diff --git a/src/main/java/org/apache/commons/math/special/Erf.java b/src/main/java/org/apache/commons/math/special/Erf.java
index 8338c7228..5b8b1779b 100644
--- a/src/main/java/org/apache/commons/math/special/Erf.java
+++ b/src/main/java/org/apache/commons/math/special/Erf.java
@@ -17,6 +17,7 @@
package org.apache.commons.math.special;
import org.apache.commons.math.MathException;
+import org.apache.commons.math.util.FastMath;
/**
* This is a utility class that provides computation methods related to the
@@ -34,24 +35,58 @@ public class Erf {
}
/**
- * Returns the error function erf(x).
+ * Returns the error function
+ * erf(x) = 2/√π 0∫x e-t2dt
*
- * The implementation of this method is based on:
- *
+ * This implementation computes erf(x) using the
+ * {@link Gamma#regularizedGammaP(double, double, double, int) regularized gamma function},
+ * following Erf, equation (3)
+ *
+ * The value returned is always between -1 and 1 (inclusive). If {@code abs(x) > 40}, then
+ * {@code erf(x)} is indistinguishable from either 1 or -1 as a double, so the appropriate extreme
+ * value is returned.
*
* @param x the value.
* @return the error function erf(x)
* @throws MathException if the algorithm fails to converge.
+ * @see Gamma#regularizedGammaP(double, double, double, int)
*/
public static double erf(double x) throws MathException {
+ if (FastMath.abs(x) > 40) {
+ return x > 0 ? 1 : -1;
+ }
double ret = Gamma.regularizedGammaP(0.5, x * x, 1.0e-15, 10000);
if (x < 0) {
ret = -ret;
}
return ret;
}
+
+ /**
+ * Returns the complementary error function
+ * erfc(x) = 2/√π x∫∞ e-t2dt
+ * = 1 - {@link #erf(double) erf(x)}
+ *
+ * This implementation computes erfc(x) using the
+ * {@link Gamma#regularizedGammaQ(double, double, double, int) regularized gamma function},
+ * following Erf, equation (3).
+ *
+ * The value returned is always between 0 and 2 (inclusive). If {@code abs(x) > 40}, then
+ * {@code erf(x)} is indistinguishable from either 0 or 2 as a double, so the appropriate extreme
+ * value is returned.
+ *
+ * @param x the value
+ * @return the complementary error function erfc(x)
+ * @throws MathException if the algorithm fails to converge
+ * @see Gamma#regularizedGammaQ(double, double, double, int)
+ * @since 2.2
+ */
+ public static double erfc(double x) throws MathException {
+ if (FastMath.abs(x) > 40) {
+ return x > 0 ? 0 : 2;
+ }
+ final double ret = Gamma.regularizedGammaQ(0.5, x * x, 1.0e-15, 10000);
+ return x < 0 ? 2 - ret : ret;
+ }
}
+
diff --git a/src/site/xdoc/changes.xml b/src/site/xdoc/changes.xml
index 530883571..f76be1566 100644
--- a/src/site/xdoc/changes.xml
+++ b/src/site/xdoc/changes.xml
@@ -52,6 +52,13 @@ The type attribute can be add,update,fix,remove.
If the output is not quite correct, check for invisible trailing spaces!
-->
+
+ Added complementary error function, erfc.
+
+
+ Modified erf (and erfc) to return extreme values for x with abs(x) > 40.
+ For these arguments, the true value is indistinguishable from an extrema as a double.
