Trying Julia

In my previous post I tried building Williams designs in R. Since that code was running a bit slow, this was an ideal test for Julia. Big enough to be at least slightly realistic, small enough that it is doable.
I am very impressed. Almost twenty fold speed increase, even though this was the best I could do in R, the most naive way possible in Julia.
                                       R              Julia        Ratio
Double Williams design 4, 100 times    3.97 sec       0.212 sec    0.053   
Williams design 5, 10 times          289.5 sec       18.54  sec    0.064 


I'd surely love to use Julia more. For instance, if I could port some of the algorithm's of Professor Ng Machine Learning class to Julia? I don't think it is possible yet, but what is not, may come.

Julia code

macro timeit(ex,name,num)

    quote

        t0 = 0

        for i=1:$num

            t0 = t0 + @elapsed $ex

        end

        println("julia,", $name, ",", t0)

        #gc()

    end

end

function gendesign(ncol)

  nrow=ncol*2

  desmat = zeros(Uint8,nrow,ncol)

  desmat[1,1:ncol] = [1:ncol]

  for i = [1:ncol]

    desmat[2*i-1,1] = i

    desmat[2*i,1]=i

  end

  carover = zeros(Uint8,ncol,ncol)

  for i = 1:(ncol-1)

    carover[i,i+1] = 1

  end

  count   = 0

  addpoint( desmat , carover,count)

end

function numzero(matin) 

  length(matin) - nnz(matin) 

end   

 

function first0(matin)

   if numzero(matin)==0

      return -1

   end   

   nrow, ncol = size(matin)

   for row = 1:nrow

      for col = 1:ncol

         if matin[row,col] == 0

            return row, col

         end

      end

    end   

end   

function addpoint(desmat,carover,count)

  if nnz(desmat) == length(desmat)

     count +=1

     print("x")

     return count

  end

  row,col  = first0(desmat)

  for i = [1:size(desmat,2)]

     if numzero(desmat[row,:]-i) == 0

        if numzero(desmat[:,col]-i) < 2

           if carover[desmat[row,col-1],i] < 2 

              if (col !=2) | (desmat[row,1] != desmat[row-1,1]) | (desmat[row-1,col] < i)

                 desmat[row,col]=i

                 carover[desmat[row,col-1],i] +=1

                 count = addpoint(desmat,carover,count)

                 desmat[row,col]=0

                 carover[desmat[row,col-1],i] -=1

              end

            end 

         end 

      end 

   end 

   return count

end

@timeit gendesign(4) "design 4 " 100

@timeit gendesign(5) "design 5 " 10

Note

Both designs were created using the same script. If you ask an even number of design points using the odd algorithm, then this will work. You just get a design with double the rows, carry over balanced, every treatment equally often in each row and each column.