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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
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

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
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.