In this tutorial we will deal with some common programming structures and also alternative conditionally statements. These statements exist as well in almost all high-level programming languages. In Matlab a common programming construction is a if or a switch statement. To repeat a number of statements, can be solved with a for or a while loop.

In the following examples we will see how this is implemented in Matlab, but nevertheless how good programmers we are, some mistakes will happen. This also motivates a brief view of the debugger in Matlab.

### For Loop in MATLAB

The general expression for a for-loop is:

for variable=expression
control statements
end |

for variable=expression
control statements
end

#### Example 1:

Let us write an m-file that calculates the sum: The sum to be calculated is: 1+1/2^{2}+1/3^{2}+…..+1/10^{2}.

i=1;
the_sum=0;
for i=1:10
the_sum=the_sum+1/(i^2);
end
fprintf('The sum of 10 elements gives: %f ', the_sum) |

i=1;
the_sum=0;
for i=1:10
the_sum=the_sum+1/(i^2);
end
fprintf('The sum of 10 elements gives: %f ', the_sum)

The execution of the code in Matlab command window gives: The sum of elements gives: 1.549768

Read more »

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Matlab Tutorials | admin, July 5, 2010 8:47 am | Comments Off on Matlab Tutorial 7: Common Programming Structures and Conditional Statements

In this Matlab tutorial we will deal with linear equations, the least square method, condition numbers over & under-determined equations.

Let’s start with an example.

**Example 1**

We have an equation system with three unknown variables and three equations. What will be the solution to the system below?

3w-2y+4z=8

5w+8y-6z=-5

9w-2y+7z=-17

Assume a matrix A containing the coefficients multiplied with x, y and z, and a vector with the numbers on the right-hand side of the equations. We can thus rewrite our equations as:

AX=b , where X contains the unknown (w, y and z), A and b are shown below.

b= A=
8 3 -2 4
-5 5 8 -6
-17 9 -2 7 |

b= A=
8 3 -2 4
-5 5 8 -6
-17 9 -2 7

How will we find the solution?

or

both gives a correct answer. The last method produces a Gaussian elimination if A is a quadratic matrix. In our case X becomes:

X=
-36.7778
71.2778
65.2222 |

X=
-36.7778
71.2778
65.2222

This is no exact solution, only an approximation. Try also a specific command: Read more »

Tags: coefficients, complex conjugated, cubical functions, diagonal elements, differential equations, eigenvalues, eigenvectors, equation system, linear equations, linear system, linearly independent, Matlab Tutorials, quadratical functions, sparse matrices, tic, toc

Matlab Tutorials | admin, June 13, 2009 4:06 am | Comments Off on Matlab Tutorial 5: Linear Equations