[1] | 1 | package agents.anac.y2015.Phoenix.GP;/* This file is part of the jgpml Project.
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| 2 | * http://github.com/renzodenardi/jgpml
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| 3 | *
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| 4 | * Copyright (c) 2011 Renzo De Nardi and Hugo Gravato-Marques
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| 5 | *
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| 6 | * Permission is hereby granted, free of charge, to any person
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| 7 | * obtaining a copy of this software and associated documentation
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| 8 | * files (the "Software"), to deal in the Software without
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| 9 | * restriction, including without limitation the rights to use,
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| 10 | * copy, modify, merge, publish, distribute, sublicense, and/or sell
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| 11 | * copies of the Software, and to permit persons to whom the
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| 12 | * Software is furnished to do so, subject to the following
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| 13 | * conditions:
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| 14 | *
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| 15 | * The above copyright notice and this permission notice shall be
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| 16 | * included in all copies or substantial portions of the Software.
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| 17 | *
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| 18 | * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
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| 19 | * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
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| 20 | * OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
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| 21 | * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
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| 22 | * HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
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| 23 | * WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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| 24 | * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
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| 25 | * OTHER DEALINGS IN THE SOFTWARE.
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| 26 | */
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| 27 |
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| 28 | import static agents.anac.y2015.Phoenix.GP.MatrixOperations.*;
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| 29 |
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| 30 | import java.util.Arrays;
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| 31 |
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| 32 | import agents.Jama.Matrix;
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| 33 |
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| 34 |
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| 35 | /** Squared Exponential covariance function with Automatic Relevance Detemination
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| 36 | * (ARD) distance measure. The covariance function is parameterized as:
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| 37 | * <p>
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| 38 | * k(x^p,x^q) = sf2 * exp(-(x^p - x^q)'*inv(P)*(x^p - x^q)/2)
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| 39 | * <p>
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| 40 | * where the P matrix is diagonal with ARD parameters ell_1^2,...,ell_D^2, where
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| 41 | * D is the dimension of the input space and sf2 is the signal variance. The
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| 42 | * hyperparameters are:
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| 43 | * <p>
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| 44 | * [ log(ell_1)
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| 45 | * log(ell_2)
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| 46 | * .
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| 47 | * log(ell_D)
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| 48 | * log(sqrt(sf2))]
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| 49 | */
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| 50 | public class CovSEard implements CovarianceFunction {
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| 51 |
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| 52 | private int D;
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| 53 | private int numParameters;
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| 54 | private Matrix K=null;
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| 55 |
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| 56 | /**
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| 57 | * Creates a new <code>PhoenixAlpha.CovSEard PhoenixAlpha.CovarianceFunction<code>
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| 58 | * @param inputDimension muber of dimension of the input
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| 59 | */
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| 60 | public CovSEard(int inputDimension){
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| 61 | this.D = inputDimension;
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| 62 | numParameters = D+1;
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| 63 | }
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| 64 |
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| 65 | /**
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| 66 | * Returns the number of hyperparameters of <code>PhoenixAlpha.CovSEard</code>
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| 67 | * @return number of hyperparameters
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| 68 | */
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| 69 | public int numParameters() {
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| 70 | return numParameters;
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| 71 | }
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| 72 |
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| 73 | /**
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| 74 | * Compute covariance matrix of a dataset X
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| 75 | * @param loghyper column <code>Matrix</code> of hyperparameters
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| 76 | * @param X input dataset
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| 77 | * @return K covariance <code>Matrix</code>
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| 78 | */
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| 79 | public Matrix compute(Matrix loghyper, Matrix X) {
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| 80 |
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| 81 | if(X.getColumnDimension()!=D)
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| 82 | throw new IllegalArgumentException("The number of dimensions specified on the covariance function "+D+" must agree with the size of the input vector"+X.getColumnDimension());
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| 83 | if(loghyper.getColumnDimension()!=1 || loghyper.getRowDimension()!=numParameters)
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| 84 | throw new IllegalArgumentException("Wrong number of hyperparameters, "+loghyper.getRowDimension()+" instead of "+numParameters);
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| 85 |
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| 86 | final Matrix ell = exp(loghyper.getMatrix(0,D-1,0,0)); // characteristic length scales
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| 87 | final double sf2 = Math.exp(2*loghyper.get(D,0)); // signal variance
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| 88 |
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| 89 | Matrix diag = new Matrix(D,D);
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| 90 | for(int i=0; i<D; i++)
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| 91 | diag.set(i,i,1/ell.get(i,0));
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| 92 |
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| 93 | K = exp(squareDist(diag.times(X.transpose())).times(-0.5)).times(sf2); // SE covariance
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| 94 |
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| 95 | return K;
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| 96 | }
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| 97 |
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| 98 | /**
