java.lang.Object
- org.hipparchus.special.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. $\erf (x) = \frac{2}{\sqrt{π}} \int_{t = 0}^{x} e^{- t^{2}} d t$
`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. $\erf (x) = \frac{2}{\sqrt{π}} \int_{t = 0}^{x} e^{- t^{2}} d t$
`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. $e r f c (x) = \frac{2}{\sqrt{π}} \int_{x}^{\infty} e^{- t^{2}} d t = 1 - e r f (x)$
`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.

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. $\erf (x) = \frac{2}{\sqrt{π}} \int_{t = 0}^{x} e^{- t^{2}} d t$
    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. $\erf (x) = \frac{2}{\sqrt{π}} \int_{t = 0}^{x} e^{- t^{2}} d t$
    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. $e r f c (x) = \frac{2}{\sqrt{π}} \int_{x}^{\infty} e^{- t^{2}} d t = 1 - e r f (x)$
    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)

Class Erf

Method Summary

Methods inherited from class java.lang.Object

Method Detail

erf

erf

erfc

erfc

erf

erf

erfInv

erfInv

erfcInv

erfcInv