How to find a minimum in this matrix ?

Hi all,

I need your help doday because I can not get rid of my problem :

I have a 6D matrix, 'C', filled with costs values. The six dimensions are : speed, acceleration, and 4 'control variables' : U1,U2,U3,U4.

I want to find the position (the value of the control variables) of the minimum cost for each pair of speed and acceleration. The result could be a matrix, attached. If several equal minimums are found, we could keep only one.

The main point is that I run Matlab 2016b, which does not support "vector directions" minimum. The second point is that my 6D 'C' cost matrix is HUUUUUGE and is about 1/100 of my total RAM capacity !

Thank you a lot for your help,

Simon :)

Answer 1

[Stephen23]

I have no idea how this will compare to using a few loops:

A = randi(999,8,7,6,5,4,3); % fake data in 8x7x6x5x4x3 array.
S = size(A);
B = reshape(A,S(1),S(2),[]);
[M,X] = min(B,[],3); % M = matrix of the minimum values.
[R,C] = ndgrid(1:S(1),1:S(2));
[~,~,U1,U2,U3,U4] = ind2sub(S,sub2ind(size(B),R,C,X))

which gives:

U1 =
   3   2   6   4   5   4   3
   1   4   2   5   4   5   1
   3   5   6   2   2   4   1
   4   2   1   4   6   4   3
   2   1   4   5   1   4   6
   5   1   6   6   5   2   1
   6   4   5   5   3   6   1
   5   3   2   6   1   3   5
U2 =
   1   3   2   5   5   3   1
   3   2   1   1   5   4   1
   5   5   3   1   5   2   4
   5   2   1   4   3   5   2
   1   1   5   4   5   5   1
   5   1   2   1   3   3   1
   3   5   5   1   5   4   5
   5   1   2   4   4   3   2
U3 =
   4   2   3   4   3   4   4
   2   3   4   4   1   4   2
   4   3   2   4   1   3   1
   4   2   3   3   2   4   2
   2   3   2   2   2   4   1
   4   2   2   1   3   2   2
   3   1   3   3   2   3   1
   2   1   3   3   2   2   2
U4 =
   3   2   3   2   3   2   2
   1   1   1   2   1   1   3
   3   2   1   3   1   1   3
   1   2   3   3   3   3   3
   1   1   2   3   1   3   2
   1   1   3   1   3   3   2
   3   2   3   3   2   2   1
   2   1   1   1   2   1   2

And checking one of them (here I picked row=1 col=2 as an example):

>> M % minimum values for each row/column of A
M =
  1    9    1    4    1    1    9
  3    4    7    1    3    1   18
  1    3    1    5   10    2    3
  2    4    2    3    2    7    2
  2    1    7    8    4    1    1
  4    2    2    3    2   10    2
  1    5    1    7    2    6    2
  3    5    1    1    2    1    2
>> A(1,2,2,3,2,2) % A(row,col,U1(row,col),U2(row,col),...)
ans =  9
>> Z = A(1,2,:,:,:,:); % A(row,col,:,:,:,:)
>> min(Z(:))
ans =  9

[Ameye Simon]

WOW ! Amazing !! Very elegant way of doing. Thank you very much Stephen, this is exactly what I needed