Question

In GSL a real n * m matrix M is represented internally as an array of size n*m. To access the (i,j) element of M, internally GSL has to access the (i-1) * n + j - 1 location of the array, which involves integer multiplications and additions.

In Numerical Recipes for C, they recommend the alternative method of declaring an array of n pointers, each pointing to an array of m numbers. Then to access the (i,j) element, one puts M[i-1][j-1]. They claim that this is more efficient because it avoids the integer multiplication. The downside is that one has to initialize each pointer separately.

I am wondering, what are the advantages/disadvantages of each approach?

Answer 1

In C:

#define n 2
#define m 3

int M[n*m];

is the same as

int M[n][m];

in C matrices are said to be stored in row-major order

http://en.wikipedia.org/wiki/Row-major_order

In C,

M[1][2]

is the same as

*(M + 1*m + 2) // if M is define as M[n][m]

You could define M as an array of n pointers, but you still have to put the data somewhere and the best place is probably a 2D array. I would suggest:

int M[n][m];

int* Mrows[n] = {M[0], M[1]};

You can then do a direct offset into rows to get to the row you want. Then:

Mrows[1][2]

is the same as

*((*(Mrows + 1)) + 2)

Its more work for the programmer and probably only worth it if you want to go really fast. In that case you may want to look into more optimizations such as specific machine instructions. Also, depending on your algorithm, you may be able to just use + operations (like if you are iterating over the matrix)