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* 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.
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package org.apache.commons.math4.analysis.differentiation;
import java.util.Arrays;
import java.util.List;
import org.apache.commons.math4.ExtendedFieldElementAbstractTest;
import org.apache.commons.math4.TestUtils;
import org.apache.commons.math4.analysis.polynomials.PolynomialFunction;
import org.apache.commons.rng.UniformRandomProvider;
import org.apache.commons.rng.simple.RandomSource;
import org.apache.commons.math4.util.FastMath;
import org.junit.Assert;
import org.junit.Test;
public class SparseGradientTest extends ExtendedFieldElementAbstractTest<SparseGradient> {
@Override
protected SparseGradient build(final double x) {
return SparseGradient.createVariable(0, x);
}
@Test
public void testConstant() {
double c = 1.0;
SparseGradient grad = SparseGradient.createConstant(c);
Assert.assertEquals(c, grad.getValue(), 1.0e-15); // returns the value
Assert.assertEquals(0, grad.numVars(), 1.0e-15); // has no variables
}
@Test
public void testVariable() {
double v = 1.0;
int id = 0;
SparseGradient grad = SparseGradient.createVariable(id, v);
Assert.assertEquals(v, grad.getValue(), 1.0e-15); // returns the value
Assert.assertEquals(1, grad.numVars(), 1.0e-15); // has one variable
Assert.assertEquals(1.0, grad.getDerivative(id), 1.0e-15); // derivative wr.t itself is 1
}
@Test
public void testVarAddition() {
final double v1 = 1.0;
final double v2 = 2.0;
final int id1 = -1;
final int id2 = 3;
final SparseGradient var1 = SparseGradient.createVariable(id1, v1);
final SparseGradient var2 = SparseGradient.createVariable(id2, v2);
final SparseGradient sum = var1.add(var2);
Assert.assertEquals(v1 + v2, sum.getValue(), 1.0e-15); // returns the value
Assert.assertEquals(2, sum.numVars());
Assert.assertEquals(1.0, sum.getDerivative(id1), 1.0e-15);
Assert.assertEquals(1.0, sum.getDerivative(id2), 1.0e-15);
}
@Test
public void testSubtraction() {
final double v1 = 1.0;
final double v2 = 2.0;
final int id1 = -1;
final int id2 = 3;
final SparseGradient var1 = SparseGradient.createVariable(id1, v1);
final SparseGradient var2 = SparseGradient.createVariable(id2, v2);
final SparseGradient sum = var1.subtract(var2);
Assert.assertEquals(v1 - v2, sum.getValue(), 1.0e-15); // returns the value
Assert.assertEquals(2, sum.numVars());
Assert.assertEquals(1.0, sum.getDerivative(id1), 1.0e-15);
Assert.assertEquals(-1.0, sum.getDerivative(id2), 1.0e-15);
}
@Test
public void testDivision() {
final double v1 = 1.0;
final double v2 = 2.0;
final int id1 = -1;
final int id2 = 3;
final SparseGradient var1 = SparseGradient.createVariable(id1, v1);
final SparseGradient var2 = SparseGradient.createVariable(id2, v2);
final SparseGradient out = var1.divide(var2);
Assert.assertEquals(v1 / v2, out.getValue(), 1.0e-15); // returns the value
Assert.assertEquals(2, out.numVars());
Assert.assertEquals(1 / v2, out.getDerivative(id1), 1.0e-15);
Assert.assertEquals(-1 / (v2 * v2), out.getDerivative(id2), 1.0e-15);
}
@Test
public void testMult() {
final double v1 = 1.0;
final double c1 = 0.5;
final double v2 = 2.0;
final int id1 = -1;
final int id2 = 3;
final SparseGradient var1 = SparseGradient.createVariable(id1, v1);
final SparseGradient unit1 = var1.multiply(c1);
final SparseGradient unit2 = SparseGradient.createVariable(id2, v2).multiply(var1);
final SparseGradient sum = unit1.add(unit2);
Assert.assertEquals(v1 * c1 + v2 * v1, sum.getValue(), 1.0e-15); // returns the value
Assert.assertEquals(2, sum.numVars());
Assert.assertEquals(c1 + v2, sum.getDerivative(id1), 1.0e-15);
Assert.assertEquals(v1, sum.getDerivative(id2), 1.0e-15);
}
@Test
public void testVarMultInPlace() {
final double v1 = 1.0;
final double c1 = 0.5;
final double v2 = 2.0;
final int id1 = -1;
final int id2 = 3;
final SparseGradient var1 = SparseGradient.createVariable(id1, v1);
final SparseGradient sum = var1.multiply(c1);
final SparseGradient mult = SparseGradient.createVariable(id2, v2);
mult.multiplyInPlace(var1);
sum.addInPlace(mult);
Assert.assertEquals(v1 * c1 + v2 * v1, sum.getValue(), 1.0e-15); // returns the value
Assert.assertEquals(2, sum.numVars());
Assert.assertEquals(c1 + v2, sum.getDerivative(id1), 1.0e-15);
Assert.assertEquals(v1, sum.getDerivative(id2), 1.0e-15);
}
@Test
public void testPrimitiveAdd() {
checkF0F1(SparseGradient.createVariable(0, 1.0).add(5), 6.0, 1.0, 0.0, 0.0);
checkF0F1(SparseGradient.createVariable(1, 2.0).add(5), 7.0, 0.0, 1.0, 0.0);
checkF0F1(SparseGradient.createVariable(2, 3.0).add(5), 8.0, 0.0, 0.0, 1.0);
}
@Test
public void testAdd() {
SparseGradient x = SparseGradient.createVariable(0, 1.0);
SparseGradient y = SparseGradient.createVariable(1, 2.0);
SparseGradient z = SparseGradient.createVariable(2, 3.0);
