Matlab Some Basics Data

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7.1 Some basics 7.2 m-files 7.3 Good practices

At the user's level Matlab is an interpreted language that accesses compiled software. This has disadvantages

and advantages.

The advantage of this is that Matlab code is easy to debug. When I write Matlab code, I have an editor open

in one window and I run Matlab in another window. Then I write a few lines of code, and I cut that code out

of the edit window and paste it into the Matlab window to test it. This is very useful and fast.

The disadvantage is that the interpreter is extremely slow. Therefore, to make Matlab a useful tool for

numerical simulation, it is critical that you try to write code that utilizes the compiled (and consequently, fast)

subroutines more than it utilizes the interpreter. I talk about this more below.

7.1 Some basics

Looping is done with theforcommand. The syntax is

>> for i = first : increment : last

commands

end

The default increment is one. For example,

>> for i = 1:n

sum = sum + x(i)*y(i);

end

calculate the dot product of x and y.

Conditional statements are evaluated with the if, while and switch commands. The syntax for ifis

>> if expression

commands

elseif expression

commands

else

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commands

end

7.2 m-files

Matlab allows the user to write programs, save them on the disk, and then to execute them. These programsare called m-files. By convention, they are namedfoo.m. To see an example of an m-file type

>> help function

This shows a function for computing the mean and standard deviation of a vector x.

The format for a matlab m-file is shown in the stat function. Copy that format for your m-files. Another

version of a m-file was shown in the ODE section of this web-page,

>> type lotka

This file specifies the right hand side of an ordinary differential equation that models a population of

predators and their prey.

7.3 Good practices

My standard of good may be a bit different from what other standards of good are, but by "good Matlab

code", I mean, code that runs fast and is understandable to people beyond its author.

Its relatively easy to write code that others can understand. Add comments to your code to explain what you

are doing. If a segment of code needs more than a few of lines of comments, break it up into smaller parts and

comment those, or put it into an m-file.

Code that runs fast is code that does not invoke the Matlab interpreter disproprotionately often compared to

the Matlab software. Obviously, this is more important for large and difficult problems, but its a good thing to

keep in mind at all times.

To demostrate the Matlab interpreter's slow speed, we will consider the problem of multiplying two 100 by

100 matrices. In the following code segment, I define three matrices, A, B and C, and multiply them together

by computing the inner product of the rows of A with the columns of B. This code is similar to code you

would write if you were using C or FORTRAN.

>> % Matrix multiplication example using full looping

>>

>> n = 100; A = rand(n); B=rand(n); C=zeros(n);

>> t = cputime;

>> for i=1:n,

for j=1:n,

for k=1:n

C(i,j) = C(i,j) + (A(i,k)*B(k,j));

end

end

end

>> t = cputime-t


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t = 97.9600

Notice that this segment of code required 98 seconds to compute the answer on my SGI O2. There are nine

permutations of this scheme, and all have similar timings.

We now consider using the colon range operator to compute the product of A and B by looping over all of the

elements of the resulting matrix C. Notice that what is being computed for a given i and j is the dot product of

the i^(th) row of A with the j^(th) column of B.

>> % Matrix multiplication example using inner products

>>

>> t = cputime;

>> for i=1:n,

for j=1:n

C(i,j) = A(i,:)*B(:,j);

end

end

>> t = cputime-t

t =

2.6600

This segment of code took 2.66 seconds to complete the calculation. By eliminating the inner loop, we have

decreased the effort required to compute C by a factor of 37 times!

Finally, we make use of the * operator, i.e. we use the full compiled code to compute C.

>> t = cputime; C = A*B; t = cputime-t

t =

0.0400

This segment of code took 0.04 seconds, a savings of 2450 times over the fully looped calculation and 66

times over the inner product calculation.

You would not want to program matrix multiplication if you are using Matlab, but this example should serve

as an illustration of the kind of code that you should avoid writting if possible.

On the other hand, be careful that you don't get too carried away with this process. The following code

segments assign a vector to the sum the first j elements of another vector, i.e.

y_j = x_1 + x_2 + ... + x_j

clear; n=2000; x = 1:n; x = x(:); y = zeros(n,1);

% case 1 -- no vectorization

t=cputime; for j=1:n, for k=1:j, y(j)=y(j)+x(k); end, end, cputime-t

% case 2 -- partial vectorization

t=cputime; for j=1:n, y(j)=sum(x(1:j)); end, cputime-t

% case 3 -- full vectorization


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