obtaining a wrong matrix size

I would like to know why I am obtaining as a result in this code, a matrix (15x1) and not a number. I am computing a test statistics equation that involves matrices products, so I am multiplying this matrix sizes:

((1x15)*(15x15)*(15x1))X((1x15)*(15x15)*(15x1))^2

I guess I am supposed to achieve a number, from this matrices products, but as I have said, MATLAB returns me as a solution of this equation a 15x1 matrix. Otherwise, at the end I have put the command size(T), to know the matrix size of T, and it returns me that is a 1x1 matrix (a number). Does anybody know why this two things doesn't match?

Following, here is my MATLAB code attached if you want to take a look at it

[Image Analyst]

The attached code also requires .xlsx workbooks, which were not attached. Attach the workbooks if you want us to try the code.

Answer 1

[Star Strider]

It is difficult to read your code and I can’t run it. I ran a simulation of the matrix operation you describe, and got a scalar result as expected.

I suggest you check the sizes of the matrices in your equation. One of your vectors may actually be a matrix.

[Josep]

I have forgotten you don't have the excel files, so obviously, you are not able to run it.

I don't understand what you mean, saying the one of my vectors may actually be a matrix. All my values operating in the equation are matrices.

Here i attach you what I receive from MATLAB in a PDF file

[Star Strider]

If the vector in the .pdf is T, then something is wrong. The size should be (15x1), not (1x1).

Again, please post the actual line of your code that is doing that calculation, and the sizes of all the vectors and matrices that are in it.

[Josep]

Okay, here is the code that is doing the calculation:

 for j=1:Nby,
    Fk(:,j)
    T = inv(Fk(:,j)'*inv(V)*Fk(:,j))*(Fk(:,j)'*inv(V)*r)^2;

    size(T)
end

Matrix sizes:

Fk(15x1)

V(15x15)

r(15x1)

[Guillaume]

The lines of code you just posted would give the result you wrote in your PDF. You're asking matlab to print Fk(:, j) which is indeed 15x1 and checking the size of T which is 1x1. Everything is as expected.

Change your lines to

for j = 1:Nby
  T = inv(Fk(:,j)'*inv(V)*Fk(:,j))*(Fk(:,j)'*inv(V)*r)^2;
  disp(T); %better to be explicit that you want this printed, than playing around with semi-colons
end

[Star Strider]

I don’t understand why that’s not producing scalar values for T.

However, if you intend to save the Nby individual values for T, you have to index them. Since the individual matrix operation terms both produce scalar values, divide the second term by the first rather than using inv on the first term:

for j=1:Nby,
    Fk(:,j)
    T(j) = ((Fk(:,j)'*inv(V)*r)^2)/(Fk(:,j)'*inv(V)*Fk(:,j));

    size(T(j))
end

[Josep]

Guillaume, that works now. As you said, I needed to ask matlab to print T, not Fk. Sorry for this mistake, I am new on Matlab.

Star Strider, why putting this / ?

Do yo get the same results? Why are you always trying to avoid inv?

[Star Strider]

It makes the code simpler and faster to divide scalars using ‘/’ than inv.

I avoid inv where possible because the ‘\’ operator is a much more efficient and computationally stable method of multiplying by inv, although sometimes it is unavoidable. Here, inv on the first term (a scalar) is the the same as 1/(Fk(:,j)'*inv(V)*Fk(:,j)), so it makes sense to compute it as a scalar.

[Josep]

Nice!

Thanks Star Strider one more time

[Star Strider]

My pleasure!