source: src/main/java/agents/anac/y2015/Phoenix/GP/CovNNone.java@ 346

Last change on this file since 346 was 1, checked in by Wouter Pasman, 6 years ago

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1package agents.anac.y2015.Phoenix.GP;/* This file is part of the jgpml Project.
2 * http://github.com/renzodenardi/jgpml
3 *
4 * Copyright (c) 2011 Renzo De Nardi and Hugo Gravato-Marques
5 *
6 * Permission is hereby granted, free of charge, to any person
7 * obtaining a copy of this software and associated documentation
8 * files (the "Software"), to deal in the Software without
9 * restriction, including without limitation the rights to use,
10 * copy, modify, merge, publish, distribute, sublicense, and/or sell
11 * copies of the Software, and to permit persons to whom the
12 * Software is furnished to do so, subject to the following
13 * conditions:
14 *
15 * The above copyright notice and this permission notice shall be
16 * included in all copies or substantial portions of the Software.
17 *
18 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
19 * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
20 * OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
21 * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
22 * HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
23 * WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
24 * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
25 * OTHER DEALINGS IN THE SOFTWARE.
26 */
27
28import agents.Jama.Matrix;
29
30/**
31 * Neural network covariance function with a single parameter for the distance
32 * measure. The covariance function is parameterized as:
33 * <P>
34 * k(x^p,x^q) = sf2 * asin(x^p'*P*x^q / sqrt[(1+x^p'*P*x^p)*(1+x^q'*P*x^q)])
35 * <P>
36 * where the x^p and x^q vectors on the right hand side have an added extra bias
37 * entry with unit value. P is ell^-2 times the unit matrix and sf2 controls the
38 * signal variance. The hyperparameters are:
39 * <P>
40 * [ log(ell)
41 * log(sqrt(sf2) ]
42 */
43
44public class CovNNone implements CovarianceFunction{
45
46 double[][] k;
47 double[][] q;
48
49 public CovNNone(){}
50
51
52 /**
53 * Returns the number of hyperparameters of this<code>PhoenixAlpha.CovarianceFunction</code>
54 *
55 * @return number of hyperparameters
56 */
57 public int numParameters() {
58 return 2;
59 }
60
61 /**
62 * Compute covariance matrix of a dataset X
63 *
64 * @param loghyper column <code>Matrix</code> of hyperparameters
65 * @param X input dataset
66 * @return K covariance <code>Matrix</code>
67 */
68 public Matrix compute(Matrix loghyper, Matrix X) {
69
70 if(loghyper.getColumnDimension()!=1 || loghyper.getRowDimension()!=numParameters())
71 throw new IllegalArgumentException("Wrong number of hyperparameters, "+loghyper.getRowDimension()+" instead of "+numParameters());
72
73 final double ell = Math.exp(loghyper.get(0,0));
74 final double em2 = 1/(ell*ell);
75 final double oneplusem2 = 1+em2;
76 final double sf2 = Math.exp(2*loghyper.get(1,0));
77
78
79 final int m = X.getRowDimension();
80 final int n = X.getColumnDimension();
81 double[][] x= X.getArray();
82
83// Matrix Xc= X.times(1/ell);
84//
85// Q = Xc.times(Xc.transpose());
86// System.out.print("Q=");Q.print(Q.getColumnDimension(), 8);
87
88// Q = new Matrix(m,m);
89// double[][] q = Q.getArray();
90 q = new double[m][m];
91
92 for(int i=0;i<m;i++){
93 for(int j=0;j<m;j++){
94 double t = 0;
95 for(int k=0;k<n;k++){
96 t+=x[i][k]*x[j][k]*em2;
97 }
98 q[i][j]=t;
99 }
100 }
101// System.out.print("q=");Q.print(Q.getColumnDimension(), 8);
102
103// Matrix dQ = diag(Q);
104// Matrix dQT = dQ.transpose();
105// Matrix Qc = Q.copy();
106// K = addValue(Qc,em2).arrayRightDivide(sqrt(addValue(dQ,1+em2)).times(sqrt(addValue(dQT,1+em2))));
107// System.out.print("K=");K.print(K.getColumnDimension(), 8);
108
109 double[] dq = new double[m];
110 for(int i=0;i<m;i++){
111 dq[i]=Math.sqrt(oneplusem2+q[i][i]);
112 }
113
114 //K = new Matrix(m,m);
115 Matrix A = new Matrix(m,m);
