Gradient of a cell array with optimizer

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Spyros Polychronopoulos 2017-12-15

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https://ww2.mathworks.cn/matlabcentral/answers/373142-gradient-of-a-cell-array-with-optimizer

编辑： Spyros Polychronopoulos 2017-12-15

Hi everyone, I have a function with various variables z, as can be seen in the example below. I would like to take the gradient in x,y (coordinates) and then use an optimizer to get 1000 z values to minimize the function. The problem is that gradient function does not work with cell arrays. If I try storing the function in symbolic matrix then simulated annealing doesn't work cause only there is only one z.

Cells approach example:

A=rand(10^3,1);
for k2=1:10^3
a{k2}=@(z) z*A(k2);
end
%preparing the array for the gradient
l=1;
for k3=1:10
for k4=1:10
for k5=1:10
q2(k3).p{k4,k5}=@(z) a{l}(z);
l=l+1;
end
end
end
clear k1 k2 k3 k4 k5 l
% now I want to do what I have done with the matrix above but I have functions this returns 1 value so doesn't work
for k1=1:10
[part_x2{k1}.p,part_y2{k1}.p]=@(z) (cellfun(@gradient,q2(k1)));
end
%this doesn't work either
for k1=1:10^3
[part_x2{k1}.p,part_y2{k1}.p]=arrayfun(@(z) gradient(q2(k1)));
end

Symbolic matrix approach example, this does work but then the optimizer doesn't work:

A=rand(2,2);
syms x
f = sin(x) * A;
for k1=1:2
  for k2=1:2
F(k1,k2)=gradient(f(k1,k2),x);
  end
end
% now the optimizer doesn't work
fun=F(1,:);
z0 = zeros(length(A(1,:)),1);
LB(1:length(A(1,:)),1) = -2; % LB - lower bound vector or array, must be the same size as z0
UB(1:length(A(1,:)),1)= 2; % UB - upper bound vector or array, must be the same size as z0
[z_ref,P_T]=simulannealbnd(fun,z0,LB,UB); %simulated annealing