Augmenting Latin Hypercube Points in MATLAB - matlab

Question

I would like to know what are the commands to create a LHS design and then augment it with more points later on if the model is not good enough? For example, I will first create a 50 points LHS design, then add more points (perhaps in batches of 20) incrementally until the model is accurate enough.
For example:
Set1=lhsdesign(5,5); %5x5 matrix
%Use of set 1, then determine more points are needed
Set2=%some command that adds 20 points to Set1 to make it a 25x5 matrix
The difficulty in running lhsdesign again for the 20 new points do not take account of the original points. There is also work done using the original points and so by generating a new set of points from scratch wastes this work as the new points are not included in the new set.

Answer 1

I was able to make a function that solves this problem. I am not sure the final matrix is a true latin hypercube, but it adds the required number of points to the given points and moves them to the closest available open 'channel' (Sub range where no point exists) if need be.
Usage is as follows:
x1=lhsdesign(200,17);
xF=lhsaugment(x1,200);
Which adds 200 points to the x1 set of points, resulting in xF being a 400x17 matrix. Function is as follows:
function xF = lhsaugment(x1,nPoi)
%function xF = lhsaugment(x1,nPoi)
%Function to augment a given latin hypercube x1 by a number of points,
%nPoi. Only the length is changed, i.e. points are added to the length.
%The original points are left unctouched and appear first in the output
%xF. Thus the size of xF is [size(x1,1)+nPoi size(x1,2)].
x2=lhsdesign(nPoi,size(x1,2));
nPoi=size(x2,1);
oPoi=size(x1,1);
tPoi=nPoi+oPoi;
fInt=1/tPoi;
for i=1:tPoi
cBound(i,:)=[(i-1)*fInt i*fInt];
end
xF=zeros(tPoi,size(x1,2));
bX1=zeros(size(x1));
bX2=zeros(size(x2));
bF=zeros(tPoi,size(x1,2));
iF=zeros(1,size(x1,2));
iMove=0;
for i=1:oPoi
for j=1:size(cBound,1)
for l=1:size(x1,2)
if (x1(i,l)>cBound(j,1))&&(x1(i,l)<=cBound(j,2))&&(bF(j,l)==0)
iF(1,l)=iF(1,l)+1;
xF(iF(1,l),l)=x1(i,l);
bX1(i,l)=1;
bF(j,l)=1;
elseif (x1(i,l)>cBound(j,1))&&(x1(i,l)<=cBound(j,2))&&(bF(j,l)~=0)
iMin=size(cBound,1);
pMin=size(cBound,1);
for m=j:-1:1
if (bF(m,l)==0)
iMin=m;
pMin=j-m;
break
end
end
for m=j:size(cBound,1)
if (bF(m,l)==0)&&(m-j<pMin)
iMin=m;
pMin=j+m;
break
end
end
iF(1,l)=iF(1,l)+1;
xF(iF(1,l),l)=x1(i,l);
bX1(i,l)=1;
bF(iMin,l)=1;
end
end
end
end
for i=1:nPoi
for j=1:size(cBound,1)
for l=1:size(x2,2)
if (x2(i,l)>cBound(j,1))&&(x2(i,l)<=cBound(j,2))&&(bF(j,l)==0)
iF(1,l)=iF(1,l)+1;
xF(iF(1,l),l)=x2(i,l);
bX2(i,l)=1;
bF(j,l)=1;
elseif (x2(i,l)>cBound(j,1))&&(x2(i,l)<=cBound(j,2))&&(bF(j,l)~=0)
iMin=size(cBound,1);
pMin=size(cBound,1);
for m=j:-1:1
if (bF(m,l)==0)
iMin=m;
pMin=j-m;
break
end
end
for m=j:size(cBound,1)
if (bF(m,l)==0)&&(m-j<pMin)
iMin=m;
pMin=j+m;
break
end
end
iF(1,l)=iF(1,l)+1;
xF(iF(1,l),l)=(x2(i,l)-(floor(x2(i,l)/fInt)*fInt))+((iMin-1)*fInt);
bX2(i,l)=1;
bF(iMin,l)=1;
if l==1
iMove=iMove+1;
end
end
end
end
end