C# Class Artemis.Engine.Maths.SpecialFunctions

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Public Methods

Method	Description
Acosh ( double x ) : double	Returns the hyperbolic arc cosine of the specified number.
AiryA ( double x ) : double	Return the value of the Airy Ai function at x.
AiryB ( double x ) : double	Return the value of the Airy Bi function at x.
Asinh ( double xx ) : double	Returns the hyperbolic arc sine of the specified number.
Atanh ( double x ) : double	Returns the hyperbolic arc tangent of the specified number.
BivariateNormDistr ( double x, double y ) : double	Return the value of the bivariate normal distribution at (x, y) (e^(-x^2 - y^2)).
ChiSqrd ( double df, double x ) : double	Returns the chi-square function (left hand tail).
CiApprox ( double x ) : double	Approximately evaluate the cosine integral at x. This approximation only converges for \|x\| <= 5π. The cosine integral is defined as x / Ci(x) = γ + ln(x) + \| (cos(t) - 1)/t dt / 0
ComplementedChiSqrd ( double df, double x ) : double	Returns the chi-square function (right hand tail).
ComplementedIncompleteGamma ( double a, double x ) : double	Returns the complemented incomplete gamma function.
ComplementedPoissonDistribution ( int k, double x ) : double	Returns the sum of the terms k+1 to infinity of the Poisson distribution.
CosSqrd ( double x ) : double	Return the value of cos(x)^2.
CumulativeNormalDistribution ( double a ) : double	Returns the area under the Gaussian probability density function, integrated from minus infinity to a.
Digamma ( double x ) : double	Return the value of the digamma function (the logarithmic derivative of the gamma function) at x.
Erf ( double x ) : double	Returns the error function of the specified number.
Erfc ( double a ) : double	Returns the complementary error function of the specified number.
FuzzySoftMax ( double x, double y, double k ) : double	A scaled version of the SoftMax function with smoothing parameter `k`.
FuzzySoftMin ( double x, double y, double k ) : double	A scaled version of the SoftMin function with smoothing parameter `k`.
Gamma ( double x ) : double	Returns the gamma function of the specified number.
IncompleteBeta ( double aa, double bb, double xx ) : double	Returns the incomplete beta function evaluated from zero to xx.
IncompleteGamma ( double a, double x ) : double	Returns the incomplete gamma function.
J0 ( double x ) : double	Returns the Bessel function of order 0 of the specified number.
J1 ( double x ) : double	Returns the Bessel function of order 1 of the specified number.
JN ( int n, double x ) : double	Returns the Bessel function of order n of the specified number.
Log10 ( double x ) : double	Returns the base 10 logarithm of the specified number.
LogGamma ( double x ) : double	Returns the natural logarithm of gamma function.
NormDistr ( double x ) : double	Return the value of the normal distribution at x (e^(-x^2)).
PoissonDistribution ( int k, double x ) : double	Returns the sum of the first k terms of the Poisson distribution.
SiApprox ( double x ) : double	Approximately evaluate the sine integral at x. This approximation only converges for \|x\| <= 5π. The sine integral is defined as x / Si(x) = \| sinc(t) dt / 0 with sinc(t) = sin(t)/t.
SineSqrd ( double x ) : double	Return the value of sin(x)^2.
SoftMax ( double x, double y ) : double	SoftMax is an infinitely differentiable approximation of the standard Max function (i.e. it is smooth).
SoftMin ( double x, double y ) : double	SoftMin is an infinitely differentiable approximation of the standard Min function (i.e. it is smooth).
Y0 ( double x ) : double	Returns the Bessel function of the second kind, of order 0 of the specified number.
Y1 ( double x ) : double	Returns the Bessel function of the second kind, of order 1 of the specified number.
YN ( int n, double x ) : double	Returns the Bessel function of the second kind, of order n of the specified number.

Private Methods

Method	Description
Stirf ( double x ) : double	Return the gamma function computed by Stirling's formula.
incbcf ( double a, double b, double x ) : double	Returns the continued fraction expansion #1 for incomplete beta integral.
incbd ( double a, double b, double x ) : double	Returns the continued fraction expansion #2 for incomplete beta integral.
p1evl ( double x, double coef, int N ) : double	Evaluates polynomial of degree N with assumtion that coef[N] = 1.0
polevl ( double x, double coef, int N ) : double	Evaluates polynomial of degree N
pseries ( double a, double b, double x ) : double	Returns the power series for incomplete beta integral. Use when b*x is small and x not too close to 1.