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| 99 | * Compute compute test set covariances
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| 100 | * @param loghyper column <code>Matrix</code> of hyperparameters
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| 101 | * @param X input dataset
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| 102 | * @param Xstar test set
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| 103 | * @return [K(Xstar,Xstar) K(X,Xstar)]
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| 104 | */
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| 105 | public Matrix[] compute(Matrix loghyper, Matrix X, Matrix Xstar) {
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| 106 |
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| 107 | if(X.getColumnDimension()!=D)
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| 108 | throw new IllegalArgumentException("The number of dimensions specified on the covariance function "+D+" must agree with the size of the input vector"+X.getColumnDimension());
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| 109 | if(loghyper.getColumnDimension()!=1 || loghyper.getRowDimension()!=numParameters)
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| 110 | throw new IllegalArgumentException("Wrong number of hyperparameters, "+loghyper.getRowDimension()+" instead of "+numParameters);
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| 111 |
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| 112 | final Matrix ell = exp(loghyper.getMatrix(0,D-1,0,0)); // characteristic length scales
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| 113 | final double sf2 = Math.exp(2*loghyper.get(D,0)); // signal variance
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| 114 |
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| 115 | double[] a = new double[Xstar.getRowDimension()];
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| 116 | Arrays.fill(a,sf2);
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| 117 | Matrix A = new Matrix(a,Xstar.getRowDimension());
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| 118 |
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| 119 | Matrix diag = new Matrix(D,D);
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| 120 | for(int i=0; i<D; i++)
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| 121 | diag.set(i,i,1/ell.get(i,0));
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| 122 |
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| 123 | Matrix B = exp(squareDist(diag.times(X.transpose()),diag.times(Xstar.transpose())).times(-0.5)).times(sf2);
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| 124 |
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| 125 | return new Matrix[]{A,B};
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| 126 | }
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| 127 |
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| 128 |
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| 129 | /**
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| 130 | * Coompute the derivatives of this <code>PhoenixAlpha.CovarianceFunction</code> with respect
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| 131 | * to the hyperparameter with index <code>idx</code>
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| 132 | *
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| 133 | * @param loghyper hyperparameters
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| 134 | * @param X input dataset
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| 135 | * @param index hyperparameter index
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| 136 | * @return <code>Matrix</code> of derivatives
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| 137 | */
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| 138 | public Matrix computeDerivatives(Matrix loghyper, Matrix X, int index){
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| 139 |
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| 140 | if(X.getColumnDimension()!=D)
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| 141 | throw new IllegalArgumentException("The number of dimensions specified on the covariance function "+D+" must agree with the size of the input vector"+X.getColumnDimension());
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| 142 | if(loghyper.getColumnDimension()!=1 || loghyper.getRowDimension()!=numParameters)
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| 143 | throw new IllegalArgumentException("Wrong number of hyperparameters, "+loghyper.getRowDimension()+" instead of "+numParameters);
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| 144 | if(index>numParameters()-1)
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| 145 | throw new IllegalArgumentException("Wrong hyperparameters index "+index+" it should be smaller or equal to "+(numParameters()-1));
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| 146 |
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| 147 | Matrix A=null;
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| 148 |
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| 149 | final Matrix ell = exp(loghyper.getMatrix(0,D-1,0,0)); // characteristic length scales
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| 150 | final double sf2 = Math.exp(2*loghyper.get(D,0)); // signal variance
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| 151 | // noise variance
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| 152 |
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| 153 | if(K.getRowDimension()!=X.getRowDimension() || K.getColumnDimension()!=X.getRowDimension()){
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| 154 | Matrix diag = new Matrix(D,D);
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| 155 | for(int i=0; i<D; i++)
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| 156 | diag.set(i,i,1/ell.get(i,0));
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| 157 |
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| 158 | K = exp(squareDist(diag.times(X.transpose())).times(-0.5)).times(sf2); // SE covariance
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| 159 | }
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| 160 |
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| 161 | if(index<D){ //length scale parameters
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| 162 | Matrix col = squareDist(X.getMatrix(0,X.getRowDimension()-1,index,index).transpose().times(1/ell.get(index,0)));
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| 163 |
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| 164 | A = K.arrayTimes(col);
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| 165 | } else { // magnitude parameter
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| 166 | A=K.times(2);
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| 167 | K = null;
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| 168 | }
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| 169 |
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| 170 | return A;
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| 171 | }
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| 172 |
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| 173 | private static Matrix squareDist(Matrix a){
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| 174 | return squareDist(a,a);
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| 175 | }
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| 176 |
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| 177 | private static Matrix squareDist(Matrix a, Matrix b){
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| 178 | Matrix C = new Matrix(a.getColumnDimension(),b.getColumnDimension());
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| 179 | final int m = a.getColumnDimension();
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| 180 | final int n = b.getColumnDimension();
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| 181 | final int d = a.getRowDimension();
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| 182 |
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| 183 | for (int i=0; i<m; i++){
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| 184 | for (int j=0; j<n; j++) {
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| 185 | double z = 0.0;
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| 186 | for (int k=0; k<d; k++) { double t = a.get(k,i) - b.get(k,j); z += t*t; }
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| 187 | C.set(i,j,z);
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| 188 | }
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| 189 | }
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| 190 |
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| 191 | return C;
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| 192 | }
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| 193 |
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| 194 | }
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