Indexing for 4-D Arrays

Hello,

I am currently having trouble pulling data from a 4-D array through indexing.

I start with a 3-D array which represents the 3D coordinates of my system. At each point in the 3D matrix I assign a random 3D vector, making it 4-D. I would like to pull the corresponding vector from many different points within the array. The 3D coordinates of the points I want to pull are stored in a 2D array with the columns being the (x,y,z) points.

%% Build array
dim = 40;
totalLocations = dim^3;
randomVec = rand(totalLocations,3);
volume = reshape(randomVec,dim,dim,dim,3);

%% Request data from 4d array
vec = [1 1 1];
ind = [1:3];

vector1 = (volume(vec(:,1),vec(:,2),vec(:,3),ind))

Output:

vector1(:,:,1,1) =

    0.4150


vector1(:,:,1,2) =

    0.0820


vector1(:,:,1,3) =

    0.0865

The above is an example of how I pull the corresponding vector from the position (1,1,1). Since this is only one point I can squeeze out the extra dimensions and end up with the desired vector. My issue is when I try and expand this to multiple (x,y,z) positions by adding additional rows to vec. For example:

    %% Build array
dim = 40;
totalLocations = dim^3;
randomVec = rand(totalLocations,3);
volume = reshape(randomVec,dim,dim,dim,3);

%% Request data from 4d array
vec = [1 1 1;1 1 2];
ind = [1:3];
clc
vector1 = volume(vec(:,1),vec(:,2),vec(:,3),ind)

My output is:

vector1(:,:,1,1) =

    0.4150    0.4150
    0.4150    0.4150


vector1(:,:,2,1) =

    0.5320    0.5320
    0.5320    0.5320


vector1(:,:,1,2) =

    0.0820    0.0820
    0.0820    0.0820


vector1(:,:,2,2) =

    0.4980    0.4980
    0.4980    0.4980


vector1(:,:,1,3) =

    0.0865    0.0865
    0.0865    0.0865


vector1(:,:,2,3) =

    0.7612    0.7612
    0.7612    0.7612

Which appears to give me the correct numbers but they all appear (number of rows in vec)^2 times. Can anyone help me with how to pull the vectors from many points in the 3-D space through use of a list of (x,y,z) coordinates. I need to do this without loops due to the size of my arrays.

Please let me know if more clarification is needed.

Thanks.

Answer 1

[Stephen23]

You could use sub2ind:

%% Build array
dim = 40;
volume = rand(dim,dim,dim,3); % simpler!

%% Request data from 4d array
vec = [1,1,1;1,1,2];
ind = 1:3;
idv = zeros(1,numel(ind));
id4 = repmat(ind,size(vec,1),1);
idx = sub2ind(size(volume),vec(:,1+idv),vec(:,2+idv),vec(:,3+idv),id4);
vector1 = volume(idx)

vector1 = 2×3

0.0996 0.0540 0.8415 0.3888 0.0559 0.9637

Compare:

volume(1,1,1,ind)

ans = 
ans(:,:,1,1) =

    0.0996


ans(:,:,1,2) =

    0.0540


ans(:,:,1,3) =

    0.8415

volume(1,1,2,ind)

ans = 
ans(:,:,1,1) =

    0.3888


ans(:,:,1,2) =

    0.0559


ans(:,:,1,3) =

    0.9637

[J12345]

Thanks, this worked perfectly!