Matrix Toolkit Java

<h2 id="capabilities">Capabilities</h2>
<p>The following is an overview of MTJ's capabilities, as listed on the project's website:
</p>
<ul><li>Datastructures for dense and structured sparse matrices in the following formats:
<ul><li>Dense, column major.</li>
<li>Banded matrices, which store only a few diagonals.</li>
<li>Packed matrices, storing only half the matrices (for triangular or symmetric matrices).</li>
<li>Tridiagonal and symmetric tridiagonal matrices.</li></ul></li>
<li>Transparent support for symmetric and triangular storage.</li>
<li>Datastructures for unstructured sparse matrices in these formats:
<ul><li>Compressed row or column storage (CRS/CCS).</li>
<li>Flexible CRS/CCS, using growable sparse vectors.</li>
<li>Compressed diagonal storage (CDS).</li></ul></li>
<li>The dense and structured sparse matrices are built on top of BLAS and LAPACK, and include the following intrinsic operations:
<ul><li>Matrix/vector multiplication.</li>
<li>Matrix/matrix multiplication.</li>
<li>Rank updates by matrices or vectors.</li>
<li>Direct matrix solvers.</li></ul></li>
<li>The unstructured sparse matrices supports the same operations as the structured ones, except they do not have direct solvers. However, their matrix/vector multiplication methods are optimised for use in iterative solvers.</li>
<li>Matrix decompositions of dense and structured sparse matrices:
<ul><li>LU and Cholesky.</li>
<li>Eigenvalue decompositions for unsymmetrical dense matrices.</li>
<li>Singular value decompositions for unsymmetrical dense matrices.</li>
<li>Eigenvalue decompositions for symmetrical matrices (tridiagonal, banded, packed and dense).</li>
<li><a href="/facts/Orthogonal_matrix/WDXBXYB5">Orthogonal matrix</a> decompositions for dense matrices (QR, RQ, LQ, and QL).</li></ul></li>
<li>Iterative solvers for unstructured sparse matrices from the Templates project:
<ul><li>BiConjugate gradients.</li>
<li>BiConjugate gradients stabilized.</li>
<li>Conjugate gradients.</li>
<li>Conjugate gradients squared.</li>
<li>Chebyshev iteration.</li>
<li>Generalized minimal residual (GMRES).</li>
<li>Iterative refinement (Richardson's method).</li>
<li>Quasi-minimal residual.</li></ul></li>
<li>A selection of algebraic preconditioners:
<ul><li>Diagonal preconditioning.</li>
<li>Symmetrical successive overrelaxation.</li>
<li>Incomplete Cholesky.</li>
<li>Incomplete LU.</li>
<li>Incomplete LU with fill-in using thresholding.</li>
<li>Algebraic multigrid by smoothed aggregation.</li></ul></li></ul>
<h2 id="usage-examples">Usage Examples</h2>
<p>Example of Singular Value Decomposition (SVD):
</p>
SVD svd = new SVD(matA.numRows(),matA.numColumns());
SVD s = svd.factor(matA);
DenseMatrix U = s.getU();
DenseMatrix S = s.getS();
DenseMatrix Vt = s.getVt();

<p>Example of matrix multiplication:
</p>
DenseMatrix result = new DenseMatrix(matA.numRows(),matB.numColumns());
matA.mult(matB,result);

<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/List_of_numerical_analysis_software/yKFzDBDK">List of numerical analysis software</a></li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>"MTJ Project Page". MTJ. Retrieved November 30, 2012. <a href="https://code.google.com/p/matrix-toolkits-java/" target="_blank">https://code.google.com/p/matrix-toolkits-java/</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>McMahan, H.B.; Gordon, G.J. (2005). "Fast exact planning in Markov decision processes" (PDF). Proc. of the 15th International Conference on Automated Planning and Scheduling (ICAPS-05). <a href="https://www.cs.cmu.edu/~ggordon/mcmahan-gordon.fast-mdp.pdf" target="_blank">https://www.cs.cmu.edu/~ggordon/mcmahan-gordon.fast-mdp.pdf</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
<li id="fn:3"><p>"Java Matrix Benchmark". Retrieved December 6, 2012. <a href="https://code.google.com/p/java-matrix-benchmark/" target="_blank">https://code.google.com/p/java-matrix-benchmark/</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li>
</ol>

Matrix Toolkit Java open-in-new

Matrix Toolkit Java