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Java example source code file (ErfTest.java)

This example Java source code file (ErfTest.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Learn more about this Java project at its project page.

Java - Java tags/keywords

erftest, test

The ErfTest.java Java example source code

/*
 * 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.math3.special;

import org.apache.commons.math3.TestUtils;
import org.apache.commons.math3.util.FastMath;

import org.junit.Test;
import org.junit.Assert;

/**
 */
public class ErfTest {
    @Test
    public void testErf0() {
        double actual = Erf.erf(0.0);
        double expected = 0.0;
        Assert.assertEquals(expected, actual, 1.0e-15);
        Assert.assertEquals(1 - expected, Erf.erfc(0.0), 1.0e-15);
    }

    @Test
    public void testErf1960() {
        double x = 1.960 / FastMath.sqrt(2.0);
        double actual = Erf.erf(x);
        double expected = 0.95;
        Assert.assertEquals(expected, actual, 1.0e-5);
        Assert.assertEquals(1 - actual, Erf.erfc(x), 1.0e-15);

        actual = Erf.erf(-x);
        expected = -expected;
        Assert.assertEquals(expected, actual, 1.0e-5);
        Assert.assertEquals(1 - actual, Erf.erfc(-x), 1.0e-15);
    }

    @Test
    public void testErf2576() {
        double x = 2.576 / FastMath.sqrt(2.0);
        double actual = Erf.erf(x);
        double expected = 0.99;
        Assert.assertEquals(expected, actual, 1.0e-5);
        Assert.assertEquals(1 - actual, Erf.erfc(x), 1e-15);

        actual = Erf.erf(-x);
        expected = -expected;
        Assert.assertEquals(expected, actual, 1.0e-5);
        Assert.assertEquals(1 - actual, Erf.erfc(-x), 1.0e-15);
    }

    @Test
    public void testErf2807() {
        double x = 2.807 / FastMath.sqrt(2.0);
        double actual = Erf.erf(x);
        double expected = 0.995;
        Assert.assertEquals(expected, actual, 1.0e-5);
        Assert.assertEquals(1 - actual, Erf.erfc(x), 1.0e-15);

        actual = Erf.erf(-x);
        expected = -expected;
        Assert.assertEquals(expected, actual, 1.0e-5);
        Assert.assertEquals(1 - actual, Erf.erfc(-x), 1.0e-15);
    }

    @Test
    public void testErf3291() {
        double x = 3.291 / FastMath.sqrt(2.0);
        double actual = Erf.erf(x);
        double expected = 0.999;
        Assert.assertEquals(expected, actual, 1.0e-5);
        Assert.assertEquals(1 - expected, Erf.erfc(x), 1.0e-5);

        actual = Erf.erf(-x);
        expected = -expected;
        Assert.assertEquals(expected, actual, 1.0e-5);
        Assert.assertEquals(1 - expected, Erf.erfc(-x), 1.0e-5);
    }

    /**
     * MATH-301, MATH-456
     */
    @Test
    public void testLargeValues() {
        for (int i = 1; i < 200; i*=10) {
            double result = Erf.erf(i);
            Assert.assertFalse(Double.isNaN(result));
            Assert.assertTrue(result > 0 && result <= 1);
            result = Erf.erf(-i);
            Assert.assertFalse(Double.isNaN(result));
            Assert.assertTrue(result >= -1 && result < 0);
            result = Erf.erfc(i);
            Assert.assertFalse(Double.isNaN(result));
            Assert.assertTrue(result >= 0 && result < 1);
            result = Erf.erfc(-i);
            Assert.assertFalse(Double.isNaN(result));
            Assert.assertTrue(result >= 1 && result <= 2);
        }
        Assert.assertEquals(-1, Erf.erf(Double.NEGATIVE_INFINITY), 0);
        Assert.assertEquals(1, Erf.erf(Double.POSITIVE_INFINITY), 0);
        Assert.assertEquals(2, Erf.erfc(Double.NEGATIVE_INFINITY), 0);
        Assert.assertEquals(0, Erf.erfc(Double.POSITIVE_INFINITY), 0);
    }

    /**
     * Compare Erf.erf against reference values computed using GCC 4.2.1 (Apple OSX packaged version)
     * erfl (extended precision erf).
     */
    @Test
    public void testErfGnu() {
        final double tol = 1E-15;
        final double[] gnuValues = new double[] {-1, -1, -1, -1, -1,
        -1, -1, -1, -0.99999999999999997848,
        -0.99999999999999264217, -0.99999999999846254017, -0.99999999980338395581, -0.99999998458274209971,
        -0.9999992569016276586, -0.99997790950300141459, -0.99959304798255504108, -0.99532226501895273415,
        -0.96610514647531072711, -0.84270079294971486948, -0.52049987781304653809,  0,
         0.52049987781304653809, 0.84270079294971486948, 0.96610514647531072711, 0.99532226501895273415,
         0.99959304798255504108, 0.99997790950300141459, 0.9999992569016276586, 0.99999998458274209971,
         0.99999999980338395581, 0.99999999999846254017, 0.99999999999999264217, 0.99999999999999997848,
         1,  1,  1,  1,
         1,  1,  1,  1};
        double x = -10d;
        for (int i = 0; i < 41; i++) {
            Assert.assertEquals(gnuValues[i], Erf.erf(x), tol);
            x += 0.5d;
        }
    }

