The command window serves as an immediate response for testing code. Most likely, your math courses will expect you to build functions and run them on the command window in order to progress and learn the methods step by step. Some useful command window tools are:
clear %used to remove all varaibles in your workspace
clc %used to remove all previous outputs in your command window
help *insert function here* % to find Matlab documentation for any built in function
additionally, using the up arrow key will allow you to immediately retype a previous command in order to rerun a code or adjust it. You can also type the start of the code before pressing up to find only the past lines that have the same starting
% sqrt(x), x^(y),exp(x),sin(x),cos(x),tan(x),pi,asin,acos,atan,factorial(n),1e-n
% you can also use inline functions to creat your own
y = @(x) exp(x)*sin(x);
sprintf('y(5) = %.2f',y(5))
% or you can also call other m file functions
Matlabtest(20) v = [1 2 3] %you can also do v = [1,2,3]
w = [4;5;6] %using ; allows us to make column vectors
length(v) %gives the size of the vector
%% use parenthesis in order to index entries
v(2) % to grab second entry
v(end) % lets you grab the last entry
v(end-1)
%% logical vectors
idx = w > 4
nnz(idx) %tells you how many of the entries are true
w(idx)
%% max function for vectors
max(v)
[largest, idx] = max(v) A = [1 2 3; 4 5 6;7 8 9]
%A = [7 2 1; 0 3 -1;-3 4 2]
%% indexing matrices
A(1,3) %acces with A(i,j)
A(:,3) %to grab every row of column 3 and vice versa for every column of a row
A(4)
%if you put only one input it will treat it as a stacked column. A(4)
%will give us 2 A(6) will give us 8
%% max function for matrices
%basically treats it as if u put in seperate column vectors
max(A) %returns a row with the highest entries of each column
max(A,[],2) % returns a column with the highest entries of each row
max(A,2) %compares the number 2 with each entry and returns the max of that comparison
B = [1 2 4;4 1 1 ; 10 12 11]
max(A,B) %compares entrywise between two matrices det(A)
inv(A) %will not work for A = [1:3;4:6;7:9] since condition number is large
A*inv(A)
cond(A) b = [1 2 3]'
x1 = inv(A)*b
x2 = A\b A' %Changes columns to rows but conjugates entries
A(1) = 1 + i;
A' %use format short to avoid cluster of 0s
A.' % will not conjugate entries
A*B %Will do the matrix mulitplication as we have shown above from A*inv(A)
A.*B %Will do an entrywise mutliplication instead of matrix multiplicationWhen solving for general cases, it might be helpful to use the symbolic math function in Matlab. A caveat, however, is to be aware of the conjugate transpose previously mentioned as syms automatically creates complex variables.
%% Symbolic math
syms a b c
v = [a b c]
v*v'
v' %gives column vector of cojugates
v*v.'
%alternate
syms a b c real
w = [a b c]
w'
det(v.'*v) %determinant of any outer product is zero
syms a b c d e f g h i
det([a b c;d e f;g h i]) %3x3 determinant formula%% shortcuts
v = [1:3]
A = [1:3;4:6;7:9]
v = [1:2:10] %odd numbers from 1 to 10
v = [10:-2:1] %deceding even numbers from 10 to 1
%Problem: build a vector of 10 entries evenly spaced from 0 to 1
v = linspace(0,1,10) %% concatenate matrices and vectors
v = [1:3]
w = [4:6]
y = [v;w] %stacks vectors on top
z = [v w] %concatenates from the right
Useful functions for building specific matrices
zeros(n,m) #NxM matrix of zeroes
ones(n,m) #NxM matrix of ones
eye(n) #NxN identity matrix
diag(X) #makes a diagonal matrix with vector as the diagonal
tril(A) #takes lower triangle of A
triu(A) #takes upper triangle of A For independent functions it is required to save the file identical to the name of your function as an .m file. The first block of comments in your code will serve as a summary of the function. Thus, when running the code: help Matlabtest -> it will return "Test function for MATLAB workshop"
% Test function for MATLAB workshop
% wobble wobble
function y = Matlabtest(x) %We would save this file as Matlabtest.m
%% for loop example1: indexing from a vector
x = 10;
sum1 = 0;
for i = 1:x %you can index from linspace since it is a vector but you generally don't
%to index backward simply build the backward vector x:-1:1
sum1 = sum1 + i;
end
sprintf('sum of first %.f integers is %.f',x,sum1)
%% for loop example3: indexing from a matrix
sum3 = 0 ;
A = [1:3;4:6;7:9]; %never really do this but this is what happens if you do
for i = A
sum3 = sum3 + i;
end
sum3
%% While loops
% generally use while loops when you don't know when to stop
% thus you need an exit criteria (an epislon or an upper bound)
% and/or an index
%Exaple: from taylor approximation we know when x is close to 0, sin(x) is
%approximately x.
