Table of Contents

1 Elementary Matlab

1.1 Notation for this demo

<C-c> specifies control-C
<Tab> tab key
<function> any function

1.2 Intro

Why do you want to use matlab specifically?
other people are using it
one of the easiest to learn
"high level"
no need to compile necessary
matrices

Some things to consider;
not free
not open/free
bulky
not flexible

Alternative "high level" languages:
Python - numpy - uses the same code base for matrices
R
Julia
Ruby

Personally like them better, because they succeed where matlab fails
Many principles taught here will apply to other languages

May seem like a lot, but it comes down to just a couple of things
matrices
operators - about a dozen
functions - MANY
a few data-types
number type
characters
Hardest part is remembering functions
This is posted online on my website.
Recommendation - go home and make a cheat sheet of all the functions we create
Our goal here: get you to use this as a simple calculator whenever you can.
This session only uses the commandline, workspace, and filebrowser

1.3 Operators

%matlab works a lot like a scientific/graphic calculator
8+5 %+ is an operator
8*5 %multiplication
%Anything after a percent sign is a comment - it will not be evaluated
ans + 3
%ans is an automatically assigned variable
b=3
b2 %exponent
(b+3)/2 %order of operations apply!

somelongtexthere<C-c>
%<c-C> cleans gets you a new command-line
%Press Up and down to browse history
clc *Cleans workspace
variableA=1
vari<Tab>2 + b2
%tab autocompletes variables shown in your workspace

1.4 Functions

sqrt(5)
*functions have parentheses
b=6
abs(3-b)
*inputs can be simplified before being evaluated in functions
mod(10,2)
*multiple inputs seperated by a commma

*several variations on rounding
round(7/2) %normal rounding
floor(7/2) %round down
ceil(7/2) %round up
fix(7/2) %round towards zero

%more help on a function:
help <function>
doc <function>
%these have links to similar functions you can tab complete to get full name of function you only know beginning of

1.5 Workspace

%you can also…
<click on A in workspace> %get more info and edit if not too big

save('fname') %no error means successfully saved
clear %clears all variables from workspace
load('fname') %restores workspace that was saved
save('fname1','a','b') %saves only variables A & B
load('fname1')
clear
load('fname')

where are we saving to? default is home directory
pwd %lists current directory
ls %lists files in current directory
mkdir('test1')
cd('tes<Tab>') %You can autocomplete files that are in your path
cd('test1')
save('fname2')
cd('') %'' shortcut for home on linux/mac
cd('..') %double dots is back a directory
load('fname2') %doesn't work

%Your path consists of
%1. Current directory
%2. Directories that are listed in your path variable
%Add directories to your path under HOME-> ENVIRONMENT-> PATH
%Anything file/directory in your path can be autocompleted and loaded without an explicit structure

%WARNING: If you have multiple files of the same name, matlab will use the first one it finds without any warning
which <filename> %lists which one matlab will use

%why the quoatation?
%non-quotations are read as variables.
%quotations are read as strings
%variables don't have to be numerical, they can be strings
S='/home/dambam/test1'
cd(S)
%You can also use the file browser for most things
%.m file extension specify scripts and functions (plaintext format)
%.mat specifies data (binary format)

1.6 Matrices

A=[7/2 11/3 3/2] %a row vector (1x3 matrix)
B=[7/2, 11/3, 3/2] %also a row vector
C=[7/2; 11/3; 3/2] %Column vector (3x1 matrix)
A=[7/2 11/3 3/2; 3 2 1; 3, 2, 1] %a 3x3 matrix
%new column with comma and/or space
%either a comma or space is required
%can have both

round(A)
%functions typically apply to whole matrices

%matlab is optimized for matrices/vectors
%All inputs and outputs are interpreted as matrices
%8 is a 1x1 matrix

%loaded variables - you can use these variables in another function
round(A)
round(ans)

1.7 Matrices Example

A=[3,1]
B=[2,4]
A+B %matrix addition
A-B %subtraction
A*B %matrix multiplication (in linear algebra, matrices are like functions. Matrix multiplication is like combining to [linear] functions)
A*B %matrix operations (insides must dimensions match)
A*A' %transpose
A.*B %element wise
A./B %element wise
C=[A,B]
C=[A;B]
det(C) %determinant
if you have matlab
help jacobian
%doesn't exist in octave by default
%if it doesn't exist in octave by default, chances are you can find a function on github or elsewhere

%not super practical to write everything out manually
1:9 - %range
1:2:9 - increment
1:2:8 - non inclusive
L=linspace(1,9,10) %10 values equally spaced between 1 and 9
meshgrid(L,L)

