Finding the indices of all minimum elements in a matrix

In Matlab, by the function min（）， one can get only one single minimum element of a matrix, even if there can be several equal minimum elements. How to get the indices of all minimum elements in a matrix?

Answer 1

[Image Analyst]

You can do it in one line of code. You just first need to decide if you want to locate occurrences of the global min, or if you want to find local mins (using imregionalmin), AND if you want a vector of logical indexes or a vector of actual indexes. Since you didn't say, I'm giving all 4 possibilities:

% Create sample data:
vec = [1,1,2,2,1,2,1,3,0,-1,4,0,3,-1,5];
% Find local mins as a logical index.
localMinIndexes = imregionalmin(vec)
% Find global mins as a logical index.
globalMin = min(vec);
globaMinIndexes = vec == globalMin

% If you want/need actual indexes, use find:
% Find local mins as actual indexes.
localMinIndexes = find(imregionalmin(vec))
% Find global mins as actual indexes.
globaMinIndexes = find(vec == min(vec))

[Hari]

Thank you

[Nicolás Sánchez]

Hey! What if the global mimimus along the vector have not the same value?

[Image Analyst]

The same value as what? Please give an example of your input and desired output.

• You can have only one global miminum though that value can occur in 1 or more places.
• You can have several local minima, and they could possibly all have different values, and, of course, they are located in different places.

[Rekha Dhanekula]

I have two matrices P=[5 0 3 0;0 4 1 2] and N=[0.01 0.02 0.025 0.015;0.027 0.03 0.029 0.035]. (r,c) = find(P==min(min(P))) gives indices corresponding to all the minimum values in matrix P. Now I want to access elements of N corresponding to that indices (r,c) Note: i tried N(r,c) which gave a 3*3 matrix which is wrong. I just want N21,N12,N14 for this problem

[Image Analyst]

@Rekha Dhanekula, try this:

P = [5 0 3 0;0 4 1 2]
N = [0.01 0.02 0.025 0.015;
	0.027 0.03 0.029 0.035]
[r, c] = find( P == min(P(:)))
for k = 1 : length(r)
	extractedN(k) = N(r(k), c(k));
end

[james sinos]

can you give an example of 2 d matrix.

thkx

[Image Analyst]

@james sinos that was an example for 2-D matrices. Both P and N are 2-D. Of course extractedN is 1-D. Not sure what you're looking for.

Here's another 2-D example where I also add the creation of a masked 2-D array where the location of the mins in m2 are also the same value in the same locations for m3.

% Demo by Image Analyst
clc;    % Clear the command window.
close all;  % Close all figures (except those of imtool.)
clear;  % Erase all existing variables. Or clearvars if you want.
workspace;  % Make sure the workspace panel is showing.
format short g;
format compact;
fontSize = 20;

% Create some arbitrary matrix.
m1 = 1000 * rand(8, 8)
% Create sample data with the min at multiple locations:
m2 = randi(9, 8, 8)
% Determine the min value:
minValue = min(m2(:))
% Find rows and columns where the min occurs:
[r, c] = find(m2 == minValue)
% Extract those locations of m1 into a new matrix
for k = 1 : length(r)
	extractedN(k) = m1(r(k), c(k));
end
% Show 1-D extracted numbers in command window:
extractedN

% Make a 2-D matrix where everything is -99999 (or whatever you want)
% except for where there's a min in m2.
m3 = -99999 * ones(8,8);
m3(m2 == minValue) = minValue