org.apache.commons.math3.special
Class Erf

java.lang.Object
  extended by org.apache.commons.math3.special.Erf

public class Erf
extends Object

This is a utility class that provides computation methods related to the error functions.

Version:
$Id: Erf.java 1416643 2012-12-03 19:37:14Z tn $

Method Summary
static double erf(double x)
          Returns the error function.
static double erf(double x1, double x2)
          Returns the difference between erf(x1) and erf(x2).
static double erfc(double x)
          Returns the complementary error function.
 
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
 

Method Detail

erf

public static double erf(double x)
Returns the error function.

erf(x) = 2/√π 0x e-t2dt

This implementation computes erf(x) using the regularized gamma function, following Erf, equation (3)

The value returned is always between -1 and 1 (inclusive). If abs(x) > 40, then erf(x) is indistinguishable from either 1 or -1 as a double, so the appropriate extreme value is returned.

Parameters:
x - the value.
Returns:
the error function erf(x)
Throws:
MaxCountExceededException - if the algorithm fails to converge.
See Also:
Gamma.regularizedGammaP(double, double, double, int)

erfc

public static double erfc(double x)
Returns the complementary error function.

erfc(x) = 2/√π x e-t2dt
= 1 - erf(x)

This implementation computes erfc(x) using the regularized gamma function, following Erf, equation (3).

The value returned is always between 0 and 2 (inclusive). If abs(x) > 40, then erf(x) is indistinguishable from either 0 or 2 as a double, so the appropriate extreme value is returned.

Parameters:
x - the value
Returns:
the complementary error function erfc(x)
Throws:
MaxCountExceededException - if the algorithm fails to converge.
Since:
2.2
See Also:
Gamma.regularizedGammaQ(double, double, double, int)

erf

public static double erf(double x1,
                         double x2)
Returns the difference between erf(x1) and erf(x2). The implementation uses either erf(double) or erfc(double) depending on which provides the most precise result.

Parameters:
x1 - the first value
x2 - the second value
Returns:
erf(x2) - erf(x1)


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