The purpose of these exercises is not to amount to killer speed-ups (a laptop is not the right hardware for that), but rather to run and modify a few examples, become comfortable with APIs, and implement some simple parallel programs.
Write a simple python program using the mpi4py module which imports mpi4py.MPI and displays the COMM_WORLD.rank, size and MPI.Get_processor_name() on each process. It is always handy to have such a program around to verify that the MPI environment is working as expected. In a distributed environment, the processor name will further inform you that your MPI execution was spawned accross machine boundaries, and how many processes are allocated per machine.
Note: To run your program mpi4py, it must be started as if it was any MPI program, i.e. as follows:
$ mpiexec -n X python <program.py>
For ipython, you need to start an ipcluster:
$ ipcluster start -n X # or similar for your ipython version, see lecture notes
Where -n X is the number of slave processes to start.
First, quantify the degree of inbalance by gathering and plotting the distribution of execution times per pixel. Assuming you used chunked decomposition as for matrix multiplication, how does this per-pixel imbalance translate into a per-chunk inbalance?
Second, Can you modify the decomposition of the problem to provide each worker with work-loads which are more equal?
ipython: read-up on the LoadBalancedView here: http://ipython.org/ipython-doc/rel-0.13/parallel/parallel_task.html mpi4py: a pure mpi4py approach is more tricky. One method might be to use asynchronous messaging (Isend, Irecv) to a set of workers and let a master (e.g. rank 0) re-assign work as workers complete.
Using the ipython approach, get a collection of processes to count the occurrences of a word in a collection of documents, and then reduce the results to a total count per word on the master process.