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18 package org.apache.commons.math4.legacy.analysis;
19
20 import org.apache.commons.math4.legacy.analysis.differentiation.DerivativeStructure;
21 import org.apache.commons.math4.legacy.analysis.differentiation.MultivariateDifferentiableFunction;
22 import org.apache.commons.math4.legacy.analysis.differentiation.UnivariateDifferentiableFunction;
23 import org.apache.commons.math4.legacy.analysis.function.Add;
24 import org.apache.commons.math4.legacy.analysis.function.Constant;
25 import org.apache.commons.math4.legacy.analysis.function.Cos;
26 import org.apache.commons.math4.legacy.analysis.function.Cosh;
27 import org.apache.commons.math4.legacy.analysis.function.Divide;
28 import org.apache.commons.math4.legacy.analysis.function.Identity;
29 import org.apache.commons.math4.legacy.analysis.function.Inverse;
30 import org.apache.commons.math4.legacy.analysis.function.Log;
31 import org.apache.commons.math4.legacy.analysis.function.Max;
32 import org.apache.commons.math4.legacy.analysis.function.Min;
33 import org.apache.commons.math4.legacy.analysis.function.Minus;
34 import org.apache.commons.math4.legacy.analysis.function.Multiply;
35 import org.apache.commons.math4.legacy.analysis.function.Pow;
36 import org.apache.commons.math4.legacy.analysis.function.Power;
37 import org.apache.commons.math4.legacy.analysis.function.Sin;
38 import org.apache.commons.math4.legacy.analysis.function.Sinc;
39 import org.apache.commons.math4.legacy.exception.DimensionMismatchException;
40 import org.apache.commons.math4.legacy.exception.NumberIsTooLargeException;
41 import org.apache.commons.math4.core.jdkmath.JdkMath;
42 import org.junit.Assert;
43 import org.junit.Test;
44
45
46
47
48 public class FunctionUtilsTest {
49 private final double EPS = JdkMath.ulp(1d);
50
51 @Test
52 public void testCompose() {
53 UnivariateFunction id = new Identity();
54 Assert.assertEquals(3, FunctionUtils.compose(id, id, id).value(3), EPS);
55
56 UnivariateFunction c = new Constant(4);
57 Assert.assertEquals(4, FunctionUtils.compose(id, c).value(3), EPS);
58 Assert.assertEquals(4, FunctionUtils.compose(c, id).value(3), EPS);
59
60 UnivariateFunction m = new Minus();
61 Assert.assertEquals(-3, FunctionUtils.compose(m).value(3), EPS);
62 Assert.assertEquals(3, FunctionUtils.compose(m, m).value(3), EPS);
63
64 UnivariateFunction inv = new Inverse();
65 Assert.assertEquals(-0.25, FunctionUtils.compose(inv, m, c, id).value(3), EPS);
66
67 UnivariateFunction pow = new Power(2);
68 Assert.assertEquals(81, FunctionUtils.compose(pow, pow).value(3), EPS);
69 }
70
71 @Test
72 public void testComposeDifferentiable() {
73 UnivariateDifferentiableFunction id = new Identity();
74 Assert.assertEquals(1, FunctionUtils.compose(id, id, id).value(new DerivativeStructure(1, 1, 0, 3)).getPartialDerivative(1), EPS);
75
76 UnivariateDifferentiableFunction c = new Constant(4);
77 Assert.assertEquals(0, FunctionUtils.compose(id, c).value(new DerivativeStructure(1, 1, 0, 3)).getPartialDerivative(1), EPS);
78 Assert.assertEquals(0, FunctionUtils.compose(c, id).value(new DerivativeStructure(1, 1, 0, 3)).getPartialDerivative(1), EPS);
