A ReintroductiontoMatlaband Making...

AERO 325 CodingTutorial

Dalle

Introduction

Motivation

Goal

List

Vectors andMatrices

Problem 1

MLint

Debugging

Functions

Problem 2

Vectorization

Problem 3

Readability

Problem 4

AERO 325 Coding TutorialA Reintroduction to Matlab and Making

Code Readable and ScalableDerek J. Dalle

University of Michigan, Ann Arbor, MI 48109

Fall 2012

AERO 325 Coding Tutorial, Using functions 1/25


Dalle

Introduction

Motivation

Goal

List

Vectors andMatrices

Problem 1

MLint

Debugging

Functions

Problem 2

Vectorization

Problem 3

Readability

Problem 4

What to get out of this tutorialStart writing programs like this!

z

Streamlineplotter

FIGURE

F(z)

w(z)

z0Source

Q

LEGEND

x

Source

FIGURE

Input/Output

Function

Figure or plot

Information flowAERO 325 Coding Tutorial, Using functions 2/25


Dalle

Introduction

Motivation

Goal

List

Vectors andMatrices

Problem 1

MLint

Debugging

Functions

Problem 2

Vectorization

Problem 3

Readability

Problem 4

What do you mean, “Program like this?”

Things I don’t mean

Use SIMULINK

Draw a bunch offlowcharts everywhereyou go

Really just this

Use functions!

Write modular code thatcan be upgradedwithout starting over

Your programs shouldbe easy to understandand read

z

Streamlineplotter

FIGURE

F(z)

w(z)

z0Source

Q

LEGEND

x

Source

FIGURE

Input/Output

Function

Figure or plot

Information flow



Dalle

Introduction

Motivation

Goal

List

Vectors andMatrices

Problem 1

MLint

Debugging

Functions

Problem 2

Vectorization

Problem 3

Readability

Problem 4

This is what engineers usually do.

FIGUREMY FUNCTION



Dalle

Introduction

Motivation

Goal

List

Vectors andMatrices

Problem 1

MLint

Debugging

Functions

Problem 2

Vectorization

Problem 3

Readability

Problem 4

Why do you want us to do that?

z

Streamlineplotter

FIGURE

F(z)

w(z)

z0Source

Q

LEGEND

x

Source

FIGURE

Input/Output

Function

Figure or plot

Information flowAERO 325 Coding Tutorial, Using functions 5/25


Dalle

Introduction

Motivation

Goal

List

Vectors andMatrices

Problem 1

MLint

Debugging

Functions

Problem 2

Vectorization

Problem 3

Readability

Problem 4

Why do you want us to do that?Construct more complicated flows using most of the same code

z

Streamlineplotter

FIGURE

F(z)

w(z)

z1Source

Q1

z2Source

Q2

z3Vortex

Γ3

αFreestream

U∞

Combined stream function



Dalle

Introduction

Motivation

Goal

List

Vectors andMatrices

Problem 1

MLint

Debugging

Functions

Problem 2

Vectorization

Problem 3

Readability

Problem 4

Why do you want us to do that?Many panels plus a freestream velocity

z

Streamlineplotter

FIGURE

F(z)

w(z)

αFreestream

U∞

z1,...,zn

Q1,...,QnSource



Dalle

Introduction

Motivation

Goal

List

Vectors andMatrices

Problem 1

MLint

Debugging

Functions

Problem 2

Vectorization

Problem 3

Readability

Problem 4

The goal of today’s tutorialThis is only a small modification from the previous slide.

Q1,...,Qn

Normalvelocity

w1,...,wn

Linearsolver

vN1,...,vNn

Sorry this is so crowded!

The lesson: The combination of these blocks is a function that takes z1, ..., zn along with α and U∞ and returns a set of source strengths.

αFreestream

U∞

z1,...,zn Unit source



Dalle

Introduction

Motivation

Goal

List

Vectors andMatrices

Problem 1

MLint

Debugging

Functions

Problem 2

Vectorization

Problem 3

Readability

Problem 4

Laundry listBasically my priorities on good (or at least readable) Matlab coding

General

Basic mechanics(Editor/command line)

Functions and not scripts!