SparseGradient xyz = x.add(y.add(z));
checkF0F1(xyz, x.getValue() + y.getValue() + z.getValue(), 1.0, 1.0, 1.0);
}
@Test
public void testPrimitiveSubtract() {
checkF0F1(SparseGradient.createVariable(0, 1.0).subtract(5), -4.0, 1.0, 0.0, 0.0);
checkF0F1(SparseGradient.createVariable(1, 2.0).subtract(5), -3.0, 0.0, 1.0, 0.0);
checkF0F1(SparseGradient.createVariable(2, 3.0).subtract(5), -2.0, 0.0, 0.0, 1.0);
}
@Test
public void testSubtract() {
SparseGradient x = SparseGradient.createVariable(0, 1.0);
SparseGradient y = SparseGradient.createVariable(1, 2.0);
SparseGradient z = SparseGradient.createVariable(2, 3.0);
SparseGradient xyz = x.subtract(y.subtract(z));
checkF0F1(xyz, x.getValue() - (y.getValue() - z.getValue()), 1.0, -1.0, 1.0);
}
@Test
public void testPrimitiveMultiply() {
checkF0F1(SparseGradient.createVariable(0, 1.0).multiply(5), 5.0, 5.0, 0.0, 0.0);
checkF0F1(SparseGradient.createVariable(1, 2.0).multiply(5), 10.0, 0.0, 5.0, 0.0);
checkF0F1(SparseGradient.createVariable(2, 3.0).multiply(5), 15.0, 0.0, 0.0, 5.0);
}
@Test
public void testMultiply() {
SparseGradient x = SparseGradient.createVariable(0, 1.0);
SparseGradient y = SparseGradient.createVariable(1, 2.0);
SparseGradient z = SparseGradient.createVariable(2, 3.0);
SparseGradient xyz = x.multiply(y.multiply(z));
checkF0F1(xyz, 6.0, 6.0, 3.0, 2.0);
}
@Test
public void testNegate() {
checkF0F1(SparseGradient.createVariable(0, 1.0).negate(), -1.0, -1.0, 0.0, 0.0);
checkF0F1(SparseGradient.createVariable(1, 2.0).negate(), -2.0, 0.0, -1.0, 0.0);
checkF0F1(SparseGradient.createVariable(2, 3.0).negate(), -3.0, 0.0, 0.0, -1.0);
}
@Test
public void testReciprocal() {
for (double x = 0.1; x < 1.2; x += 0.1) {
SparseGradient r = SparseGradient.createVariable(0, x).reciprocal();
Assert.assertEquals(1 / x, r.getValue(), 1.0e-15);
final double expected = -1 / (x * x);
Assert.assertEquals(expected, r.getDerivative(0), 1.0e-15 * FastMath.abs(expected));
}
}
@Test
public void testPow() {
for (int n = 0; n < 10; ++n) {
SparseGradient x = SparseGradient.createVariable(0, 1.0);
SparseGradient y = SparseGradient.createVariable(1, 2.0);
SparseGradient z = SparseGradient.createVariable(2, 3.0);
List<SparseGradient> list = Arrays.asList(x, y, z,
x.add(y).add(z),
x.multiply(y).multiply(z));
if (n == 0) {
for (SparseGradient sg : list) {
Assert.assertEquals(sg.getField().getOne(), sg.pow(n));
}
} else if (n == 1) {
for (SparseGradient sg : list) {
Assert.assertEquals(sg, sg.pow(n));
}
} else {
for (SparseGradient sg : list) {
SparseGradient p = sg.getField().getOne();
for (int i = 0; i < n; ++i) {
p = p.multiply(sg);
}
Assert.assertEquals(p, sg.pow(n));
}
}
}
}
@Test
public void testPowDoubleDS() {
for (int maxOrder = 1; maxOrder < 5; ++maxOrder) {
SparseGradient x = SparseGradient.createVariable(0, 0.1);
SparseGradient y = SparseGradient.createVariable(1, 0.2);
SparseGradient z = SparseGradient.createVariable(2, 0.3);
List<SparseGradient> list = Arrays.asList(x, y, z,
x.add(y).add(z),
x.multiply(y).multiply(z));
for (SparseGradient sg : list) {
// the special case a = 0 is included here
for (double a : new double[] { 0.0, 0.1, 1.0, 2.0, 5.0 }) {
SparseGradient reference = (a == 0) ?
x.getField().getZero() :
SparseGradient.createConstant(a).pow(sg);
SparseGradient result = SparseGradient.pow(a, sg);
Assert.assertEquals(reference, result);
}
}
// negative base: -1^x can be evaluated for integers only, so value is sometimes OK, derivatives are always NaN
SparseGradient negEvenInteger = SparseGradient.pow(-2.0, SparseGradient.createVariable(0, 2.0));
Assert.assertEquals(4.0, negEvenInteger.getValue(), 1.0e-15);
Assert.assertTrue(Double.isNaN(negEvenInteger.getDerivative(0)));
SparseGradient negOddInteger = SparseGradient.pow(-2.0, SparseGradient.createVariable(0, 3.0));
Assert.assertEquals(-8.0, negOddInteger.getValue(), 1.0e-15);
Assert.assertTrue(Double.isNaN(negOddInteger.getDerivative(0)));
SparseGradient negNonInteger = SparseGradient.pow(-2.0, SparseGradient.createVariable(0, 2.001));
Assert.assertTrue(Double.isNaN(negNonInteger.getValue()));
Assert.assertTrue(Double.isNaN(negNonInteger.getDerivative(0)));
SparseGradient zeroNeg = SparseGradient.pow(0.0, SparseGradient.createVariable(0, -1.0));
Assert.assertTrue(Double.isNaN(zeroNeg.getValue()));
Assert.assertTrue(Double.isNaN(zeroNeg.getDerivative(0)));
SparseGradient posNeg = SparseGradient.pow(2.0, SparseGradient.createVariable(0, -2.0));
Assert.assertEquals(1.0 / 4.0, posNeg.getValue(), 1.0e-15);
Assert.assertEquals(FastMath.log(2.0) / 4.0, posNeg.getDerivative(0), 1.0e-15);
// very special case: a = 0 and power = 0
SparseGradient zeroZero = SparseGradient.pow(0.0, SparseGradient.createVariable(0, 0.0));
// this should be OK for simple first derivative with one variable only ...
