Package org.hipparchus.special

Class Erf

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

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. $$erfc(x)=\frac{2}{\sqrt{\pi }}{\int }_x^{\mathrm{\infty }}{e}^{-t^2}dt=1-erf(x)$$
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.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Details

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. $$erfc(x)=\frac{2}{\sqrt{\pi }}{\int }_x^{\mathrm{\infty }}{e}^{-t^2}dt=1-erf(x)$$

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)