Accessing the nth dimension in a variable sized multidimensional array

I have a large array of values, and before the execution I don't know how many dimension I need.

How can I extract a single column from this? Or even a specific value?

I tried things like writing a vector of the indices, but that didn't return a single value.

Example: I have a matrix A, how do I get A(1,1,...,1,:) when I don't know how many dimensions A has?

And what if I want to set a single dimension to a specific value like A(1,:,:,...,:)

Alternatively: is there another good way of storing high-dimensional scalar fields? I tried a list of index vectors like in a sparse matrix, but finding a specific value becomes very inefficient that way right?

Answer 1

[Stephen23]

"...how do I get A(1,1,...,1,:) when I don't know how many dimensions A has?"

You use a comma-separated list, which you can easily generate from a cell array:

C = {1,1,1,...1,,':'};
A(C{:})

https://www.mathworks.com/help/matlab/matlab_prog/comma-separated-lists.html

https://www.mathworks.com/matlabcentral/answers/320713-how-to-operate-on-comma-separated-lists

You can create the cell array using repmat or num2cell or similar. The function ndims will also be useful here.

"...what if I want to set a single dimension to a specific value like A(1,:,:,...,:)"

Use a comma-separated list. Lets try a more practical example, where we define the size of C automatically:

C = repmat({':'},1,ndims(A));
C{1} = 1; % C{dim} = index
val = A(C{:})

[Jan Bode]

And as a follow up: is there a way to use things like 'n:end' somehow? To me those give out Index out of Bounds exceptions even when I explicitely use 4:5 in an array with size 6

[Stephen23]

"...is there a way to use things like 'n:end' somehow?"

I guess you mean for some arbitrary dimension. As far as I know, there is no easy way to use end with this comma-separated list syntax. You would have to get the size of that dimension yourself and create a numeric vector within that size, and then use that vector in another comma-separated list to obtain the subset that you want.

It is worth noting that using the end method in indexing already does something similar, accessing the array first to get the size and then with the indexing to get the required subarray.

[Walter Roberson]

subsref twice? That does not sound right. end calls the end method; https://www.mathworks.com/help/matlab/matlab_oop/object-end-indexing.html

[Jan Bode]

Well okay, guess I will do it manually then

Answer 2

[Walter Roberson]

nd = ndims(YourArray);

dim_wanted = randi(nd);
proto = repmat({1}, 1, nd);
proto{dim_wanted} = ':';
just_that_dim = YourArray(proto{:});

dim_one = randi(nd);
proto = repmat({':'}, 1, nd);
proto{dim_one} = 1;
all_except_that_dim = YourArray(proto{:});

proto = arrayfun(@randi, size(YourArray), 'uniform', 0);
dim_wanted = randi(nd);
proto{dim_wanted} = ':';
random_vector_in_N_space = YourArray(proto{:});

[Walter Roberson]

My Answer showed how to index by any arbitrary dimension: repmat() the most common index, and replace the specific choices, then use cell expansion as the index expression. You could make a helper function, such as

IndexDim = @(A,n,index) A(struct('t',[repmat({':'},1,n-1),index,repmat({':'},1,ndims(A)-2+(n==1))]).t)

Note: doing this on one line requires a fairly new version of MATLAB; I do not recall at the moment if it needs R2020a or R2019b, but R2019a would be expected to fail for this.