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* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.apache.commons.math4.analysis;
import org.apache.commons.math4.analysis.differentiation.DerivativeStructure;
import org.apache.commons.math4.analysis.differentiation.MultivariateDifferentiableFunction;
import org.apache.commons.math4.analysis.differentiation.UnivariateDifferentiableFunction;
import org.apache.commons.math4.analysis.function.Add;
import org.apache.commons.math4.analysis.function.Constant;
import org.apache.commons.math4.analysis.function.Cos;
import org.apache.commons.math4.analysis.function.Cosh;
import org.apache.commons.math4.analysis.function.Divide;
import org.apache.commons.math4.analysis.function.Identity;
import org.apache.commons.math4.analysis.function.Inverse;
import org.apache.commons.math4.analysis.function.Log;
import org.apache.commons.math4.analysis.function.Max;
import org.apache.commons.math4.analysis.function.Min;
import org.apache.commons.math4.analysis.function.Minus;
import org.apache.commons.math4.analysis.function.Multiply;
import org.apache.commons.math4.analysis.function.Pow;
import org.apache.commons.math4.analysis.function.Power;
import org.apache.commons.math4.analysis.function.Sin;
import org.apache.commons.math4.analysis.function.Sinc;
import org.apache.commons.math4.exception.DimensionMismatchException;
import org.apache.commons.math4.exception.NotStrictlyPositiveException;
import org.apache.commons.math4.exception.NumberIsTooLargeException;
import org.apache.commons.math4.util.FastMath;
import org.junit.Assert;
import org.junit.Test;
/**
* Test for {@link FunctionUtils}.
*/
public class FunctionUtilsTest {
private final double EPS = FastMath.ulp(1d);
@Test
public void testCompose() {
UnivariateFunction id = new Identity();
Assert.assertEquals(3, FunctionUtils.compose(id, id, id).value(3), EPS);
UnivariateFunction c = new Constant(4);
Assert.assertEquals(4, FunctionUtils.compose(id, c).value(3), EPS);
Assert.assertEquals(4, FunctionUtils.compose(c, id).value(3), EPS);
UnivariateFunction m = new Minus();
Assert.assertEquals(-3, FunctionUtils.compose(m).value(3), EPS);
Assert.assertEquals(3, FunctionUtils.compose(m, m).value(3), EPS);
UnivariateFunction inv = new Inverse();
Assert.assertEquals(-0.25, FunctionUtils.compose(inv, m, c, id).value(3), EPS);
UnivariateFunction pow = new Power(2);
Assert.assertEquals(81, FunctionUtils.compose(pow, pow).value(3), EPS);
}
@Test
public void testComposeDifferentiable() {
UnivariateDifferentiableFunction id = new Identity();
Assert.assertEquals(1, FunctionUtils.compose(id, id, id).value(new DerivativeStructure(1, 1, 0, 3)).getPartialDerivative(1), EPS);
UnivariateDifferentiableFunction c = new Constant(4);
Assert.assertEquals(0, FunctionUtils.compose(id, c).value(new DerivativeStructure(1, 1, 0, 3)).getPartialDerivative(1), EPS);
Assert.assertEquals(0, FunctionUtils.compose(c, id).value(new DerivativeStructure(1, 1, 0, 3)).getPartialDerivative(1), EPS);
UnivariateDifferentiableFunction m = new Minus();
Assert.assertEquals(-1, FunctionUtils.compose(m).value(new DerivativeStructure(1, 1, 0, 3)).getPartialDerivative(1), EPS);
Assert.assertEquals(1, FunctionUtils.compose(m, m).value(new DerivativeStructure(1, 1, 0, 3)).getPartialDerivative(1), EPS);
UnivariateDifferentiableFunction inv = new Inverse();
Assert.assertEquals(0.25, FunctionUtils.compose(inv, m, id).value(new DerivativeStructure(1, 1, 0, 2)).getPartialDerivative(1), EPS);
UnivariateDifferentiableFunction pow = new Power(2);
Assert.assertEquals(108, FunctionUtils.compose(pow, pow).value(new DerivativeStructure(1, 1, 0, 3)).getPartialDerivative(1), EPS);
UnivariateDifferentiableFunction log = new Log();
double a = 9876.54321;
