How to pre-allocate arrays in multi-loop iteration - arrays

Question

I need to pre-allocate arrays in my code below.
I don't quite understand how to pre-allocate arrays in multi-loop iteration.
a=0:1:2;
b=0:1:2;
c=0:1:2;
xx1=[];yy1=[];zz1=[];xx2=[];yy2=[];zz2=[];
for k=1:length(c)-1;
z1=c(k); z2=c(k+1);
for w=1:length(b)-1;
y1=b(w); y2=b(w+1);
for q=1:length(a)-1;
x1=a(q); x2=a(q+1);
xx1=[xx1;x1]; xx2=[xx2;x2];
yy1=[yy1;y1]; yy2=[yy2;y2];
zz1=[zz1;z1]; zz2=[zz2;z2];
end
end
end
The expected results are:
[xx1 xx2 yy1 yy2 zz1 zz2]
ans =
0 1 0 1 0 1
1 2 0 1 0 1
0 1 1 2 0 1
1 2 1 2 0 1
0 1 0 1 1 2
1 2 0 1 1 2
0 1 1 2 1 2
1 2 1 2 1 2

Answer 1

Increase a counter in the innermost loop to keep track of which entry of xx1 etc you should fill.
a = 0:1:2;
b = 0:1:2;
c = 0:1:2;
xx1 = NaN((length(a)-1)*(length(b)-1)*(length(c)-1),1); %// preallocate
xx2 = NaN((length(a)-1)*(length(b)-1)*(length(c)-1),1);
yy1 = NaN((length(a)-1)*(length(b)-1)*(length(c)-1),1);
yy2 = NaN((length(a)-1)*(length(b)-1)*(length(c)-1),1);
zz1 = NaN((length(a)-1)*(length(b)-1)*(length(c)-1),1);
zz2 = NaN((length(a)-1)*(length(b)-1)*(length(c)-1),1);
n = 0; %// initiallize counter
for k=1:length(c)-1;
z1=c(k); z2=c(k+1);
for w=1:length(b)-1;
y1=b(w); y2=b(w+1);
for q=1:length(a)-1;
n = n + 1; %// increase counter;
x1 = a(q);
x2 = a(q+1);
xx1(n) = x1; %// fill values
xx2(n) = x2;
yy1(n) = y1;
yy2(n) = y2;
zz1(n) = z1;
zz2(n) = z2;
end
end
end
Anyway, it can be done without loops, adapting the procedure given in this answer. This has two advantages:
It may be faster if a, b, c are large.
The same code works for any number of vectors, not just 3. Simply define vectors1 and vectors2 accordingly in the code below.
Code without loops:
a = 0:1:2;
b = 0:1:2;
c = 0:1:2;
vectors1 = { a(1:end-1), b(1:end-1), c(1:end-1) };
vectors2 = { a(2:end), b(2:end), c(2:end) };
n = numel(vectors1);
combs1 = cell(1,n);
[combs1{:}] = ndgrid(vectors1{end:-1:1});
combs1 = reshape(cat(n+1, combs1{:}),[],n);
combs2 = cell(1,n);
[combs2{:}] = ndgrid(vectors2{end:-1:1});
combs2 = reshape(cat(n+1, combs2{:}),[],n);
result(:,2:2:2*n) = combs2;
result(:,1:2:2*n) = combs1;