Assert.assertEquals(1.0, zeroZero.getValue(), 1.0e-15);
Assert.assertEquals(Double.NEGATIVE_INFINITY, zeroZero.getDerivative(0), 1.0e-15);
Assert.assertEquals(0.0, zeroZero.getDerivative(1), 1.0e-15);
Assert.assertEquals(0.0, zeroZero.getDerivative(2), 1.0e-15);
}
}
@Test
public void testExpression() {
double epsilon = 2.5e-13;
for (double x = 0; x < 2; x += 0.2) {
SparseGradient sgX = SparseGradient.createVariable(0, x);
for (double y = 0; y < 2; y += 0.2) {
SparseGradient sgY = SparseGradient.createVariable(1, y);
for (double z = 0; z >- 2; z -= 0.2) {
SparseGradient sgZ = SparseGradient.createVariable(2, z);
// f(x, y, z) = x + 5 x y - 2 z + (8 z x - y)^3
SparseGradient sg =
sgZ.linearCombination(1, sgX,
5, sgX.multiply(sgY),
-2, sgZ,
1, sgZ.linearCombination(8, sgZ.multiply(sgX), -1, sgY).pow(3));
double f = x + 5 * x * y - 2 * z + FastMath.pow(8 * z * x - y, 3);
Assert.assertEquals(f, sg.getValue(), FastMath.abs(epsilon * f));
// df/dx = 1 + 5 y + 24 (8 z x - y)^2 z
double dfdx = 1 + 5 * y + 24 * z * FastMath.pow(8 * z * x - y, 2);
Assert.assertEquals(dfdx, sg.getDerivative(0), FastMath.abs(epsilon * dfdx));
}
}
}
}
@Test
public void testCompositionOneVariableX() {
double epsilon = 1.0e-13;
for (double x = 0.1; x < 1.2; x += 0.1) {
SparseGradient sgX = SparseGradient.createVariable(0, x);
for (double y = 0.1; y < 1.2; y += 0.1) {
SparseGradient sgY = SparseGradient.createConstant(y);
SparseGradient f = sgX.divide(sgY).sqrt();
double f0 = FastMath.sqrt(x / y);
Assert.assertEquals(f0, f.getValue(), FastMath.abs(epsilon * f0));
double f1 = 1 / (2 * FastMath.sqrt(x * y));
Assert.assertEquals(f1, f.getDerivative(0), FastMath.abs(epsilon * f1));
}
}
}
@Test
public void testTrigo() {
double epsilon = 2.0e-12;
for (double x = 0.1; x < 1.2; x += 0.1) {
SparseGradient sgX = SparseGradient.createVariable(0, x);
for (double y = 0.1; y < 1.2; y += 0.1) {
SparseGradient sgY = SparseGradient.createVariable(1, y);
for (double z = 0.1; z < 1.2; z += 0.1) {
SparseGradient sgZ = SparseGradient.createVariable(2, z);
SparseGradient f = sgX.divide(sgY.cos().add(sgZ.tan())).sin();
double a = FastMath.cos(y) + FastMath.tan(z);
double f0 = FastMath.sin(x / a);
Assert.assertEquals(f0, f.getValue(), FastMath.abs(epsilon * f0));
double dfdx = FastMath.cos(x / a) / a;
Assert.assertEquals(dfdx, f.getDerivative(0), FastMath.abs(epsilon * dfdx));
double dfdy = x * FastMath.sin(y) * dfdx / a;
Assert.assertEquals(dfdy, f.getDerivative(1), FastMath.abs(epsilon * dfdy));
double cz = FastMath.cos(z);
double cz2 = cz * cz;
double dfdz = -x * dfdx / (a * cz2);
Assert.assertEquals(dfdz, f.getDerivative(2), FastMath.abs(epsilon * dfdz));
}
}
}
}
@Test
public void testSqrtDefinition() {
for (double x = 0.1; x < 1.2; x += 0.001) {
SparseGradient sgX = SparseGradient.createVariable(0, x);
SparseGradient sqrt1 = sgX.pow(0.5);
SparseGradient sqrt2 = sgX.sqrt();
SparseGradient zero = sqrt1.subtract(sqrt2);
checkF0F1(zero, 0.0, 0.0);
}
}
@Test
public void testRootNSingularity() {
for (int n = 2; n < 10; ++n) {
SparseGradient sgZero = SparseGradient.createVariable(0, 0.0);
SparseGradient rootN = sgZero.rootN(n);
Assert.assertEquals(0.0, rootN.getValue(), 1.0e-5);
Assert.assertTrue(Double.isInfinite(rootN.getDerivative(0)));
Assert.assertTrue(rootN.getDerivative(0) > 0);
}
}
@Test
public void testSqrtPow2() {
for (double x = 0.1; x < 1.2; x += 0.001) {
SparseGradient sgX = SparseGradient.createVariable(0, x);
SparseGradient rebuiltX = sgX.multiply(sgX).sqrt();
SparseGradient zero = rebuiltX.subtract(sgX);
checkF0F1(zero, 0.0, 0.0);
}
}
@Test
public void testCbrtDefinition() {
for (double x = 0.1; x < 1.2; x += 0.001) {
SparseGradient sgX = SparseGradient.createVariable(0, x);
SparseGradient cbrt1 = sgX.pow(1.0 / 3.0);
SparseGradient cbrt2 = sgX.cbrt();
SparseGradient zero = cbrt1.subtract(cbrt2);
checkF0F1(zero, 0.0, 0.0);
}
}
@Test
public void testCbrtPow3() {
for (double x = 0.1; x < 1.2; x += 0.001) {
SparseGradient sgX = SparseGradient.createVariable(0, x);
SparseGradient rebuiltX = sgX.multiply(sgX.multiply(sgX)).cbrt();
SparseGradient zero = rebuiltX.subtract(sgX);
checkF0F1(zero, 0.0, 0.0);
}
}
@Test
public void testPowReciprocalPow() {
for (double x = 0.1; x < 1.2; x += 0.01) {
SparseGradient sgX = SparseGradient.createVariable(0, x);
for (double y = 0.1; y < 1.2; y += 0.01) {
SparseGradient sgY = SparseGradient.createVariable(1, y);
SparseGradient rebuiltX = sgX.pow(sgY).pow(sgY.reciprocal());
SparseGradient zero = rebuiltX.subtract(sgX);
checkF0F1(zero, 0.0, 0.0, 0.0);
}
}
}
@Test
public void testHypotDefinition() {
for (double x = -1.7; x < 2; x += 0.2) {
SparseGradient sgX = SparseGradient.createVariable(0, x);
for (double y = -1.7; y < 2; y += 0.2) {
SparseGradient sgY = SparseGradient.createVariable(1, y);
SparseGradient hypot = SparseGradient.hypot(sgY, sgX);
SparseGradient ref = sgX.multiply(sgX).add(sgY.multiply(sgY)).sqrt();
SparseGradient zero = hypot.subtract(ref);
