How to return a 2D matrix containing the heighest non-NaN values from a 3D matrix

Hi,

I have a large 3D matrix of data where in the 3rd dimension where some values are NaN and some values are non-NaN. Call it M with size m*n*p.

A 2D matrix P (size m*n) contains the number of non-NaN values held within the pages returned in the array M(m,n).

Also, take one value of P, t=P(m,n); then each of M(m,n,1:t) contains a non-NaN value, and each of M(m,n,t+1:end) contains a NaN value. That is, all the non-NaN values in M are stacked from the p=1 to p=nth pages.

An example of the data is created with this code:

P = ceil(rand(4,4) * 4);
for x = 1:4
for y = 1:4
for z = 1:4
if P(x,y) >= z
M(x,y,z) = ceil(rand*10);
else
M(x,y,z) = NaN;
end
end
end
end

For example:

M(:,:,1) =

       9    10     4     4
      10     4    10     3
       3     3    10     9
       3     8     5     9

M(:,:,2) =

       9   NaN   NaN     3
       6   NaN     9     3
       6     3     7     4
       8     4     9     8

M(:,:,3) =

       4   NaN   NaN     9
       5   NaN   NaN   NaN
      10   NaN    10     4
       8   NaN     4     4

M(:,:,4) =

     NaN   NaN   NaN     9
       7   NaN   NaN   NaN
       1   NaN     2   NaN
       2   NaN    10   NaN

I am looking for an efficient way to return the 'pth-most' values of M, which is essentially the last non-NaN value of each M(m,n) array. For the example dataset this would be:

result =

       4    10     4     9
       7     4     9     3
       1     3     2     4
       2     4    10     4

Does anyone have any clever suggestions?

Thank you Steven

Answer 1

[Andrei Bobrov]

s = size(M);
[i1,i2] = ndgrid(1:s(1),1:s(2));
result = M(sub2ind(s,i1,i2,s(3) - sum(isnan(M),3)));

ADD

s = size(M);
[i1,i2] = ndgrid(1:s(1),1:s(2));
i3 = s(3) - sum(isnan(M),3);
i3(i3==0)=1;
result = M(sub2ind(s,i1,i2,i3));

[Steven]

Great thank you!

[Steven]

I wonder if you can help me further; how would you handle the situation where some of the arrays returned by M(m,n) are entirely NaN's?

In this instance, sum(isnan(M),3) == s(3), and the sub2ind function call will be badly formed?

[Andrei Bobrov]

Please see ADD part.