 2
array_length = 100
theta_array = np.linspace(theta_min, theta_max, array_length)

# load the array of ordinate (y axis) values:

f_of_theta_array = np.sqrt(axis_asq - (axis_asq - axis_bsq) * np.sin(theta_array)**2)

# now make the graph. open a new window for the plot we are about to make

plt.figure()

# now draw the plot

plt.plot(theta_array, f_of_theta_array)

# now label the axes and give the plot a title. "gca" is "get current axes"

ax = plt.gca()

ax.set_xlabel("theta (radians)")
ax.set_ylabel("integrand")
ax.set_title("integrand of the second kind")
 
# now save the plot to a png (portable network graphics) file

plt.savefig("unit04_elliptic_integrand.png")

print("all done")

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