Matrices with not constant values

Question

I'm trying to make a program that uses a two-dimensional matrix. The problem is that to avoid to have limit, I don't know how to declare the matrix because the dimensions are not constant. I saw to how to realize vectors with not-constant dimension, creating objects. But for matrices nothing... How can I resolve?

Answer 1

If you know how to handle variable dimensioned vectors you can already solve your problem:

E.g. you can store a vector of column vectors of the m x n matrix A = (a_1, .., a_n), or a vector of row vectors A^t = (a_1, .., a_m).

Or you can sequentially store the m x n elements of such a matrix into a single vector. You would only need some enumeration of the elements to transform the indices i and j of element a_ij into a single index k.

E.g. enumerating row wise:

• k = f(i,j) = [m (i-1) + (j-1)] + 1 = m (i-1) + j

if i from {1,..,m}, j from {1,.., n} and k from {1, .., mn}.

The inverse, calculating i and j from k is:

• i = g_1(k) = ((k-1) div m) + 1

• j = g_2(k) = k - m (i-1) = k - m (g_1(k)-1)

If you do not care how this is done in principle but just need some working code, you should search for some C++ matrix library.