79
80 UnivariateDifferentiableFunction m = new Minus();
81 Assert.assertEquals(-1, FunctionUtils.compose(m).value(new DerivativeStructure(1, 1, 0, 3)).getPartialDerivative(1), EPS);
82 Assert.assertEquals(1, FunctionUtils.compose(m, m).value(new DerivativeStructure(1, 1, 0, 3)).getPartialDerivative(1), EPS);
83
84 UnivariateDifferentiableFunction inv = new Inverse();
85 Assert.assertEquals(0.25, FunctionUtils.compose(inv, m, id).value(new DerivativeStructure(1, 1, 0, 2)).getPartialDerivative(1), EPS);
86
87 UnivariateDifferentiableFunction pow = new Power(2);
88 Assert.assertEquals(108, FunctionUtils.compose(pow, pow).value(new DerivativeStructure(1, 1, 0, 3)).getPartialDerivative(1), EPS);
89
90 UnivariateDifferentiableFunction log = new Log();
91 double a = 9876.54321;
92 Assert.assertEquals(pow.value(new DerivativeStructure(1, 1, 0, a)).getPartialDerivative(1) / pow.value(a),
93 FunctionUtils.compose(log, pow).value(new DerivativeStructure(1, 1, 0, a)).getPartialDerivative(1), EPS);
94 }
95
96 @Test
97 public void testAdd() {
98 UnivariateFunction id = new Identity();
99 UnivariateFunction c = new Constant(4);
100 UnivariateFunction m = new Minus();
101 UnivariateFunction inv = new Inverse();
102
103 Assert.assertEquals(4.5, FunctionUtils.add(inv, m, c, id).value(2), EPS);
104 Assert.assertEquals(4 + 2, FunctionUtils.add(c, id).value(2), EPS);
105 Assert.assertEquals(4 - 2, FunctionUtils.add(c, FunctionUtils.compose(m, id)).value(2), EPS);
106 }
107
108 @Test
109 public void testAddDifferentiable() {
110 UnivariateDifferentiableFunction sin = new Sin();
111 UnivariateDifferentiableFunction c = new Constant(4);
112 UnivariateDifferentiableFunction m = new Minus();
113 UnivariateDifferentiableFunction inv = new Inverse();
114
115 final double a = 123.456;
116 Assert.assertEquals(- 1 / (a * a) -1 + JdkMath.cos(a),
117 FunctionUtils.add(inv, m, c, sin).value(new DerivativeStructure(1, 1, 0, a)).getPartialDerivative(1),
118 EPS);
119 }
120
121 @Test
122 public void testMultiply() {
123 UnivariateFunction c = new Constant(4);
124 Assert.assertEquals(16, FunctionUtils.multiply(c, c).value(12345), EPS);
125
126 UnivariateFunction inv = new Inverse();
127 UnivariateFunction pow = new Power(2);
128 Assert.assertEquals(1, FunctionUtils.multiply(FunctionUtils.compose(inv, pow), pow).value(3.5), EPS);
129 }
130
131 @Test
132 public void testMultiplyDifferentiable() {
133 UnivariateDifferentiableFunction c = new Constant(4);
134 UnivariateDifferentiableFunction id = new Identity();
135 final double a = 1.2345678;
136 Assert.assertEquals(8 * a, FunctionUtils.multiply(c, id, id).value(new DerivativeStructure(1, 1, 0, a)).getPartialDerivative(1), EPS);
137
138 UnivariateDifferentiableFunction inv = new Inverse();
139 UnivariateDifferentiableFunction pow = new Power(2.5);
140 UnivariateDifferentiableFunction cos = new Cos();
141 Assert.assertEquals(1.5 * JdkMath.sqrt(a) * JdkMath.cos(a) - JdkMath.pow(a, 1.5) * JdkMath.sin(a),
142 FunctionUtils.multiply(inv, pow, cos).value(new DerivativeStructure(1, 1, 0, a)).getPartialDerivative(1), EPS);
