001/**
002 * Copyright (c) 2011, The University of Southampton and the individual contributors.
003 * All rights reserved.
004 *
005 * Redistribution and use in source and binary forms, with or without modification,
006 * are permitted provided that the following conditions are met:
007 *
008 *   *  Redistributions of source code must retain the above copyright notice,
009 *      this list of conditions and the following disclaimer.
010 *
011 *   *  Redistributions in binary form must reproduce the above copyright notice,
012 *      this list of conditions and the following disclaimer in the documentation
013 *      and/or other materials provided with the distribution.
014 *
015 *   *  Neither the name of the University of Southampton nor the names of its
016 *      contributors may be used to endorse or promote products derived from this
017 *      software without specific prior written permission.
018 *
019 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
020 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
021 * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
022 * DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
023 * ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
024 * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
025 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
026 * ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
027 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
028 * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
029 */
030package org.openimaj.math.matrix;
031
032import java.util.Random;
033
034import no.uib.cipr.matrix.DenseVector;
035import no.uib.cipr.matrix.Vector;
036import no.uib.cipr.matrix.Vector.Norm;
037
038import org.openimaj.util.function.Function;
039
040/**
041 * Perform the Gram-Schmid process on a vector, returning the orthogonal basis set 
042 * whose first vector is the input
043 * 
044 * http://zintegra.net/archives/738
045 * @author Sina Samangooei (ss@ecs.soton.ac.uk)
046 */
047public class GramSchmidtProcess implements Function<double[],Vector[]>{
048        
049        Random r = new Random();
050        /**
051         * an unseeded random start
052         */
053        public GramSchmidtProcess() {
054        }
055        /**
056         * Set the random seed of the purtubations
057         * @param seed
058         */
059        public GramSchmidtProcess(int seed) {
060                this.r = new Random(seed);
061        }
062
063        private Vector project(Vector v, Vector u){
064                return u.copy().scale((v.dot(u) / u.dot(u)));
065        }
066
067        @Override
068        public Vector[] apply(double[] in) {
069                Vector[] vmat = new Vector[in.length];
070                
071                vmat[0] = new DenseVector(in);
072                double norm = vmat[0].norm(Norm.Two);
073                vmat[0].scale(1/norm);
074                for (int j = 1; j < in.length; j++) {
075                        Vector randvec = randvec(vmat[0].size(),norm);
076                        vmat[j] = new DenseVector(vmat[0]).add(randvec);
077                        for (int i = 0; i < j; i++) {
078                                vmat[j].add(-1, project(vmat[j],vmat[i]));
079                        }
080                        vmat[j].scale(1/vmat[j].norm(Norm.Two));
081                }
082                return vmat;
083        }
084
085        private Vector randvec(int nvec, double d) {
086                double[] ret = new double[nvec];
087                for (int i = 0; i < ret.length; i++) {
088                        ret[i] = d * r.nextDouble();
089                }
090                return new DenseVector(ret);
091        }
092        
093        /**
094         * @param args
095         */
096        public static void main(String[] args) {
097                GramSchmidtProcess proc = new GramSchmidtProcess();
098                
099                Vector[] allvec = proc.apply(new double[]{0,0,1});
100                for (Vector vector : allvec) {
101                        System.out.println(vector);
102                }
103        }
104        /**
105         * @param dir
106         * @return construct and perform a {@link GramSchmidtProcess}
107         */
108        public static Vector[] perform(double[] dir) {
109                
110                return new GramSchmidtProcess(0).apply(dir);
111        }
112        
113}