Selecting simultaneously not NaN values in multiple matrices - matlab

Question

I have three matlab matrices A, B, and C with the same size:
A = [1:3; 4:6; 7:9];
B = [2 NaN 5; NaN NaN 7; 0 1 NaN];
C = [3 NaN 2; 1 NaN NaN; 1 NaN 5];
%>> A = %>>B = %>>C =
% 1 2 3 % 2 NaN 5 % 3 NaN 2
% 4 5 6 % NaN NaN 7 % 1 NaN NaN
% 7 8 9 % 0 1 NaN % 1 NaN 5
I would like the three matrices to keep only values for which each of the 3 matrices does not have a NaN in that specific position. That is, I would like to obtain the following:
%>> A = %>>B = %>>C =
% 1 NaN 3 % 2 NaN 5 % 3 NaN 2
% NaN NaN NaN % NaN NaN NaN % NaN NaN NaN
% 7 NaN NaN % 0 NaN NaN % 1 NaN NaN
In my attempt, I'm stacking the three matrices along the third dimension of a new matrix ABC with size 3x3x3 and then I'm using a for loop to make sure all the three matrices do not have NaN in that specific position.
ABC(:,:,1)=A; ABC(:,:,2)=B; ABC(:,:,3)=C;
for i=1:size(A,1)
for j=1:size(A,2)
count = squeeze(ABC(i,j,:));
if sum(~isnan(count))<size(ABC,3)
A(i,j)=NaN;
B(i,j)=NaN;
C(i,j)=NaN;
end
end
end
This code works fine. However, as I have more than 30 matrices of bigger size I was wondering whether there is a more elegant solution to this problem.
Thank you for your help.

Answer 1

Lets do fancy indexing!
First, the solution:
indnan=sum(isnan(cat(3,A,B,C)),3)>0;
A(indnan)=NaN;
B(indnan)=NaN;
C(indnan)=NaN;
What this code does is essentially creates a 3D matrix, and computes how many NaN there are in each (i,j,:) arrays. Then, if there are more than 0 (i.e.any of them is NaN) it gets a logical index for it. Finally, we fill up all those with NaN, leaving only the non-NaN alive.

Answer 2

Ander’s answer is good, but for very large matrices it might be expensive to create that 3D matrix.
First of all, I would suggest putting the matrices into a cell array. That makes it a lot easier to programmatically manage many arrays. That is, instead of A, B, etc, work with C{1}, C{2}, etc:
C = {A,B,C};
It takes essentially zero cost to make this change.
Now, to find all elements where one of the matrices is NaN:
M = isnan(C{1});
for ii=2:numel(C)
M = M | isnan(C{ii});
end
A similar loop then sets the corresponding elements to NaN:
for ii=1:numel(C)
C{ii}(M) = NaN,
end
This latter loop can be replaced by a call to cellfun, but I like explicit loops.
EDIT: Here are some timings. This is yet another example of loops being faster in modern MATLAB than the equivalent vectorized code. Back in the old days, the loop code would have been 100x slower.
This is the test code:
function so(sz) % input argument is the size of the arrays
C3 = cell(1,3);
for ii=1:numel(C3)
C3{ii} = create(sz,0.05);
end
C20 = cell(1,20);
for ii=1:numel(C20)
C20{ii} = create(sz,0.01);
end
if(~isequal(method1(C3),method2(C3))), error('not equal!'), end
if(~isequal(method1(C20),method2(C20))), error('not equal!'), end
fprintf('method 1, 3 arrays: %f s\n',timeit(#()method1(C3)))
fprintf('method 2, 3 arrays: %f s\n',timeit(#()method2(C3)))
fprintf('method 1, 20 arrays: %f s\n',timeit(#()method1(C20)))
fprintf('method 2, 20 arrays: %f s\n',timeit(#()method2(C20)))
% method 1 is the vectorized code from Ander:
function mask = method1(C)
mask = sum(isnan(cat(3,C{:})),3)>0;
% method 2 is the loop code from this answer:
function mask = method2(C)
mask = isnan(C{1});
for ii=2:numel(C)
mask = mask | isnan(C{ii});
end
function mat = create(sz,p)
mat = rand(sz);
mat(mat<p) = nan;
These are the results on my machine (with R2017a):
>> so(500)
method 1, 3 arrays: 0.003215 s
method 2, 3 arrays: 0.000386 s
method 1, 20 arrays: 0.016503 s
method 2, 20 arrays: 0.001257 s
The loop is 10x faster! For small arrays I see much less of a difference, but the loop code is still several times faster, even for 5x5 arrays.