Sum of a function

Hello everyone, I am stucked on how to write particular code for a Nash-Cournout oligopolistic equilibrium problem. I have written everything correctly and it ran successfully. The only situation I am in presently is trying to vary a particular step. To be more precise

I need code for the following:

is random for every

is random for every and

is random for every . I need to execute the following Quad program $c_j(x_j) = \frac{1}{2}x{_j}^{'} P_j x_j+ {q_j}^{'} x{_j}$. I will be glad if I can get a prompt help on this.

https://www.mathworks.com/matlabcentral/answers/uploaded_files/226241/Screenshot_20190625-093751.png

Thanks

Answer 1

[Himanshu Rai]

The expression below should solve your problem. Also write questions properly - would be scalar, so c is a vector. P and x are normal matrices, and q is a vector. This should solve your problem.

PS - Also update your question, and attach the image file there

c = x' * P * x / 2 + q' * x

[Olawale Kazeem]

Note $x_j$ is not a scalar, $x_j$ is a vector generated randomly in the interval (0,1] for each $j=1 \cdots 10.$

[Himanshu Rai]

From what is specified in the question appears to be a scalar value. The same goes for and

[Olawale Kazeem]

Sorry I need to include that, $x_j$ is a vector generated randomly in (0,1] for each j, $P_j$ is a matrix generated randomly in [1,40] and $q_j$ is also a vector generated randomly in [1,40]. Suppose $j$ runs from 1 to 10 and the dimension of the vector and matrix is m=3

[Himanshu Rai]

From your comment , and , are the dimensions of your matrices. But this doesn't satisfy usual matix operation rules for the evaluation of you expression. Please specify more clearly, what (dimension of the) vector you are referring to, and by size of matrix to be 3 do you mean it is a square matrix ?

[Olawale Kazeem]

Thanks for your response. The matrix $P_j$ is a 3x3 matrix generated randomly in the interval [1,40]. $q_j$ is a 3x1$ generated randomly in [1,40] , $x_j$ is a 3x1 by matrix generated randomly in (0,1]. The indexed $j = 1 \cdots 10.$ This implies we have to generate $P_1$ $P_2$ up to $P_10.$ Same for $q_j$ and $x_j$.

[Himanshu Rai]

All right, so now I got what your question is, but still your dimensions doesn't satisfy rules of matrix opeations.

is , is , so will be .

is , is , so will be .

But we can't add these two results.

[Olawale Kazeem]

We need q_j to be 1by 3 as well

[Himanshu Rai]

Well if is , then can't be calculated, because again the matrices are incompatible

Answer 2

[Olawale Kazeem]

I just checked the mistake, hopefully I have not disturbed you too much. I am attaching a file that contains what I need.

[Himanshu Rai]

I have updated my answer based on the image file you provided. Update your question, attach this file in the question and also don't comment as answer

[Olawale Kazeem]

Thanks, but I still don't understand how to treat the js, should I write each differently? I mean getting $c_1(x_1)$, $c_2(x_2)$, ⋯ . separately. I need a code that can run everything together once.

[Olawale Kazeem]

How do I get a function going by what you suggested up there?

[Himanshu Rai]

Use

sum(c) % here c is what you get from the expression in the answer

[Olawale Kazeem]

I get that, I hope this is my final question. What if my N is greater than the dimension of the matrices? It is clear now that the s are the entries of the vector x. If the vector is of dimension 10, but I need to sum up to $N=20$, how possible is this?

[Himanshu Rai]

This doesn't make any sense - how can we add 20 elements, if there are only 10 elements in vector.

[Olawale Kazeem]

What I found out is that $c = sum(c) .$ Can you check that for me? Since c is scalar from the operation above.

[Himanshu Rai]

is a scalar, whereas c is a vector.

[Olawale Kazeem]

I suppose my definition of x is wrong. I defined ; ; and ; . $c = 0.5*x'*P*x+q'*x$. This gives a matrix.

[Himanshu Rai]

This is not x, but . is a vector but x is a matrix. And what you denote by c above is actually