116 double[][] k = new double[m][m];//K.getArray();
117 double[][] a =A.getArray();
118 for(int i=0;i<m;i++){
119 final double dqi = dq[i];
120 for(int j=0;j<m;j++){
121 final double t = (em2+q[i][j])/(dqi*dq[j]);
122 k[i][j]=t;
123 a[i][j]=sf2*Math.asin(t);
124 }
125 }
126// System.out.print("k=");K.print(K.getColumnDimension(), 8);
127// System.out.println("");
128
129// Matrix A = asin(K).times(sf2);
130 return A;
131 }
132
133 /**
134 * Compute compute test set covariances
135 *
136 * @param loghyper column <code>Matrix</code> of hyperparameters
137 * @param X input dataset
138 * @param Xstar test set
139 * @return [K(Xstar,Xstar) K(X,Xstar)]
140 */
141 public Matrix[] compute(Matrix loghyper, Matrix X, Matrix Xstar) {
142
143 if(loghyper.getColumnDimension()!=1 || loghyper.getRowDimension()!=numParameters())
144 throw new IllegalArgumentException("Wrong number of hyperparameters, "+loghyper.getRowDimension()+" instead of "+numParameters());
145
146 final double ell = Math.exp(loghyper.get(0,0));
147 final double em2 = 1/(ell*ell);
148 final double oneplusem2 = 1+em2;
149 final double sf2 = Math.exp(2*loghyper.get(1,0));
150
151
152
153 final int m = X.getRowDimension();
154 final int n = X.getColumnDimension();
155 double[][] x= X.getArray();
156 final int mstar = Xstar.getRowDimension();
157 final int nstar = Xstar.getColumnDimension();
158 double[][] xstar= Xstar.getArray();
159
160
161 double[] sumxstardotTimesxstar = new double[mstar];
162 for(int i=0; i<mstar; i++){
163 double t =0;
164 for(int j=0; j<nstar; j++){
165 final double tt = xstar[i][j];
166 t+=tt*tt*em2;
167 }
168 sumxstardotTimesxstar[i]=t;
169 }
170
171 Matrix A = new Matrix(mstar,1);
172 double[][] a = A.getArray();
173 for(int i=0; i<mstar; i++){
174 a[i][0]=sf2*Math.asin((em2+sumxstardotTimesxstar[i])/(oneplusem2+sumxstardotTimesxstar[i]));
175 }
176
177
178
179// X = X.times(1/ell);
180// Xstar = Xstar.times(1/ell);
181// Matrix tmp = sumRows(Xstar.arrayTimes(Xstar));
182//
183// Matrix tmp2 = tmp.copy();
184// addValue(tmp,em2);
185// addValue(tmp2,oneplusem2);
186// Matrix A = asin(tmp.arrayRightDivide(tmp2)).times(sf2);
187
188
189 double[] sumxdotTimesx = new double[m];
190 for(int i=0; i<m; i++){
191 double t =0;
192 for(int j=0; j<n; j++){
193 final double tt = x[i][j];
194 t+=tt*tt*em2;
195 }
196 sumxdotTimesx[i]=t+oneplusem2;
197 }
198
199 Matrix B = new Matrix(m,mstar);
200 double[][] b = B.getArray();
201 for(int i=0; i<m; i++){
202 final double[] xi = x[i];
203 for(int j=0; j<mstar; j++){
204 double t=0;
205 final double[] xstarj = xstar[j];
206 for(int k=0; k<n; k++){
207 t+=xi[k]*xstarj[k]*em2;
208 }
209 b[i][j]=t+em2;
210 }
211 }
212
213 for(int i=0; i<m; i++){
214 for(int j=0; j<mstar; j++){
215 b[i][j] = sf2*Math.asin(b[i][j]/Math.sqrt((sumxstardotTimesxstar[j]+oneplusem2)*sumxdotTimesx[i]));
216 }
217 }
218
219
220
221// tmp = sumRows(X.arrayTimes(X));
222// addValue(tmp,oneplusem2);
223//
224// tmp2=tmp2.transpose();
225//
226// tmp = addValue(X.times(Xstar.transpose()),em2).arrayRightDivide(sqrt(tmp.times(tmp2)));
227// Matrix B = asin(tmp).times(sf2);
228
229 //System.out.println("");
230 return new Matrix[]{A,B};
231 }
232
233 /**
234 * Coompute the derivatives of this <code>PhoenixAlpha.CovarianceFunction</code> with respect
235 * to the hyperparameter with index <code>idx</code>
236 *
237 * @param loghyper hyperparameters
238 * @param X input dataset
239 * @param index hyperparameter index
240 * @return <code>Matrix</code> of derivatives
241 */
242 public Matrix computeDerivatives(Matrix loghyper, Matrix X, int index) {
243
244 if(loghyper.getColumnDimension()!=1 || loghyper.getRowDimension()!=numParameters())
245 throw new IllegalArgumentException("Wrong number of hyperparameters, "+loghyper.getRowDimension()+" instead of "+numParameters());
246 if(index>numParameters()-1)
247 throw new IllegalArgumentException("Wrong hyperparameters index "+index+" it should be smaller or equal to "+(numParameters()-1));
248
