# Min of each column of a sparse matrix?

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Elvira123 on 13 Feb 2018
Edited: Jan on 28 Jun 2022
How can I compute the min of each column of a sparse matrix excluding empty cells? I'm trying with: MIN = min(MATRIX, [], 1);
But the results is a column vector of zeros.
Thank you Elvira

Paras Gupta on 28 Jun 2022
Hi,
The ‘min’ function generally works for full matrices (or dense matrices) only. In the case of sparse matrices, the ‘min’ function would consider the missing zero elements thereby giving the result as 0.
The following code illustrates how a vector with the minimum of each column can be computed in the case of sparse matrices.
% MATRIX is the given sparse matrix
% First, we use the find the row and column indices for non-zero elements
[ii,jj] = find(MATRIX);
% MIN is the vector with min of each column
% We use the accumarray function to apply the @min function on the selected
% index groups jj
MIN = accumarray(jj,nonzeros(MATRIX),[],@min)
You can refer to the documentation on sparse matrices, find, nonzeros, and accumarray for more information to understand how the above code works. A different method as proposed in the following answer can also be referred to compute the desired result. https://in.mathworks.com/matlabcentral/answers/35309-max-min-of-sparse-matrices
Hope this helps!

Matt J on 28 Jun 2022
Edited: Matt J on 28 Jun 2022
result = -log( max( spfun(@(x)exp(-x), yourMatrix) ,[],1) );

Jan on 28 Jun 2022
Edited: Jan on 28 Jun 2022
For large inputs a loop is faster than accumarray:
X = sprand(2000, 20000, 0.2);
tic;
for k = 1:10
[ii,jj] = find(X);
MIN = accumarray(jj, nonzeros(X), [], @min);
end
toc
Elapsed time is 1.261082 seconds.
tic;
for k = 1:10
MIN2 = myMin(X);
end
toc
Elapsed time is 1.008365 seconds.
isequal(MIN, MIN2.')
ans = logical
1
function M = myMin(X);
[i1, i2, v] = find(X);
M = Inf(1, size(X, 2));
for k = 1:numel(v)
if M(i2(k)) > v(k)
M(i2(k)) = v(k);
end
end
end