将数组中值的特定索引与数组MatLab的大小相关的方程式

Question

I'm trying to come up with an equation that relates the index of a value within a 3D array, to the index of the same array but reshaped into a column vector.

Consider the following.

A = randi([1,10],3,2,2);
A2 = reshape(A,3*2*2,1);

A and A2 have the same number of elements, but the arrangement of the elements is different for each array. If I lay out a possible example for A and A2 here it is clear geometrically how each index lines up.

A(:,:,1) = [9 10; 10 7;  2  1]
A(:,:,2) = [3 10;  6 2; 10 10]

A2 = [9; 10; 2; 10; 7; 1; 3; 6; 10; 10; 2; 10]

Let's say n=1:1:3*2*2 , this is an array that is the same length as A2 and numbers each of the elements. The value of A(2,2,2)=2 and has indices [i,j,k]=[2,2,2] . I would like to have an equation relating i, j, k, and n.

I've looked into the built-in functions ind2sub and sub2ind but it seems that I inadvertently shaped my i, j, and k coordinates (which correspond with real x, y, and z points) differently than how MatLab does. This makes it difficult for me to change everything now, and is why I need an equation.

Answer 1

The conversion between 3D index and linear (1D) index is given by:

n=i+(j-1)*M + (k-1)*M*N

The reverse can be obtained recursively as:

k = floor((n-1)/(M*N)) +1 
n = n - (k-1)*M*N
j = floor((n-1)/M) + 1
i = n - (j-1)*M 

I haven't tested it, but I think it will give you what you are expeccting.