Parameter sweep with meshgrid using a function containing a for loop

I am calculating the time evolution of the following system using a for loop as in the code below.

trainLen = 30;
initLen = 3;
data = [1:1:trainLen]; %%Some data

inSize = 1; 
resSize = 50;

Win = (rand(resSize,1+inSize)-0.5) .* 1;
W = rand(resSize,resSize)-0.5;
a = 0.95;

X = zeros(1+inSize+resSize,trainLen-initLen);
x = rand(resSize,trainLen);

for t = 1:trainLen
    u = data(t);
    x(:,t+1) = (1-a)*x(:,t) + a*tanh( Win*[1;u] + W*x(:,t) );
    if t > initLen
        X(:,t-initLen) = [1;u;x(:,t)];
    end
end

I would like to perform a parameter sweep over the variables a (a scalar) and W (a matrix) using meshgrid to try and avoid using two for loops, but I am struggling rewriting the (time evolution) for loop as an anonymous function to be used with a and W, as in this example.

Any help would be appreciated.

[KSSV]

You mean to say you want to change the code to the case where variables a, w are matrices? Show us the code which is not working for you.

[Valentina Baccetti]

Thanks KSSV, apologies I didn't make myself clear. In my original code a and W are, respectively, a scalar and a matrix. What I have done so far is performing the parameter sweep using two for loops

trainLen = 30;
initLen = 3;
data = [1:1:trainLen]; %%Some data

inSize = 1; 
resSize = 50;

Win = (rand(resSize,1+inSize)-0.5) .* 1;
W = rand(resSize,resSize)-0.5;

a = [0.2,0.5,0.7,0.95]; %Now a vector
Wmult = [0.13, 0.144, 0.18, 0.2]; 

X = zeros(1+inSize+resSize,trainLen-initLen, size(a,2),size(Wmult,2));
x = rand(resSize,trainLen,size(a,2),size(Wmult,2));

for l = 1:size(a,2) 
    for m = 1:size(Wmult,2)
        for t = 1:trainLen
            u = data(t);
            x(:,t+1,l,m) = (1-a(l))*x(:,t,l,m)+ a(l)*tanh( Win*[1;u] + W(m)*W*x(:,t,l,m)) ;
            if t > initLen
                X(:,t-initLen,l,m) = [1;u;x(:,t,l,m)];
            end
        end
    end
end
 
 

My idea would be to first put a and Wmult into a matrix using meshgrid first

[aValue,WValue] = meshgrid(a,Wmult);

and then define a function of the kind (commented out so not to break the compiler)

%timeEvolution = @(a,Wmult)(for l = 1:size(a,2) 
%     for m = 1:size(Wmult,2)
%         for t = 1:trainLen
%             u = data(t);
%             x(:,t+1,l,m) = (1-a(l))*x(:,t,l,m)+ a(l)*tanh( Win*[1;u] + W(m)*W*x(:,t,l,m)) ;
%             if t > initLen
%                 X(:,t-initLen,l,m) = [1;u;x(:,t,l,m)];
%             end
%         end
%     end
% end)

Is there any way to do this?

Answer 1

[Ramtej]

Hi Valentina,

I understand that you are trying to avoid using two for-loops to perform parameter sweep using an anonymous function.

You cannot reduce the for loops in your case using “meshgrid” and anonymous functions because of the following two reasons.

1. The code provided uses both the index value "l" and the value of the vector "a" at index "l" in the inner for loops. However, you will only be passing the values "[aValue, WValue]" when using meshgrid and an anonymous function.
2. Anonymous functions cannot contain explicit “for” loops and “if” clause statements.

Hope this helps!