Question

Suppose that f is a function of one parameter whose output is an n-dimensional (m₁ × m₂… × m_n) array, and that B is a vector of length k whose elements are all valid arguments for f.

I am looking for a convenient, and more importantly, “shape-agnostic”, MATLAB expression (or recipe) for producing the (n+1)-dimensional (m₁ × m₂ ×…× m_n × k) array obtained by “stacking” the k n-dimensional arrays f(b), where the parameter b ranges over B.

To do this in numpy, I would use an expression like this one:

C = concatenate([f(b)[..., None] for b in B], -1)

In case it’s of any use, I’ll unpack this numpy expression below (see APPENDIX), but the feature of it that I want to emphasize now is that it is entirely agnostic about the shapes/sizes of f(b) and B. For the types of applications I have in mind, the ability to write such “shape-agnostic” code is of utmost importance. (I stress this point because much MATLAB code I come across for doing this sort of manipulation is decidedly not “shape-agnostic”, and I don’t know how to make it so.)

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APPENDIX

In general, if A is a numpy array, then the expression A[..., None] can be thought as “reshaping” A so that it gets one extra, trivial, dimension. Thus, if f(b) is an n-dimensional (m₁ × m₂… × m_n) array, then, f(b)[..., None] is the corresponding (n+1)-dimensional (m₁ × m₂ ×…× m_n × 1) array. (The reason for adding this trivial dimension will become clear below.)

With this clarification out of the way, the meaning of the first argument to concatenate, namely:

[f(b)[..., None] for b in B]

is not too hard to decipher. It is a standard Python “list comprehension”, and it evaluates to the sequence of the k (n+1)-dimensional (m₁ × m₂ ×…× m_n × 1) arrays f(b)[..., None], as the parameter b ranges over the vector B.

The second argument to concatenate is the “axis” along which the concatenation is to be performed, expressed as the index of the corresponding dimension of the arrays to be concatenated. In this context, the index -1 plays the same role as the end keyword does in MATLAB. Therefore, the expression

concatenate([f(b)[..., None] for b in B], -1)

says “concatenate the arrays f(b)[..., None] along their last dimension”. It is in order to provide this “last dimension” to concatenate over that it becomes necessary to reshape the f(b) arrays (with, e.g., f(b)[..., None]).

Answer 1

One way of doing that is:

 % input:
 f=@(x) x*ones(2,2)
 b=1:3;
 %%%%
 X=arrayfun(f,b,'UniformOutput',0);
 X=cat(ndims(X{1})+1,X{:});

Maybe there are more elegant solutions?