Extract sub array from d-dimensional array given indices for each dimension

Suppose I have a d-dimensional array A which is size d_1 by d_2 by....by d_d and for each dimension i have a index vector vd_i such that vd_i(1)>=1 and vd_i(end)<= size(A, i). How do I extract the sub array A(vd_1,vd_2,...,vd_3) when d is arbitrary?

Edit: as mentioned by the wonderful Matt J, I meant that 1<= vd_i(j)<= size(A,i) for all i,j.

[Matt J]

and for each dimension i have a index vector vd_i such that vd_i(1)>=1 and vd_i(end)<= size(A, i).

I think what you really mean is 1<= vd_i(j)<= size(A,i) for all i,j. If that's not what you meant then, well, you should check that it's true, because it's a requirement in any subscript indexing operation.

[Michael Van de Graaff]

yes, that's true my bad

Answer 1

[Matt J]

If you have your vd_i in a cell array V={vd_1,vd_2,...,vd_d}, you can do

A(V{:})

[Michael Van de Graaff]

Thank You! knew i was missing something trivial.

Answer 2

[Voss]

% random 4-D (4x8x5x10) array A:
d_siz = [4 8 5 10];
A = randn(d_siz);
size(A)

ans = 1×4

4 8 5 10

% make the index vectors for each dimension
% into a cell array:
vd = {[2 3] [1 3 5 7] [2 3 4] 4:8};

% index into A in each dimension:
A_subs = A(vd{:});

size(A_subs)

ans = 1×4

2 4 3 5

[Michael Van de Graaff]

thank you! the A(vd{:}) was what i needed.

[Voss]

You're welcome!

Answer 3

[dpb]

Did you try the obvious???

Smallish example, but works in general...

>> d=3;A=reshape(1:4^d,4,4,[])              % make up a sample array to play with that can read
>> A
A(:,:,1) =
     1     5     9    13
     2     6    10    14
     3     7    11    15
     4     8    12    16
A(:,:,2) =
    17    21    25    29
    18    22    26    30
    19    23    27    31
    20    24    28    32
A(:,:,3) =
    33    37    41    45
    34    38    42    46
    35    39    43    47
    36    40    44    48
A(:,:,4) =
    49    53    57    61
    50    54    58    62
    51    55    59    63
    52    56    60    64
>> 
>> v1=2:3;v2=v1;v3=v1;          % pick middle two of each dimension
>> A(v1,v2,v3)
ans(:,:,1) =
    22    26
    23    27
ans(:,:,2) =
    38    42
    39    43
>>

is, by inspection, the array elements of 2nd, 3rd plane and the central four elements of each, respectively.