checkF0F1(zero, 0.0, 0.0, 0.0);
}
}
}
@Test
public void testHypotNoOverflow() {
SparseGradient sgX = SparseGradient.createVariable(0, +3.0e250);
SparseGradient sgY = SparseGradient.createVariable(1, -4.0e250);
SparseGradient hypot = SparseGradient.hypot(sgX, sgY);
Assert.assertEquals(5.0e250, hypot.getValue(), 1.0e235);
Assert.assertEquals(sgX.getValue() / hypot.getValue(), hypot.getDerivative(0), 1.0e-10);
Assert.assertEquals(sgY.getValue() / hypot.getValue(), hypot.getDerivative(1), 1.0e-10);
SparseGradient sqrt = sgX.multiply(sgX).add(sgY.multiply(sgY)).sqrt();
Assert.assertTrue(Double.isInfinite(sqrt.getValue()));
}
@Test
public void testHypotNeglectible() {
SparseGradient sgSmall = SparseGradient.createVariable(0, +3.0e-10);
SparseGradient sgLarge = SparseGradient.createVariable(1, -4.0e25);
Assert.assertEquals(sgLarge.abs().getValue(),
SparseGradient.hypot(sgSmall, sgLarge).getValue(),
1.0e-10);
Assert.assertEquals(0,
SparseGradient.hypot(sgSmall, sgLarge).getDerivative(0),
1.0e-10);
Assert.assertEquals(-1,
SparseGradient.hypot(sgSmall, sgLarge).getDerivative(1),
1.0e-10);
Assert.assertEquals(sgLarge.abs().getValue(),
SparseGradient.hypot(sgLarge, sgSmall).getValue(),
1.0e-10);
Assert.assertEquals(0,
SparseGradient.hypot(sgLarge, sgSmall).getDerivative(0),
1.0e-10);
Assert.assertEquals(-1,
SparseGradient.hypot(sgLarge, sgSmall).getDerivative(1),
1.0e-10);
}
@Test
public void testHypotSpecial() {
Assert.assertTrue(Double.isNaN(SparseGradient.hypot(SparseGradient.createVariable(0, Double.NaN),
SparseGradient.createVariable(0, +3.0e250)).getValue()));
Assert.assertTrue(Double.isNaN(SparseGradient.hypot(SparseGradient.createVariable(0, +3.0e250),
SparseGradient.createVariable(0, Double.NaN)).getValue()));
Assert.assertTrue(Double.isInfinite(SparseGradient.hypot(SparseGradient.createVariable(0, Double.POSITIVE_INFINITY),
SparseGradient.createVariable(0, +3.0e250)).getValue()));
Assert.assertTrue(Double.isInfinite(SparseGradient.hypot(SparseGradient.createVariable(0, +3.0e250),
SparseGradient.createVariable(0, Double.POSITIVE_INFINITY)).getValue()));
}
@Test
public void testPrimitiveRemainder() {
for (double x = -1.7; x < 2; x += 0.2) {
SparseGradient sgX = SparseGradient.createVariable(0, x);
for (double y = -1.7; y < 2; y += 0.2) {
SparseGradient remainder = sgX.remainder(y);
SparseGradient ref = sgX.subtract(x - FastMath.IEEEremainder(x, y));
SparseGradient zero = remainder.subtract(ref);
checkF0F1(zero, 0.0, 0.0, 0.0);
}
}
}
@Test
public void testRemainder() {
for (double x = -1.7; x < 2; x += 0.2) {
SparseGradient sgX = SparseGradient.createVariable(0, x);
for (double y = -1.7; y < 2; y += 0.2) {
SparseGradient sgY = SparseGradient.createVariable(1, y);
SparseGradient remainder = sgX.remainder(sgY);
SparseGradient ref = sgX.subtract(sgY.multiply((x - FastMath.IEEEremainder(x, y)) / y));
SparseGradient zero = remainder.subtract(ref);
checkF0F1(zero, 0.0, 0.0, 0.0);
}
}
}
@Override
@Test
public void testExp() {
for (double x = 0.1; x < 1.2; x += 0.001) {
double refExp = FastMath.exp(x);
checkF0F1(SparseGradient.createVariable(0, x).exp(), refExp, refExp);
}
}
@Test
public void testExpm1Definition() {
for (double x = 0.1; x < 1.2; x += 0.001) {
SparseGradient sgX = SparseGradient.createVariable(0, x);
SparseGradient expm11 = sgX.expm1();
SparseGradient expm12 = sgX.exp().subtract(sgX.getField().getOne());
SparseGradient zero = expm11.subtract(expm12);
checkF0F1(zero, 0.0, 0.0);
}
}
@Override
@Test
public void testLog() {
for (double x = 0.1; x < 1.2; x += 0.001) {
checkF0F1(SparseGradient.createVariable(0, x).log(), FastMath.log(x), 1.0 / x);
}
}
@Test
public void testLog1pDefinition() {
for (double x = 0.1; x < 1.2; x += 0.001) {
SparseGradient sgX = SparseGradient.createVariable(0, x);
SparseGradient log1p1 = sgX.log1p();
SparseGradient log1p2 = sgX.add(sgX.getField().getOne()).log();
SparseGradient zero = log1p1.subtract(log1p2);
checkF0F1(zero, 0.0, 0.0);
}
}
@Test
public void testLog10Definition() {
for (double x = 0.1; x < 1.2; x += 0.001) {
SparseGradient sgX = SparseGradient.createVariable(0, x);
SparseGradient log101 = sgX.log10();
SparseGradient log102 = sgX.log().divide(FastMath.log(10.0));
SparseGradient zero = log101.subtract(log102);
checkF0F1(zero, 0.0, 0.0);
}
}
@Test
public void testLogExp() {
for (double x = 0.1; x < 1.2; x += 0.001) {
SparseGradient sgX = SparseGradient.createVariable(0, x);
SparseGradient rebuiltX = sgX.exp().log();
SparseGradient zero = rebuiltX.subtract(sgX);
checkF0F1(zero, 0.0, 0.0);
}
}
@Test
public void testLog1pExpm1() {
for (double x = 0.1; x < 1.2; x += 0.001) {
SparseGradient sgX = SparseGradient.createVariable(0, x);
SparseGradient rebuiltX = sgX.expm1().log1p();
SparseGradient zero = rebuiltX.subtract(sgX);
checkF0F1(zero, 0.0, 0.0);
}
}
@Test
public void testLog10Power() {
for (double x = 0.1; x < 1.2; x += 0.001) {
SparseGradient sgX = SparseGradient.createVariable(0, x);
