#matrix #sparse #solver

bin+lib russell_sparse

Sparse matrix tools and solvers

12 unstable releases (3 breaking)

Uses new Rust 2021

0.4.1 Jun 28, 2022
0.3.1 Jun 28, 2022
0.3.0 May 14, 2022
0.2.6 Oct 22, 2021
0.1.1 Sep 4, 2021

#114 in Math

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Used in 2 crates

MIT license

550KB
11K SLoC

Russell Sparse - Sparse matrix tools and solvers

Crates.io

This crate is part of Russell - Rust Scientific Library

This repository contains tools for handling sparse matrices and functions to solve large sparse systems.

Documentation:

Installation

Install some libraries:

sudo apt-get install \
    liblapacke-dev \
    libmumps-seq-dev \
    libopenblas-dev \
    libsuitesparse-dev

Add this to your Cargo.toml (choose the right version):

[dependencies]
russell_sparse = "*"

Optional: Use a locally compiled MUMPS library

The standard Debian libmumps-seq-dev does not come with Metis or OpenMP that may lead to faster calculations. Therefore, it may be advantageous to use a locally compiled MUMPS library.

We just need the include files in /usr/local/include/mumps and a library file named libdmumps_open_seq_omp in /usr/local/lib/mumps.

Follow the instructions from https://github.com/cpmech/script-install-mumps and then set the environment variable USE_LOCAL_MUMPS=1:

export USE_LOCAL_MUMPS=1

Number of threads

By default OpenBLAS will use all available threads, including Hyper-Threads that make the performance worse. Thus, it is best to set the following environment variable:

export OPENBLAS_NUM_THREADS=<real-core-count>

Furthermore, if working on a multi-threaded application, it is recommended to set:

export OPENBLAS_NUM_THREADS=1

Examples

Solve a sparse linear system

use russell_lab::{Matrix, Vector};
use russell_sparse::{ConfigSolver, Solver, SparseTriplet, Symmetry, StrError};

fn main() -> Result<(), StrError> {
    // allocate a square matrix
    let mut trip = SparseTriplet::new(3, 3, 5, Symmetry::No)?;
    trip.put(0, 0, 0.2)?;
    trip.put(0, 1, 0.2)?;
    trip.put(1, 0, 0.5)?;
    trip.put(1, 1, -0.25)?;
    trip.put(2, 2, 0.25)?;
    
    // print matrix
    let (m, n) = trip.dims();
    let mut a = Matrix::new(m, n);
    trip.to_matrix(&mut a)?;
    let correct = "┌                   ┐\n\
                   │   0.2   0.2     0 │\n\
                   │   0.5 -0.25     0 │\n\
                   │     0     0  0.25 │\n\
                   └                   ┘";
    assert_eq!(format!("{}", a), correct);
    
    // allocate rhs
    let rhs1 = Vector::from(&[1.0, 1.0, 1.0]);
    let rhs2 = Vector::from(&[2.0, 2.0, 2.0]);
    
    // calculate solution
    let config = ConfigSolver::new();
    let (mut solver, x1) = Solver::compute(config, &trip, &rhs1)?;
    let correct1 = "┌   ┐\n\
                    │ 3 │\n\
                    │ 2 │\n\
                    │ 4 │\n\
                    └   ┘";
    assert_eq!(format!("{}", x1), correct1);
    
    // solve again
    let mut x2 = Vector::new(trip.dims().0);
    solver.solve(&mut x2, &rhs2)?;
    let correct2 = "┌   ┐\n\
                    │ 6 │\n\
                    │ 4 │\n\
                    │ 8 │\n\
                    └   ┘";
    assert_eq!(format!("{}", x2), correct2);
    Ok(())
}

Sparse solvers

We wrap two direct sparse solvers: UMFPACK (aka UMF) and MUMPS (aka MMP). The default solver is UMF; however UMF may run out of memory for large matrices, whereas MMP still may work. The MMP solver is not thread-safe and thus must be used in single-threaded applications.

Tools

This crate includes a tool named solve_mm_build to study the performance of the available sparse solvers (currently MMP and UMF). The _build suffix is to disable the coverage tool.

solve_mm_build reads a Matrix Market file and solves the linear system:

a ⋅ x = rhs

with a right-hand-side containing only ones.

The data directory contains an example of Matrix Market file named bfwb62.mtx and you may download more matrices from https://sparse.tamu.edu/

Run the command:

cargo run --release --bin solve_mm_build -- data/matrix_market/bfwb62.mtx

Or

cargo run --release --bin solve_mm_build -- --help

for more options.

Dependencies

~8–11MB
~210K SLoC