# MSPA 400 Session 8 Python Module #2

# Reading assignment:

# "Think Python" 2nd Edition Chapter 11 (11.1-11.8)

# "Think Python" 3rd Edition Chapter 11 (pages 121-132)

# Module #2 objectives: 1) demonstrate how to handle negative areas with

# numerical integration, 2) plot results using Python fill_between, and 3)

# demonstrate the use of an inequality for plotting different colors.

import matplotlib.pyplot

from matplotlib.pyplot import *

import numpy

from numpy import *

# Function from Lial Section 15.4 Example 6

def f(x):

f = x*x-4.0 #Students can supply a function at this point.

return f

# Integrate is a general numerical integration function. It requires

# an interval [a,b] and n = the number of subintervals used for integration.

# Integrate uses the function defined as f above. For details refer

# to Lial Section 15.3.

def integrate(a,b,n):

sum = 0.0

delta = (b-a)/n

i = 0

while i < n:

sum = sum + delta*(f(a+delta*(i+1))+f(a+delta*i))/2

i = i+1

return sum

#This defines the parameters for integration.

c = 4.0

b = 2.0

a = 0.0

n=100

# One area is negative and the other is positive. We integrate them separately

# and combine their absolute values.

area1 = integrate(a,b,n)

area2 = integrate(b,c,n)

area = abs(area1)+np.abs(area2)

print "Final Estimate of Area= %r" %area

# The next section of code shows how to plot different colors by

# dividing the interval based on which area is negative.

x = arange(0.0,2.1,0.1) # This defines the interval for the color red.

y = f(x)

# fill_between() requires an array for x and two functions for y between

# which the color is filled. In this case we use 0.0 for the x-axis and y.

# alpha controls the intensity of the color.

fill_between(x,0,y,color='r',alpha=0.8)

x = arange(2.0,4.1,0.1) # This defines the interval for the color blue.

y1 = f(x)

fill_between(x,0.0,y1,color='b',alpha=0.8)

# This section sets up the dimensions of the plot and creates it. We have to

# consider both plots and find the min and max of y for plot limits.

ymin = min(min(y),min(y1))

ymax = max(max(y),max(y1))

xlim(-0.5,4.5)

ylim(ymin-1.0,ymax+1.0)

xlabel('x-axis')

ylabel('y-axis')

title('Plot Showing Color Coded Integration Areas')

show()

# This section of code shows how to plot different colors using a

# logical operator in the plotting statement. The operator will

# control when each color is used.

figure() # This separates the two plots from each other.

x = arange(0.0,4.1,0.1) # This defines the interval for color filling.

y = f(x)

plot(x,y,c='k')

# This shows how to fill between the lines using an inequality.

fill_between(x,0.0,y,where= y < 0.0, facecolor = 'y',interpolate=True)

fill_between(x,0.0,y,where= y > 0.0, facecolor = 'g', interpolate=True)

xlim(-0.5,4.5)

ylim(ymin-1.0,ymax+1.0)

xlabel('x-axis')

ylabel('y-axis')

title('Plot Showing Color Coded Integration Areas')

show()

# Assignment #1: Refer to Lial Section 15.4 Exercise 42. Modify the code

# to reproduce the plot shown in the exercise. Compare to the answer sheet.