SparseGradient rebuiltX = SparseGradient.pow(10.0, sgX).log10();
SparseGradient zero = rebuiltX.subtract(sgX);
checkF0F1(zero, 0.0, 0.0);
}
}
@Test
public void testSinCos() {
for (double x = 0.1; x < 1.2; x += 0.001) {
SparseGradient sgX = SparseGradient.createVariable(0, x);
SparseGradient sin = sgX.sin();
SparseGradient cos = sgX.cos();
double s = FastMath.sin(x);
double c = FastMath.cos(x);
checkF0F1(sin, s, c);
checkF0F1(cos, c, -s);
}
}
@Test
public void testSinAsin() {
for (double x = 0.1; x < 1.2; x += 0.001) {
SparseGradient sgX = SparseGradient.createVariable(0, x);
SparseGradient rebuiltX = sgX.sin().asin();
SparseGradient zero = rebuiltX.subtract(sgX);
checkF0F1(zero, 0.0, 0.0);
}
}
@Test
public void testCosAcos() {
for (double x = 0.1; x < 1.2; x += 0.001) {
SparseGradient sgX = SparseGradient.createVariable(0, x);
SparseGradient rebuiltX = sgX.cos().acos();
SparseGradient zero = rebuiltX.subtract(sgX);
checkF0F1(zero, 0.0, 0.0);
}
}
@Test
public void testTanAtan() {
for (double x = 0.1; x < 1.2; x += 0.001) {
SparseGradient sgX = SparseGradient.createVariable(0, x);
SparseGradient rebuiltX = sgX.tan().atan();
SparseGradient zero = rebuiltX.subtract(sgX);
checkF0F1(zero, 0.0, 0.0);
}
}
@Test
public void testTangentDefinition() {
for (double x = 0.1; x < 1.2; x += 0.001) {
SparseGradient sgX = SparseGradient.createVariable(0, x);
SparseGradient tan1 = sgX.sin().divide(sgX.cos());
SparseGradient tan2 = sgX.tan();
SparseGradient zero = tan1.subtract(tan2);
checkF0F1(zero, 0.0, 0.0);
}
}
@Override
@Test
public void testAtan2() {
for (double x = -1.7; x < 2; x += 0.2) {
SparseGradient sgX = SparseGradient.createVariable(0, x);
for (double y = -1.7; y < 2; y += 0.2) {
SparseGradient sgY = SparseGradient.createVariable(1, y);
SparseGradient atan2 = SparseGradient.atan2(sgY, sgX);
SparseGradient ref = sgY.divide(sgX).atan();
if (x < 0) {
ref = (y < 0) ? ref.subtract(FastMath.PI) : ref.add(FastMath.PI);
}
SparseGradient zero = atan2.subtract(ref);
checkF0F1(zero, 0.0, 0.0);
}
}
}
@Test
public void testAtan2SpecialCases() {
SparseGradient pp =
SparseGradient.atan2(SparseGradient.createVariable(1, +0.0),
SparseGradient.createVariable(1, +0.0));
Assert.assertEquals(0, pp.getValue(), 1.0e-15);
Assert.assertEquals(+1, FastMath.copySign(1, pp.getValue()), 1.0e-15);
SparseGradient pn =
SparseGradient.atan2(SparseGradient.createVariable(1, +0.0),
SparseGradient.createVariable(1, -0.0));
Assert.assertEquals(FastMath.PI, pn.getValue(), 1.0e-15);
SparseGradient np =
SparseGradient.atan2(SparseGradient.createVariable(1, -0.0),
SparseGradient.createVariable(1, +0.0));
Assert.assertEquals(0, np.getValue(), 1.0e-15);
Assert.assertEquals(-1, FastMath.copySign(1, np.getValue()), 1.0e-15);
SparseGradient nn =
SparseGradient.atan2(SparseGradient.createVariable(1, -0.0),
SparseGradient.createVariable(1, -0.0));
Assert.assertEquals(-FastMath.PI, nn.getValue(), 1.0e-15);
}
@Test
public void testSinhDefinition() {
for (double x = 0.1; x < 1.2; x += 0.001) {
SparseGradient sgX = SparseGradient.createVariable(0, x);
SparseGradient sinh1 = sgX.exp().subtract(sgX.exp().reciprocal()).multiply(0.5);
SparseGradient sinh2 = sgX.sinh();
SparseGradient zero = sinh1.subtract(sinh2);
checkF0F1(zero, 0.0, 0.0);
}
}
@Test
public void testCoshDefinition() {
for (double x = 0.1; x < 1.2; x += 0.001) {
SparseGradient sgX = SparseGradient.createVariable(0, x);
SparseGradient cosh1 = sgX.exp().add(sgX.exp().reciprocal()).multiply(0.5);
SparseGradient cosh2 = sgX.cosh();
SparseGradient zero = cosh1.subtract(cosh2);
checkF0F1(zero, 0.0, 0.0);
}
}
@Test
public void testTanhDefinition() {
for (double x = 0.1; x < 1.2; x += 0.001) {
SparseGradient sgX = SparseGradient.createVariable(0, x);
SparseGradient tanh1 = sgX.exp().subtract(sgX.exp().reciprocal()).divide(sgX.exp().add(sgX.exp().reciprocal()));
SparseGradient tanh2 = sgX.tanh();
SparseGradient zero = tanh1.subtract(tanh2);
checkF0F1(zero, 0.0, 0.0);
}
}
@Test
public void testSinhAsinh() {
for (double x = 0.1; x < 1.2; x += 0.001) {
SparseGradient sgX = SparseGradient.createVariable(0, x);
SparseGradient rebuiltX = sgX.sinh().asinh();
SparseGradient zero = rebuiltX.subtract(sgX);
checkF0F1(zero, 0.0, 0.0);
}
}
@Test
public void testCoshAcosh() {
for (double x = 0.1; x < 1.2; x += 0.001) {
SparseGradient sgX = SparseGradient.createVariable(0, x);
SparseGradient rebuiltX = sgX.cosh().acosh();
SparseGradient zero = rebuiltX.subtract(sgX);
checkF0F1(zero, 0.0, 0.0);
}
}
@Test
public void testTanhAtanh() {
for (double x = 0.1; x < 1.2; x += 0.001) {
SparseGradient sgX = SparseGradient.createVariable(0, x);
SparseGradient rebuiltX = sgX.tanh().atanh();
SparseGradient zero = rebuiltX.subtract(sgX);
checkF0F1(zero, 0.0, 0.0);
}
}
@Test
public void testCompositionOneVariableY() {
for (double x = 0.1; x < 1.2; x += 0.1) {
SparseGradient sgX = SparseGradient.createConstant(x);
for (double y = 0.1; y < 1.2; y += 0.1) {