143
144 UnivariateDifferentiableFunction cosh = new Cosh();
145 Assert.assertEquals(1.5 * JdkMath.sqrt(a) * JdkMath.cosh(a) + JdkMath.pow(a, 1.5) * JdkMath.sinh(a),
146 FunctionUtils.multiply(inv, pow, cosh).value(new DerivativeStructure(1, 1, 0, a)).getPartialDerivative(1), 8 * EPS);
147 }
148
149 @Test
150 public void testCombine() {
151 BivariateFunction bi = new Add();
152 UnivariateFunction id = new Identity();
153 UnivariateFunction m = new Minus();
154 UnivariateFunction c = FunctionUtils.combine(bi, id, m);
155 Assert.assertEquals(0, c.value(2.3456), EPS);
156
157 bi = new Multiply();
158 UnivariateFunction inv = new Inverse();
159 c = FunctionUtils.combine(bi, id, inv);
160 Assert.assertEquals(1, c.value(2.3456), EPS);
161 }
162
163 @Test
164 public void testCollector() {
165 BivariateFunction bi = new Add();
166 MultivariateFunction coll = FunctionUtils.collector(bi, 0);
167 Assert.assertEquals(10, coll.value(new double[] {1, 2, 3, 4}), EPS);
168
169 bi = new Multiply();
170 coll = FunctionUtils.collector(bi, 1);
171 Assert.assertEquals(24, coll.value(new double[] {1, 2, 3, 4}), EPS);
172
173 bi = new Max();
174 coll = FunctionUtils.collector(bi, Double.NEGATIVE_INFINITY);
175 Assert.assertEquals(10, coll.value(new double[] {1, -2, 7.5, 10, -24, 9.99}), 0);
176
177 bi = new Min();
178 coll = FunctionUtils.collector(bi, Double.POSITIVE_INFINITY);
179 Assert.assertEquals(-24, coll.value(new double[] {1, -2, 7.5, 10, -24, 9.99}), 0);
180 }
181
182 @Test
183 public void testSinc() {
184 BivariateFunction div = new Divide();
185 UnivariateFunction sin = new Sin();
186 UnivariateFunction id = new Identity();
187 UnivariateFunction sinc1 = FunctionUtils.combine(div, sin, id);
188 UnivariateFunction sinc2 = new Sinc();
189
190 for (int i = 0; i < 10; i++) {
191 double x = JdkMath.random();
192 Assert.assertEquals(sinc1.value(x), sinc2.value(x), EPS);
193 }
194 }
195
196 @Test
197 public void testFixingArguments() {
198 UnivariateFunction scaler = FunctionUtils.fix1stArgument(new Multiply(), 10);
199 Assert.assertEquals(1.23456, scaler.value(0.123456), EPS);
200
201 UnivariateFunction pow1 = new Power(2);
202 UnivariateFunction pow2 = FunctionUtils.fix2ndArgument(new Pow(), 2);
203
204 for (int i = 0; i < 10; i++) {
205 double x = JdkMath.random() * 10;
206 Assert.assertEquals(pow1.value(x), pow2.value(x), 0);
207 }
208 }
209
210 @Test
211 public void testToDifferentiableUnivariate() {
212
213 final UnivariateFunction f0 = new UnivariateFunction() {
214 @Override
215 public double value(final double x) {
216 return x * x;
217 }
218 };
219 final UnivariateFunction f1 = new UnivariateFunction() {
220 @Override
221 public double value(final double x) {
222 return 2 * x;
223 }
224 };
225 final UnivariateFunction f2 = new UnivariateFunction() {
226 @Override
227 public double value(final double x) {
228 return 2;
229 }
230 };
231 final UnivariateDifferentiableFunction f = FunctionUtils.toDifferentiable(f0, f1, f2);
232
233 for (double t = -1.0; t < 1; t += 0.01) {
234
235 DerivativeStructure dsT = new DerivativeStructure(1, 2, 0, t);
236 DerivativeStructure y = f.value(dsT.sin());
