The If Statement

In this tutorial we will assume that you know how to create vectors and matrices, know how to index into them, and know about loops. For more information on those topics see one of our tutorials on vectors, matrices, vector operations, loops, plotting, executable files, or subroutines.

There are times when you want your code to make a decision. For example, if you are approximating a differential equation, and the rate of change is discontinuous, you may want to change the rate depending on what time step you are on.

Here we will define an executable file that contains an if statement. The file is called by Matlab, and it constructs a second derivative finite difference matrix with boundary conditions. There is a variable in the file called decision. If this variable is less than 3, the file will find and plot the eigen values of the matrix, if it is greater than 3 the eigen values of the inverse of the matrix are found and plotted, otherwise, the system is inverted to find an approximation to y'=sin(x) according to the specified boundary conditions.

If you are not familiar with creating exectable files see our tutorial on the subject. Otherwise, copy the following script into a file called ifDemo.m. 
decision = 3;
leftx = 0;
rightx = 1;

lefty = 1;
righty = 1;

N= 10;
h = (rightx-leftx)/(N-1);
x = [leftx:h:rightx]';

A = zeros(N);

for i=2:N-1,
   A(i,i-1:i+1) = [1 -2 1];
end

A = A/h^2;

A(1,1) = 1;
A(N,N) = 1;

b = sin(x);
b(1) = lefty;
b(N) = righty;

if(decision<3)

    % Find and plot the eigen values
    [e,v] = eig(A);
    e = diag(e);
    plot(real(e),imag(e),'rx');
    title('Eigen Values of the matrix');

elseif(decision>3)

    % Find and plot the eigen values of inv(A)
    [e,v] = eig(inv(A));
    e = diag(e);
    plot(real(e),imag(e),'rx');
    title('Eigen Values of the inverse of the matrix');

else

   
    % Solve the system
    y = A\b;
    linear = (lefty-righty+sin(leftx)-sin(rightx))/(leftx-rightx);
    constant = lefty + sin(leftx) - linear*leftx;
    true = -sin(x) + linear*x + constant;

    subplot(1,2,1);
    plot(x,y,'go',x,true,'y');
    title('True Solution and Approximation');
    xlabel('x');
    ylabel('y');
    subplot(1,2,2);
    plot(x,abs(y-true),'cx');
    title('Error');
    xlabel('x');
    ylabel('|Error|');


end
You can execute the instructions in the file by simply typing ifDemo at the matlab prompt. Try changing the value of the variable decision to see what actions the script will take. Also, try changing the other variables and experiment.

The basic form of the if-block is demonstrated in the program above. You are not required to have an elseif or else block, but you are required to end the if-block with the endif statement.

The previous tutorial is an introduction to subroutines.

This tutorial written by Kelly Black.