The little orange marks on theside are your friend

Debugging

Coding basics

Declaring a function with inputsand outputs

for loops

Basic vectors/matrices

Handling exceptions

Vectorizing code

Can always go without this, butit makes life much easier (foryou and your computer)

“Dot” operators, .*, .^, etc.

Initializing vectors and matrices

Aerodynamics

If you do everything just right, thecode you can write today can bemodified to make any 2D panelcode. The method we will use isparticularly bad.



Dalle

Introduction

Motivation

Goal

List

Vectors andMatrices

Problem 1

MLint

Debugging

Functions

Problem 2

Vectorization

Problem 3

Readability

Problem 4

AgendaThe farther we get, the easier your next homework will be

We’ll be going back and forth between me talking and you coding.

1 Basic introduction (this) (20 min)2 Matrix construction example (ex1.m) (5 min)3 Tips not directly about code or syntax (5 min)4 FUNCTIONS, function syntax, input, and output (5 min)5 Potential functions for point source and freestream (ex2.m) (5 min)6 Introduction to vectorization! (5 min)7 Lots of sources plus one freestream (ex3.m) (10 min)8 Writing readable code and when to use loops (5 min)9 Create a point-source panel code (ex4.m) (whatever’s left)

Please follow the instructions within the example files (ex1.m, etc.)about naming new files.



Dalle

Introduction

Motivation

Goal

List

Vectors andMatrices

Problem 1

MLint

Debugging

Functions

Problem 2

Vectorization

Problem 3

Readability

Problem 4

Vectors and MatricesIntroduction

In Matlab, scalars, vectors, and matrices are really all the same thing.

Suppose A is a matrix, x is a columnvector, and c is a scalar. You can usethe size command to find out how manyrows and columns each variable has.

>> size(A)ans =

5 4>> size(x)ans =

4 1>> size(c)ans =

1 1

To see the value of one entry of a matrixor vector, use the following notation

>> A(2, 3)ans =

-1

This is the third entry of the second row.Use this to change a single entry of amatrix, too.

>> A(2, 3) = 4;>> A(2, 3)ans =

4



Dalle

Introduction

Motivation

Goal

List

Vectors andMatrices

Problem 1

MLint

Debugging

Functions

Problem 2

Vectorization

Problem 3

Readability

Problem 4

Creating vectors and matricesThe right way

Small arrays

For a small vector or matrix, if you know all the values, construct it directly.

A = [1, 0; 2, -1; 3, 0];

Use commas to separate entries within a row and semicolons to separate rows.

Large arrays

Initialize large arrays to the correct size using a vector command. This creates amatrix of all zeros with 100 rows and 20 columns.

A = zeros(100, 20);

See also the commands ones, eye (identity matrix), and nan (not a number).Matlab will let you get away with not doing this, but it’s a really bad idea!



Dalle

Introduction

Motivation

Goal

List

Vectors andMatrices

Problem 1

MLint

Debugging

Functions

Problem 2

Vectorization

Problem 3

Readability

Problem 4

Creating a large matrix or vectorObviously a big matrix full of zeros is not that interesting

1 Decide how many rows and columns you need.

m = 21; n = 21;2 Initialize the matrix and/or vector.

A = zeros(m, n); b = zeros(m, 1);3 Now loop through the rows and columns to set the entries to what

you really want.

for i = 1:mfor j = 1:n

A(i, j) = ???endb(i) = ???

end4 Suppose you want each entry in the kth row to be 1.

A(k, :) = 1;5 Use this to solve the linear system Ax = b

x = A \ b;AERO 325 Coding Tutorial, Using functions 11/25


Dalle

Introduction

Motivation

Goal

List

Vectors andMatrices

Problem 1

MLint

Debugging

Functions

Problem 2

Vectorization

Problem 3

Readability

Problem 4

Problem 1Create a specified linear system

Open the files ex1.m and make_matrix.m in Matlab.

The files contain the instructions that you need. Your task is to create thematrix and vector

A =

1 −1 0 0 0 0−1 2 −1 0 0 00 −1 3 −1 0 00 0 −1 4 −1 00 0 0 −1 5 −10 0 0 0 −1 6

b =

123456

but for arbitrary size. This would be for n = 6.

Then you must solve the linear system Ax = b.



