Method Detail

• erf

  public static double erf(double x)

  Returns the error function.

  erf(x) = 2/√π ₀∫^x 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)

• erfInv

  public static double erfInv(double x)

  Returns the inverse erf.

  This implementation is described in the paper: Approximating the erfinv function by Mike Giles, Oxford-Man Institute of Quantitative Finance, which was published in GPU Computing Gems, volume 2, 2010. The source code is available here.

  Parameters:

  x - the value

  Returns:

  t such that x = erf(t)

  Since:

  3.2

• erfcInv

  public static double erfcInv(double x)

  Returns the inverse erfc.

  Parameters:

  x - the value

  Returns:

  t such that x = erfc(t)

  Since:

  3.2