+
Added a getUniqueCount() method to Frequency to return the number of unique
values included in the frequency table.
diff --git a/src/test/java/org/apache/commons/math/special/ErfTest.java b/src/test/java/org/apache/commons/math/special/ErfTest.java
index 35e30ede7..78d8bb56b 100644
--- a/src/test/java/org/apache/commons/math/special/ErfTest.java
+++ b/src/test/java/org/apache/commons/math/special/ErfTest.java
@@ -18,6 +18,7 @@
package org.apache.commons.math.special;
import org.apache.commons.math.MathException;
+import org.apache.commons.math.TestUtils;
import org.apache.commons.math.util.FastMath;
import junit.framework.TestCase;
@@ -30,7 +31,8 @@ public class ErfTest extends TestCase {
public void testErf0() throws MathException {
double actual = Erf.erf(0.0);
double expected = 0.0;
- assertEquals(expected, actual, 1.0e-5);
+ assertEquals(expected, actual, 1.0e-15);
+ assertEquals(1 - expected, Erf.erfc(0.0), 1.0e-15);
}
public void testErf1960() throws MathException {
@@ -38,10 +40,12 @@ public class ErfTest extends TestCase {
double actual = Erf.erf(x);
double expected = 0.95;
assertEquals(expected, actual, 1.0e-5);
+ assertEquals(1 - actual, Erf.erfc(x), 1.0e-15);
actual = Erf.erf(-x);
expected = -expected;
assertEquals(expected, actual, 1.0e-5);
+ assertEquals(1 - actual, Erf.erfc(-x), 1.0e-15);
}
public void testErf2576() throws MathException {
@@ -49,10 +53,12 @@ public class ErfTest extends TestCase {
double actual = Erf.erf(x);
double expected = 0.99;
assertEquals(expected, actual, 1.0e-5);
+ assertEquals(1 - actual, Erf.erfc(x), 1e-15);
actual = Erf.erf(-x);
expected = -expected;
assertEquals(expected, actual, 1.0e-5);
+ assertEquals(1 - actual, Erf.erfc(-x), 1.0e-15);
}
public void testErf2807() throws MathException {
@@ -60,10 +66,12 @@ public class ErfTest extends TestCase {
double actual = Erf.erf(x);
double expected = 0.995;
assertEquals(expected, actual, 1.0e-5);
+ assertEquals(1 - actual, Erf.erfc(x), 1.0e-15);
actual = Erf.erf(-x);
expected = -expected;
assertEquals(expected, actual, 1.0e-5);
+ assertEquals(1 - actual, Erf.erfc(-x), 1.0e-15);
}
public void testErf3291() throws MathException {
@@ -71,20 +79,112 @@ public class ErfTest extends TestCase {
double actual = Erf.erf(x);
double expected = 0.999;
assertEquals(expected, actual, 1.0e-5);
+ assertEquals(1 - expected, Erf.erfc(x), 1.0e-5);
actual = Erf.erf(-x);
expected = -expected;
assertEquals(expected, actual, 1.0e-5);
+ assertEquals(1 - expected, Erf.erfc(-x), 1.0e-5);
}
-
+
/**
- * MATH-301
+ * MATH-301, MATH-456
*/
public void testLargeValues() throws Exception {
- for (int i = 1; i < 200; i++) {
+ for (int i = 1; i < 200; i*=10) {
double result = Erf.erf(i);
assertFalse(Double.isNaN(result));
assertTrue(result > 0 && result <= 1);
+ result = Erf.erf(-i);
+ assertFalse(Double.isNaN(result));
+ assertTrue(result >= -1 && result < 0);
+ result = Erf.erfc(i);
+ assertFalse(Double.isNaN(result));
+ assertTrue(result >= 0 && result < 1);
+ result = Erf.erfc(-i);
+ assertFalse(Double.isNaN(result));
+ assertTrue(result >= 1 && result <= 2);
+ }
+ assertEquals(-1, Erf.erf(Double.NEGATIVE_INFINITY), 0);
+ assertEquals(1, Erf.erf(Double.POSITIVE_INFINITY), 0);
+ assertEquals(2, Erf.erfc(Double.NEGATIVE_INFINITY), 0);
+ 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).
+ */
+ public void testErfGnu() throws Exception {
+ 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++) {
+ 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).
+ */
+ public void testErfcGnu() throws Exception {
+ 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++) {
+ 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
+ */
+ public void testErfcMaple() throws Exception {
+ 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]/Math.sqrt(2));
+ assertEquals(ref[i][1], result, 1E-15);
+ TestUtils.assertRelativelyEquals(ref[i][1], result, 1E-13);
}
}
}