Dalle

Introduction

Motivation

Goal

List

Vectors andMatrices

Problem 1

MLint

Debugging

Functions

Problem 2

Vectorization

Problem 3

Readability

Problem 4

Matlab code checker (formerly called MLint)Matlab is surprisingly good at improving your code

On the right-hand side of any fileopened in the Matlab editor there isa helpful bar. The top right cornerhas a box that gives a quicksynopsis of your code. This is reallyhelpful; try to make the squaregreen!

Bad (code will not run):

Better (problems detected): Good (doesn’t mean perfect):



Dalle

Introduction

Motivation

Goal

List

Vectors andMatrices

Problem 1

MLint

Debugging

Functions

Problem 2

Vectorization

Problem 3

Readability

Problem 4

Matlab code checker (formerly called MLint)Individual suggestions

The rest of the bar gives an individuallisting of each error or suggestion thatMLint has found in your file. You canmouse over a mark to read MLint’ssuggestion or click on the mark to takeyou to the line with the problem.

It’s not always possible to get rid of allthe orange marks, but you shouldcertainly consider each suggestion. A lotof errors, like variables that are neverused, are trivial to fix.

Sometimes MLint suggests a correctionon its own.

Each mark represents an error orsuggestion.



Dalle

Introduction

Motivation

Goal

List

Vectors andMatrices

Problem 1

MLint

Debugging

Functions

Problem 2

Vectorization

Problem 3

Readability

Problem 4

DebuggingCode doesn’t work? Put a break point right before the error.

The bar on the left side of the editor is for breakpoints. The program will stop each time it gets to aline with a red dot to the left of it. You can add andremove the break points (red dots) by left-clicking onthem one time.

Once you’re at a break point, you can see the valuesthat each variable has and use them from theMatlab command line.

Debugging toolbar

Just click on these buttons while in debug mode;you’ll quickly figure out what they all do and whenthey’re useful.



Dalle

Introduction

Motivation

Goal

List

Vectors andMatrices

Problem 1

MLint

Debugging

Functions

Problem 2

Vectorization

Problem 3

Readability

Problem 4

FunctionsHow to use them

1 Create a file for each function. (Just like you are probably used todoing) (This example: mypotential.m)

2 Define the inputs and outputs with the first line in your file.

function [F, w] = mypotential(x, y)......

3 The inputs are x and y, and the outputs are F and w. You can haveas many inputs or outputs as you want.

4 Code the rest of the program the way you normally would (exceptdon’t define x and y; their values are taken from outside).



Dalle

Introduction

Motivation

Goal

List

Vectors andMatrices

Problem 1

MLint

Debugging

Functions

Problem 2

Vectorization

Problem 3

Readability

Problem 4

Functions (and not scripts)Why to use them

Reusability and Readability

Suppose you have to do a complicated task that you need to do many times.

A = point_source(z, z1, Q1) + point_source(z, z2, Q2);

Suppose you made a small mistake in your function. Now you only need to fix itin one place! It’s also far easier to understand what’s going on (including to you!).

Scripts are bad!

Scripts have global scope–which means they affect variables outside thefunction. Consider this example where my_dumb_script is a file that begins withthe command clear all and then does some other task.

>> F = complicated_model(1e10); % This might take hours.>> my_dumb_script>> FUndefined function or variable 'F'.

It’s gone! Never put clear all in your programs!!!!!!AERO 325 Coding Tutorial, Using functions 17/25


Dalle

Introduction

Motivation

Goal

List

Vectors andMatrices

Problem 1

MLint

Debugging

Functions

Problem 2

Vectorization

Problem 3

Readability

Problem 4

Problem 2

Open the file ex2.m in Matlab.

The file contains the instructions that you need. Your task is to create twocomplex potential functions: point_source.m for a source centered atz0 with strength Q and freestream.m for a freestream velocity of U atan angle of α. The main purpose of this task is to practice creatingfunctions.

