CODEWITHSUNDEEP
matlabmatrix
karfai
karfai

Reputation: 906

Sum of element in Vector to get the correspond Matrix

Currently, I need to develop an algorithm to solve the Optimization Problem

I encounter a problem about my way to calculate the distance between facility is not efficient enough.

Now, I given the matrices, which is the length of facilities.

A = [0.0300     % The left most facility
    0.0400      % 2nd
    0.0500      % 3rd
    0.0200      % 4th
    0.0600];    % The right most facility

Say, I want to find the distance between the center of two facilities.(Assume no gap between) For example:

Distance between center of 2nd and 5th facility = 0.0400/2 + 0.0500 + 0.0200 + 0.0600/2 = 0.1200

From that, we can form a matrix B which is the output I want (can be symmetrical matrix also)

B = [0      0.0350  0.0800  0.1150  0.1550
    0       0       0.0450  0.0800  0.1200
    0       0       0       0.0350  0.0750
    0       0       0       0       0.0400
    0       0       0       0       0];

I was try to avoid nested for loop. This is the best that I can think off in order the get matrix B.

n = numel(A);
x = triu(repmat(A,1,n));
B = zeros(5);
x = x - diag(diag(x)/2);
for i=1:4
    x(i,:) = x(i,:)/2;
    y = x;
    B(i,:) = sum(y);
    x(i,:) = 0;
end
B = B - diag(diag(B))

Of course, the matrix size very large in reality and my way is not efficient enough. Is there any trick to get the matrix B instead of using for loop?

Upvotes: 0

Views: 57

Answers (1)

MrAzzaman
MrAzzaman

Reputation: 4768

You could think about the problem in a different way - essentially what you're calculating is the average of the distance between the start points of each facility and the end points of each facility. i.e.

           <------start dist------>
[    A    ][  B  ][       C       ][         D         ]
                  <--------------end dist-------------->

You can calculate the start and end points of each facility using:

end_pts = cumsum(A);
start_pts = end_pts - A;

You can then calculate the start and end distances using:

start_dist = abs(bsxfun(@minus,start_pts,start_pts'));
end_dist = abs(bsxfun(@minus,end_pts,end_pts'));

You then take the average of these matrices to find the distance between the centres:

B = (start_dist + end_dist)./2;

Upvotes: 1

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