Calculating distances between coordinates from a matrix

Hello users,

I am a new user of MATLAB and I am working on a final project for a class. This is my forst class using the app and I am at beginner level, so please bear with me ;) (Also, english is a second language, so please excuse any grammar mistakes)

Here is my question: I have a matrix wich represents individuals, along with their coordinates and other variables.

So far, my population matrix looks like this:

Pop = [1 1 2; 2 3 3; 3 5 1; 4 7 6; 5 8 2 ];

Where the first column is the ID of each individual, and columns 2 and 3 represent their location in X and Y respectively.

I am trying to make a distance matrix which would have the distances between each individual. I want a result that would look like this:

    1      2       3
1   0     2.23    7.21
2  2.23    0      2.82
3  7.21   2.82     0
And so on for each individual (5 in that case)

Here is the code I have figured out so far:

Pop = [1 1 2; 2 3 3; 3 5 1; 4 7 6; 5 8 2 ]; %Col1=ID; Col2=positionX; Col3=PositionY

Dist = zeros (length(Pop(:,1))); %create distance matrix filled with zeroes

for j=1:length(Pop(:,1)) %go through each column
    for i=1:length(Pop(:,1)) %go through each row
        for t=1:length(Pop(:,1)); %do this loop the number of times we have people
            Dist(i,j)=sqrt(((Pop(i,j+1)-Pop(i+1,j+1))^2)+(Pop(i,j+2)-Pop(i+1,j+2))^2) %euclidian distance
            t+1 %iteration+1
        end
    end
end

Dist %show resulting matrix

The problem is that when it reaches the end of the lines of Pop, the are no more values so it stops. Also, for some reason, it does not calculate the distance between two same points as 0.

Thanks in advance for any help!

[Junaid Asmat]

I also want to write the code same as it is but I want to calculate distance between coordinates atleast 500. Want should I do?

Answer 1

[Chandra Kurniawan]

Pop = [1 1 2; 
       2 3 3;
       3 5 1; 
       4 7 6; 
       5 8 2]; 
[m n] = size(Pop);
n = m;
Dist = zeros(m, n);
for i = 1 : m 
  for j = 1 : n
      Dist(i, j) = sqrt((Pop(i, 1) - Pop(j, 1)) ^ 2 + ...
                        (Pop(i, 2) - Pop(j, 2)) ^ 2);
  end     
end
Dist

---------------------------------------------------------------- Dist =

         0    2.2361    4.4721    6.7082    8.0623
    2.2361         0    2.2361    4.4721    5.8310
    4.4721    2.2361         0    2.2361    3.6056
    6.7082    4.4721    2.2361         0    1.4142
    8.0623    5.8310    3.6056    1.4142         0

>>

[Florian]

Thanks, I noticed though that you calculate the distance using the first column of Pop as X, but that's just a detail and I figured it out.

Answer 2

[Andrei Bobrov]

use function dist from Neural Network Toolbox

Dist = dist(Pop(:,2:3)')

variant 2 with use function pdist from Statistics Toolbox

Dist = tril(ones(5),-1)
Dist(logical(Dist))= pdist(Pop(:,2:3))
Dist = Dist + Dist.'

variant 3

Dist = sqrt(bsxfun(@minus,Pop(:,2),Pop(:,2)').^2+bsxfun(@minus,Pop(:,3),Pop(:,3)').^2);

variant 4

x = Pop(:,2);
y = Pop(:,3);
n = size(Pop,1);
K = nchoosek(1:n,2);
Dist = accumarray(K,hypot(diff(x(K),1,2),diff(y(K),1,2)),[n n]);
Dist = Dist + Dist.'

Answer 3

[Alex]

1. Your third loop over t is not needed. t isn't even used in your distance calculation.

2. your distance is measured wrong.

Dist(i,j) represents the distance between the ith & jth person.

So, it should be Dist(i,j) = sqrt( (xi - xj) ^2 + (yi - yj)^2);

Your current Dist is Dist(i,j) = sqrt( (xi - x(i+1))^2 + (yi - y(i+1)^2);

A simple test of would be to manually calculate Dist(1,1)

Using your current Dist()

Dist(1,1) = sqrt( (pop(1,2) - pop(2,2))^2 + (pop(1,3) - pop(2,3))^2)

Dist(1,1) = sqrt( ({x of person 1} - {x of person 2})^2 + ({y of person 1} - {y of person 2})^2)

Answer 4

[Florian]

Thank you everyone! I used a combination of Chandra's code, along with dist function suggested by Andrei.

Have a nice day all of you!