3D Matrix Flatten algorithm
Let's first start of with a 2D matrix Q [n x m] (where n is the number of rows and m is the number of columns). to be flattened we'll need a 1D matrix L of length n * m.
We know that: Q[0, 0] = L[0] and that Q[0, 1] = L[1] and that Q[0, m - 1] = L[m - 1] and that Q[1, 0] = L[m] and that Q[1, 1] = L[m + 1].
From the above the we can conclude that every time we move from a row to another row, we jump m (the number of elements in a single row) elements.
So, the equation for 2D matrix flattening would be (assuming indexing using i, j for the 2D matrix and y for the 1D matrix): y = j + i * m.
This can be generalized for 3D matrix flattening where the 3D matrix Q [n x m x p] is to be flattened to L of length q = n * m * p.
We know that Q[1, 1, 0] = L[m + 1] and that Q[n - 1, m - 1, 0] = L[m - 1 + (n - 1) * m] = L[nm - 1], So Q[0, 0, 1] = L[nm] and Q[0, 1, 1] = L[nm + 1].
From the above, it can be concluded that every time we jump 1 plane (from k = 0 to k = 1 for example), we jump nm elements
So, the equation for 3D matrix flattening would be (assuming indexing using i, j, k for the 3D matrix and y for the 1D matrix): y = j + i * m + k * n * m.