ENGG1811 Computing for Engineersen1811/19T2/lecs/week03/... · 2019-02-06 · The goal for this...

ENGG1811 © UNSW, CRICOS Provider No: 00098G1 slide 1

Week 3: Functions, list, for, plotting

ENGG1811 Computing for Engineers

The goal for this week

• We will cover 4 different topics this week. They are:– Functions– List– For-loop– Plotting

• The reason why we have put these 4 topics together is that you can do something useful by combining them

• We will work on a project with makes use of these four topics. We will start by telling you the project’s goal and show you the end product.

• We will then look at these 4 topics one by one.

ENGG1811 © UNSW, CRICOS Provider No: 00098G slide 2

Project: goal

• If you drop an object of mass m in a medium with drag coefficient d and acceleration due to gravity g, then the object’s speed v(t) at time t is given by:


• Given the numerical value of m, g and d, the goal of the project is to plot v(t) against t– for t = 0, 0.5, 1, 1.5, …., 39.5, 40

• You certainly know how to do this by using pen, paper and calculator

• You may also need a bit of perseverance because it does get a bit repetitive

Project: end product

• Goal: Given the numerical value of m, g and d, the goal of the project is to plot v(t) against t– for t = 0, 0.5, 1, 1.5, …., 39.5, 40


• You will do it in Python

• The end product

This week’s topics

• Functions • List• For-loop• Plotting


Functions

• We talked about functions in Week 1 and you used it in your lab in Week 2


• We will show you how to write your own functions

Your first function

• You know that when you use the function math.cos(), you input a value and get an output


• You will now write a function which squares the input value and then outputs it

math.cos()1.34 cosine of 1.34

my_square()• Open the file my_square_prelim.py that comes with this

week’s lecture• Type in Lines 12-14 as shown below

– Don’t forget the : at the end of Line 12– The indentation in Lines 13-14 is important

• And then run the program


Anatomy of a function• Line 12:

– def means you want to define a function– The name of the function is my_square– x is the identifier you give to the input

• Lines 13 and 14 are indented relative to def so they belong to the function definition

• Lines 16 and 17 are not indented, so they are not part of the function


Mechanics of function evaluation (1)• Line 17: The function my_square is called

– Terminology: Calling a function means executing the code inside a function

• Because the variable a has the value of 5, the identifier x in the function is assigned the value of 5

• The code inside the function is executed sequentially• Line 13: the identifier y is assigned the value of 25


Mechanics of function evaluation (2)

• return y in Line 14 means the value of y (which is 25) is to be put at the place where the function is called

• The right-hand-side of Line 17 is now 25 • b is then assigned the value of 25


Multiple inputs

• Code in my_power.py• You can have multiple inputs to a function

– For example, the function my_power has two inputs (Line 12)• When the function my_power is called in Lines 15 and 17,

there are 2 values inside the parentheses separated by a comma


Orderly assignment

x ← 5 n ← 2


x ← 2 n ← 5

Local scope• The code is in local.py• Note that there is a variable y in the function and there is

also a variable y outside the function• Are they the same?


def my_power(x,n): y = x ** n return y

y = 4z = my_power(y,2)

print('y = ' ,y)print('z = ' ,z)

We will copy the code to the Python tutor website which allows us to visualise the execution of the code

http://pythontutor.com/visualize.html

Local variable scope• The variables in the function are stored in a separate

memory space– This applies to data types int, float, str, bool– But not for all data types, will tell you more later

• We say the scope of the variable is local to the function


def my_power(x,n): y = x ** n return y

y = 4z = my_power(y,2)

print('y = ' ,y)print('z = ' ,z)

Memory space for my_power

x

n

4

2

Base memory space

y 4

y 16

Multiple outputs

• Code in my_power3.py


x ← 5 n1 ← 2n2 ← 3n3 ← 4

Functions can call other functions • The code is in my_power3_improved.py• A function can call other functions


Function must be defined before they can be called

• Python expects that you define the functions before they are called

• The following code will not work because the function my_square is called in Line 13 but its definition is only found later in Line 16


DOESN’T WORK

Function must be defined before they can be called (cont’d)


• Consider the code my_power3_improved.py where the function my_power3() calls the function my_power()

• The function my_power3() is called the first time in Line 22. So my_power3() and the function it calls must all be defined before this line.

