Java example source code file (ErfTest.java)

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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);
        }
    }
}