237 Assert.assertEquals(JdkMath.sin(t) * JdkMath.sin(t), f.value(JdkMath.sin(t)), 1.0e-15);
238 Assert.assertEquals(JdkMath.sin(t) * JdkMath.sin(t), y.getValue(), 1.0e-15);
239 Assert.assertEquals(2 * JdkMath.cos(t) * JdkMath.sin(t), y.getPartialDerivative(1), 1.0e-15);
240 Assert.assertEquals(2 * (1 - 2 * JdkMath.sin(t) * JdkMath.sin(t)), y.getPartialDerivative(2), 1.0e-15);
241 }
242
243 try {
244 f.value(new DerivativeStructure(1, 3, 0.0));
245 Assert.fail("an exception should have been thrown");
246 } catch (NumberIsTooLargeException e) {
247 Assert.assertEquals(2, e.getMax());
248 Assert.assertEquals(3, e.getArgument());
249 }
250 }
251
252 @Test
253 public void testToDifferentiableMultivariate() {
254
255 final double a = 1.5;
256 final double b = 0.5;
257 final MultivariateFunction f = new MultivariateFunction() {
258 @Override
259 public double value(final double[] point) {
260 return a * point[0] + b * point[1];
261 }
262 };
263 final MultivariateVectorFunction gradient = new MultivariateVectorFunction() {
264 @Override
265 public double[] value(final double[] point) {
266 return new double[] { a, b };
267 }
268 };
269 final MultivariateDifferentiableFunction mdf = FunctionUtils.toDifferentiable(f, gradient);
270
271 for (double t = -1.0; t < 1; t += 0.01) {
272
273 DerivativeStructure dsT = new DerivativeStructure(1, 1, 0, t);
274 DerivativeStructure y = mdf.value(new DerivativeStructure[] { dsT.sin(), dsT.cos() });
275 Assert.assertEquals(a * JdkMath.sin(t) + b * JdkMath.cos(t), y.getValue(), 1.0e-15);
276 Assert.assertEquals(a * JdkMath.cos(t) - b * JdkMath.sin(t), y.getPartialDerivative(1), 1.0e-15);
277 }
278
279 for (double u = -1.0; u < 1; u += 0.01) {
280 DerivativeStructure dsU = new DerivativeStructure(2, 1, 0, u);
281 for (double v = -1.0; v < 1; v += 0.01) {
282 DerivativeStructure dsV = new DerivativeStructure(2, 1, 1, v);
283 DerivativeStructure y = mdf.value(new DerivativeStructure[] { dsU, dsV });
284 Assert.assertEquals(a * u + b * v, mdf.value(new double[] { u, v }), 1.0e-15);
285 Assert.assertEquals(a * u + b * v, y.getValue(), 1.0e-15);
286 Assert.assertEquals(a, y.getPartialDerivative(1, 0), 1.0e-15);
287 Assert.assertEquals(b, y.getPartialDerivative(0, 1), 1.0e-15);
288 }
289 }
290
291 try {
292 mdf.value(new DerivativeStructure[] { new DerivativeStructure(1, 3, 0.0), new DerivativeStructure(1, 3, 0.0) });
293 Assert.fail("an exception should have been thrown");
294 } catch (NumberIsTooLargeException e) {
295 Assert.assertEquals(1, e.getMax());
296 Assert.assertEquals(3, e.getArgument());
297 }
298 }
299
300 @Test
301 public void testToDifferentiableMultivariateInconsistentGradient() {
302
303 final double a = 1.5;
304 final double b = 0.5;
305 final MultivariateFunction f = new MultivariateFunction() {
306 @Override
307 public double value(final double[] point) {
308 return a * point[0] + b * point[1];
309 }
310 };
311 final MultivariateVectorFunction gradient = new MultivariateVectorFunction() {
312 @Override
313 public double[] value(final double[] point) {
314 return new double[] { a, b, 0.0 };
315 }
316 };
