Is there any better alternative of four nested loops?

Hi,

I have certain matrices e1, e2, e3 & e4 corresponding to u1, u2, u3 & u4 of sizes h1, h2, h3, & h4 respectively. I have to search for

(a row of e1)+(a row of e2)+ (a row of e3) = -(a row of e4)

and report corresponding rows of u1, u2, u3 & u4 with name A, B, C & D. Here is my code:

for i1=1:h1(1,1)

for j1=1:h2(1,1)

for k1=1:h3(1,1)

R=[e1(i1,:)+e2(j1,:)+e3(k1,:), i1, j1, k1];

for z=1:h4(1,1)

if e4(z,:)==-R(1:(length(R)-3))

A=u1(R(1,length(R)-2),:)

B=u2(R(1,length(R)-1),:)

C=u3(R(1,length(R)),:)

D=u4(z,:)

end

end

end

end

end

Is there any short cut? Please help me.

Thank you in advance.

[DGM]

How large are the arrays? What class are they? If they are floating point, to what tolerance must they match?

[Sheet]

u1,u2... have integer entries >0

e1, e2. ... have integer entries +ve, -ve & 0.

Suppose n=19, k1=8. My code for u1 and e1:

s1=1:(n-1);

u1=nchoosek(s1,k1);

q1=size(u1);

e1=zeros(nchoosek((n-1),k1),(n-1)/2);

for i1=1:q1(1,1)

for l=1:(n-1)/2

a1=l*ones(1,k1);

A1=mod(u1(i1,:)+a1, n);

r1=length(setdiff(A1,u1(i1,:)));

e1(i1,l)=n-4*r1;

end

end

[DGM]

Let's simplify for sake of example. Let's say you wanted to check rowofe1 + rowofe2 == rowofe3 (only two terms in the sum). Let's say each array is 10x5.

% integer-valued
h = 10;
w = 5;
e1 = randi([0 9],h,w);
e2 = randi([0 9],h,w);
e3 = randi([0 9],h,w);

% generate sum by implicit array expansion
e1pluse2 = e1 + permute(e2,[3 2 1]);
e1pluse2 = reshape(permute(e1pluse2,[1 3 2]),[],w);

% find matching rows
[matches idx] = ismember(e1pluse2,e3,'rows');

size(e1pluse2)

ans = 1×2

100 5

So the size of the array holding all possible row sums between N 2D arrays is rows^N x cols.

In your case, that would be 43578^3 x 8. You don't have enough memory.

[Sheet]

Thank you.

Can we implement genetic algorithm or any other search method into it? How?

[DGM]

I don't know. I wouldn't be the one to ask about GA stuff.

If the values in the arrays have some sort of order to them, there might be simplifications.

Answer 1

[Constantino Carlos Reyes-Aldasoro]

Hi

In Matlab, if you think in matrices you can avoid many many many loops. For example, if you want to find if a column of a certain matrix (call that a) is equal to a different matrix (call that b), you can do that directly in a single command:

a = [1 2 3 4; 2 3 4 5; 3 4 5 6; 1 2 3 9;0 1 0 1]

a = 5×4

1 2 3 4 2 3 4 5 3 4 5 6 1 2 3 9 0 1 0 1

b = [2 3 4 2 1]';
a==repmat(b,[1 4])

ans = 5×4 logical array
   0   1   0   0
   0   1   0   0
   0   1   0   0
   0   1   0   0
   0   1   0   1

So, I compared matrix b with all the columns of a, to do that I repeated b (repmat) 4 times. You will see that all the elements of the second column are the same as those elements of b and thus all are 1. In the fourth column, there is just one element that is the same. So, what I want is all the elements to be the same, so I will use all, and eventually, what I want is to know which column is the one that matches, so I will use find:

all(a==repmat(b,[1 4]))

ans = 1×4 logical array
   0   1   0   0

find(all(a==repmat(b,[1 4])))

ans = 2

So without any loops, I have found which column of a matches b. Use these ideas and you may still need one loop but in general using matrices and matrix operations is much faster and efficient than using loops.