README.md

Project Structure

• include: contains all required headers.
• src: contains all implementations of classes (.cpp):
  • solver: this folder contains files and classes that are responsible for solving equations. It has an abstract class named base_solver which implemented by two types of solvers, simple_solver and sparse_solver. New solvers can be added to this folder and implement the base_solver.
  • storage: this folder contains files and classes that are responsible for storing data and reading them. It has an abstract class named base_storage_format. Another abstract class derived from base_storage_format named csc_storage_format, representing CSC storage format, which implemented by two other classes, mtx_matrix and mtx_vector. New storage formats can be added to this folder and implement the base_storage_format or available ones such as csc_storage_format.
  • utils: contains utility classes which are needed by other classes. In this case, it has a dfs for traversing a graph.
• tests: all tests of these project will go here.
  • lib: contains googletest framework sources.
  • data: all test data required for testing.
  • solver_tests: tests for different algorithms.

Algorithms

In this section, different algorithms are described for Lx=b where L is a n x n lower triangular matrix.

Simple Algorithm

This algorithm basically is iterating over none-zero elements of matrix L and computes the final answers.

Sparse Algorithm

In this algorithm, a graph of G=(V,E), where V={1,2,3,...,n} and E={(i, j) | Lji != 0, is created. Then, a DFS is run starting from none-zero elements of b. The resulting set is named reach-set of b. Finally, the solver algorithm is run for vertices inside this reach-set instead of all none-zero elements of L.

Parallel Sparse Algorithm

In order to make the sparse algorithm parallel, the nodes are grouped into levels. Their levels are computed based on wavefront algorithm which defines a depth for each node base on the following formula:

depth(i) = 1 + max_j{depth(j), where L(i,j) != 0}

In this approach, first the reach-set of b is computed and then the wavefront algorithm executed. All nodes inside each level can be run in parallel.

Install and Build

tests

In order to run the tests, the googletest framework needed to be installed.

cli

List of available switches

	-v vector_file_path, e.g: -v ./b.mtx
	-m matrix_file_path, e.g: -m ./L.mtx
	-o output_directory_path, e.g: -o ./
	-a algorithm_type[simple, sparse, par_sparse], e.g: -a par_sparse

demo

TODO

• add a CMakeLists file.
• add support for testing.
  • add the googletest framework.
  • write tests for utils classes.
  • write tests for storage classes.
    • add tests for dense mtx_vector
    • add tests for dense mtx_matrix
    • add tests for sparse mtx_vector
    • add tests for sparse mtx_matrix
  • write tests for solver classes.
    • write tests for simple_solver
    • write tests for sparse_solver
    • write tests for parallel sparse_solver
• update readme with algorithms descriptions.
• add more solvers with support of parallelism.
  • wavefront based parallelism.
• try to setup Travis CI with this repo.
• add a test coverage tool.