Find the minimum of 3 2d arrays at each position.

Hi, I have 3 2d arrays with same dimensions(or a 3d array with 3 layers), and I want to find the the minimum position of each point. e.g. function could tell which array (or layer has the minimum value of each point).

I know how to do that with for loop, but that cost a lot of time dealing with large scale arrays. So is there a more efficient way to do that?

   D=rand(1000,1000,3);
  [row,col,~]=size(D);  
  for i=1:row
          for j=1:col
              close=min(D(i,j,:));    %minimum value
              if size(find(D(i,j,:)==close))==1    %if only one minimum
                  position(i,j)=(find(D(i,j,:)==close));
              else
                  n=find(D(i,j,:)==close);    %if 2 or more
                  position(i,j)=n(1);
              end
          end
  end

Answer 1

[Ji Hoon Jeong]

Hi Li zifan

Your algorithm is fine, but several parts can be fixed to make it much faster.

1. Preallocation is critical In your code, the size of the variable "position" is not fixed. Please add this line before the for loops

 position = zeros(1000,1000);

2. Less the number of functions, Faster the script if statement and 3 find function will slower your code

use

 find(D(i,j,:)==close

code only once in your for loop

3. index of min value can be found by min function min function can spit out two output, one is min value itself, and the other one is location(=index) of the min value.

Altogether, faster version of your code

 D=rand(1000,1000,3);
 position = zeros(1000,1000);
 [row,col,~]=size(D);  
 for i=1:row
       for j=1:col
           [~,index_of_min_value] = min(D(i,j,:));
           position(i,j) = index_of_min_value;
       end
 end

[Li zifan]

That helps me a lot! Thank you so much for the advice and the improved function!

But I don't understand whats gonna happen if there are 2 or more positions contain the minimum value, what index will be shown?

[Ji Hoon Jeong]

Thinking about "more than 2 minimum value" is a really smart move. In my example, function "min" is used to find the index of the minimum value. When there are more than 2 minimum values exist, the function returns the smallest index of the minimum value.

"If the minimum value occurs more than once, then min returns the index corresponding to the first occurrence."

-from matlab's min function document

 values = [3,1,5,2,1,5];
 [v,i] = min(values);

 v = 1
 i = 2 ( 2 and 5 has the same minimum value 1 )

Usually, this does not make any problem with your algorithm, but sometimes this can bias the output to the smaller index value. If this characteristic bothers you, then you should write custom min function.