Assert.assertEquals(pow.value(new DerivativeStructure(1, 1, 0, a)).getPartialDerivative(1) / pow.value(a),
FunctionUtils.compose(log, pow).value(new DerivativeStructure(1, 1, 0, a)).getPartialDerivative(1), EPS);
}
@Test
public void testAdd() {
UnivariateFunction id = new Identity();
UnivariateFunction c = new Constant(4);
UnivariateFunction m = new Minus();
UnivariateFunction inv = new Inverse();
Assert.assertEquals(4.5, FunctionUtils.add(inv, m, c, id).value(2), EPS);
Assert.assertEquals(4 + 2, FunctionUtils.add(c, id).value(2), EPS);
Assert.assertEquals(4 - 2, FunctionUtils.add(c, FunctionUtils.compose(m, id)).value(2), EPS);
}
@Test
public void testAddDifferentiable() {
UnivariateDifferentiableFunction sin = new Sin();
UnivariateDifferentiableFunction c = new Constant(4);
UnivariateDifferentiableFunction m = new Minus();
UnivariateDifferentiableFunction inv = new Inverse();
final double a = 123.456;
Assert.assertEquals(- 1 / (a * a) -1 + FastMath.cos(a),
FunctionUtils.add(inv, m, c, sin).value(new DerivativeStructure(1, 1, 0, a)).getPartialDerivative(1),
EPS);
}
@Test
public void testMultiply() {
UnivariateFunction c = new Constant(4);
Assert.assertEquals(16, FunctionUtils.multiply(c, c).value(12345), EPS);
UnivariateFunction inv = new Inverse();
UnivariateFunction pow = new Power(2);
Assert.assertEquals(1, FunctionUtils.multiply(FunctionUtils.compose(inv, pow), pow).value(3.5), EPS);
}
@Test
public void testMultiplyDifferentiable() {
UnivariateDifferentiableFunction c = new Constant(4);
UnivariateDifferentiableFunction id = new Identity();
final double a = 1.2345678;
Assert.assertEquals(8 * a, FunctionUtils.multiply(c, id, id).value(new DerivativeStructure(1, 1, 0, a)).getPartialDerivative(1), EPS);
UnivariateDifferentiableFunction inv = new Inverse();
UnivariateDifferentiableFunction pow = new Power(2.5);
UnivariateDifferentiableFunction cos = new Cos();
Assert.assertEquals(1.5 * FastMath.sqrt(a) * FastMath.cos(a) - FastMath.pow(a, 1.5) * FastMath.sin(a),
FunctionUtils.multiply(inv, pow, cos).value(new DerivativeStructure(1, 1, 0, a)).getPartialDerivative(1), EPS);
UnivariateDifferentiableFunction cosh = new Cosh();
Assert.assertEquals(1.5 * FastMath.sqrt(a) * FastMath.cosh(a) + FastMath.pow(a, 1.5) * FastMath.sinh(a),
FunctionUtils.multiply(inv, pow, cosh).value(new DerivativeStructure(1, 1, 0, a)).getPartialDerivative(1), 8 * EPS);
}
@Test
public void testCombine() {
BivariateFunction bi = new Add();
UnivariateFunction id = new Identity();
UnivariateFunction m = new Minus();
UnivariateFunction c = FunctionUtils.combine(bi, id, m);
Assert.assertEquals(0, c.value(2.3456), EPS);
bi = new Multiply();
UnivariateFunction inv = new Inverse();
c = FunctionUtils.combine(bi, id, inv);
Assert.assertEquals(1, c.value(2.3456), EPS);
}
@Test
public void testCollector() {
BivariateFunction bi = new Add();
MultivariateFunction coll = FunctionUtils.collector(bi, 0);
Assert.assertEquals(10, coll.value(new double[] {1, 2, 3, 4}), EPS);
bi = new Multiply();
coll = FunctionUtils.collector(bi, 1);
Assert.assertEquals(24, coll.value(new double[] {1, 2, 3, 4}), EPS);
bi = new Max();
coll = FunctionUtils.collector(bi, Double.NEGATIVE_INFINITY);
Assert.assertEquals(10, coll.value(new double[] {1, -2, 7.5, 10, -24, 9.99}), 0);
bi = new Min();
coll = FunctionUtils.collector(bi, Double.POSITIVE_INFINITY);
Assert.assertEquals(-24, coll.value(new double[] {1, -2, 7.5, 10, -24, 9.99}), 0);
}
@Test
public void testSinc() {
BivariateFunction div = new Divide();
UnivariateFunction sin = new Sin();
UnivariateFunction id = new Identity();
UnivariateFunction sinc1 = FunctionUtils.combine(div, sin, id);
UnivariateFunction sinc2 = new Sinc();
for (int i = 0; i < 10; i++) {
double x = FastMath.random();
Assert.assertEquals(sinc1.value(x), sinc2.value(x), EPS);
}
}
@Test
