In order to understand how to perform computations on top of a sparse matrix and the resulting benefits thereof, we will be looking at an example and comparing the difference between having a sparse matrix and not having a sparse matrix.

Solving a system of equations

As discussed in the Solving linear systems using matrices recipe, a system of equations is solved using the solve function in scipy.linalg.

In order to compare the difference between sparse matrix computation and non-sparse matrix computation, we will perform the following tasks:

• Import relevant packages
• Initialize a 10,000 x 10,000 matrix named A
• Impute very few values with some random numbers
• Set the diagonal, so that the rank of matrix is not reduced by a lot
• Initialize a set of values for the output b so that the equation A*x = b is set up
• Solve for the values of x once with the sparse matrix and another time without the sparse matrix format
• Compare the differences in the speed of computation by using the sparse matrix format