SparseGradient sgY = SparseGradient.createVariable(0, y);
SparseGradient f = sgX.divide(sgY).sqrt();
double f0 = FastMath.sqrt(x / y);
double f1 = -x / (2 * y * y * f0);
checkF0F1(f, f0, f1);
}
}
}
@Test
public void testTaylorPolynomial() {
for (double x = 0; x < 1.2; x += 0.1) {
SparseGradient sgX = SparseGradient.createVariable(0, x);
for (double y = 0; y < 1.2; y += 0.2) {
SparseGradient sgY = SparseGradient.createVariable(1, y);
for (double z = 0; z < 1.2; z += 0.2) {
SparseGradient sgZ = SparseGradient.createVariable(2, z);
SparseGradient f = sgX.multiply(3).add(sgZ.multiply(-2)).add(sgY.multiply(5));
for (double dx = -0.2; dx < 0.2; dx += 0.2) {
for (double dy = -0.2; dy < 0.2; dy += 0.1) {
for (double dz = -0.2; dz < 0.2; dz += 0.1) {
double ref = 3 * (x + dx) + 5 * (y + dy) -2 * (z + dz);
Assert.assertEquals(ref, f.taylor(dx, dy, dz), 3.0e-15);
}
}
}
}
}
}
}
@Test
public void testTaylorAtan2() {
double x0 = 0.1;
double y0 = -0.3;
SparseGradient sgX = SparseGradient.createVariable(0, x0);
SparseGradient sgY = SparseGradient.createVariable(1, y0);
SparseGradient atan2 = SparseGradient.atan2(sgY, sgX);
double maxError = 0;
for (double dx = -0.05; dx < 0.05; dx += 0.001) {
for (double dy = -0.05; dy < 0.05; dy += 0.001) {
double ref = FastMath.atan2(y0 + dy, x0 + dx);
maxError = FastMath.max(maxError, FastMath.abs(ref - atan2.taylor(dx, dy)));
}
}
double expectedError = 0.0241;
Assert.assertEquals(expectedError, maxError, 0.01 * expectedError);
}
@Override
@Test
public void testAbs() {
SparseGradient minusOne = SparseGradient.createVariable(0, -1.0);
Assert.assertEquals(+1.0, minusOne.abs().getValue(), 1.0e-15);
Assert.assertEquals(-1.0, minusOne.abs().getDerivative(0), 1.0e-15);
SparseGradient plusOne = SparseGradient.createVariable(0, +1.0);
Assert.assertEquals(+1.0, plusOne.abs().getValue(), 1.0e-15);
Assert.assertEquals(+1.0, plusOne.abs().getDerivative(0), 1.0e-15);
SparseGradient minusZero = SparseGradient.createVariable(0, -0.0);
Assert.assertEquals(+0.0, minusZero.abs().getValue(), 1.0e-15);
Assert.assertEquals(-1.0, minusZero.abs().getDerivative(0), 1.0e-15);
SparseGradient plusZero = SparseGradient.createVariable(0, +0.0);
Assert.assertEquals(+0.0, plusZero.abs().getValue(), 1.0e-15);
Assert.assertEquals(+1.0, plusZero.abs().getDerivative(0), 1.0e-15);
}
@Override
@Test
public void testSignum() {
SparseGradient minusOne = SparseGradient.createVariable(0, -1.0);
Assert.assertEquals(-1.0, minusOne.signum().getValue(), 1.0e-15);
Assert.assertEquals( 0.0, minusOne.signum().getDerivative(0), 1.0e-15);
SparseGradient plusOne = SparseGradient.createVariable(0, +1.0);
Assert.assertEquals(+1.0, plusOne.signum().getValue(), 1.0e-15);
Assert.assertEquals( 0.0, plusOne.signum().getDerivative(0), 1.0e-15);
SparseGradient minusZero = SparseGradient.createVariable(0, -0.0);
Assert.assertEquals(-0.0, minusZero.signum().getValue(), 1.0e-15);
Assert.assertTrue(Double.doubleToLongBits(minusZero.signum().getValue()) < 0);
Assert.assertEquals( 0.0, minusZero.signum().getDerivative(0), 1.0e-15);
SparseGradient plusZero = SparseGradient.createVariable(0, +0.0);
Assert.assertEquals(+0.0, plusZero.signum().getValue(), 1.0e-15);
Assert.assertTrue(Double.doubleToLongBits(plusZero.signum().getValue()) == 0);
Assert.assertEquals( 0.0, plusZero.signum().getDerivative(0), 1.0e-15);
}
@Test
public void testCeilFloorRintLong() {
SparseGradient x = SparseGradient.createVariable(0, -1.5);
Assert.assertEquals(-1.5, x.getValue(), 1.0e-15);
Assert.assertEquals(+1.0, x.getDerivative(0), 1.0e-15);
Assert.assertEquals(-1.0, x.ceil().getValue(), 1.0e-15);
Assert.assertEquals(+0.0, x.ceil().getDerivative(0), 1.0e-15);
Assert.assertEquals(-2.0, x.floor().getValue(), 1.0e-15);
Assert.assertEquals(+0.0, x.floor().getDerivative(0), 1.0e-15);
Assert.assertEquals(-2.0, x.rint().getValue(), 1.0e-15);
Assert.assertEquals(+0.0, x.rint().getDerivative(0), 1.0e-15);
Assert.assertEquals(-2.0, x.subtract(x.getField().getOne()).rint().getValue(), 1.0e-15);
Assert.assertEquals(-1l, x.round(), 1.0e-15);
}
@Test
public void testCopySign() {
SparseGradient minusOne = SparseGradient.createVariable(0, -1.0);
Assert.assertEquals(+1.0, minusOne.copySign(+1.0).getValue(), 1.0e-15);
Assert.assertEquals(-1.0, minusOne.copySign(+1.0).getDerivative(0), 1.0e-15);
Assert.assertEquals(-1.0, minusOne.copySign(-1.0).getValue(), 1.0e-15);
Assert.assertEquals(+1.0, minusOne.copySign(-1.0).getDerivative(0), 1.0e-15);
Assert.assertEquals(+1.0, minusOne.copySign(+0.0).getValue(), 1.0e-15);
Assert.assertEquals(-1.0, minusOne.copySign(+0.0).getDerivative(0), 1.0e-15);
Assert.assertEquals(-1.0, minusOne.copySign(-0.0).getValue(), 1.0e-15);
Assert.assertEquals(+1.0, minusOne.copySign(-0.0).getDerivative(0), 1.0e-15);
Assert.assertEquals(+1.0, minusOne.copySign(Double.NaN).getValue(), 1.0e-15);
Assert.assertEquals(-1.0, minusOne.copySign(Double.NaN).getDerivative(0), 1.0e-15);
