/*
* 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.function;
import org.apache.commons.math4.analysis.differentiation.DerivativeStructure;
import org.apache.commons.math4.util.FastMath;
import org.junit.Assert;
import org.junit.Test;
/**
* Test for all classes in org.apache.commons.math4.analysis.function that implement UnivariateDifferentiableFunction explicitly.
*/
public class UnivariateDifferentiableFunctionTest {
private static final double EPS = Math.ulp(1d);
@Test
public void testAcos() {
Acos acos = new Acos();
Assert.assertEquals(FastMath.PI/3, acos.value(0.5), EPS);
Assert.assertEquals(FastMath.PI/4, acos.value(Double.valueOf(1/FastMath.sqrt(2))), EPS);
double a = 0.5;
Assert.assertEquals(-1/FastMath.sqrt(1-FastMath.pow(a,2)), acos.value(new DerivativeStructure(1,1,0,a)).getPartialDerivative(1), EPS);
}
@Test
public void testAcosh() {
Acosh acosh = new Acosh();
Assert.assertEquals(0,acosh.value(1), EPS);
double a = 1.2345;
Assert.assertEquals(a,acosh.value(FastMath.cosh(a)), EPS);
Assert.assertEquals(1/(FastMath.sqrt(a-1)*FastMath.sqrt(a+1)),acosh.value(new DerivativeStructure(1,1,0,a)).getPartialDerivative(1), EPS);
}
@Test
public void testAsin() {
Asin asin = new Asin();
double a = 1.2345;
Assert.assertEquals(a, asin.value(FastMath.sin(a)), EPS);
Assert.assertEquals(1/FastMath.sqrt(1 - FastMath.pow(a,2)), asin.value(new DerivativeStructure(1,1,0,a)).getPartialDerivative(1), EPS);
}
@Test
public void testAsinh() {
Asinh asinh = new Asinh();
double a = 1.2345;
Assert.assertEquals(a, asinh.value(FastMath.sinh(a)), EPS);
Assert.assertEquals(1/FastMath.sqrt(FastMath.pow(a,2.0) + 1), asinh.value(new DerivativeStructure(1,1,0,a)).getPartialDerivative(1), EPS);
}
@Test
public void testAtan() {
Atan atan = new Atan();
double a = 1.2345;
Assert.assertEquals(a, atan.value(FastMath.tan(a)), EPS);
Assert.assertEquals(1/(FastMath.pow(a,2.0) + 1), atan.value(new DerivativeStructure(1,1,0,a)).getPartialDerivative(1), EPS);
}
@Test
public void testAtanh() {
Atanh atanh = new Atanh();
double a = 1.2345;
Assert.assertEquals(a, atanh.value(FastMath.tanh(a)), EPS);
Assert.assertEquals(1/(1 - FastMath.pow(a,2.0)), atanh.value(new DerivativeStructure(1,1,0,a)).getPartialDerivative(1), EPS);
}
@Test
public void testCbrt() {
Cbrt cbrt = new Cbrt();
double a = 1.2345;
Assert.assertEquals(a, cbrt.value(FastMath.pow(a,3)), EPS);
Assert.assertEquals(1.0/(3.0*FastMath.pow(a, 2.0/3.0)), cbrt.value(new DerivativeStructure(1,1,0,a)).getPartialDerivative(1), EPS);
}
@Test
public void testConstant() {
double a = 123.456;
Constant constantNeg1 = new Constant(-1);
Constant constant0 = new Constant(0);
Constant constant5 = new Constant(5);
Assert.assertEquals(-1, constantNeg1.value(a), EPS);
Assert.assertEquals(0, constant0.value(a), EPS);
Assert.assertEquals(5, constant5.value(a), EPS);
Assert.assertEquals(0, constantNeg1.value(new DerivativeStructure(1,1,0,a)).getPartialDerivative(1), EPS);
Assert.assertEquals(0, constant0.value(new DerivativeStructure(1,1,0,a)).getPartialDerivative(1), EPS);
Assert.assertEquals(0, constant5.value(new DerivativeStructure(1,1,0,a)).getPartialDerivative(1), EPS);
}
@Test
public void testCos() {
Cos cos = new Cos();
double a = 0.987;
Assert.assertEquals(a, cos.value(FastMath.acos(a)), EPS);
Assert.assertEquals(-FastMath.sin(a), cos.value(new DerivativeStructure(1,1,0,a)).getPartialDerivative(1), EPS);
}
@Test
public void testCosh() {
Cosh cosh = new Cosh();
double a = 1.2345;
Assert.assertEquals(a, cosh.value(FastMath.acosh(a)), EPS);
