Help vectorising for loop for kernel density

I am having a devil of a time figuring out how to vectorise the following for loopp

dens = NaN(length(y),1);
for i=1:length(y)
   dens(i) = (1/(n*h))*sum(kernel((Y-y(i))/h));
end

Where Y has 1000 points and y has 50 points, i think perhaps it could be done by subtracting each element in y from Y such that i get a 1000 by 50 matrix. And then i can sum across columns to get the result perhaps ? but that would requre some fairly large matrices for changed dimensions and i also dont know how to do it

any help will be greatly appreciated

[Matt Fig]

What are n and h, and where is the kernel function?

[DoVile Last Name:]

n = 1000 (number of simulated variables = length(Y), h is the bandwidth = 0.15 and the kernel function i have declared already so when the loop calls kernel(x) it should call that function, the function it self is:

K_Gauss =@(z) exp((-z.^2)./2)./sqrt(2*pi);

Answer 1

[Matt Fig]

With these values for Y and y:

Y = rand(10,1)*10;
y = rand(5,1)*10;

This gives the same result as your FOR loop:

D = (1/(n*h))*sum(kernel(bsxfun(@minus,Y.',y)/h),2);

Here is the code I used to check the equality of the two approaches, in case it helps you:

Y = rand(1000,1)*10;
y = rand(50,1)*10;
dens = NaN(length(y),1);
n = length(Y);
h = .15;
kernel = @(z) exp((-z.^2)./2)./sqrt(2*pi);

for i=1:length(y)
   dens(i) = (1/(n*h))*sum(kernel((Y-y(i))/h));
end

D = (1/(n*h))*sum(kernel(bsxfun(@minus,Y.',y)/h),2);
isequal(dens,D)  % Check for equality.

[DoVile Last Name:]

Hi Matt,

I get the strangest error when i try to apply your code, it says

??? Error using ==> bsxfun
Non-singleton dimensions of the two input arrays must match each other.

However the dimensions seem to match the code you have above, so i cant really see where it would go wrong. Any suggestions ?

[Matt Fig]

What are the dimensions of Y and y?

whos y Y

[DoVile Last Name:]

    Name         Size            Bytes  Class     Attributes

    Y         1000x1              8000  double              
    y            1x50              400  double

[Matt Fig]

So is it working now? Did you copy and paste my test code to see that it is working? Those dimensions are identical to my test code. Are you sure about the other variables being as I show, and the kernel function?

[DoVile Last Name:]

It unfortunately is not working, i accepted the answer by mistake :)

I tested the example code you posted and it works fine, however my main code still does not. I have zipped to a rar file here http://www.mediafire.com/?9o846f8f481q7sr.

Thanks alot for your help btw Matt, i am trying to get into the habbit of vectorizing my code.