SparseGradient plusOne = SparseGradient.createVariable(0, +1.0);
Assert.assertEquals(+1.0, plusOne.copySign(+1.0).getValue(), 1.0e-15);
Assert.assertEquals(+1.0, plusOne.copySign(+1.0).getDerivative(0), 1.0e-15);
Assert.assertEquals(-1.0, plusOne.copySign(-1.0).getValue(), 1.0e-15);
Assert.assertEquals(-1.0, plusOne.copySign(-1.0).getDerivative(0), 1.0e-15);
Assert.assertEquals(+1.0, plusOne.copySign(+0.0).getValue(), 1.0e-15);
Assert.assertEquals(+1.0, plusOne.copySign(+0.0).getDerivative(0), 1.0e-15);
Assert.assertEquals(-1.0, plusOne.copySign(-0.0).getValue(), 1.0e-15);
Assert.assertEquals(-1.0, plusOne.copySign(-0.0).getDerivative(0), 1.0e-15);
Assert.assertEquals(+1.0, plusOne.copySign(Double.NaN).getValue(), 1.0e-15);
Assert.assertEquals(+1.0, plusOne.copySign(Double.NaN).getDerivative(0), 1.0e-15);
}
@Test
public void testToDegreesDefinition() {
double epsilon = 3.0e-16;
for (int maxOrder = 0; maxOrder < 6; ++maxOrder) {
for (double x = 0.1; x < 1.2; x += 0.001) {
SparseGradient sgX = SparseGradient.createVariable(0, x);
Assert.assertEquals(FastMath.toDegrees(x), sgX.toDegrees().getValue(), epsilon);
Assert.assertEquals(180 / FastMath.PI, sgX.toDegrees().getDerivative(0), epsilon);
}
}
}
@Test
public void testToRadiansDefinition() {
double epsilon = 3.0e-16;
for (int maxOrder = 0; maxOrder < 6; ++maxOrder) {
for (double x = 0.1; x < 1.2; x += 0.001) {
SparseGradient sgX = SparseGradient.createVariable(0, x);
Assert.assertEquals(FastMath.toRadians(x), sgX.toRadians().getValue(), epsilon);
Assert.assertEquals(FastMath.PI / 180, sgX.toRadians().getDerivative(0), epsilon);
}
}
}
@Test
public void testDegRad() {
for (double x = 0.1; x < 1.2; x += 0.001) {
SparseGradient sgX = SparseGradient.createVariable(0, x);
SparseGradient rebuiltX = sgX.toDegrees().toRadians();
SparseGradient zero = rebuiltX.subtract(sgX);
checkF0F1(zero, 0, 0);
}
}
@Test
public void testCompose() {
PolynomialFunction poly =
new PolynomialFunction(new double[] { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 });
for (double x = 0.1; x < 1.2; x += 0.001) {
SparseGradient sgX = SparseGradient.createVariable(0, x);
SparseGradient sgY1 = sgX.getField().getZero();
for (int i = poly.degree(); i >= 0; --i) {
sgY1 = sgY1.multiply(sgX).add(poly.getCoefficients()[i]);
}
SparseGradient sgY2 = sgX.compose(poly.value(x), poly.polynomialDerivative().value(x));
SparseGradient zero = sgY1.subtract(sgY2);
checkF0F1(zero, 0.0, 0.0);
}
}
@Test
public void testField() {
SparseGradient x = SparseGradient.createVariable(0, 1.0);
checkF0F1(x.getField().getZero(), 0.0, 0.0, 0.0, 0.0);
checkF0F1(x.getField().getOne(), 1.0, 0.0, 0.0, 0.0);
Assert.assertEquals(SparseGradient.class, x.getField().getRuntimeClass());
}
@Test
public void testLinearCombination1DSDS() {
final SparseGradient[] a = new SparseGradient[] {
SparseGradient.createVariable(0, -1321008684645961.0 / 268435456.0),
SparseGradient.createVariable(1, -5774608829631843.0 / 268435456.0),
SparseGradient.createVariable(2, -7645843051051357.0 / 8589934592.0)
};
final SparseGradient[] b = new SparseGradient[] {
SparseGradient.createVariable(3, -5712344449280879.0 / 2097152.0),
SparseGradient.createVariable(4, -4550117129121957.0 / 2097152.0),
SparseGradient.createVariable(5, 8846951984510141.0 / 131072.0)
};
final SparseGradient abSumInline = a[0].linearCombination(a[0], b[0], a[1], b[1], a[2], b[2]);
final SparseGradient abSumArray = a[0].linearCombination(a, b);
Assert.assertEquals(abSumInline.getValue(), abSumArray.getValue(), 1.0e-15);
Assert.assertEquals(-1.8551294182586248737720779899, abSumInline.getValue(), 1.0e-15);
Assert.assertEquals(b[0].getValue(), abSumInline.getDerivative(0), 1.0e-15);
Assert.assertEquals(b[1].getValue(), abSumInline.getDerivative(1), 1.0e-15);
Assert.assertEquals(b[2].getValue(), abSumInline.getDerivative(2), 1.0e-15);
Assert.assertEquals(a[0].getValue(), abSumInline.getDerivative(3), 1.0e-15);
Assert.assertEquals(a[1].getValue(), abSumInline.getDerivative(4), 1.0e-15);
Assert.assertEquals(a[2].getValue(), abSumInline.getDerivative(5), 1.0e-15);
}
@Test
public void testLinearCombination1DoubleDS() {
final double[] a = new double[] {
-1321008684645961.0 / 268435456.0,
-5774608829631843.0 / 268435456.0,
-7645843051051357.0 / 8589934592.0
};
final SparseGradient[] b = new SparseGradient[] {
SparseGradient.createVariable(0, -5712344449280879.0 / 2097152.0),
SparseGradient.createVariable(1, -4550117129121957.0 / 2097152.0),
SparseGradient.createVariable(2, 8846951984510141.0 / 131072.0)
};
final SparseGradient abSumInline = b[0].linearCombination(a[0], b[0],
a[1], b[1],
a[2], b[2]);
final SparseGradient abSumArray = b[0].linearCombination(a, b);
Assert.assertEquals(abSumInline.getValue(), abSumArray.getValue(), 1.0e-15);
Assert.assertEquals(-1.8551294182586248737720779899, abSumInline.getValue(), 1.0e-15);
Assert.assertEquals(a[0], abSumInline.getDerivative(0), 1.0e-15);
