* Added erfc
* Top-coded both erf and erfc to return extreme values when true values are indistinguishable from extrema * Added tests against reference data JIRA: MATH-465, MATH-364 git-svn-id: https://svn.apache.org/repos/asf/commons/proper/math/branches/MATH_2_X@1054184 13f79535-47bb-0310-9956-ffa450edef68
This commit is contained in:
Phil Steitz
parent
6794d0afe6
commit
593ae5e9e5
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@ -17,6 +17,7 @@
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package org.apache.commons.math.special;
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import org.apache.commons.math.MathException;
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import org.apache.commons.math.util.FastMath;
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/**
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* This is a utility class that provides computation methods related to the
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@ -34,24 +35,58 @@ public class Erf {
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}
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/**
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* Returns the error function erf(x).
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* <p>Returns the error function</p>
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* <p>erf(x) = 2/√π <sub>0</sub>∫<sup>x</sup> e<sup>-t<sup>2</sup></sup>dt </p>
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*
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* The implementation of this method is based on:
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* <ul>
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* <li>
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* <a href="http://mathworld.wolfram.com/Erf.html">
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* Erf</a>, equation (3).</li>
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* </ul>
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* <p>This implementation computes erf(x) using the
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* {@link Gamma#regularizedGammaP(double, double, double, int) regularized gamma function},
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* following <a href="http://mathworld.wolfram.com/Erf.html"> Erf</a>, equation (3)</p>
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*
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* <p>The value returned is always between -1 and 1 (inclusive). If {@code abs(x) > 40}, then
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* {@code erf(x)} is indistinguishable from either 1 or -1 as a double, so the appropriate extreme
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* value is returned.</p>
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*
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* @param x the value.
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* @return the error function erf(x)
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* @throws MathException if the algorithm fails to converge.
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* @see Gamma#regularizedGammaP(double, double, double, int)
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*/
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public static double erf(double x) throws MathException {
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if (FastMath.abs(x) > 40) {
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return x > 0 ? 1 : -1;
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}
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double ret = Gamma.regularizedGammaP(0.5, x * x, 1.0e-15, 10000);
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if (x < 0) {
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ret = -ret;
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}
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return ret;
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}
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/**
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* <p>Returns the complementary error function</p>
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* <p>erfc(x) = 2/√π <sub>x</sub>∫<sup>∞</sup> e<sup>-t<sup>2</sup></sup>dt <br/>
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* = 1 - {@link #erf(double) erf(x)} </p>
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*
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* <p>This implementation computes erfc(x) using the
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* {@link Gamma#regularizedGammaQ(double, double, double, int) regularized gamma function},
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* following <a href="http://mathworld.wolfram.com/Erf.html"> Erf</a>, equation (3).</p>
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*
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* <p>The value returned is always between 0 and 2 (inclusive). If {@code abs(x) > 40}, then
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* {@code erf(x)} is indistinguishable from either 0 or 2 as a double, so the appropriate extreme
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* value is returned.</p>
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*
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* @param x the value
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* @return the complementary error function erfc(x)
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* @throws MathException if the algorithm fails to converge
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* @see Gamma#regularizedGammaQ(double, double, double, int)
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* @since 2.2
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*/
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public static double erfc(double x) throws MathException {
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if (FastMath.abs(x) > 40) {
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return x > 0 ? 0 : 2;
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}
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final double ret = Gamma.regularizedGammaQ(0.5, x * x, 1.0e-15, 10000);
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return x < 0 ? 2 - ret : ret;
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}
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}
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@ -52,6 +52,13 @@ The <action> type attribute can be add,update,fix,remove.
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If the output is not quite correct, check for invisible trailing spaces!
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-->
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<release version="2.2" date="TBD" description="TBD">
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<action dev="psteitz" type="update" issue="MATH-364" due-to="Christian Winter">
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Added complementary error function, erfc.
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</action>
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<action dev="psteitz" type="fix" issue="MATH-456">
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Modified erf (and erfc) to return extreme values for x with abs(x) > 40.
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For these arguments, the true value is indistinguishable from an extrema as a double.
