Problem with an equation

Hi!

I have a problem writing an equation in Matlab. The variables and the equation look like this:

x=(-3:0.001:3)
y=(-4:0.001:4)
z=cos(x*y)*(1+3*(exp-(x.^2+2*y.^2)))

For me one of the obvious problems is that x and y have different sizes. But surely there is a way around the problem.

The message I recieve is:

Error using * Inner matrix dimensions must agree.

So obviously something is also wrong with the dimensions but I can´t figure it out.

So my question is, how do I write this to make this equation work?

A brief explanation of why this is not working would also be appreciated!

Thank you in advance.

Answer 1

[Stephen23]

Presumably you are not intending to perform matrix multiplication, but rather element-wise multiplication. Here are two methods to get use element-wise multiplication to get an output, even if the input vectors are different lengths:

x = -3:0.01:3;
y = -4:0.01:4;
% method 1: ndgrid
[X,Y] = ndgrid(x,y);
Z1 = cos(X.*Y).*(1+3*exp(X.^2+2*Y.^2));
% method 2: bsxfun
Z2 = cos(bsxfun(@times,x(:),y)) .* (1+3*exp(bsxfun(@plus,x(:).^2,2*y.^2)));

both of these give exactly the same result:

>> isequal(Z1,Z2)
ans =
     1
>> size(Z1)
ans =
   601   801

So the Z matrices have numel(x) rows and numel(y) columns. Thus you get an output value for each element in x and y.

Note that I reduced the number of points in the vectors (from 6001 and 8001 to 601 and 801), just to make it easier to work with.

I also removed the minus sign from after the exp fucntion as this is not MATLAB syntax and I have no idea what you intended this to do (it results in a syntax error).

Explanation

It confuses many MATLAB learners that there are different ways to multiply matrices. These different ways have been explained clearly many times on this forum, and in the documentation:

http://www.mathworks.com/help/matlab/matlab_prog/array-vs-matrix-operations.html

The next topic is how to perform element-wise multiply (or any other element-wise operation) on vectors of different lengths. In short: it is not possible to do this and get a vector the length of the input vectors. What length should the output be? Consider:

[1,2,3] .* [8,9]

as an element-wise operation means:

[1*8,2*9,3*????]

Thus the error. The solution is to either:

• pad the vectors to the same length
• Orient the vectors orthogonally and operate over every pair of elements. This is what I showed above.

[Alexander Engman]

Thank you so much!

[Stephen23]

My pleasure! You can also accept the answer that best resolves your question. This gives us points and is a small token of gratitude that you can offer us.