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Matrix data structures, linear solvers, least squares methods, eigenvalue, and singular value decompositions. For larger random dense matrices (above ~ 350 x 350) matrix-matrix multiplication C = A.B is about 50% faster than MTJ.
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package no.uib.cipr.matrix.sparse;

import com.github.fommil.netlib.ARPACK;
import no.uib.cipr.matrix.*;
import org.netlib.util.doubleW;
import org.netlib.util.intW;

import java.util.Comparator;
import java.util.Map;
import java.util.TreeMap;
import java.util.logging.Logger;

/**
 * Uses ARPACK to partially solve symmetric eigensystems (ARPACK is designed to
 * compute a subset of eigenvalues/eigenvectors).
 *
 * @author Sam Halliday
 */
public class ArpackSym {

    public enum Ritz {
        /**
         * compute the NEV largest (algebraic) eigenvalues.
         */
        LA,
        /**
         * compute the NEV smallest (algebraic) eigenvalues.
         */
        SA,
        /**
         * compute the NEV largest (in magnitude) eigenvalues.
         */
        LM,
        /**
         * compute the NEV smallest (in magnitude) eigenvalues.
         */
        SM,
        /**
         * compute NEV eigenvalues, half from each end of the spectrum
         */
        BE
    }

    private static final Logger log = Logger.getLogger(ArpackSym.class.getName());

    private final ARPACK arpack = ARPACK.getInstance();

    private static final double TOL = 0.0001;

    private static final boolean EXPENSIVE_CHECKS = true;

    private final Matrix matrix;

    public ArpackSym(Matrix matrix) {
        if (!matrix.isSquare())
            throw new IllegalArgumentException("matrix must be square");
        if (EXPENSIVE_CHECKS)
            for (MatrixEntry entry : matrix) {
                if (entry.get() != matrix.get(entry.column(), entry.row()))
                    throw new IllegalArgumentException(
                            "matrix must be symmetric");
            }
        this.matrix = matrix;
    }

    /**
     * Solve the eigensystem for the number of eigenvalues requested.
     * 
     * NOTE: The references to the eigenvectors will keep alive a reference to a
     * {@code nev * n} double array, so use the {@code copy()} method to free it
     * up if only a subset is required.
     *
     * @param eigenvalues
     * @param ritz
     *            preference for solutions
     * @return a map from eigenvalues to corresponding eigenvectors.
     */
    public Map solve(int eigenvalues, Ritz ritz) {
        if (eigenvalues <= 0)
            throw new IllegalArgumentException(eigenvalues + " <= 0");
        if (eigenvalues >= matrix.numColumns())
            throw new IllegalArgumentException(eigenvalues + " >= "
                    + (matrix.numColumns()));

        int n = matrix.numRows();
        intW nev = new intW(eigenvalues);

        int ncv = Math.min(2 * eigenvalues, n);

        String bmat = "I";
        String which = ritz.name();
        doubleW tol = new doubleW(TOL);
        intW info = new intW(0);
        int[] iparam = new int[11];
        iparam[0] = 1;
        iparam[2] = 300;
        iparam[6] = 1;
        intW ido = new intW(0);

        // used for initial residual (if info != 0)
        // and eventually the output residual
        double[] resid = new double[n];
        // Lanczos basis vectors
        double[] v = new double[n * ncv];
        // Arnoldi reverse communication
        double[] workd = new double[3 * n];
        // private work array
        double[] workl = new double[ncv * (ncv + 8)];
        int[] ipntr = new int[11];

        int i = 0;
        while (true) {
            i++;
            arpack.dsaupd(ido, bmat, n, which, nev.val, tol, resid, ncv, v, n,
                    iparam, ipntr, workd, workl, workl.length, info);
            if (ido.val == 99)
                break;
            if (ido.val != -1 && ido.val != 1)
                throw new IllegalStateException("ido = " + ido.val);
            // could be refactored to handle the other types of mode
            av(workd, ipntr[0] - 1, ipntr[1] - 1);
        }

        ArpackSym.log.fine(i + " iterations for " + n);

        if (info.val != 0)
            throw new IllegalStateException("info = " + info.val);

        double[] d = new double[nev.val];
        boolean[] select = new boolean[ncv];
        double[] z = java.util.Arrays.copyOfRange(v, 0, nev.val * n);

        arpack.dseupd(true, "A", select, d, z, n, 0, bmat, n, which, nev, TOL,
                resid, ncv, v, n, iparam, ipntr, workd, workl, workl.length,
                info);
        if (info.val != 0)
            throw new IllegalStateException("info = " + info.val);

        int computed = iparam[4];
        ArpackSym.log.fine("computed " + computed + " eigenvalues");

        Map solution = new TreeMap(
                new Comparator() {
                    @Override
                    public int compare(Double o1, Double o2) {
                        // highest first
                        return Double.compare(o2, o1);
                    }
                });
        DenseVector eigenvectors = new DenseVector(z, false);
        for (i = 0; i < computed; i++) {
            double eigenvalue = d[i];
            DenseVectorSub eigenvector = new DenseVectorSub(eigenvectors,
                    i * n, n);
            solution.put(eigenvalue, eigenvector);
        }

        return solution;
    }

    private void av(double[] work, int input_offset, int output_offset) {
        DenseVector w = new DenseVector(work, false);
        Vector x = new DenseVectorSub(w, input_offset, matrix.numColumns());
        Vector y = new DenseVectorSub(w, output_offset, matrix.numColumns());
        matrix.mult(x, y);
    }
}