How to trim leading and trailing NaN values from n-dimensional array? - matlab

Question

This is easy in two dimensions, for example:
>> A = NaN(5,4)
>> A(2:4,2:3) = [1 2; 3 4; 5 6]
>> A(2,2) = NaN
>> A(4,3) = NaN
A =
NaN NaN NaN NaN
NaN NaN 2 NaN
NaN 3 4 NaN
NaN 5 NaN NaN
NaN NaN NaN NaN
>> A(~all(isnan(A),2),~all(isnan(A),1))
ans =
NaN 2
3 4
5 NaN
Note that NaN values in rows and columns that are not all NaN are retained.
How to expand this to multiple dimensions? For example if A has three dimensions:
>> A = NaN(5,4,3)
>> A(2:4,2:3,2) = [1 2; 3 4; 5 6]
>> A(2,2,2) = NaN
>> A(4,3,2) = NaN
A(:,:,1) =
NaN NaN NaN NaN
NaN NaN NaN NaN
NaN NaN NaN NaN
NaN NaN NaN NaN
NaN NaN NaN NaN
A(:,:,2) =
NaN NaN NaN NaN
NaN NaN 2 NaN
NaN 3 4 NaN
NaN 5 NaN NaN
NaN NaN NaN NaN
A(:,:,3) =
NaN NaN NaN NaN
NaN NaN NaN NaN
NaN NaN NaN NaN
NaN NaN NaN NaN
NaN NaN NaN NaN
How do I then get
ans =
NaN 2
3 4
5 NaN
I'd like to do this in four dimensions, and with much larger matrixes than the example matrix A here.

Answer 1

My solution to the problem based on the input A as posted by OP:
>> [i,j,k] = ind2sub(size(A),find(~isnan(A)));
>> l = min([i j k]);
>> u = max([i j k]);
>> B=A(l(1):u(1),l(2):u(2),l(3):u(3))
B =
NaN 2
3 4
5 NaN
>> size(B)
ans =
3 2
Since you stated that you want to do this on much larger matrices I'm not sure about the performance of #ronalchn's solution - that is all the all-calls. But I have no idea to what extend that matters - maybe someone can comment...

Answer 2

Try this:
2 dimensions
A(~all(isnan(A),2),~all(isnan(A),1))
3 dimensions
A(~all(all(isnan(A),2),3),...
~all(all(isnan(A),1),3),...
~all(all(isnan(A),1),2))
4 dimensions
A(~all(all(all(isnan(A),2),3),4),...
~all(all(all(isnan(A),1),3),4),...
~all(all(all(isnan(A),1),2),4),...
~all(all(all(isnan(A),1),2),3))
Basically, the rule is for N dimensions:
on all N dimensions you do the isnan() thing.
Then wrap it in with the all() function N-1 times,
and the 2nd argument each of the all() functions for the ith dimension should be numbers 1 to N in any order, but excluding i.
Since Theodros Zelleke wants to see whose method is faster (nice way of saying he thinks his method is so fast), here's a benchmark. Matrix A defined as:
A = NaN*ones(100,400,3,3);
A(2:4,2:3,2,2) = [1 2; 3 4; 5 6];
A(2,2,2,2) = NaN;A(4,3,2,2) = NaN;
A(5:80,4:200,2,2)=ones(76,197);
His test defined as:
tic;
for i=1:100
[i,j,k,z] = ind2sub(size(A),find(~isnan(A)));
l = min([i j k z]);
u = max([i j k z]);
B=A(l(1):u(1),l(2):u(2),l(3):u(3),l(4):u(4));
end
toc
With results:
Elapsed time is 0.533932 seconds.
Elapsed time is 0.519216 seconds.
Elapsed time is 0.575037 seconds.
Elapsed time is 0.525000 seconds.
My test defined as:
tic;
for i=1:100
isnanA=isnan(A);
ai34=all(all(isnanA,3),4);
ai12=all(all(isnanA,1),2);
B=A(~all(ai34,2),~all(ai34,1),~all(ai12,4),~all(ai12,3));
end
toc
With results:
Elapsed time is 0.224869 seconds.
Elapsed time is 0.225132 seconds.
Elapsed time is 0.246762 seconds.
Elapsed time is 0.236989 seconds.