Error using fmincon and integral2: taking integral variables theta and p as an array while performing computation

I am minimizing q for whole range of p and theta; p has limit from 2pi to 20pi and theta from 0 to pi; to find the value of d, r_g,G_g. q is function of theta, p,d, r_g, G_g.

But while computation p and theta are behaving as an array. Because of this I am getting error. I tried using "ArrayValued", true. This is also not working. How to correct this. Here my part of code

[q] = optimizeParameters();% Call optimizeParameters to define the objective function q
options = optimset('PlotFcns', @optimplotfval);% Set optimization options

d0 = [-0.5, 24, 3e6];
lb = [-1, 24, 2e6];
ub = [0, 32, 6e6];
[solution,fval] = fmincon(@(x)integral2(@(theta,p)q(theta,p,x(1),x(2),x(3)),pi/36,pi/6,2*pi,20*pi),d0,[],[],[],[],lb,ub,[],options); % minimize

function q = optimizeParameters()
   
    Vs = 250;
    k = @(p)p/Vs;
    c = @(theta)Vs./sin(theta);
    w5 = 0.001;
    n = 3;
    dl = -6;
    d1 = @(d)dl + 2 * n * d - d;

    q = @(theta, p, d, r_g, G_g) calculateObjective(theta, p, d, r_g, G_g, Vs, k, c, w5, n, dl, d1);
end


function answer = calculateObjective(theta, p, d, r_g, G_g, Vs, k, c, w5, n, dl, d1);
    % printing the p  and thetahere which is giving an array because of this error in further computation
    theta 
    p
    % rest of the code

end

[Steven Lord]

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[Manoj Manoj]

This is the error I am getting. The error is due to matrix size not compatible for multiplication. But the matrix are x2_inv and B are 4x4 matrices. Since I am using k and c as function handles it shows the size of these matrices as 56x56.

This is not working contex: I tried using "ArrayValued",true; which we use when using integral and in integral2 it is not a valid option.

Error using  * 
Incorrect dimensions for matrix multiplication. Check that the number of columns in the first matrix matches the number of rows in the second matrix. To operate on
each element of the matrix individually, use TIMES (.*) for elementwise multiplication.

Error in untitled5>calculateObjective (line 190)
Y2= x2_inv*(B*[0;0;-w5;w5]);

Error in untitled5>@(theta,p,d,r_g,G_g)calculateObjective(theta,p,d,r_g,G_g,Vs,k,c,w5,n,dl,d1) (line 35)
    q = @(theta, p, d, r_g, G_g) calculateObjective(theta, p, d, r_g, G_g, Vs, k, c, w5, n, dl, d1);

Error in untitled5>@(theta,p)q(theta,p,x(1),x(2),x(3)) (line 11)
[solution,fval] = fmincon(@(x)integral2(@(theta,p)q(theta,p,x(1),x(2),x(3)),pi/36,pi/6,2*pi,20*pi,'Method','tiled'),d0,[],[],[],[],lb,ub,[],options); % minimize

Error in integral2Calc>integral2t/tensor (line 228)
        Z = FUN(X,Y);  NFE = NFE + 1;

Error in integral2Calc>integral2t (line 55)
[Qsub,esub] = tensor(thetaL,thetaR,phiB,phiT);

Error in integral2Calc (line 9)
    [q,errbnd] = integral2t(fun,xmin,xmax,ymin,ymax,optionstruct);

Error in integral2 (line 105)
    Q = integral2Calc(fun,xmin,xmax,yminfun,ymaxfun,opstruct);

Error in untitled5>@(x)integral2(@(theta,p)q(theta,p,x(1),x(2),x(3)),pi/36,pi/6,2*pi,20*pi,'Method','tiled') (line 11)
[solution,fval] = fmincon(@(x)integral2(@(theta,p)q(theta,p,x(1),x(2),x(3)),pi/36,pi/6,2*pi,20*pi,'Method','tiled'),d0,[],[],[],[],lb,ub,[],options); % minimize

Error in fmincon (line 568)
      initVals.f = feval(funfcn{3},X,varargin{:});

Error in untitled5 (line 11)
[solution,fval] = fmincon(@(x)integral2(@(theta,p)q(theta,p,x(1),x(2),x(3)),pi/36,pi/6,2*pi,20*pi,'Method','tiled'),d0,[],[],[],[],lb,ub,[],options); % minimize

Caused by:
    Failure in initial objective function evaluation. FMINCON cannot continue.

Answer 1

[Torsten]

Take care that you pass k, c and d1 as values, not as function handles to your objective function.

Thus (as in all your questions before) use

q = @(theta, p, d, r_g, G_g) calculateObjective(theta, p, d, r_g, G_g, Vs, k(p), c(theta), w5, n, dl, d1(d));

instead of

q = @(theta, p, d, r_g, G_g) calculateObjective(theta, p, d, r_g, G_g, Vs, k, c, w5, n, dl, d1);

!!!

[q] = optimizeParameters();% Call optimizeParameters to define the objective function q
options = optimset('PlotFcns', @optimplotfval);% Set optimization options
d0 = [-0.5, 24, 3e6];
lb = [-1, 24, 2e6];
ub = [0, 32, 6e6];
[solution,fval] = fmincon(@(x)integral2(@(theta,p)arrayfun(@(theta,p)q(theta,p,x(1),x(2),x(3)),theta,p),pi/36,pi/6,2*pi,20*pi),d0,[],[],[],[],lb,ub,[],options) % minimize
function q = optimizeParameters()   
    Vs = 250;
    k = @(p)p/Vs;
    c = @(theta)Vs./sin(theta);
    w5 = 0.001;
    n = 3;
    dl = -6;
    d1 = @(d)dl + 2 * n * d - d;
    q = @(theta, p, d, r_g, G_g) calculateObjective(theta, p, d, r_g, G_g, Vs, k(p), c(theta), w5, n, dl, d1(d));
end
function answer = calculateObjective(theta, p, d, r_g, G_g, Vs, k, c, w5, n, dl, d1);
    % printing the p  and thetahere which is giving an array because of this error in further computation
    answer = theta + p;
    % rest of the code
end