la4j (Linear Algebra for Java)

The la4j is an open source and 100% Java library that provides Linear Algebra primitives (matrices and vectors) and algorithms. The la4j library was initially designed to be a lightweight and simple tool for passionate Java developers. It has been started as student project and turned into one of the most popular Java packages for matrices and vectors.

The key features of the la4j are listed bellow:

• Great performance allied with beautiful design
• No dependencies and tiny size (~150kb jar)
• Fluent and object-oriented/functional API
• Sparse (CRS, CCS) and dense (1D/2D arrays) matrices and vectors
• Linear systems solving (Gaussian, Jacobi, Seidel, Square Root, Sweep and other)
• Matrices decomposition (Eigenvalues/Eigenvectors, SVD, QR, LU, Cholesky and other)
• Functors support: predicates, functions, procedures and accumulators
• MatrixMarket/CSV IO formats support

Samples

Building the matrix

// We will use a CRS (Compressed Row Storage) matrix builder
// We will use a 2D array matrix builder
Matrix b = Matrices.asBuilder(LinearAlgebra.BASIC2D_FACTORY)
           .shape(25, 25)    // We want a 25x25 matrix
           .source(3.14)     // ... with all the elements equal '3.14'
           .buildDiagonal(); // ... and it should be a diagonal matrix

// We wil use a CCS (Compressed Column Storage) matrix builder
Matrix c = Matrices.asBuilder(LinearAlgebra.CCS_FACTORY)
           .shape(14, 14)         // We want a 14x14 matrix
           .source(new Random())  // ... with random elements
           .buildSymmetric();     // ... and it should be a symmetric matrix

Building the vector

// We will use a dense vector builder
Vector a = Vectors.asBuilder(LinearAlgebra.DENSE_FACTORY)
           .length(10)            // We want 10 elements vector
           .source(new Random())  // ... with random values
           .build();

Vector a = Vectors.asBuilder(LinearAlgebra.DENSE_FACTORY)
           .length(10)                    // We want 10 elements vector
           .source(new double[] { 1.0 })  // ... with the values from an array
           .build();                      // ... and it should be extended to a requested size

Matrix inversion

// We want a simple dense matrix that uses 2D array as internal representation
Matrix a = new Basic2DMatrix(new double[][] {
   { 1.0, 2.0, 3.0 },
   { 4.0, 5.0, 6.0 },
   { 7.0, 8.0, 9.0 }
});

// We will use Gauss-Jordan method for inverting
MatrixInverter inverter = a.withInverter(LinearAlgebra.GAUSS_JORDAN);
// The 'b' matrix will be dense
Matrix b = inverter.inverse(LinearAlgebra.DENSE_FACTORY);

System of linear equations

// The coefficient matrix 'a' is a CRS (Compressed Row Storage) matrix
Matrix a = new CRSMatrix(new double[][] {
   { 1.0, 2.0, 3.0 },
   { 4.0, 5.0, 6.0 },
   { 7.0, 8.0, 9.0 }
});

// A right hand side vector, which is simple dense vector
Vector b = new BasicVector(new double[] {
   1.0, 2.0, 3.0
});

// We will use standard Forward-Back Substitution method,
// which is based on LU decomposition and can be used with square systems
LinearSystemSolver solver = a.withSolver(LinearAlgebra.FORWARD_BACK_SUBSTITUTION);
// The 'x' vector will be sparse
Vector x = solver.solve(b, LinearAlgebra.SPARSE_FACTORY);

Matrix decomposition

// We want simple dense matrix, which is based on 1D double array
Matrix a = new Basic1DMatrix(new double[][] {
   { 1.0, 2.0, 3.0 },
   { 4.0, 5.0, 6.0 },
   { 7.0, 8.0, 9.0 }
});

// We will use LU decompositor
MatrixDecompositor decompositor = a.withDecompositor(LinearAlgebra.LU);
// The result should be treated as: L = lup[0], U = lup[1], P = lup[2]
Matrix[] lup = decompositor.decompose(LinearAlgebra.DENSE_FACTORY);

Changelog

See CHANGELOG.md

Download

Details of the last version of the la4j can be found on the project web site http://la4j.org or its GitHub page https://github.com/vkostyukov/la4j.

Licensing

This software is licensed under the terms you may find in the file named "LICENSE" in this directory.

How To Contribute

• Fork it
• Create your feature branch (git checkout -b my-new-feature)
• Commit your changes (git commit -am 'Add some feature')
• Push to the branch (git push origin my-new-feature)
• Create new Pull Request

Contributors

See CONTRIBUTORS.md

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by Vladimir Kostyukov, 2011-2014