249 final double ell = Math.exp(loghyper.get(0,0));
250 final double em2 = 1/(ell*ell);
251 final double oneplusem2 = 1+em2;
252 final double twosf2 = 2*Math.exp(2*loghyper.get(1,0));
253
254 final int m = X.getRowDimension();
255 final int n = X.getColumnDimension();
256 double[][] x= X.getArray();
257
258// Matrix X = XX.times(1/ell);
259
260 if(q==null || q.length!=m || q[0].length!=m) {
261 q = new double[m][m];
262
263 for(int i=0;i<m;i++){
264 for(int j=0;j<m;j++){
265 double t = 0;
266 for(int k=0;k<n;k++){
267 t+=x[i][k]*x[j][k]*em2;
268 }
269 q[i][j]=t;
270 }
271 }
272 }
273
274 double[] dq = new double[m];
275 for(int i=0;i<m;i++){
276 dq[i]=Math.sqrt(oneplusem2+q[i][i]);
277 }
278
279 if(k==null || k.length!=m || k[0].length!=m) {
280 k = new double[m][m];
281 for(int i=0;i<m;i++){
282 final double dqi = dq[i];
283 for(int j=0;j<m;j++){
284 final double t = (em2+q[i][j])/(dqi*dq[j]);
285 k[i][j]=t;
286 }
287 }
288 }
289
290// Matrix Xc= XX.times(1/ell);
291// Matrix Q = Xc.times(Xc.transpose());
292//
293// Matrix dQ = diag(Q);
294// Matrix dQT = dQ.transpose();
295// Matrix K = addValue(Q.copy(),em2).arrayRightDivide(sqrt(addValue(dQ.copy(),1+em2)).times(sqrt(addValue(dQT,1+em2))));
296// Matrix dQc = dQ.copy();
297
298 Matrix A;
299 if(index==0){
300 for(int i=0;i<m;i++){
301 dq[i]=oneplusem2+q[i][i];
302 }
303 double[] v = new double[m];
304 for(int i=0; i<m; i++){
305 double t =0;
306 for(int j=0; j<n; j++){
307 final double xij = x[i][j];
308 t+=xij*xij*em2;
309 }
310 v[i]=(t+em2)/(dq[i]);
311 }
312
313// Matrix test = addValue(sumRows(X.arrayTimes(X)),em2);
314// Matrix tmp = addValue(dQc,1+em2);
315// Matrix V = addValue(sumRows(X.arrayTimes(X)),em2).arrayRightDivide(tmp);
316//
317// tmp = sqrt(tmp);
318// tmp = addValue(Q.copy(),em2).arrayRightDivide(tmp.times(tmp.transpose()));
319
320 for(int i=0; i<m; i++){
321 final double vi = v[i];
322 for(int j=0; j<m; j++){
323 double t =(q[i][j]+em2)/(Math.sqrt(dq[i])*Math.sqrt(dq[j]));
324 final double kij = k[i][j];
325 q[i][j]=-twosf2*((t-(0.5*kij*(vi+v[j])))/Math.sqrt(1-kij*kij));
326 }
327 }
328
329// Matrix tmp2 = new Matrix(m,m);
330// for(int j=0; j<m; j++)
331// tmp2.setMatrix(0,m-1,j,j,V);
332//
333// tmp = tmp.minus(K.arrayTimes(tmp2.plus(tmp2.transpose())).times(0.5));
334//
335// A = tmp.arrayRightDivide(sqrtOneMinusSqr(K)).times(-twosf2);
336
337 A = new Matrix(q);
338// System.out.println("");
339 q=null;
340 } else{
341 for(int i=0; i<m; i++){
342 for(int j=0; j<m; j++){
343 k[i][j]=Math.asin(k[i][j])*twosf2;
344 }
345 }
346// A = asin(K).times(twosf2);
347// K=null;
348 A = new Matrix(k);
349 k=null;
350 }
351
352
353 return A;
354 }
355
356// private static Matrix sqrtOneMinusSqr(Matrix in){
357// Matrix out = new Matrix(in.getRowDimension(),in.getColumnDimension());
358// for(int i=0; i<in.getRowDimension(); i++)
359// for(int j=0; j<in.getColumnDimension(); j++) {
360// final double tmp = in.get(i,j);
361// out.set(i,j,Math.sqrt(1-tmp*tmp));
362// }
363// return out;
364// }
365
366 public static void main(String[] args) {
367
368 CovNNone cf = new CovNNone();
369
370 Matrix X = Matrix.identity(6,6);
371 Matrix logtheta = new Matrix(new double[][]{{0.1},{0.2}});
372
373 Matrix z =new Matrix(new double[][]{{1,2,3,4,5,6},{1,2,3,4,5,6}});
374
375// System.out.println("")
376//
377// long start = System.currentTimeMillis()
378//
379// Matrix K = cf.compute(logtheta,X);
380// long stop = System.currentTimeMillis();
381// System.out.println(""+(stop-start));
382
383// K.print(K.getColumnDimension(), 15);
384
385// long start = System.currentTimeMillis();
386// Matrix[] res = cf.compute(logtheta,X,z);
387// long stop = System.currentTimeMillis();
388// System.out.println(""+(stop-start));
389
390// res[0].print(res[0].getColumnDimension(), 8);
391// res[1].print(res[1].getColumnDimension(), 8);
392
393 Matrix d = cf.computeDerivatives(logtheta,X,1);
394
395 d.print(d.getColumnDimension(), 8);
396
397 }
398}
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