1.8 Indexing

A=rand(10) %random integers between 1 & 10, in a 5x5 matrix)
%we want to access only certain parts of this matrix
A(1) %first elements
A(1:3) %elements 1 through 3
A(:) %All elements
A(1:end) %elements 1 through the last
A(2:end-1) %second element to the second to last element
B=A(:) %Matrix to column vector

%indexing runs down columns then rows:

1 4 7
2 5 8
3 6 9

1.9 Subscripts

A(1,3) %element in first row, third column
A(1:3,1:2) %elements in 1-3 rows with 1-2 columns
A(1,:) %everything in the first row
A(2:end,:) %everything but the first row

*subscripts - specifies rows then columns

1,1 2,1 3,1
1,2 2,2 3,2
1,3 2,3 3,3

%trick to remember:
%Index - Individual
%subscripts - begins with s - plural

1.10 Vectors Matrices & Tensors

%Many functions exist to create matrices, alter matrices, or query matrix properties
%These take the following form:
<function>(nRows,nColumns)
OR
<function>(nRows/Columns) %if square matrix

%random matrices are good for trying things out
rand(3,1) %3x1 matrix with elements sampled uniform distribution between zero and 1
rand(1,3) %1x3 matrix
rand(3,3) %3x3 matrix
rand(3) %3x3 matrix

%Many times you need some regular matrix, but no function exists
%no function to sample between -30 & 30 exists
%how to get values between -30 & 30?
rand(3,3)*60-30

%what happens if we do more than 2 dimensions)?
rand(3,3,3) %3D matrix aka tensor
%can't show a 3d matrix at once, so it shows slices
%showing subscripts of each dimensio
%':' means all elements

rand(100,100,100) %Should produce a large output
<C-c> %Cancels operation
rand(100,100,100); %semi-colon supresses output
rand(1000,1000,1000); %you should get an error about memory limitations
%maybe trouble on windows!

%semicolon can also be used to separate commands and run them on the same line
A=rand(100); B=rand(200);

%Some other useful functions
eye() %identity matrix
ones() %matrix of just ones
zeros() %matrix of zeros
randi(100,3,2) %3x2 matrix with random integers between 1 & 100

%what is this telling me?
length(zeros(10,1)); %size of largest dimension
length(zeros(1,10); %size of largest dimension

size(1,2) %size of all dimensions
numel(zeros(3,3)) %number of elements in matrix

sum(A,1) %Add all elements accross rows
sum(A,2) %Add all elements accross columns
sum(A) %default to sum accross rows (dimension 1), leaving row vector
min(A,1) %minimum values in rows
max(A,2) %maximum values in rows

1.11 Logic

2>1 %1 is equivalent to true
2<1 %0 is equivalent to false
2==2
2~=2

%All the operators for logical indexing are
= %equal to ~ %not equal to
> %greater than
>= %greater than or equal to
< %less than
<= %less than or equal to
& %and

%or

%Compound statements can be created with & and |
A=2;
B=1;
A>B | A<3 %or
A>B & B<(A+4) %and
(A>-3 | A<3) & B==1; %Group with parentheses

[A A] = [B 2]; %works element wise in matrices [1 2 3; 1 2 3]=[1 1; 1 1] %invalid
%output when from matrices are called "logical indices"
A=randi(10,10)
I=A>4
A(I) %returns everything that has a 1 logical index
A(A>2)=0 %sets everything that has a 1 logical index to have a value of 0
A(A==0)=[] %removes elements that have a 1 logical index
%NOTE: Removing and setting values matrix values also works with regular indexing and subscripting

A=randi(10,10)
ind=find(A==8) %Get regular index from logical index
A(ind)
[n,m]=find(A==8) %get subscripts from logical index
A(n,m)
%Note the form for functions with multiple outputs
[n,m]=find(A<8 & A>4)
ind=find(A==8 | A==4)
find([0 8]) %simple way of finding index of that are not zeros
~[0 1 1 1 0] %flip 0s to 1s and 1s to 0s
find([~0 8]) %find all zero elements

%Other very useful functions
any(A>1) %check if any of the logical indices in a dimension are 1
all() %checks if all logical indices are 1
rand(3)./0 %infinity
isinf(ans) %checks if values are infinity
isinf(8)

1.12 Sets

%Treating matrix elements across a dimension like part of a set
A=rand(10);
B=sort(A,1); %sort across rows

C=unique(A); %All elements in A without repeats

A = [5 7 1];
B = [3 1 1];
union(A,B) %All elements in A and B without repeats
unique([A B]) %All elements in A and B without repeats

C = intersect(A,B) %elements that are present in both A and B

ismember([3 2 1], [2 1 3])