%Question: how close to 0 do we have to be for |sin(x) - x| < epsilon
epsilon = 1e-5;
x = 0.5;
counter = 1;
while(abs(sin(x) - x) > epsilon)
x = x - 1e-6; %Use ctrl + c to break out of loops in command window if you get stuck in infinite loop
counter = counter + 1;
end
sprintf('after %.f iterations we get x = %f',counter,x)
%% If and if-else
%Requires logicals:
% & (and)
% == (check equivalence)
% | (or = and/or since its a "math" or)
% ~ (negation)
a = 10;
b = 5;
if a == 10 & b ~= 5
sprintf('a is 10 and b is not 5')
elseif a == 15 | b == 5
sprintf('a is 15 or b is 5')
else
sprintf('Neither')
end
y = 10; % since we defined the function to spit out a y,
%this is what it will return if we try to assing the function to a variable
end
data = readtable('WalMart~MATLAB.csv'); summary(data)
data.Properties %to see what properties your data has
data.Properties.VariableNames{3} = 'Temp' %If you want to change varable names column1 = data(:,1) %will return a table
column1 = data{:,1} %will return a vector of the entries in that table column
%sometimes you might be to lazy to find the column number for something so
%you can just type the varable name to pull it
Temp = data{:,'Temp'};
%you can also pull multiple columns with either numbers or via variable id
%We shall grab everything with numbers
storestuff = data(:,[1 3 4 10 11]);
%you can also pull the values of a variable with dot notation
data.Temp
%% cell Array
% basically vectors but for strings
a = {'Male' 'Female' 'Male' 'Female' 'Female'}
%can use cell arrays to pull the columns via varaible id
storestuff2 = data(:,{'Store','Temp','Fuel_Price','CPI','Unemployment'}); %% categorical vectors
%The values for Store are saved as doubles when they are actually just
%labels. In our case since they are numbers we can still index into them
%using data(data.Store == 1,:) to grab all the rows with store 1. However,
%if the labels were strings instead we would not be able to index with
%a == 'Male
%Thus we change it into a categorical array/vector instead
b = categorical(a)
b == 'Male'
%Another benefit of using categorical arrays is the amount of space used
%since we are now just treating 1 or 'Male' as a label instead of a double
%or a string
whos a b
c = categorical(data.Store);
whos c column1 % We need to change the str variables into doubles first
storestuff.CPI = str2double(storestuff.CPI);
storestuff.Unemployment = str2double(storestuff.Unemployment);
mean_storestuff = grpstats(storestuff,'Store',@mean); %applies the mean fucntion to everything in the data frame grouped by 'Store'
mean_storestuff.GroupCount = []; % to remove a column we dont want
mean(storestuff.CPI) %will return NaN since there are NaN values in CPI data
mean(storestuff.CPI,'omitnan') %will omit all the N/A entries when using the mean functions holidays = data(:,{'Store','IsHoliday'});
holidays.IsHoliday = categorical(holidays.IsHoliday); %change to categorical
holidays.IsHoliday = holidays.IsHoliday == 'TRUE'; %change to 0/1
sum_holidays = grpstats(holidays,'Store',@sum);
sum_holidays.GroupCount = []; Pretty useless info since it just tells us that all the stores had 13 holidays each i.e. the data is spread among the same days. We can use this to filter out the holidays from the original data but we will just use it to play around with the join function
%% Joining tables
mean_both = join(mean_storestuff,sum_holidays); If you want to join tables of different length, the second table has to be smaller row wise
%test = join(mean_storeNtemp,storeNtemp) %will fail
test = join(storestuff,mean_storestuff); %if you want the left hand table to be smaller you can use an inner which
%will keep those with match values
testi = innerjoin(mean_storestuff,storestuff); %in this case every row has a matching key %whereas inner join removes rows without matching keys, oter join will keep
%everything and just put NA for columns that do not have matching keys
testO = outerjoin(mean_storestuff,storestuff);
%outer join, however, will create seperate columns for each key of the
%respective tables %We use 'mergekey' to avoid this
testO = outerjoin(mean_storestuff,storestuff,'Mergekey',true); %we can use the discretize function to seperate our temperatures into bins
%in order to help find patterns
x = mean_storestuff.mean_Temp; %dummy var for convenience
y = discretize(x,linspace(min(x),max(x),4),'Categorical',{'Low','Middle','High'}); %4 number vector to have 3 bins
mean_both.Tgroups = y; %add in a new column called Tgroups with our categories Graphs unemployment vs CPI color coded by our temp groups
Use interactive graph tool to adjust whatever you'd like
f = gscatter(mean_both.mean_Unemployment,mean_both.mean_CPI,mean_both.Tgroups)
%graphs unemployment vs CPI color coded by our temp groups
%use interactive graph tool to adjust whatever you'd like
%% adding stuff manually
xlabel('Unemployment')
ylabel('CPI')
title('Unemployment vs CPI')
grid('on') gname(mean_both.Store) %12 28 38 have same means weird
%% etc/indexing
data.Store = categorical(data.Store);
idx = any(data.Store == {'12' '28' '38'},2);
test = data(idx,{'Store','Unemployment','CPI'});
test.Unemployment = str2double(test.Unemployment);
test.CPI = str2double(test.CPI);
test.Store = categorical(test.Store);
test{test.Store == '12',2} == test{test.Store =='28',2} % weird - All data matches, only reason there is 0 at the end is because NaN == NaN
- Returns false
- Double check in excel to see that all 3 are the same