Suppose you have a sparse matrix A[i][j] defined, where there can only
 be values if 0 <= 2i <= j <= i+n.  You could declare a rectangular array:

 float A[n][2n];

 but that would be wasteful, since the actual content of the array is
 roughly a fourth of what you allocated.  Instead, you can define arrays

 float B[m];

 int offset[n];

 where m is the number of pairs (i,j) in the domain of A.  (In this case,
 m = n(n+1)/2.)

 in such a way that the function fetch returns the value of A[i][j] for
 all legal i and j.

 int index(int i, int j)
  {
   return offset[i] + j;
  }

 float fetch(int i, int j)
  {
   return B[index(i,j)];
  }

 How do you compute B?  For this example:

 B[0] = 0;
 B[1] = n-1;
 B[2] = 2*n-3;
 B[3] = 3*n-6;

 etc.