• However, my_power3() and the functions it calls can appear in any order.

Can exchange the order but both must be defined before my_power3() is called

Project (Part 1)• mass m, drag coefficient d, acceleration due to gravity g• speed v(t) at time t is:


• Exercise:

– Open the file project_prelim.py– Write a function called free_fall() to compute v(t)

• The def line of the function is given in Line 16:�

• The calculation requires:– Constant g – defined in Line 13 – The math library (imported in Line 9) and math.exp() to calculate

exponential. E.g math.exp(-2.1) gives e-2.1

• The function should return the computed speed• Testing: Lines 28 & 29 have the expected values

def free_fall(t,mass,drag):




List • You have come across a number of data types:

– int, float, str, bool, etc.

• We will now introduce a new data type called list

• A list consists of a sequence of objects enclosed in [ ] and separated by commas


List is useful because you can use them with loops

Why using loops in programming?


• Let us hear from Mark Zuckerberg (founder of Facebook) on why you need loops in programming

• https://www.youtube.com/watch?v=mgooqyWMTxk

ENGG1811 © UNSW, CRICOS Provider No: 00098G W6 slide 24

Iteration (Repetition)

• Often need to execute statements repeatedly

• Loops are statements that can do this

• Process is called iteration

• Kinds of loop:– For (iterate a fixed number of times)

– While (iterate as long as something is True)• We will spend a part of the lecture in the next few

weeks to learn about loops

ENGG1811 © UNSW, CRICOS Provider No: 00098G W6 slide 25

G’day, mate!

• I wish to say G’day to each student in an ENGG1811 class.

• I’ve created a list of names. There are 484 names.

Let us type the following code:


There are still 468 lines L

The enlightened way


These two lines of code print out the 484 G’day

• The code is in gday.py

For loop

for name in ["Charlie", "Hannah", "Olivia", "Usman"]: print("G'day, ",name)


• The code is in gday_explained.py

• Let us copy the code to Python Tutor and see how it is executed

• http://pythontutor.com/

The for-loop explained

• The variable name is called the loop variable • Code under for-loop is indented• The loop variable is assigned to the first item in the list• name is now the string "Charlie”. The code in the for-loop is

executed assuming this value of name• After executing the code under the for-loop, execution return

to the for-line. The computer checks whether there is a next item in the list. Yes, there is so the computer assigned "Hannah" to the variable name. The code in the for-loop is executed assuming this value of name

• This is repeated until all items in the list have been usedENGG1811 © UNSW, CRICOS Provider No: 00098G slide 29

for name in ["Charlie", "Hannah", "Olivia", "Usman"]: print("G'day, ",name)

Flowchart

http://interactivepython.org/runestone/static/thinkcspy/PythonTurtle/FlowofExecutionoftheforLoop.html


Examples of for-loop

• We will switch to Spyder to look at a number of examples of using for-loop – File name: for_examples.py

• Spyder allows us to divide the code into cells and we can run the code in each cell independently – Good for testing and debugging code– To run a cell, make sure your mouse cursor is in that cell

and click


For-loop exercise:

• �You are asked to write a for-loop to print out all the negative numbers in a given list of numbers

• You can do it in for_exercise_prelim.py


range()

• range() is a Python function that generates a sequence of integers

• The function can take 1 to 3 inputs and its behaviour depends on the number of inputs

• Examples in range_ex.py


range() expression sequence explanationrange(5) 0,1,2,3,4 One input. Starting from 0. Keep

increasing by 1. Does not including the number specified by the input.