D=randi(10,1,8);
E=randi(10,1,8);
F=randi(10,1,8);
G=randi(10,1,8);
X=1:8
A=[X; D; X; E]
B=[F; X; G; X]
ismember(A,B,'rows') %rows that are present in both A and B

1.13 Matrix manipulation

A=1:1000;
B=reshape(A,100,10); %reshape 1x1000 to 100 x 10, number of elements need to remain the same
size(B)

A=randi(10,2);
B=repmat(A,2,1) %Duplicates a matrix and appends it to the first dimension
size(B);
B=repmat(A,3,2) %Duplicates a matrix and appends it to 5 times to the first dimension & 2 times to the 2nd
size(B);

A=randi(10,3)
B=repelem(A,2,3) %Duplicates each element in place by specified dimensions

%WHAT ARE THESE GOOD FOR?
%row-wise multiplication
A=randi(10,3,2)
B=[1.5 2]
C=repmat(B,size(A,1),1);
D=A.*C;

1.14 Datatypes

%Before we go any further
%Everything is a matrix, but the elements take on specific types
Numbers :
double %most precise, takes up most memory
single %half as precise as double
int %less preciese as double
int8, int16,…
logical %least precise, least amount of memory. Default type when using logical operators
%Use double (default) and logical unless you need to save on memory
convert between types using double(), single(), int8(), etc.
Char - just letters or non evaluatable numbers
'a'
'1'
' '
%99% of the time only double, logical, and char are used

1.15 Strings

%Strings are not a datatype! They are an array of char
A='this is a string'
size(A)

%This means we can combine them like matrices
var='8'
string=['the variable equals ' var '.'] %concatenation
string=['the variable ''var'' equals ' var '.'] %literal quotations
%numerically the same as
a=1
b=[2 1]
[a b [1 3 4]]
disp(string) %print string
disp(['the variable equals ' var '.']) %print string
[ 'number' num2str(80000) '.']
newline %newline character
fname=[filesep 'home' filesep 'dambam' filesep 'test1'] %OS agnostic slash
r=input('Is matlab fun? ','s') %prompt for input

1.16 Plotting

figure(1) %initiates figure 1
x=linspace(1,100,1000) %x values of what is being plotted
y=1./x; %y values of what is being plotted
plot(x,y) %plot - by default uses connected line
plot(x,y,'+') %plot unconnected plus siges
plot(x,y,':') %plot connected dots
plot(x,y,'–') %plot connected dashed lines
plot(x,y,'r.') %plot red points
%check out all the different shapes and color with help plot
title('1/x') %create title

plot(x,y,'r.','MarkerSize',10) %change size of markers
plot(x,y,'r','LineWidth',10) %change size of connecting line
plot(x,y,'ro','MarkerEdgeColor','b') %change collor of marker edge
plot(x,y,'ro','MarkerEdgeColor','b','MarkerFaceColor',[.5 .6 .2]) %change edge and face colors, the latter using RBG values
%field, then value

xlabel('x') %label x axis
ylabel('y') %label y axis
xlim([0 40]) %set x axis limits
ylim([0 .4]) %set y axis limits
legend('Responses') %add legend with label 'Responses'

z=1./(x.2)
plot(x,z) %erases what we've done

plot(x,y)
hold on %specifies that you don't want to redraw plot
plot(x,z)
legend('Responses1','Responses2') %add legend with 2 labels
hold off

figure(2)
x=-2:0.25:2;
[X,Y]=meshgrid(x); %2D equivalent of linspace: creating X and Y values that will be evaluated along Z
z=X.*exp(-X.2-Y.2);
imagesc(z) %third dimension is represented by color
colorbar
colormap winter
help graph3d
colorbar

close %close current figure
surf(z) %third dimension is represented by color and space

%Different ways of displaying images
imshow('board.tif')
open()
load spine
imagesc(X)
colormap gray
axis image

figure(1)
x=-2:0.25:2;
y1=exp(x)
y2=log(x)
y3=abs(x)
y4=x.2

%Plot multiple things seperately in one figure
subplot(2,3,1)
plot(x,y1)
subplot(2,3,2)
plot(x,y2)
subplot(2,3,3)
plot(x,y3)
subplot(2,3,4)
plot(x,y4)

%You can return to a specific subplot whenever you like
subplot(2,3,2)
ylim([-3 1])

figure(2)
A=randn(1000,1) %Normally distributed random numbers
histogram(A) %histogram, automatically setting the number of bins
histogram(A,10) %set number of bins to 10

close all %close all figures

1.17 Grouping

%Cells are a collection of matrices
%Essential for grouping strings and matrices of different sizes
%Don't use unless you have to - rules for cell manipulation can be tricky!

