Programming with Matlab: files, loops, conditionals, etc.

In this practice we will focus essentially on the aspects of Matlab linked to programming. Matlab uses its own high-level language that is compiled with C ++ (which is properly the development language). The fact that it is a compiled language means that if we do not do things right the speed of calculation can be significantly reduced.

Matlab File Types: scripts and functions

Matlab files have the extension .m and can be classified into two types, function files and scripts.

Script files: Script files are simply files with instruction lines with Matlab that run in the order they are written.
Function files: These are files that are designed to be called from script files to make a certain calculation from input variables and return output variables. Function files are very easily recognized because they must start with the keyword function.

The syntax of a function file is:

[out1, out2,...] = functionName (input1,input2,...)

Where the input values are the input variables and the output variables.

Note: Function files must be named as the function name. So, for example, maxFunc.m will be the name of the file that contains the maxFunc function.

Example: Suppose that, as an example, we want to calculate the maximum between two functions when we evaluate them at an x-point. We will do this for these two functions:

This forces us to create a script that initializes the value of x and calls the function. We will need to create the function, give it a name, and define the input and output variables. The script file would be: (must be created, named and saved)

x=0.2;
[maxF,indFun] = maximFunc(x); %call the function maximFunc
fprintf('For x= %e, the max= %e value, for the function %d \n',x,maxF,indFun)
For x= 2.000000e-01, the max= 1.960133e-01 value, for the function 2 
%
% The file for the function must be named maximFunc.m and it can be found at the end of this page
%

Loops: for and while

The two options for looping in a Matlab program are (as in most programming languages) the for and while loops.

As a general rule we will use a for loop if we know exactly how many times we will do the loop (such as traversing an array or vector, etc.). If the number of iterations depends on a condition and therefore it is not clear how many iterations will be needed, then we will use a while loop.

The for always usually has a counter that updates automatically, while the while needs to do so explicitly.

First example: Compute the norm of vector

% ---- for loop example
x = 1:10; %initalize the vector
suma = 0;
for i = 1:length(x)
    suma = suma+x(i)^2;
end
norma = sqrt(suma) % make the sum in a 'manual' way
norma = 19.6214
norm(x) % compare with the Matlab function
ans = 19.6214
sqrt(sum(x.^2)) %another possibility with Matlab functions
ans = 19.6214
%------ the same with while loop (NOT appropriate in this case)
x = 1:10; %initalize the vector
suma = 0;
cm = 1;
while (cm <= length(x))
    suma = suma+x(cm)^2;
    cm = cm+1; %you have to increase the counter
end
norma = sqrt(suma) % compute the norm
norma = 19.6214

Second example: Compute how many terms of the numerical series

are needed to approximate the sum value with a precission less of

. That is, compute the K in order to have

%------ while loop example:
n = 1;
S(1) = 1;
while (abs(S(n)-pi^2/6) > 1.e-4)
    n = n+1;
    S(n) = S(n-1)+1/n^2;
end
K = n
K = 10000

Exercise 1:

Add all the components of an mxn array: A = rand (m, n) using two for loops one for rows and the other for columns. Compare the result with the Matlab sum (A (:)) statement.

Exercise 2:

Use a while to calculate the number of iterations required for the terms of the sequence

, taking

until

Conditionals: if, else, elseif

When programming an algorithm, conditionals are essential. For the simplest case (two options), in Matlab the syntax is

if (condition)

do some computations

else (condition)

do some other computations

For example: Compute the absolute value of a number

x=-3; 
if (x > 0)
    ax = x;
else
    ax = -x;
end
ax
ax = 3

If there are consecutive (nested) conditions then the syntax is:

if (condition)

do some computations

elseif (condition)

do some other computations

...............

elseif (condition)

do some other computations

 x=rand(); %random value in [0,1]
 if (x < 0.3) 
     val = 1;
 elseif((x >= 0.3) && (x < 0.6)) %two simultaneous conditions 
     val = 2;
 elseif((x >= 0.6) && (x <= 1))
     val = 3;
 end
 [x, val]
ans = 1×2
    0.9706    3.0000

Needed Functions:

function [maxF, indFun]=maximFunc(x)
    y1 = x^2*sin(x); %only scalar values can be computed
    y2 = x*cos(x);
    [maxim, ind] = max([y1,y2]); %the max function give us all the information
    maxF = maxim;
    indFun = ind;
end