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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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/*
 * Copyright (C) 2003-2006 Bjørn-Ove Heimsund
 * 
 * This file is part of MTJ.
 * 
 * This library is free software; you can redistribute it and/or modify it
 * under the terms of the GNU Lesser General Public License as published by the
 * Free Software Foundation; either version 2.1 of the License, or (at your
 * option) any later version.
 * 
 * This library is distributed in the hope that it will be useful, but WITHOUT
 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License
 * for more details.
 * 
 * You should have received a copy of the GNU Lesser General Public License
 * along with this library; if not, write to the Free Software Foundation,
 * Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
 */

package no.uib.cipr.matrix;

import java.util.Arrays;
import java.util.Iterator;

/**
 * Partial implementation of a banded matrix
 */
abstract class AbstractBandMatrix extends AbstractMatrix {

    /**
     * Matrix data
     */
    double[] data;

    /**
     * Number of upper and lower diagonals
     */
    int kl, ku;

    /**
     * Size of the matrix. It is always square
     */
    int n;

    /**
     * Constructor for AbstractBandMatrix
     * 
     * @param n
     *            Size of the matrix. Since the matrix must be square, this
     *            equals both the number of rows and columns
     * @param kl
     *            Number of diagonals below the main diagonal
     * @param ku
     *            Number of diagonals above the main diagonal
     */
    public AbstractBandMatrix(int n, int kl, int ku) {
        super(n, n);

        this.n = n;
        if (kl < 0 || ku < 0)
            throw new IllegalArgumentException("kl < 0 || ku < 0");
        this.kl = kl;
        this.ku = ku;

        data = new double[numColumns * (1 + kl + ku)];
    }

    /**
     * Constructor for AbstractBandMatrix
     * 
     * @param A
     *            Matrix to copy from
     * @param kl
     *            Number of diagonals below the main diagonal
     * @param ku
     *            Number of diagonals above the main diagonal
     */
    public AbstractBandMatrix(Matrix A, int kl, int ku) {
        this(A, kl, ku, true);
    }

    /**
     * Constructor for AbstractBandMatrix
     * 
     * @param A
     *            Matrix to copy from
     * @param kl
     *            Number of diagonals below the main diagonal
     * @param ku
     *            Number of diagonals above the main diagonal
     * @param deep
     *            True if a deep copy is made. For a shallow copy,
     *            A must be a banded matrix
     */
    public AbstractBandMatrix(Matrix A, int kl, int ku, boolean deep) {
        super(A);

        if (kl < 0 || ku < 0)
            throw new IllegalArgumentException("kl < 0 || ku < 0");
        if (!isSquare())
            throw new IllegalArgumentException("Band matrix must be square");
        this.n = numRows;
        this.kl = kl;
        this.ku = ku;

        if (deep) {
            data = new double[numColumns * (1 + kl + ku)];
            copy(A);
        } else
            this.data = ((AbstractBandMatrix) A).getData();
    }

    /**
     * Returns the matrix contents
     */
    public double[] getData() {
        return data;
    }

    @Override
    public void add(int row, int column, double value) {
        checkBand(row, column);
        data[getIndex(row, column)] += value;
    }

    @Override
    public void set(int row, int column, double value) {
        checkBand(row, column);
        data[getIndex(row, column)] = value;
    }

    @Override
    public double get(int row, int column) {
        if (!inBand(row, column))
            return 0;
        return data[getIndex(row, column)];
    }

    /**
     * Returns the number of lower diagonals
     */
    public int numSubDiagonals() {
        return kl;
    }

    /**
     * Returns the number of upper diagonals
     */
    public int numSuperDiagonals() {
        return ku;
    }

    /**
     * Returns true if the given indices are within the band
     */
    boolean inBand(int row, int column) {
        return column - ku <= row && row <= column + kl;
    }

    /**
     * Checks that the indices are within the band
     */
    void checkBand(int row, int column) {
        if (!inBand(row, column))
            throw new IndexOutOfBoundsException("Insertion index out of band");
    }

    /**
     * Checks the row and column indices, and returns the linear data index
     */
    int getIndex(int row, int column) {
        check(row, column);
        return ku + row - column + column * (kl + ku + 1);
    }

    /**
     * Set this matrix equal to the given matrix
     */
    void copy(Matrix A) {
        for (MatrixEntry e : A)
            if (inBand(e.row(), e.column()))
                set(e.row(), e.column(), e.get());
    }

    @Override
    public Matrix set(Matrix B) {
        if (!(B instanceof AbstractBandMatrix))
            return super.set(B);

        checkSize(B);

        AbstractBandMatrix Bb = (AbstractBandMatrix) B;
        if (Bb.kl != kl)
            throw new IllegalArgumentException("B.kl != kl");
        if (Bb.ku != ku)
            throw new IllegalArgumentException("B.ku != ku");

        double[] Bd = Bb.getData();

        if (Bd == data)
            return this;

        System.arraycopy(Bd, 0, data, 0, data.length);

        return this;
    }

    @Override
    public Matrix zero() {
        Arrays.fill(data, 0);
        return this;
    }

    @Override
    public Iterator iterator() {
        return new BandMatrixIterator();
    }

    /**
     * Iterator over a band matrix
     */
    class BandMatrixIterator extends RefMatrixIterator {

        /**
         * Matrix bandwidths. Cannot be taken directly from the matrix since
         * that breaks iterating over symmetrical matrices
         */
        private final int lkl, lku;

        public BandMatrixIterator(int lkl, int lku) {
            this.lkl = lkl;
            this.lku = lku;
        }

        public BandMatrixIterator() {
            this(kl, ku);
        }

        @Override
        public MatrixEntry next() {
            entry.update(row, column);

            // Traversal first down the columns, then the rows
            if (row < Math.min(column + lkl, n - 1)
                    && row >= Math.max(column - lku, 0))
                row++;
            else {
                column++;
                row = Math.max(column - lku, 0);
            }

            return entry;
        }

    }

}