I have a 3d matrix (n-by-m-by-t) in MATLAB representing n-by-m measurements in a grid over a period of time. I would like to have a 2d matrix, where the spatial information is gone and only n*m measurements over time t are left (ie: n*m-by-t)
How can I do this?
You need the command reshape:
Say your initial matrix is (just for me to get some data):
a=rand(4,6,8); Then, if the last two coordinates are spatial (time is 4, m is 6, n is 8) you use:
a=reshape(a,[4 48]); and you end up with a 4x48 array.
If the first two are spatial and the last is time (m is 4, n is 6, time is 8) you use:
a=reshape(a,[24 8]); and you end up with a 24x8 array.
This is a fast, O(1) operation (it just adjusts it header of what the shape of the data is). There are other ways of doing it, e.g. a=a(:,:) to condense the last two dimensions, but reshape is faster.
Reshape is of course the standard solution to reshaping an array. (What else would they call it?) There are still a few tricks to uncover.
First of all, the simplest way to turn an array of size [n,m,p] into an array of size [n*m,p]?
B = reshape(A,n*m,p); But better is this:
B = reshape(A,[],p); If you leave one of the arguments to reshape empty, then reshape computes the size for you! Be careful, if you try this and the size of A does not conform, then you will get an error. Thus:
reshape(magic(3),[],2) ??? Error using ==> reshape Product of known dimensions, 2, not divisible into total number of elements, 9. Logically, we cannot create an array of with two columns from something that has 9 elements in it. I did put a function called wreshape on the MATLAB Central exchange that would pad as necessary to do this operation with no error generated.
Of course, you can always use tricks like
B = A(:); to create a vector directly from a matrix. This is equivalent to the form
B=reshape(A,[],1); A better solution to this problem is to use nshape.m available from Rasmus Bro's N-Way Toolbox. That will allow you to reshape along a given mode, which is a little more tricky with the reshape command.
The toolbox is available at the following link:
https://www.mathworks.com/matlabcentral/fileexchange/1088-the-n-way-toolbox
There are some other excellent tools there to help with array manipulation as well.