In this tutorial we will assume that you know how to create vectors and matrices and know how to index into them. For more information on those topics see one of our tutorials on either vectors, matrices, or vector operations.
The "for" loop allows us to repeat certain commands. If you want to repeat some action in a predetermined way, you can use the "for" loop. All of the loop structures in matlab are started with a keyword such as "for", or "while" and they all end with the word "end". Another deep thought, eh.
The "for" loop will loop around some statement, and you must tell Matlab where to start and where to end. Basically, you give a vector in the "for" statement, and Matlab will loop through for each value in the vector:
For example, a simple loop will go around four times:
>> for j=1:4,
j
end
j =
1
j =
2
j =
3
j =
4
>>
Once Matlab reads the "end" statement, it will loop through and print out j each time.
For another example, if we define a vector and later want to change the entries, we can step though and change each individual entry:
>> v = [1:3:10]
v =
1 4 7 10
>> for j=1:4,
v(j) = j;
end
>> v
v =
1 2 3 4
Note, that this is a simple example and is a nice
demonstration to show you how a "for" loop works.
However, DO NOT DO THIS IN PRACTICE!!!!
Matlab is an interpreted language and looping through
a vector like this is the slowest possible way to change
a vector. The notation used in the first statement
is much faster than the loop.
A better example, is one in which we want to perform operations on the rows of a matrix. If you want to start at the second row of a matrix and subtract the previous row of the matrix and then repeat this operation on the following rows, a "for" loop can do this in short order:
>> A = [ [1 2 3]' [3 2 1]' [2 1 3]']
A =
1 3 2
2 2 1
3 1 3
>> B = A;
>> for j=2:3,
A(j,:) = A(j,:) - A(j-1,:)
end
A =
1 3 2
1 -1 -1
3 1 3
A =
1 3 2
1 -1 -1
2 2 4
For a more realistic example, since we can now
use loops and perform row operations on a matrix,
Gaussian Elimination can be performed using only
two loops and one statement:
>> for j=2:3,
for i=j:3,
B(i,:) = B(i,:) - B(j-1,:)*B(i,j-1)/B(j-1,j-1)
end
end
B =
1 3 2
0 -4 -3
3 1 3
B =
1 3 2
0 -4 -3
0 -8 -3
B =
1 3 2
0 -4 -3
0 0 3
Another example where loops come in handy is the approximation
of differential equations. The following example approximates
the D.E. y'=x^2-y^2, y(0)=1, using Euler's Method. First, the step
size, h, is defined. Once done, the grid points are found,
and an approximation is found. The approximation is simply
a vector, y, in which the entry y(j) is the approximation at
x(j).
>> h = 0.1;
>> x = [0:h:2];
>> y = 0*x;
>> y(1) = 1;
>> size(x)
ans =
1 21
>> for i=2:21,
y(i) = y(i-1) + h*(x(i-1)^2 - y(i-1)^2);
end
>> plot(x,y)
>> plot(x,y,'go')
>> plot(x,y,'go',x,y)
If you don't like the "for" loop, you can also
use a "while" loop. The "while" loop repeats
a sequence of commands as long as some condition
is met. In this example the D.E. y'=x-|y|, y(0)=1,
is approximated using Euler's Method:
>> h = 0.001;
>> x = [0:h:2];
>> y = 0*x;
>> y(1) = 1;
>> i = 1;
>> size(x)
ans =
1 2001
>> max(size(x))
ans =
2001
>> while(i<max(size(x)))
y(i+1) = y(i) + h*(x(i)-abs(y(i)));
i = i + 1;
end
>> plot(x,y,'go')
>> plot(x,y)
This tutorial written by Kelly Black.