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matlabloopsfunction-handle

Create flexible function handle

I am using numerical integration in MATLAB, with one varibale to integrate over but the function also contains a variable number of terms depending on the dimension of my data. Right now this looks like the following for the 2-dimensional case:

for t = 1:T  
   fxt = @(u)  exp(-0.5*(x(t,1)-theta*norminv(u,0,1)).^2) .* ...
         exp(-0.5*(x(t,2) -theta*norminv(u,0,1)).^2);
   f(t) = integral(fxt,1e-4,1-1e-4,'AbsTol',1e-3); 
end

I would like to have this function flexible in the sense that there could be any number of data points in, each in the following term:

exp(-0.5*(x(t,i) -theta*norminv(u,0,1)).^2);

I hope this is understandable.

Solution

  • If x and u have a valid dimension match (vector-vector or array-scalar) for the subtraction, you can put the whole matrix x into the handle and pass it to the integral function using the name-parameter pair ('ArrayValued',true):

    fxt = @(u)  exp(-0.5*(x - theta*norminv(u,0,1)).^2) .* ...
            exp(-0.5*(x - theta*norminv(u,0,1)).^2);
f   = integral(fxt,1e-4,1-1e-4,'AbsTol',1e-3,'ArrayValued',true);

    [Documentation]

    You may need a loop if integral ever passes a vector u into the handle. But in looking at how the integral function is written, the integration nodes are entered as scalars for array-valued functions, so the loop shouldn't be necessary unless some weird dimension-mismatch error is thrown.


    Array-Valued Output

    In response to the comments below, you could try this function handle:

    fx = @(u,t,k)  prod(exp(-0.5*(x(t,1:k)-theta*norminv(u,0,1)).^2),2);

    Then your current loop would look like

    fx = @(u,t,k) prod(exp(-0.5*(x(t,1:k)-theta*norminv(u,0,1)).^2),2);
k  = 2;
for t = 1:T
  f(t) = integral(@(u)fx(u,t,k),1e-4,1-1e-4,'AbsTol',1e-3,'ArrayValued',true);
end

    The ArrayValued flag is needed since x and u will have a dimension mismatch. In this form, another loop would be needed to sweep through the k indexes. However, we can improve this function by skipping the loop altogether since each iterate of the loop is independent by using the ArrayValued mode:

    fx = @(u,k) prod(exp(-0.5*(x(:,1:k)-theta*norminv(u,0,1)).^2),2);
k  = 2;
f  = integral(@(u)fx(u,k),1e-4,1-1e-4,'AbsTol',1e-3,'ArrayValued',true);


    Vector-Valued Output

    If ArrayValued is not desired, which may be the case if the integration requires a lot of subdivisions and a vector-valued u is preferable, you can also try a recursive version of the handle using cell arrays:

    % x has size [T,K]
fx = cell(K,1);
fx{1} = @(u,t) exp(-0.5*(x(t,1) - theta*norminv(u,0,1)).^2);
for k = 2:K
    fx{k} = @(u,t) fx{k-1}(u,t).*exp(-0.5*(x(t,k) - theta*norminv(u,0,1)).^2);
end

f(T) = 0;
k    = 2;
for t = 1:T
    f(t) = integral(@(u)fx{k}(u,t),1e-4,1-1e-4,'AbsTol',1e-3);
end