317 final MultivariateDifferentiableFunction mdf = FunctionUtils.toDifferentiable(f, gradient);
318
319 try {
320 DerivativeStructure dsT = new DerivativeStructure(1, 1, 0, 0.0);
321 mdf.value(new DerivativeStructure[] { dsT.sin(), dsT.cos() });
322 Assert.fail("an exception should have been thrown");
323 } catch (DimensionMismatchException e) {
324 Assert.assertEquals(2, e.getDimension());
325 Assert.assertEquals(3, e.getArgument());
326 }
327 }
328
329 @Test
330 public void testDerivativeUnivariate() {
331
332 final UnivariateDifferentiableFunction f = new UnivariateDifferentiableFunction() {
333
334 @Override
335 public double value(double x) {
336 return x * x;
337 }
338
339 @Override
340 public DerivativeStructure value(DerivativeStructure x) {
341 return x.multiply(x);
342 }
343 };
344
345 final UnivariateFunction f0 = FunctionUtils.derivative(f, 0);
346 final UnivariateFunction f1 = FunctionUtils.derivative(f, 1);
347 final UnivariateFunction f2 = FunctionUtils.derivative(f, 2);
348
349 for (double t = -1.0; t < 1; t += 0.01) {
350 Assert.assertEquals(t * t, f0.value(t), 1.0e-15);
351 Assert.assertEquals(2 * t, f1.value(t), 1.0e-15);
352 Assert.assertEquals(2, f2.value(t), 1.0e-15);
353 }
354 }
355
356 @Test
357 public void testDerivativeMultivariate() {
358
359 final double a = 1.5;
360 final double b = 0.5;
361 final double c = 0.25;
362 final MultivariateDifferentiableFunction mdf = new MultivariateDifferentiableFunction() {
363
364 @Override
365 public double value(double[] point) {
366 return a * point[0] * point[0] + b * point[1] * point[1] + c * point[0] * point[1];
367 }
368
369 @Override
370 public DerivativeStructure value(DerivativeStructure[] point) {
371 DerivativeStructure x = point[0];
372 DerivativeStructure y = point[1];
373 DerivativeStructure x2 = x.multiply(x);
374 DerivativeStructure y2 = y.multiply(y);
375 DerivativeStructure xy = x.multiply(y);
376 return x2.multiply(a).add(y2.multiply(b)).add(xy.multiply(c));
377 }
378 };
379
380 final MultivariateFunction f = FunctionUtils.derivative(mdf, new int[] { 0, 0 });
381 final MultivariateFunction dfdx = FunctionUtils.derivative(mdf, new int[] { 1, 0 });
382 final MultivariateFunction dfdy = FunctionUtils.derivative(mdf, new int[] { 0, 1 });
383 final MultivariateFunction d2fdx2 = FunctionUtils.derivative(mdf, new int[] { 2, 0 });
384 final MultivariateFunction d2fdy2 = FunctionUtils.derivative(mdf, new int[] { 0, 2 });
385 final MultivariateFunction d2fdxdy = FunctionUtils.derivative(mdf, new int[] { 1, 1 });
386
387 for (double x = -1.0; x < 1; x += 0.01) {
388 for (double y = -1.0; y < 1; y += 0.01) {
389 Assert.assertEquals(a * x * x + b * y * y + c * x * y, f.value(new double[] { x, y }), 1.0e-15);
390 Assert.assertEquals(2 * a * x + c * y, dfdx.value(new double[] { x, y }), 1.0e-15);
391 Assert.assertEquals(2 * b * y + c * x, dfdy.value(new double[] { x, y }), 1.0e-15);
392 Assert.assertEquals(2 * a, d2fdx2.value(new double[] { x, y }), 1.0e-15);
393 Assert.assertEquals(2 * b, d2fdy2.value(new double[] { x, y }), 1.0e-15);
394 Assert.assertEquals(c, d2fdxdy.value(new double[] { x, y }), 1.0e-15);
395 }
396 }
397 }
398 }