range(2,8) 2,3,4,5,6,7 Two inputs. 1st number in list = 1st input

• With 2 inputs, the function has the form range(start,stop)– range(0,stop) is the same as range(stop)

• #elements in the list = stop - start

range()


range() expression

sequence explanation

range(2,20,4) 2,6,10,14,16 The first input (=2 in this example) is the starting value of the sequence. The last input (= 4 in this example) is the increment. The next element of the sequence is obtained by adding the increment to the element before:

2, 2 + 4, 2 + 4 + 4

Keep incrementing until a number >= the last input (= 20 in this case) is reached. Stop but don’t include the last number generated.

• The general form is range(start,stop,inc)• #elements in the list = ceil ((stop-start)/inc)

– ceil(x) = smallest integer greater than or equal to x



– Another application of list is to use it with experimental data


Tensile testing machine

• To understand how materials behave under tensile force • Pull the specimen and measure its length


Source: Holly Moore, Matlab for Engineers. p.197

Data from a test

Load [lbf] Length [inches]0 2.000

1650 2.0023400 2.0045200 2.0066850 2.0087750 2.0108650 2.0209300 2.040

10100 2.08010400 2.120


Source: Holly Moore, Matlab for Engineers. p.197

• Make two lists – One for load– The other for length

• Plot load on the horizontal axis and length on the vertical axis

Plotting graph • The code is in plot_demo.py


Code for graph plotting


Short form Lines 11-15Put the data in 2 lists

Lines 17-27 Plotting graphs

Import library

matplotlib

• matplotlib is a large library with many functions• You can do plots of many different styles

– Pie chart, histogram, log-log, log-linear, 3D and even animation

• And also to customise them in many ways • We will only show you the basic plot types • The library is well documented and its website has

many examples – https://matplotlib.org


Operations on list

• You know how to append an element to a list • There are other operations that you can do on a list

– Finding the maximum or minimum element in a list– Sum the elements in a list – Determining the number of elements in a list

• Terminology: length of a list = number of elements in a list – Sort a list

• See list_processing.py


Line continuation

• Sometimes you have a long line of code, it is best that split it into multiple lines so that you don’t have to scroll to the right to read

• Python uses two methods to say that code typed in multiple lines of code is in fact one line of code– Implicit continuation with brackets (), [], {}– Explicit continuation with \

• Demo code in continuation.py


Project (Part 2)

• We will spend the rest of the lecture to complete the project

• Goal: Given the numerical value of m, g and d, the goal of the project is to plot speed v(t) against t– for t = 0, 0.5, 1, 1.5, …., 39.5, 40


• Note that you have already got a function that can compute the speed, so you should make use of it

Project: Producing the graph

• You want to plot a graph of the free fall speed against time• In order to produce the graph, you need to create two lists


List of time instants

• There are 81 numbers in the list and of course you are not going to type these 81 numbers in

• The function range() will be useful here but you need to know range() can only generate a sequence of integers, it cannot generate numbers with decimal points

• The hints are:– You can generate this list by using range() together with a

for-loop– The numbers are all multiples of a constant


• The first list is a list of time instants (in seconds). We ask you to use:

[0 0.5 1 1.5 2 2.5 39.5 40]

List of speeds


• The second list is a list of speeds• If you do this manually, you will do:

– Time is 0. Use the speed formula. Speed = 0.– Time is 0.5. Use the speed formula. Speed = 4.692400935– Time is 1. Use the speed formula. Speed = 8.98399681455

– Time is 40. Use the speed formula. Speed = 54.8885179036

• Of course, you aren’t going to do the manual way since you have seen the trick

• You should use the list of times and the function you wrote • File project_prelim.py

Summary

• Functions– Writing functions

• New data types: List and range • Using functions from matplotlib• For-loop

– To repeatedly do some actions


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ENGG1811 Computing for Engineersen1811/19T2/lecs/week03/... · 2019-02-06 · The goal for this...

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