Vectorizable FIND function with if statement MATLAB

Question

I have a matrix u, I want to go across all rows and all columns and do the following. If the element is non zero, I return the value of the row index. If the element is zero, find the row index the next non zero element after this element. I can do this easily using two for loops with a find function. But I need to do this many many times (not because of the size of the matrix but because this is called many times). How can I do it faster?

here is the for loop code:

     for w=scenario_size:-1:1
            for t=1:time_size
                l = u(t,w) ;
                if l~=0
                    tprime = t ;
                else
                    tprime = t+ find(u(t:end,w),1,'first') -1 ;
                end
                i(t,w)       = tprime ;
                boo(t,w)     = number(tprime,w)/u(tprime,w) ;
            end
end

Example if one column is [0,0,5,1,0,3], the i is [3,3,3,4,6,6]. The last element of any column of u is always non-zero (I forced this by artificially adding a row of ones at the end).

Then boo is the corresponding entry to tprime for some matrix number divided by the corresponding u (which is non zero by construction).

gnovice · Accepted Answer

You can solve this using find, cummin, and some logical indexing. Starting with this example case:

>> u = randi([0 1], 10);
>> u(end, :) = 1

u =

     0     0     0     0     1     0     1     0     1     1
     1     0     1     1     1     0     0     0     0     1
     0     0     0     0     0     1     0     1     1     0
     1     1     1     0     1     1     0     0     0     0
     0     0     1     0     0     0     0     0     1     0
     1     1     1     0     0     0     0     0     0     0
     0     1     0     1     0     0     1     1     0     1
     1     1     0     1     0     1     1     1     1     1
     1     0     0     1     0     0     1     1     1     1
     1     1     1     1     1     1     1     1     1     1

The following will do what you want:

i = nan(size(u));  % Start with all nan values
[r, ~] = find(u);  % Get row indices of non-zero values
i(u ~= 0) = r;     % Place row indices in locations of non-zero values
i = cummin(i, 1, 'reverse');  % Column-wise cumulative minimum, starting from bottom

And the result:

i =

     2     4     2     2     1     3     1     3     1     1
     2     4     2     2     2     3     7     3     3     2
     4     4     4     7     4     3     7     3     3     7
     4     4     4     7     4     4     7     7     5     7
     6     6     5     7    10     8     7     7     5     7
     6     6     6     7    10     8     7     7     8     7
     8     7    10     7    10     8     7     7     8     7
     8     8    10     8    10     8     8     8     8     8
     9    10    10     9    10    10     9     9     9     9
    10    10    10    10    10    10    10    10    10    10

And you can then calculate your matrix boo by converting i to a linear index:

index = i+time_size.*repmat(0:(scenario_size-1), time_size, 1);  % Create linear index
boo = number(index)./u(index);

Alternatively, you can compute i as a linear index from the start:

i = nan(size(u));  % Start with all nan values
index = find(u);   % Get linear indices of non-zero values
i(index) = index;  % Place linear indices in locations of non-zero values
i = cummin(i, 1, 'reverse');  % Column-wise cumulative minimum, starting from bottom
boo = number(i)./u(i);

Vectorizable FIND function with if statement MATLAB

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