MATLAB:Iterative Structures

Often in solving engineering problems you will want a program to run pieces of code several times with slightly - or possibly vastly - different parameters. The number of times to run the code may depend on some logical expression or on the number of columns in a particular matrix. For these, you will use iterative structures.

Initializing Large Vectors

One of the dangers in MATLAB's ability to automatically resize a vector is the amount of time it actually takes to do that.

Iterative Resizing

Consider the following:

clear
tic
y0 = 0;
v0 = 5;
a  = -9.81;
NP = 10;
t = linspace(0, 5, NP)
for k=1:NP
   y(k) = y0 + v0*t(k) + 0.5*a*t(k).^2;
end
toc

This code takes, on average, 36 microseconds to run. If NP is increased to 100, the average time to complete goes up to about 150 microseconds. NP of 1000 increases the time to 2.25 ms. And NP of 10000 increases the time to over 10 s! The graph below shows, on a log scale, time to complete as a function of NP:

Clearly, this becomes a major problem as the number of points increases.

Initialized

Remarkably, adding a single line completely changes the timing of the program. The following program:

clear
tic
y0 = 0;
v0 = 5;
a  = -9.81;
NP = 10;
t = linspace(0, 5, NP)
y = t*0;     % here's the only thing that changed!!!
for k=1:NP
   y(k) = y0 + v0*t(k) + 0.5*a*t(k).^2;
end
toc

generates the following time vs. NP graph:

which indicates a reduction, by three orders of magnitude, of the run time. And all that was done was creating a vector y of the appropriate size before running the loop, rather than continuously changing the vector size inside the loop.

Vectorized

Of course, the fastest version of the code uses MATLAB's ability to vectorize:

clear
tic
y0 = 0;
v0 = 5;
a  = -9.81;
NP = 10;
t = linspace(0, 5, NP)
y = y0 + v0*t + 0.5*a*t.^2;
toc

which generates the following time vs. NP graph:

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