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Manipulating matrices with collectives #

In this exercise, we’ll look at some simple manipulations of matrices with collective operations.

We’ll do this with square matrices, where the number of rows (and columns) is equal to the number of processes.

We’ll implement three routines:

1. printing a matrix by gathering it to a single process and printing there;
2. transposing a matrix;
3. multiplying a matrix against a distributed vector.

For a data distribution, we will use a one-dimensional distribution where each process holds one row.

I provide a template file matrix.c in the code/mpi/collectives subdirectory of the repository.

It allocates some matrices and sets up the values.

Exercise

You should implement the three stubbed-out functions

1. print_matrix
2. transpose_matrix
3. matrix_vector_product

I provide a routine to print the vector (so you can see if you’ve implemented the matrix-vector product correctly).

Advanced (optional) #

You could think about how to extend these routines to handle the case where the matrices continue to be square, but now each process holds $k$ rows, rather than one row. The matrix is now $kP \times kP$ when running with $P$ processes. For the vector, each process will now hold $k$ entries.

Gathering the matrix for printing and computing the matrix-vector product are not much more difficult. Transposing becomes rather harder, because each process needs to send a non-contiguous block of the input data. You can either rearrange the data so that you send contiguous blocks of $k\times k$ entries to each process, or use an MPI derived datatype (see, for example, the EPCC material here).

Good luck!