How to store outputs of a function in a matrix?

I need help in storing outputs of a repeated integration in a matrix and then find the max value for each row i (Gam).

Gam = linspace(2,20,19);
Fvpa = zeros(length(Gam),length(w)); %Matrix where I want to store outputs
 for i=1:length(Gam)
    w = 0.01:0.01:0.99;
    for j=1:length(w)
        syms q %new variable that I want to use in integration
        assume (-0.99<= q <=0.99);
        ff=@(q) gamma((v+1)/2)/(gamma(0.5)*gamma(v/2))*(h/v)^0.5*(1+h/v*(q-x_T*beta_OLS).^2).^[-((v+1)/2)];
        fq1=@(q) w(j) .* exp(q) + (1-w(j)) .* exp(i_T);
        fq2 =@(q) fq1(q).^(1-Gam(i))/(1-Gam(i)); 
        fq3 =@(q) ff(q).* fq2(q);%final function that I want to integrate over q
        fqint = int(fq3, q, -0.99, 0.99); 
        Fvpa=vpa(fqint); %This must be the outputs of each integration that I want then to store 
    end
 end
display(Fvpa);

[Rizwan Khan]

% For storing the values

Fvpa(i,j) = vpa(fqint);

%for finding the maximum value of each row of output Fvpa

max = max(Fvpa ,[], 2); % max will be a column vector in which each element is a maximum value of the corresponding row.

Answer 1

[Charles Rice]

You need to move your assignment of w to above your preallocation of the Fvpa variable, or lenght(w) is meaningless. In your loop, you are assigning the output of vpa(fqint) to a single variable called Fvpa. See line 14 below for the array assignment. If you need the max value for each row, you can just run max(Fvpa, [], 2) to operate on each row. By default, max() returns a row vector containing the max of each column. See help below.

>> help max

max Maximum elements of an array.

M = max(X) is the largest element in the vector X. If X is a matrix, M

is a row vector containing the maximum element from each column.

...

M = max(X,[],DIM) or [M,I] = max(X,[],DIM) operates along the

dimension DIM.

1. Gam = linspace(2,20,19);
2. w = 0.01:0.01:0.99;
3. Fvpa = zeros(length(Gam),length(w)); %Matrix where I want to store outputs
5. for i=1:length(Gam)
6. for j=1:length(w)
7. syms q %new variable that I want to use in integration
8. assume (-0.99<= q <=0.99);
9. ff=@(q) gamma((v+1)/2)/(gamma(0.5)*gamma(v/2))*(h/v)^0.5*(1+h/v*(q-x_T*beta_OLS).^2).^[-((v+1)/2)];
10. fq1=@(q) w(j) .* exp(q) + (1-w(j)) .* exp(i_T);
11. fq2 =@(q) fq1(q).^(1-Gam(i))/(1-Gam(i));
12. fq3 =@(q) ff(q).* fq2(q);%final function that I want to integrate over q
13. fqint = int(fq3, q, -0.99, 0.99);
14. Fvpa(i, j) = vpa(fqint); %This must be the outputs of each integration that I want then to store
15. end
16. end
17. display(Fvpa);

[Federica Poli]

Thank you very much. It was really helpful

Answer 2

[Federica Poli]

Do you know how to find the "w" value related to each maximum?

Answer 3

[Charles Rice]

>> help max

M = max(X) is the largest element in the vector X. If X is a matrix, M

is a row vector containing the maximum element from each column. For

N-D arrays, max(X) operates along the first non-singleton dimension.

[M,I] = max(X) also returns the indices into operating dimension

corresponding to the maximum values. If X contains more than one

element with the maximum value, then the index of the first one

is returned.

In your case, Gam is your row variable, and w is your column variable, so:

[Fvpa_max_columns, index_columns] = max(Fvpa);

w_max = w(index_columns)

[Fvpa_max_rows, index_rows] = max(Fvpa, [], 1);

Gam_max = Gam(index_rows)