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</action>
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<action dev="psteitz" type="update" issue="MATH-448" due-to="Patrick Meyer">
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Added a getUniqueCount() method to Frequency to return the number of unique
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values included in the frequency table.
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@ -18,6 +18,7 @@
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package org.apache.commons.math.special;
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import org.apache.commons.math.MathException;
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import org.apache.commons.math.TestUtils;
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import org.apache.commons.math.util.FastMath;
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import junit.framework.TestCase;
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@ -30,7 +31,8 @@ public class ErfTest extends TestCase {
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public void testErf0() throws MathException {
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double actual = Erf.erf(0.0);
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double expected = 0.0;
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assertEquals(expected, actual, 1.0e-5);
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assertEquals(expected, actual, 1.0e-15);
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assertEquals(1 - expected, Erf.erfc(0.0), 1.0e-15);
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}
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public void testErf1960() throws MathException {
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@ -38,10 +40,12 @@ public class ErfTest extends TestCase {
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double actual = Erf.erf(x);
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double expected = 0.95;
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assertEquals(expected, actual, 1.0e-5);
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assertEquals(1 - actual, Erf.erfc(x), 1.0e-15);
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actual = Erf.erf(-x);
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expected = -expected;
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assertEquals(expected, actual, 1.0e-5);
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assertEquals(1 - actual, Erf.erfc(-x), 1.0e-15);
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}
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public void testErf2576() throws MathException {
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@ -49,10 +53,12 @@ public class ErfTest extends TestCase {
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double actual = Erf.erf(x);
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double expected = 0.99;
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assertEquals(expected, actual, 1.0e-5);
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assertEquals(1 - actual, Erf.erfc(x), 1e-15);
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actual = Erf.erf(-x);
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expected = -expected;
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assertEquals(expected, actual, 1.0e-5);
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assertEquals(1 - actual, Erf.erfc(-x), 1.0e-15);
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}
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public void testErf2807() throws MathException {
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@ -60,10 +66,12 @@ public class ErfTest extends TestCase {
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double actual = Erf.erf(x);
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double expected = 0.995;
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assertEquals(expected, actual, 1.0e-5);
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assertEquals(1 - actual, Erf.erfc(x), 1.0e-15);
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actual = Erf.erf(-x);
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expected = -expected;
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assertEquals(expected, actual, 1.0e-5);
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assertEquals(1 - actual, Erf.erfc(-x), 1.0e-15);
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}
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public void testErf3291() throws MathException {
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@ -71,20 +79,112 @@ public class ErfTest extends TestCase {
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double actual = Erf.erf(x);
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double expected = 0.999;
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assertEquals(expected, actual, 1.0e-5);
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assertEquals(1 - expected, Erf.erfc(x), 1.0e-5);
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actual = Erf.erf(-x);
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expected = -expected;
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assertEquals(expected, actual, 1.0e-5);
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assertEquals(1 - expected, Erf.erfc(-x), 1.0e-5);
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}
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/**
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* MATH-301
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* MATH-301, MATH-456
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*/
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public void testLargeValues() throws Exception {
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for (int i = 1; i < 200; i++) {
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for (int i = 1; i < 200; i*=10) {
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double result = Erf.erf(i);
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assertFalse(Double.isNaN(result));
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assertTrue(result > 0 && result <= 1);
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result = Erf.erf(-i);
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assertFalse(Double.isNaN(result));
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assertTrue(result >= -1 && result < 0);
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result = Erf.erfc(i);
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assertFalse(Double.isNaN(result));
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assertTrue(result >= 0 && result < 1);
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result = Erf.erfc(-i);
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assertFalse(Double.isNaN(result));
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assertTrue(result >= 1 && result <= 2);
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}
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assertEquals(-1, Erf.erf(Double.NEGATIVE_INFINITY), 0);
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assertEquals(1, Erf.erf(Double.POSITIVE_INFINITY), 0);
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assertEquals(2, Erf.erfc(Double.NEGATIVE_INFINITY), 0);
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assertEquals(0, Erf.erfc(Double.POSITIVE_INFINITY), 0);
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}
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/**
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* Compare Erf.erf against reference values computed using GCC 4.2.1 (Apple OSX packaged version)
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* erfl (extended precision erf).