    /**
     * Compare Erf.erfc against reference values computed using GCC 4.2.1 (Apple OSX packaged version)
     * erfcl (extended precision erfc).
     */
    @Test
    public void testErfcGnu() {
        final double tol = 1E-15;
        final double[] gnuValues = new double[] { 2,  2,  2,  2,  2,
        2,  2,  2, 1.9999999999999999785,
        1.9999999999999926422, 1.9999999999984625402, 1.9999999998033839558, 1.9999999845827420998,
        1.9999992569016276586, 1.9999779095030014146, 1.9995930479825550411, 1.9953222650189527342,
        1.9661051464753107271, 1.8427007929497148695, 1.5204998778130465381,  1,
        0.47950012218695346194, 0.15729920705028513051, 0.033894853524689272893, 0.0046777349810472658333,
        0.00040695201744495893941, 2.2090496998585441366E-05, 7.4309837234141274516E-07, 1.5417257900280018858E-08,
        1.966160441542887477E-10, 1.5374597944280348501E-12, 7.3578479179743980661E-15, 2.1519736712498913103E-17,
        3.8421483271206474691E-20, 4.1838256077794144006E-23, 2.7766493860305691016E-26, 1.1224297172982927079E-29,
        2.7623240713337714448E-33, 4.1370317465138102353E-37, 3.7692144856548799402E-41, 2.0884875837625447567E-45};
        double x = -10d;
        for (int i = 0; i < 41; i++) {
            Assert.assertEquals(gnuValues[i], Erf.erfc(x), tol);
            x += 0.5d;
        }
    }

    /**
     * Tests erfc against reference data computed using Maple reported in Marsaglia, G,,
     * "Evaluating the Normal Distribution," Journal of Statistical Software, July, 2004.
     * http//www.jstatsoft.org/v11/a05/paper
     */
    @Test
    public void testErfcMaple() {
        double[][] ref = new double[][]
                        {{0.1, 4.60172162722971e-01},
                         {1.2, 1.15069670221708e-01},
                         {2.3, 1.07241100216758e-02},
                         {3.4, 3.36929265676881e-04},
                         {4.5, 3.39767312473006e-06},
                         {5.6, 1.07175902583109e-08},
                         {6.7, 1.04209769879652e-11},
                         {7.8, 3.09535877195870e-15},
                         {8.9, 2.79233437493966e-19},
                         {10.0, 7.61985302416053e-24},
                         {11.1, 6.27219439321703e-29},
                         {12.2, 1.55411978638959e-34},
                         {13.3, 1.15734162836904e-40},
                         {14.4, 2.58717592540226e-47},
                         {15.5, 1.73446079179387e-54},
                         {16.6, 3.48454651995041e-62}
        };
        for (int i = 0; i < 15; i++) {
            final double result = 0.5*Erf.erfc(ref[i][0]/FastMath.sqrt(2));
            Assert.assertEquals(ref[i][1], result, 1E-15);
            TestUtils.assertRelativelyEquals(ref[i][1], result, 1E-13);
        }
    }

    /**
     * Test the implementation of Erf.erf(double, double) for consistency with results
     * obtained from Erf.erf(double) and Erf.erfc(double).
     */
    @Test
    public void testTwoArgumentErf() {
        double[] xi = new double[]{-2.0, -1.0, -0.9, -0.1, 0.0, 0.1, 0.9, 1.0, 2.0};
        for(double x1 : xi) {
            for(double x2 : xi) {
                double a = Erf.erf(x1, x2);
                double b = Erf.erf(x2) - Erf.erf(x1);
                double c = Erf.erfc(x1) - Erf.erfc(x2);
                Assert.assertEquals(a, b, 1E-15);
                Assert.assertEquals(a, c, 1E-15);
            }
        }
    }

    @Test
    public void testErfInvNaN() {
        Assert.assertTrue(Double.isNaN(Erf.erfInv(-1.001)));
        Assert.assertTrue(Double.isNaN(Erf.erfInv(+1.001)));
    }

    @Test
    public void testErfInvInfinite() {
        Assert.assertTrue(Double.isInfinite(Erf.erfInv(-1)));
        Assert.assertTrue(Erf.erfInv(-1) < 0);
        Assert.assertTrue(Double.isInfinite(Erf.erfInv(+1)));
        Assert.assertTrue(Erf.erfInv(+1) > 0);
    }

    @Test
    public void testErfInv() {
        for (double x = -5.9; x < 5.9; x += 0.01) {
            final double y = Erf.erf(x);
            final double dydx = 2 * FastMath.exp(-x * x) / FastMath.sqrt(FastMath.PI);
            Assert.assertEquals(x, Erf.erfInv(y), 1.0e-15 / dydx);
        }
    }

    @Test
    public void testErfcInvNaN() {
        Assert.assertTrue(Double.isNaN(Erf.erfcInv(-0.001)));
        Assert.assertTrue(Double.isNaN(Erf.erfcInv(+2.001)));
    }

    @Test
    public void testErfcInvInfinite() {
        Assert.assertTrue(Double.isInfinite(Erf.erfcInv(-0)));
        Assert.assertTrue(Erf.erfcInv( 0) > 0);
        Assert.assertTrue(Double.isInfinite(Erf.erfcInv(+2)));
        Assert.assertTrue(Erf.erfcInv(+2) < 0);
    }

    @Test
    public void testErfcInv() {
        for (double x = -5.85; x < 5.9; x += 0.01) {
            final double y = Erf.erfc(x);
            final double dydxAbs = 2 * FastMath.exp(-x * x) / FastMath.sqrt(FastMath.PI);
            Assert.assertEquals(x, Erf.erfcInv(y), 1.0e-15 / dydxAbs);
        }
    }
}

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