public void testFixingArguments() {
UnivariateFunction scaler = FunctionUtils.fix1stArgument(new Multiply(), 10);
Assert.assertEquals(1.23456, scaler.value(0.123456), EPS);
UnivariateFunction pow1 = new Power(2);
UnivariateFunction pow2 = FunctionUtils.fix2ndArgument(new Pow(), 2);
for (int i = 0; i < 10; i++) {
double x = FastMath.random() * 10;
Assert.assertEquals(pow1.value(x), pow2.value(x), 0);
}
}
@Test(expected = NumberIsTooLargeException.class)
public void testSampleWrongBounds(){
FunctionUtils.sample(new Sin(), FastMath.PI, 0.0, 10);
}
@Test(expected = NotStrictlyPositiveException.class)
public void testSampleNegativeNumberOfPoints(){
FunctionUtils.sample(new Sin(), 0.0, FastMath.PI, -1);
}
@Test(expected = NotStrictlyPositiveException.class)
public void testSampleNullNumberOfPoints(){
FunctionUtils.sample(new Sin(), 0.0, FastMath.PI, 0);
}
@Test
public void testSample() {
final int n = 11;
final double min = 0.0;
final double max = FastMath.PI;
final double[] actual = FunctionUtils.sample(new Sin(), min, max, n);
for (int i = 0; i < n; i++) {
final double x = min + (max - min) / n * i;
Assert.assertEquals("x = " + x, FastMath.sin(x), actual[i], 0.0);
}
}
@Test
public void testToDifferentiableUnivariate() {
final UnivariateFunction f0 = new UnivariateFunction() {
@Override
public double value(final double x) {
return x * x;
}
};
final UnivariateFunction f1 = new UnivariateFunction() {
@Override
public double value(final double x) {
return 2 * x;
}
};
final UnivariateFunction f2 = new UnivariateFunction() {
@Override
public double value(final double x) {
return 2;
}
};
final UnivariateDifferentiableFunction f = FunctionUtils.toDifferentiable(f0, f1, f2);
for (double t = -1.0; t < 1; t += 0.01) {
// x = sin(t)
DerivativeStructure dsT = new DerivativeStructure(1, 2, 0, t);
DerivativeStructure y = f.value(dsT.sin());
Assert.assertEquals(FastMath.sin(t) * FastMath.sin(t), f.value(FastMath.sin(t)), 1.0e-15);
Assert.assertEquals(FastMath.sin(t) * FastMath.sin(t), y.getValue(), 1.0e-15);
Assert.assertEquals(2 * FastMath.cos(t) * FastMath.sin(t), y.getPartialDerivative(1), 1.0e-15);
Assert.assertEquals(2 * (1 - 2 * FastMath.sin(t) * FastMath.sin(t)), y.getPartialDerivative(2), 1.0e-15);
}
try {
f.value(new DerivativeStructure(1, 3, 0.0));
Assert.fail("an exception should have been thrown");
} catch (NumberIsTooLargeException e) {
Assert.assertEquals(2, e.getMax());
Assert.assertEquals(3, e.getArgument());
}
}
@Test
public void testToDifferentiableMultivariate() {
final double a = 1.5;
final double b = 0.5;
final MultivariateFunction f = new MultivariateFunction() {
@Override
public double value(final double[] point) {
return a * point[0] + b * point[1];
}
};
final MultivariateVectorFunction gradient = new MultivariateVectorFunction() {
@Override
public double[] value(final double[] point) {
return new double[] { a, b };
}
};
final MultivariateDifferentiableFunction mdf = FunctionUtils.toDifferentiable(f, gradient);
for (double t = -1.0; t < 1; t += 0.01) {
// x = sin(t), y = cos(t), hence the method really becomes univariate
DerivativeStructure dsT = new DerivativeStructure(1, 1, 0, t);
DerivativeStructure y = mdf.value(new DerivativeStructure[] { dsT.sin(), dsT.cos() });
Assert.assertEquals(a * FastMath.sin(t) + b * FastMath.cos(t), y.getValue(), 1.0e-15);
Assert.assertEquals(a * FastMath.cos(t) - b * FastMath.sin(t), y.getPartialDerivative(1), 1.0e-15);
}
for (double u = -1.0; u < 1; u += 0.01) {
DerivativeStructure dsU = new DerivativeStructure(2, 1, 0, u);
for (double v = -1.0; v < 1; v += 0.01) {
DerivativeStructure dsV = new DerivativeStructure(2, 1, 1, v);
DerivativeStructure y = mdf.value(new DerivativeStructure[] { dsU, dsV });
Assert.assertEquals(a * u + b * v, mdf.value(new double[] { u, v }), 1.0e-15);
