Top n rows in a matrix?

Question

I'm trying to find a better way to do this, ideally in Octave, but I'll take NumPy as a last resort.

Say I have an axb matrix M. If I need row indexes of the maximum value in any column, [x, xi] = max(M) will return these indexes for me as a row vector.

For example, if M:

 1 3 5 2 9 1 7 2 4 

The above will return the row vector [3 2 1] as xi ; The index vector of each row that contains the maximum value for this column. It's good. I want this row vector.

But what if I want the top n such row vectors?

[edited to explain it better]

In the above example, the first such vector will be the above [3, 2, 1] (row indices with the highest values ​​for each given column). The second such vector will be [2 1 3] (row indices with second highest values ​​for each column).

I could do it iteratively, but my actual matrices have many thousands of rows, so that would be quite expensive. I cannot find any obvious matrix utility function to help me with this. Any suggestions?

Answer 1

I assume that you mean that you want to get the largest values ​​from the matrix. In this case, Obtaining indices from the n largest elements in the matrix is almost the same question as this one, except that the OP wanted to get the largest values ​​of the entire matrix, rather than individual maxima. This should provide you with what you need.

 n = 2; % The depth to get M = [ 1, 3, 5; ... 2, 9, 1; ... 7, 2, 4 ]; % The matrix to look at [m, mi] = sort(M, 'descend'); % Sort the to access them x = m(1:n, :) % Get the values xi = mi(1:n, :) % and the indices 

Answer 2

Like this?

 % N is the number of rows you want to include. [x, xi] = max(a(1:N,:)) 

This gives you:

 a = 16 2 3 13 5 11 10 8 9 7 6 12 4 14 15 1 N = 3; [x, xi] = max(a(1:N,:)) x = 16 11 10 13 xi = 1 2 2 1 

Answer 3

Here's how to do it in numpy. Please see numpy.argmax , which returns the maximum value indices along the axis. Note that these indexes are based on 0, so you might want to add / subtract 1 on it to make it 1 based on like in matlab.

Taking the same example @Stewie Griffin :-)

 In [3]: a = np.array([[16,2,3,13], [5,11,10,8], [9,7,6,12], [4,14,15,1]]) In [4]: N = 2 # A 0-based index In [5]: np.argmax(a[N], axis=0) Out[5]: array([0, 1, 1, 0]) 

Here the axis is 0 because you want the maximum indices in each column. Change it to 1 if you want maximum indices in each raw. Also numpy.argmin if you want min.

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Based on your explanation, you want the nth largest indices in each column, which is very easy with numpy.argsort .

 In [11]: A = np.argsort(a, axis=0) # returns indices of smallest to largest values in each column In [12]: A Out[12]: array([[3, 0, 0, 3], [1, 2, 2, 1], [2, 1, 1, 2], [0, 3, 3, 0]]) In [13]: N = 1 # 0-based index In [14]: A[N] # 2nd smallest indices Out[14]: array([1, 2, 2, 1]) In [14]: A[-N-1] # 2nd largest indices Out[14]: array([2, 1, 1, 2])