OUTPUT 1 OUTPUT 2 NAME INPUT 1 INPUT 2 INPUT 3F w point_source z z0 QF w freestream z U α

Point source:

F(z) =Q2π

log(z− z0) w(z) =Q

2π(z− z0)

Freestream:

F(z) = Ue−iαz w(z) = Ue−iα



Dalle

Introduction

Motivation

Goal

List

Vectors andMatrices

Problem 1

MLint

Debugging

Functions

Problem 2

Vectorization

Problem 3

Readability

Problem 4

VectorizationApplying operations to vectors and matrices to get rid of loops

Have you ever noticed what happens when you use a function like sinon a matrix? It turns out that

>> sin([1, 0.5; -2, 3])ans =

0.8415 0.4794-0.9093 0.1411

is exactly the same as

>> [sin(1), sin(0.5); sin(-2), sin(3)]ans =

0.8415 0.4794-0.9093 0.1411

This is exactly what we would want, and it means we don’t have to writeas many loops.



Dalle

Introduction

Motivation

Goal

List

Vectors andMatrices

Problem 1

MLint

Debugging

Functions

Problem 2

Vectorization

Problem 3

Readability

Problem 4

VectorizationApplied to your code: the so-called “dot operators”

This is the key to writing fast code in Matlab.

Compare two versions that calculate the following formula for eachelement of two m×n matrices

z = x2 siny

Bad versionfor i = 1:m

for j = 1:nz(i,j) = x(i,j)^2*sin(y(i,j))

endend

Good versionz = x.^2 .* sin(y)

This is simpler to write, easier to read, and much faster. It’s a good habitto always use dot operators (except .+ and .-, which are the same).



Dalle

Introduction

Motivation

Goal

List

Vectors andMatrices

Problem 1

MLint

Debugging

Functions

Problem 2

Vectorization

Problem 3

Readability

Problem 4

Vectorization and Problem 2

Think about the point_source function you wrote for Problem 2.

(1) Does it work if z is a matrix and z0 and Q are both scalars?

(2) Does it work if z is a scalar and z0 and Q are both vectors?

Test it!

Most likely the answer to (1) is yes, and the answer to (2) is no. Can youmake a very small change to your code so that both are true?



Dalle

Introduction

Motivation

Goal

List

Vectors andMatrices

Problem 1

MLint

Debugging

Functions

Problem 2

Vectorization

Problem 3

Readability

Problem 4

Problem 3A freestream with several sources and sinks

Open the files ex3.m and multi_source.m in Matlab.

The files contain the instructions that you need. The task is to create ageneric complex potential function that can plot the streamlines for onefreestream plus any number of of sources and sinks (and vortexes?).

It’s ok to use a loop for this one!

Your folder contains a function to plot the streamlines automatically. Runex3.m to test your file. If you have done everything correctly, you shouldget a streamline plot for what looks like a wavy symmetric airfoil.

x

y

−5 −4 −3 −2 −1 0 1 2 3 4 5−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1



Dalle

Introduction

Motivation

Goal

List

Vectors andMatrices

Problem 1

MLint

Debugging

Functions

Problem 2

Vectorization

Problem 3

Readability

Problem 4

CommentsSelf-documenting source code

The things we’ve covered will do a lot to make code more readable.

But there’s one thing more important than all the rest: comments.

It doesn’t take very long, and there’s no reason not to comment every line!

Ok, I thought of two reasons

1 You want to make people figure out your code as an assignment

2 You want to put a short code snippet into a document

It’s better to put comments on their own line. Compare:

% Complex potential and velocity functions for source i.[F, w] = point_source(z, z0(i), Q(i));

[F, w] = point_source(z, z0(i), Q(i)); % source i

Use blank lines

In Matlab, two percent signs, %%, is a special type of comment that you canuse to split your code into blocks.



Dalle

Introduction

Motivation

Goal

List

Vectors andMatrices

Problem 1

MLint

Debugging

Functions

Problem 2

Vectorization

Problem 3

Readability

Problem 4

Example with lots of commentsThis function is hard enough to edit with comments



Dalle

Introduction

Motivation

Goal

List

Vectors andMatrices

Problem 1

MLint

Debugging

Functions

Problem 2

Vectorization

Problem 3

Readability

Problem 4

Problem 4A point-source panel method?

Open the files ex4.m and source_panel.m in Matlab.

The instructions in those files should be adequate, but this color-codedpicture may help. Or it might be really confusing.

U

α ni

U


IntroductionMotivationGoalList

Vectors and MatricesProblem 1MLintDebuggingFunctionsProblem 2VectorizationProblem 3ReadabilityProblem 4

A ReintroductiontoMatlaband Making...

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