A simple 2D matrix class
There is a recurring question on some C++ forums about nesting std::vector’s to build a 2D matrix, i.e.:
std::vector< std::vector<double> > someMatrix;

This is not very efficient, both memorywise and speedwise.
In fact, each vector has an overhead due to the fact that it typically stores three pointers. So, e.g. in case of a 20 rows by 30 columns matrix, assuming that inner vectors represent matrix rows, the overhead is 20 rows x 3 pointers/row = 60 pointers, i.e. 60 pointers x 4 bytes/pointer = 240 bytes.
But there is also a speed penalty. In fact, dynamic memory allocated by each vector is in general scattered on the heap; instead, it would be better for locality to have contiguous memory allocated for the whole matrix.
So, a better technique consists in using just one instance of std::vector, storing all matrix elements in this very instance, using a proper ordering for elements, e.g. storing matrix elements rowwise.
The total size of the vector is rows * columns, and given a 2D index (row, column) it can be “linearized” to point to proper vector element using the following formula:
<vector index> = <column index> + <row index> * <matrix columns>
These concepts are developed in a simple reusable C++ template class attached to this blog post. This is a simple class for simple needs (i.e. just storing 2D matrix elements in an efficient way and accessing them conveniently). For more advanced matrix classes, with template metaprogramming optimizations, Blitz++ library can be considered.