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*/
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public void testErfGnu() throws Exception {
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final double tol = 1E-15;
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final double[] gnuValues = new double[] {-1, -1, -1, -1, -1,
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-1, -1, -1, -0.99999999999999997848,
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-0.99999999999999264217, -0.99999999999846254017, -0.99999999980338395581, -0.99999998458274209971,
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-0.9999992569016276586, -0.99997790950300141459, -0.99959304798255504108, -0.99532226501895273415,
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-0.96610514647531072711, -0.84270079294971486948, -0.52049987781304653809, 0,
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0.52049987781304653809, 0.84270079294971486948, 0.96610514647531072711, 0.99532226501895273415,
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0.99959304798255504108, 0.99997790950300141459, 0.9999992569016276586, 0.99999998458274209971,
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0.99999999980338395581, 0.99999999999846254017, 0.99999999999999264217, 0.99999999999999997848,
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1, 1, 1, 1,
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1, 1, 1, 1};
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double x = -10d;
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for (int i = 0; i < 41; i++) {
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assertEquals(gnuValues[i], Erf.erf(x), tol);
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x += 0.5d;
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}
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}
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/**
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* Compare Erf.erfc against reference values computed using GCC 4.2.1 (Apple OSX packaged version)
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* erfcl (extended precision erfc).
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*/
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public void testErfcGnu() throws Exception {
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final double tol = 1E-15;
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final double[] gnuValues = new double[] { 2, 2, 2, 2, 2,
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2, 2, 2, 1.9999999999999999785,
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1.9999999999999926422, 1.9999999999984625402, 1.9999999998033839558, 1.9999999845827420998,
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1.9999992569016276586, 1.9999779095030014146, 1.9995930479825550411, 1.9953222650189527342,
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1.9661051464753107271, 1.8427007929497148695, 1.5204998778130465381, 1,
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0.47950012218695346194, 0.15729920705028513051, 0.033894853524689272893, 0.0046777349810472658333,
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0.00040695201744495893941, 2.2090496998585441366E-05, 7.4309837234141274516E-07, 1.5417257900280018858E-08,
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1.966160441542887477E-10, 1.5374597944280348501E-12, 7.3578479179743980661E-15, 2.1519736712498913103E-17,
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3.8421483271206474691E-20, 4.1838256077794144006E-23, 2.7766493860305691016E-26, 1.1224297172982927079E-29,
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2.7623240713337714448E-33, 4.1370317465138102353E-37, 3.7692144856548799402E-41, 2.0884875837625447567E-45};
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double x = -10d;
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for (int i = 0; i < 41; i++) {
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assertEquals(gnuValues[i], Erf.erfc(x), tol);
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x += 0.5d;
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}
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}
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/**
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* Tests erfc against reference data computed using Maple reported in Marsaglia, G,,
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* "Evaluating the Normal Distribution," Journal of Statistical Software, July, 2004.
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* http//www.jstatsoft.org/v11/a05/paper
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*/
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public void testErfcMaple() throws Exception {
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double[][] ref = new double[][]
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{{0.1, 4.60172162722971e-01},
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{1.2, 1.15069670221708e-01},
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{2.3, 1.07241100216758e-02},
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{3.4, 3.36929265676881e-04},
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{4.5, 3.39767312473006e-06},
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{5.6, 1.07175902583109e-08},
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{6.7, 1.04209769879652e-11},
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{7.8, 3.09535877195870e-15},
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{8.9, 2.79233437493966e-19},
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{10.0, 7.61985302416053e-24},
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{11.1, 6.27219439321703e-29},
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{12.2, 1.55411978638959e-34},
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{13.3, 1.15734162836904e-40},
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{14.4, 2.58717592540226e-47},
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{15.5, 1.73446079179387e-54},
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{16.6, 3.48454651995041e-62}
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};
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for (int i = 0; i < 15; i++) {
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final double result = 0.5*Erf.erfc(ref[i][0]/Math.sqrt(2));
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assertEquals(ref[i][1], result, 1E-15);
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TestUtils.assertRelativelyEquals(ref[i][1], result, 1E-13);
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}
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}
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}
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