Create 3d matrix from 3 vectors

Question

I have 3 vectors, named a, b and c and I want to create 3D matrix, M, so that M(i,j,k) = a(i) + b(j) + c(k), where a(i) means ith element of vector a, and likewise for all vectors and matrix.

For creating 2d matrix, it is easy like a+b'. but I am not sure how I can create 3d matrix.

Answer 1

You only need permute or reshape to do the multi-dimensional equivalent of transposition:

a + b.' + reshape(c, 1, 1, []);

Assuming that a , b , c are column vectors of sizes L × 1 , M × 1 and N × 1 , this works because

• a is L × 1 , or equivalently L × 1 × 1 ;
• b.' is 1 × M × 1 ;
• reshape(c, 1, 1, [] is 1 × 1 × N .

So, by implicit expansion the result is an L × M × N 3D array.