Class 28 — Wednesday, March 30

Look both ways

• Back or ahead

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Agenda

• Slides discussing pass by value vs pass by reference, and how it relates to us.

• Learn how Python can graph any function

• Write several functions to determine info about linear equation.

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To do

• Check out and use CS 1112 Grading Issue/Late Work

• Look at Hands on Python.

• Look at function epistle.

• Look at www.python.org resources.

• Check out the Python Tutorial section on functions.

• Look over artifacts

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Slides

• Google slideset

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Examples

• Program rearrangements.py

• Module lines.py

• Program plotacular.py

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Why functions?

• Question: Why bother with functions?

• Makes modern software possible

• Question: Why bother with non-standard functions?

• Tasks important to you can be solved and reused as wanted

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Program rearrangements.py

• We provide this program to you to start our investigation of plotting a graph in python

• First, we will have to add a few new modules to our Pycharm installation. The following code block shows which libraries must be imported to produce the neat graph images.

• Note the new keyword-- as: this is to allow us to not have to type super-long module and sub-module names in order to execute the useful functions that we're interested.

import matplotlib.pyplot as plt

import numpy as np

• This program takes in a lower-bound, upper-bound and step-size as its input.

• It then feeds these values into arange which is just like range, but can deal with float (decimal) values.

• For example, if we wanted all the half-steps from 0 to 3, we could get the sequence of x-values,

• [0, 0.5, 1.0, 1.5, 2.0, 2.5]

• Next, the program calculates the value of y = x*x for every x in this sequence.

• This will produce a sequence of y-values,

• [0, 0.25, 1.0, 2.25, 4.0, 6.25]

• Note that theses ordered pairs of (x,y) values will graph a parabola.

x = np.arange( lb, ub, step )

 

print( "x-size =", len( x ) )

 

y = x ** 2

print( "y-size =", len( y ) )

 

print( len( x ) == len( y ) )

 

plt.plot( x, y )

 

Spend some time with your neighbor running rearrangements.py, and experimenting with different lower and upper bounds, and step sizes to see what you can graph!

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Module lines.py and Program 'plotacular.py'

• First, open up plotacular.py, and notice the different operations we are tasked to write as functions for module lines.py

• lines.plot_line(m1, b1) has been written for you, and plots the line represented by y = m*x + b

• lines.find_m takes in two ordered pairs, (x1, y1) and (x2, y2), and returns slope.

• lines.find_b takes in two ordered pairs, (x1, y1) and (x2, y2), and returns the y-intercept.

• lines.find_perpendicular takes in a slope value, m, and returns the opposite reciprocal slope.

• lines.fine_y takes in a slope m, a y-intercept b, and an input value of x, and returns the corresponding y value.

• We'll give you a chance to try each on your own, then we will review as a class.

import matplotlib.pyplot as plt

import numpy as np

def plot_line(m, b):

lb = -10

ub = 10

step = 0.01

x = np.arange(lb, ub, step)

y = m*x + b

plt.plot(x, y)

plt.show()

return

def find_m(x1, y1, x2, y2):

...

return m

def find_b(x1, y1, x2, y2):

...

return b

def find_perpendicular(m):

...

return perp

def find_y(m, b, x):

...

return y

 

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🦆 © 2022 Jim Cohoon

Resources from previous semesters are available.