I have a function HermitePCECoefficients which takes as inputs multiple parameters, including a column vector y, and outputs a column vector Coefficients, the same length as y:
Coefficients=HermitePCECoefficients(grid,weights,indices,y,mu,sigma,normalized)
Suppose now that y is not a column vector, but a 2D array (matrix), and I want to run HermitePCECoefficients on each of its columns, storing the corresponding outputs in a array. Doing it with a for loop is simple and clear, but it takes forever:
Coefficients=zeros(size(y));
for i=1:size(y,2)
Coefficients(:,i)=HermitePCECoefficients(grid,weights,indices,y(:,i),mu,sigma,normalized);
end
Thus, I put bsxfun to the job. Since bsxfun only works with binary functions, I created a "dummy" binary function f, which is really only a function of a single argument:
f=@(a,b) HermitePCECoefficients(grid,weights,indices,a,mu,sigma,normalized);
Then used bsxfun this way:
Coefficients=bsxfun(f,y,omega_f);
This works fine, and it's much faster than the for loop (don't worry about omega_f, it's just a vector whose length corresponds to the number of columns in y).
Question 1: do you think this is the right way to use bsxfun in this context?
Question 2: maybe a better solution would be to directly modify HermitePCECoefficients, so that it could take a generic array y as input. Inside the function, this is the only line which requires y to be a column vector:
Coefficients(i)=dot(weights,y.*Psi)/norm;
weights and Psi are two column vectors, so if I pass an array y, MATLAB complains. Any suggestions on how to modify it?
Option 2 seems better (but only testing will tell). Just replace
dot(weights,y.*Psi)/norm
by
sum(bsxfun(@times, weights.*Psi, y)/norm)
or (probably faster)
(weights.*Psi).'*y / norm
Either of the above is equivalent to computing the vector [ dot(weights,y(:,1).*Psi)/norm, dot(weights,y(:,2).*Psi)/norm, ... ] for an arbitrary number of columns of y. Each entry of this vector is the result for a column of y.