Assert.assertEquals(a * u + b * v, y.getValue(), 1.0e-15);
Assert.assertEquals(a, y.getPartialDerivative(1, 0), 1.0e-15);
Assert.assertEquals(b, y.getPartialDerivative(0, 1), 1.0e-15);
}
}
try {
mdf.value(new DerivativeStructure[] { new DerivativeStructure(1, 3, 0.0), new DerivativeStructure(1, 3, 0.0) });
Assert.fail("an exception should have been thrown");
} catch (NumberIsTooLargeException e) {
Assert.assertEquals(1, e.getMax());
Assert.assertEquals(3, e.getArgument());
}
}
@Test
public void testToDifferentiableMultivariateInconsistentGradient() {
final double a = 1.5;
final double b = 0.5;
final MultivariateFunction f = new MultivariateFunction() {
@Override
public double value(final double[] point) {
return a * point[0] + b * point[1];
}
};
final MultivariateVectorFunction gradient = new MultivariateVectorFunction() {
@Override
public double[] value(final double[] point) {
return new double[] { a, b, 0.0 };
}
};
final MultivariateDifferentiableFunction mdf = FunctionUtils.toDifferentiable(f, gradient);
try {
DerivativeStructure dsT = new DerivativeStructure(1, 1, 0, 0.0);
mdf.value(new DerivativeStructure[] { dsT.sin(), dsT.cos() });
Assert.fail("an exception should have been thrown");
} catch (DimensionMismatchException e) {
Assert.assertEquals(2, e.getDimension());
Assert.assertEquals(3, e.getArgument());
}
}
@Test
public void testDerivativeUnivariate() {
final UnivariateDifferentiableFunction f = new UnivariateDifferentiableFunction() {
@Override
public double value(double x) {
return x * x;
}
@Override
public DerivativeStructure value(DerivativeStructure x) {
return x.multiply(x);
}
};
final UnivariateFunction f0 = FunctionUtils.derivative(f, 0);
final UnivariateFunction f1 = FunctionUtils.derivative(f, 1);
final UnivariateFunction f2 = FunctionUtils.derivative(f, 2);
for (double t = -1.0; t < 1; t += 0.01) {
Assert.assertEquals(t * t, f0.value(t), 1.0e-15);
Assert.assertEquals(2 * t, f1.value(t), 1.0e-15);
Assert.assertEquals(2, f2.value(t), 1.0e-15);
}
}
@Test
public void testDerivativeMultivariate() {
final double a = 1.5;
final double b = 0.5;
final double c = 0.25;
final MultivariateDifferentiableFunction mdf = new MultivariateDifferentiableFunction() {
@Override
public double value(double[] point) {
return a * point[0] * point[0] + b * point[1] * point[1] + c * point[0] * point[1];
}
@Override
public DerivativeStructure value(DerivativeStructure[] point) {
DerivativeStructure x = point[0];
DerivativeStructure y = point[1];
DerivativeStructure x2 = x.multiply(x);
DerivativeStructure y2 = y.multiply(y);
DerivativeStructure xy = x.multiply(y);
return x2.multiply(a).add(y2.multiply(b)).add(xy.multiply(c));
}
};
final MultivariateFunction f = FunctionUtils.derivative(mdf, new int[] { 0, 0 });
final MultivariateFunction dfdx = FunctionUtils.derivative(mdf, new int[] { 1, 0 });
final MultivariateFunction dfdy = FunctionUtils.derivative(mdf, new int[] { 0, 1 });
final MultivariateFunction d2fdx2 = FunctionUtils.derivative(mdf, new int[] { 2, 0 });
final MultivariateFunction d2fdy2 = FunctionUtils.derivative(mdf, new int[] { 0, 2 });
final MultivariateFunction d2fdxdy = FunctionUtils.derivative(mdf, new int[] { 1, 1 });
for (double x = -1.0; x < 1; x += 0.01) {
for (double y = -1.0; y < 1; y += 0.01) {
Assert.assertEquals(a * x * x + b * y * y + c * x * y, f.value(new double[] { x, y }), 1.0e-15);
Assert.assertEquals(2 * a * x + c * y, dfdx.value(new double[] { x, y }), 1.0e-15);
Assert.assertEquals(2 * b * y + c * x, dfdy.value(new double[] { x, y }), 1.0e-15);
Assert.assertEquals(2 * a, d2fdx2.value(new double[] { x, y }), 1.0e-15);
Assert.assertEquals(2 * b, d2fdy2.value(new double[] { x, y }), 1.0e-15);
Assert.assertEquals(c, d2fdxdy.value(new double[] { x, y }), 1.0e-15);
}
}
}
}