C=cell(3,1);
C{1}=A
C{2}=B
C{3}='label'
C{1}(1:3) indexing matrix a, indexed in cell C

try to find a matrix solution when you can
cells can be hard to work with

%Structs allow for more organization
C=struct()
C.varA=A; %Aname is called the fieldname'
C.B=B;
C.string1='label'
C.D.A=A;
fieldnames(C) %returns all fieldnames belonging to struct C

%Even more organization with classes and objects - a bit more complex

1.18 Anonymous functions

%Last random bit
funA=@(x) exp(-x.2).*log(x).2;
%lets x remain unset
funA(linspace(1,10,100))
integral(funA,0,Inf) %integrate using anonymous functions

1.19 Conclusion

Remember doc & help
Google is your best friend
loads of people at your stage who have already asked your questions
"matlab move zero elements from matrix"
Matlab/Octave is one of the easiest languages to begin with
Use matlab/octave as your calculator whenever you can

1.20 Next time

Scripts & Functions
Conditional statements
Loops
Debugging and Error handling
Stats
Misc.

If you already know a language - could be boring
Check out my website instead

2 Exercises

2.1 1. Files

In your home directory, create directory test2 inside directory test1.
then save a with the data a='this is a test'
list the contents of the new directory
return to your home directory

2.2 2. Matrices

create a random matrix of size 3x2, matrix multiply it by an identity matrix, then element wise multiply by 10, then sum all the elements

2.3 3. Index & Subscripts

Create a random matrix of integers between -10 and 90, with 10 rows and 9 columns.
Select values between the 3rd and 4th column and the 2nd and 6th and set these values equal to 3
Remove the 4th column.
Check the number of columns in the matrix.
Remove the 10th element from the matrix.
CHeck the size of the matrix again.

2.4 4. Matrix manipulation

Create a column vector with values 3 through 1502, incrementing by 1.5
Resize the vector to be a matrix of size 20x50
Duplicate all elements in place by 3 columns and 2 row
Remove the fourth column

2.5 5. Logical indexing

Create a matrix of size 10x12 with random integers between 5 & 15
Set all values of 10 equal to 4
Add 1 to all values greater than 10
Get subscripts of all values equal to 8

2.6 6. Strings

Assign variables to the following strings: 'Strings', ' ', 'are ', 'nice' '.'
Concatenate the strings in order with a new line between 'Strings' and ' '
Create a second string with your name.
Add these two strings to a cell

2.7 7. Plotting

create an anonymous function for 1/x2 + 1/y2
generate 3000 z values between -3 and 3 for both x and y
Using 2 different plotting functions in 2 subplots
plot a 3D surface
display the colorbar
change the colormap

3 Answers

3.1 1. Files

a='test1/test2'
mkdir(a)
cd(a)

pwd
a='this is a test'
save(filename,variables)
cd('/home/dambam')
cd(~)

3.1.1 Now how do I delete this junk?

%must delete file first!
delete('somefilename.mat')
delete('test1/test2/
rmdir('test2')
rmdir('test1')
%easy to delete things you don't want to delete -> necessary to have backups!
If using tab completion, but make sure to carefully check before deleting!

plantext/mat files contain data, m files are code
good practice to keep data and code seperate

3.2 2. Matrices

sum(sum(rand(3,2)*eye(2,3)*10))
%single digits are treated as scalars, which are always element wise

3.3 3. Index & Subscripts

A=randi(100,10,9)-10
A(2:6,3:4)=3
A(:,4)=[]
size(A,2) %should be 8
A(1)=[];
size(A); should be 1x79

3.4 4. Matrix Manipulation

A=[5:1.5:3202]';
A=resize(A,4,533);
A=repelem(A,2,3):
A(:,4)=[];

3.5 5. Logical indexing

A=randi(10,10,12)+5;
A(A==4)=4;
i=(A>10);
A(i)=A(i)+1;
[n,m]=find(A==8)

3.6 6. Strings

A='Strings'
B=' '
C='are '
D='nice'
E='.'
string1=[A newline B C D E];
string2='David White'
cellA={string1, string2}
%OR
cellA{1}=string1;
cellA{2}=string2;

3.7 7. Plotting

funA = @(x,y) 1./x2 + 1./x2;
l=linspace(3000,-3,3);
[X,Y]=meshgrid(l);
Z=funA(X,Y);
subplot(2,1,1)
surf(X,Y,Z)
subplot(2,1,2)
imagesc(X,Y,Z)

Author: Dave White

Created: 2019-01-27 Sun 19:02

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