Assert.assertEquals(FastMath.sinh(a), cosh.value(new DerivativeStructure(1,1,0,a)).getPartialDerivative(1), EPS);
}
@Test
public void testExp() {
Exp exp= new Exp();
double a = 1.2345;
Assert.assertEquals(a, exp.value(FastMath.log(a)), EPS);
Assert.assertEquals(exp.value(a), exp.value(new DerivativeStructure(1,1,0,a)).getPartialDerivative(1), EPS);
}
@Test
public void testExpm1() {
Expm1 expm1 = new Expm1();
double a = 1.2345;
Assert.assertEquals(a-1, expm1.value(FastMath.log(a)), EPS);
Assert.assertEquals(FastMath.exp(a), expm1.value(new DerivativeStructure(1,1,0,a)).getPartialDerivative(1), EPS);
}
@Test
public void testIdentity() {
Identity identity = new Identity();
double a = 123.456;
Assert.assertEquals(a, identity.value(a), EPS);
Assert.assertEquals(1, identity.value(new DerivativeStructure(1,1,0,a)).getPartialDerivative(1), EPS);
}
@Test
public void testInverse() {
Inverse inverse = new Inverse();
double a = 123.456;
Assert.assertEquals(1/a, inverse.value(a), EPS);
Assert.assertEquals(-1/FastMath.pow(a,2), inverse.value(new DerivativeStructure(1,1,0,a)).getPartialDerivative(1), EPS);
}
@Test
public void testLog() {
double a = 123.456;
Log log = new Log();
Assert.assertEquals(Math.log(a), log.value(a), EPS);
Assert.assertEquals(1/a,log.value(new DerivativeStructure(1,1,0,a)).getPartialDerivative(1), EPS);
}
@Test
public void testLog10() {
Log10 log10 = new Log10();
double a =1.2345;
Assert.assertEquals(a, log10.value(FastMath.pow(10, a)), EPS);
Assert.assertEquals(1/(a*FastMath.log(10)), log10.value(new DerivativeStructure(1,1,0,a)).getPartialDerivative(1), EPS);
}
@Test
public void testLog1p() {
Log1p log1p = new Log1p();
double a = 1.2345;
Assert.assertEquals(a+1,FastMath.exp(log1p.value(a)), EPS);
Assert.assertEquals(1/(1+a), log1p.value(new DerivativeStructure(1,1,0,a)).getPartialDerivative(1), EPS);
}
@Test
public void testMinus() {
Minus minus = new Minus();
double a = 123.456;
Assert.assertEquals(-a, minus.value(a), EPS);
Assert.assertEquals(-1, minus.value(new DerivativeStructure(1,1,0,a)).getPartialDerivative(1), EPS);
}
@Test
public void testPower() {
Power squared = new Power(2);
Power power2_5 = new Power(2.5);
double a = 123.456;
Assert.assertEquals(FastMath.pow(a,2), squared.value(a), EPS);
Assert.assertEquals(FastMath.pow(a, 2.5), power2_5.value(a), EPS);
Assert.assertEquals(2*a, squared.value(new DerivativeStructure(1,1,0,a)).getPartialDerivative(1), EPS);
Assert.assertEquals(2.5*FastMath.pow(a,1.5), power2_5.value(new DerivativeStructure(1,1,0,a)).getPartialDerivative(1), EPS);
}
@Test
public void testSin() {
Sin sin = new Sin();
double a = 0.987;
Assert.assertEquals(a, sin.value(FastMath.asin(a)), EPS);
Assert.assertEquals(FastMath.cos(a), sin.value(new DerivativeStructure(1,1,0,a)).getPartialDerivative(1), EPS);
}
@Test
public void testSinh() {
Sinh sinh = new Sinh();
double a = 1.2345;
Assert.assertEquals(a, sinh.value(FastMath.asinh(a)), EPS);
Assert.assertEquals(FastMath.cosh(a), sinh.value(new DerivativeStructure(1,1,0,a)).getPartialDerivative(1), EPS);
}
@Test
public void testTan() {
Tan tan = new Tan();
double a = 0.987;
Assert.assertEquals(a, tan.value(FastMath.atan(a)), EPS);
Assert.assertEquals(1/(FastMath.pow(FastMath.cos(a),2)), tan.value(new DerivativeStructure(1,1,0,a)).getPartialDerivative(1), EPS);
}
@Test
public void testTanh() {
Tanh tanh = new Tanh();
double a = 0.987;
Assert.assertEquals(a, tanh.value(FastMath.atanh(a)), EPS);
Assert.assertEquals(1/FastMath.pow(FastMath.cosh(a),2), tanh.value(new DerivativeStructure(1,1,0,a)).getPartialDerivative(1), EPS);
}
}