Package org.hipparchus.special

Class Erf

  • public class Erf
extends Object
    This is a utility class that provides computation methods related to the error functions.

    • Method Summary

      All Methods Static Methods Concrete Methods 
      Modifier and Type Method Description
      static double erf​(double x)
      Returns the error function. \[ \mathrm{erf}(x) = \frac{2}{\sqrt{\pi}} \int_{t=0}^x e^{-t^2}dt \]
      static double erf​(double x1, double x2)
      Returns the difference between erf(x1) and erf(x2).
      static <T extends CalculusFieldElement<T>>
      T      		 erf​(T x)
      Returns the error function. \[ \mathrm{erf}(x) = \frac{2}{\sqrt{\pi}} \int_{t=0}^x e^{-t^2}dt \]
      static <T extends CalculusFieldElement<T>>
      T      		 erf​(T x1, T x2)
      Returns the difference between erf(x1) and erf(x2).
      static double erfc​(double x)
      Returns the complementary error function. \[ \mathrm{erfc}(x) = \frac{2}{\sqrt{\pi}} \int_{t=x}^\infty e^{-t^2}dt = 1 - \mathrm{erf}
      static <T extends CalculusFieldElement<T>>
      T      		 erfc​(T x)
      Returns the complementary error function. \[ erfc(x) = \frac{2}{\sqrt{\pi}} \int_x^\infty e^{-t^2}dt = 1 - erf(x) \]
      static double erfcInv​(double x)
      Returns the inverse erfc.
      static <T extends CalculusFieldElement<T>>
      T      		 erfcInv​(T x)
      Returns the inverse erfc.
      static double erfInv​(double x)
      Returns the inverse erf.
      static <T extends CalculusFieldElement<T>>
      T      		 erfInv​(T x)
      Returns the inverse erf.

    • Method Detail

      • erf

        public static double erf​(double x)
        Returns the error function. \[ \mathrm{erf}(x) = \frac{2}{\sqrt{\pi}} \int_{t=0}^x e^{-t^2}dt \]

        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:
        MathIllegalStateException - if the algorithm fails to converge.
        See Also:
        Gamma.regularizedGammaP(double, double, double, int)

      • erf

        public static <T extends CalculusFieldElement<T>> T erf​(T x)
        Returns the error function. \[ \mathrm{erf}(x) = \frac{2}{\sqrt{\pi}} \int_{t=0}^x e^{-t^2}dt \]

        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.

        Type Parameters:
        T - type of the field elements
        Parameters:
        x - the value.
        Returns:
        the error function erf(x)
        Throws:
        MathIllegalStateException - 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. \[ \mathrm{erfc}(x) = \frac{2}{\sqrt{\pi}} \int_{t=x}^\infty e^{-t^2}dt = 1 - \mathrm{erf}

        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:
        MathIllegalStateException - if the algorithm fails to converge.
        See Also:
        Gamma.regularizedGammaQ(double, double, double, int)

      • erfc

        public static <T extends CalculusFieldElement<T>> T erfc​(T x)
        Returns the complementary error function. \[ erfc(x) = \frac{2}{\sqrt{\pi}} \int_x^\infty e^{-t^2}dt = 1 - erf(x) \]

        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. This implies that the current implementation does not allow the use of Dfp with extended precision.

        Type Parameters:
        T - type of the field elements
        Parameters:
        x - the value
        Returns:
        the complementary error function erfc(x)
        Throws:
        MathIllegalStateException - if the algorithm fails to converge.
        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)

      • erf

        public static <T extends CalculusFieldElement<T>> T erf​(T x1,
                                                        T 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.

        Type Parameters:
        T - type of the field elements
        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)

      • erfInv

        public static <T extends CalculusFieldElement<T>> T erfInv​(T 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.

        Type Parameters:
        T - type of the filed elements
        Parameters:
        x - the value
        Returns:
        t such that x = erf(t)

      • erfcInv

        public static double erfcInv​(double x)
        Returns the inverse erfc.
        Parameters:
        x - the value
        Returns:
        t such that x = erfc(t)

      • erfcInv

        public static <T extends CalculusFieldElement<T>> T erfcInv​(T x)
        Returns the inverse erfc.
        Type Parameters:
        T - type of the field elements
        Parameters:
        x - the value
        Returns:
        t such that x = erfc(t)