Assert.assertEquals(a[1], abSumInline.getDerivative(1), 1.0e-15);
Assert.assertEquals(a[2], abSumInline.getDerivative(2), 1.0e-15);
}
@Test
public void testLinearCombination2DSDS() {
// we compare accurate versus naive dot product implementations
// on regular vectors (i.e. not extreme cases like in the previous test)
UniformRandomProvider random = RandomSource.create(RandomSource.WELL_1024_A,
0xc6af886975069f11l);
for (int i = 0; i < 10000; ++i) {
final SparseGradient[] u = new SparseGradient[4];
final SparseGradient[] v = new SparseGradient[4];
for (int j = 0; j < u.length; ++j) {
u[j] = SparseGradient.createVariable(j, 1e17 * random.nextDouble());
v[j] = SparseGradient.createConstant(1e17 * random.nextDouble());
}
SparseGradient lin = u[0].linearCombination(u[0], v[0], u[1], v[1]);
double ref = u[0].getValue() * v[0].getValue() +
u[1].getValue() * v[1].getValue();
Assert.assertEquals(ref, lin.getValue(), 1.0e-15 * FastMath.abs(ref));
Assert.assertEquals(v[0].getValue(), lin.getDerivative(0), 1.0e-15 * FastMath.abs(v[0].getValue()));
Assert.assertEquals(v[1].getValue(), lin.getDerivative(1), 1.0e-15 * FastMath.abs(v[1].getValue()));
lin = u[0].linearCombination(u[0], v[0], u[1], v[1], u[2], v[2]);
ref = u[0].getValue() * v[0].getValue() +
u[1].getValue() * v[1].getValue() +
u[2].getValue() * v[2].getValue();
Assert.assertEquals(ref, lin.getValue(), 1.0e-15 * FastMath.abs(ref));
Assert.assertEquals(v[0].getValue(), lin.getDerivative(0), 1.0e-15 * FastMath.abs(v[0].getValue()));
Assert.assertEquals(v[1].getValue(), lin.getDerivative(1), 1.0e-15 * FastMath.abs(v[1].getValue()));
Assert.assertEquals(v[2].getValue(), lin.getDerivative(2), 1.0e-15 * FastMath.abs(v[2].getValue()));
lin = u[0].linearCombination(u[0], v[0], u[1], v[1], u[2], v[2], u[3], v[3]);
ref = u[0].getValue() * v[0].getValue() +
u[1].getValue() * v[1].getValue() +
u[2].getValue() * v[2].getValue() +
u[3].getValue() * v[3].getValue();
Assert.assertEquals(ref, lin.getValue(), 1.0e-15 * FastMath.abs(ref));
Assert.assertEquals(v[0].getValue(), lin.getDerivative(0), 1.0e-15 * FastMath.abs(v[0].getValue()));
Assert.assertEquals(v[1].getValue(), lin.getDerivative(1), 1.0e-15 * FastMath.abs(v[1].getValue()));
Assert.assertEquals(v[2].getValue(), lin.getDerivative(2), 1.0e-15 * FastMath.abs(v[2].getValue()));
Assert.assertEquals(v[3].getValue(), lin.getDerivative(3), 1.0e-15 * FastMath.abs(v[3].getValue()));
}
}
@Test
public void testLinearCombination2DoubleDS() {
// we compare accurate versus naive dot product implementations
// on regular vectors (i.e. not extreme cases like in the previous test)
UniformRandomProvider random = RandomSource.create(RandomSource.WELL_1024_A,
0xc6af886975069f11l);
for (int i = 0; i < 10000; ++i) {
final double[] u = new double[4];
final SparseGradient[] v = new SparseGradient[4];
for (int j = 0; j < u.length; ++j) {
u[j] = 1e17 * random.nextDouble();
v[j] = SparseGradient.createVariable(j, 1e17 * random.nextDouble());
}
SparseGradient lin = v[0].linearCombination(u[0], v[0], u[1], v[1]);
double ref = u[0] * v[0].getValue() +
u[1] * v[1].getValue();
Assert.assertEquals(ref, lin.getValue(), 1.0e-15 * FastMath.abs(ref));
Assert.assertEquals(u[0], lin.getDerivative(0), 1.0e-15 * FastMath.abs(v[0].getValue()));
Assert.assertEquals(u[1], lin.getDerivative(1), 1.0e-15 * FastMath.abs(v[1].getValue()));
lin = v[0].linearCombination(u[0], v[0], u[1], v[1], u[2], v[2]);
ref = u[0] * v[0].getValue() +
u[1] * v[1].getValue() +
u[2] * v[2].getValue();
Assert.assertEquals(ref, lin.getValue(), 1.0e-15 * FastMath.abs(ref));
Assert.assertEquals(u[0], lin.getDerivative(0), 1.0e-15 * FastMath.abs(v[0].getValue()));
Assert.assertEquals(u[1], lin.getDerivative(1), 1.0e-15 * FastMath.abs(v[1].getValue()));
Assert.assertEquals(u[2], lin.getDerivative(2), 1.0e-15 * FastMath.abs(v[2].getValue()));
lin = v[0].linearCombination(u[0], v[0], u[1], v[1], u[2], v[2], u[3], v[3]);
ref = u[0] * v[0].getValue() +
u[1] * v[1].getValue() +
u[2] * v[2].getValue() +
u[3] * v[3].getValue();
Assert.assertEquals(ref, lin.getValue(), 1.0e-15 * FastMath.abs(ref));
Assert.assertEquals(u[0], lin.getDerivative(0), 1.0e-15 * FastMath.abs(v[0].getValue()));
Assert.assertEquals(u[1], lin.getDerivative(1), 1.0e-15 * FastMath.abs(v[1].getValue()));
Assert.assertEquals(u[2], lin.getDerivative(2), 1.0e-15 * FastMath.abs(v[2].getValue()));
Assert.assertEquals(u[3], lin.getDerivative(3), 1.0e-15 * FastMath.abs(v[3].getValue()));
}
}
@Test
public void testSerialization() {
SparseGradient a = SparseGradient.createVariable(0, 1.3);
SparseGradient b = (SparseGradient) TestUtils.serializeAndRecover(a);
Assert.assertEquals(a, b);
}
private void checkF0F1(SparseGradient sg, double value, double...derivatives) {
// check value
Assert.assertEquals(value, sg.getValue(), 1.0e-13);
// check first order derivatives
for (int i = 0; i < derivatives.length; ++i) {
Assert.assertEquals(derivatives[i], sg.getDerivative(i), 1.0e-13);
}
}
}