Method Details

Acosh() public static method

Returns the hyperbolic arc cosine of the specified number.

public static Acosh ( double x ) : double
x	double
return	double

AiryA() public static method

Return the value of the Airy Ai function at x.

public static AiryA ( double x ) : double
x	double
return	double

AiryB() public static method

Return the value of the Airy Bi function at x.

public static AiryB ( double x ) : double
x	double
return	double

Asinh() public static method

Returns the hyperbolic arc sine of the specified number.

public static Asinh ( double xx ) : double
xx	double
return	double

Atanh() public static method

Returns the hyperbolic arc tangent of the specified number.

public static Atanh ( double x ) : double
x	double
return	double

BivariateNormDistr() public static method

Return the value of the bivariate normal distribution at (x, y) (e^(-x^2 - y^2)).

public static BivariateNormDistr ( double x, double y ) : double
x	double
y	double
return	double

ChiSqrd() public static method

Returns the chi-square function (left hand tail).

public static ChiSqrd ( double df, double x ) : double
df	double	degrees of freedom
x	double	double value
return	double

CiApprox() public static method

Approximately evaluate the cosine integral at x. This approximation only converges for |x| <= 5π. The cosine integral is defined as x / Ci(x) = γ + ln(x) + | (cos(t) - 1)/t dt / 0

public static CiApprox ( double x ) : double
x	double
return	double

ComplementedChiSqrd() public static method

Returns the chi-square function (right hand tail).

public static ComplementedChiSqrd ( double df, double x ) : double
df	double	degrees of freedom
x	double	double value
return	double

ComplementedIncompleteGamma() public static method

Returns the complemented incomplete gamma function.

public static ComplementedIncompleteGamma ( double a, double x ) : double
a	double
x	double
return	double

ComplementedPoissonDistribution() public static method

Returns the sum of the terms k+1 to infinity of the Poisson distribution.

public static ComplementedPoissonDistribution ( int k, double x ) : double
k	int	start
x	double	double value
return	double

CosSqrd() public static method

Return the value of cos(x)^2.

public static CosSqrd ( double x ) : double
x	double
return	double

CumulativeNormalDistribution() public static method

Returns the area under the Gaussian probability density function, integrated from minus infinity to a.

public static CumulativeNormalDistribution ( double a ) : double
a	double
return	double

Digamma() public static method

Return the value of the digamma function (the logarithmic derivative of the gamma function) at x.

public static Digamma ( double x ) : double
x	double
return	double

Erf() public static method

Returns the error function of the specified number.

public static Erf ( double x ) : double
x	double
return	double

Erfc() public static method

Returns the complementary error function of the specified number.

public static Erfc ( double a ) : double
a	double
return	double

FuzzySoftMax() public static method

A scaled version of the SoftMax function with smoothing parameter k.

public static FuzzySoftMax ( double x, double y, double k ) : double
x	double
y	double
k	double
return	double

FuzzySoftMin() public static method

A scaled version of the SoftMin function with smoothing parameter k.

public static FuzzySoftMin ( double x, double y, double k ) : double
x	double
y	double
k	double
return	double

Gamma() public static method

Returns the gamma function of the specified number.

public static Gamma ( double x ) : double
x	double
return	double

IncompleteBeta() public static method

Returns the incomplete beta function evaluated from zero to xx.

public static IncompleteBeta ( double aa, double bb, double xx ) : double
aa	double
bb	double
xx	double
return	double

IncompleteGamma() public static method

Returns the incomplete gamma function.

public static IncompleteGamma ( double a, double x ) : double
a	double
x	double
return	double

J0() public static method

Returns the Bessel function of order 0 of the specified number.

public static J0 ( double x ) : double
x	double
return	double

J1() public static method

Returns the Bessel function of order 1 of the specified number.

public static J1 ( double x ) : double
x	double
return	double

JN() public static method

Returns the Bessel function of order n of the specified number.

public static JN ( int n, double x ) : double
n	int
x	double
return	double

Log10() public static method

Returns the base 10 logarithm of the specified number.

public static Log10 ( double x ) : double
x	double
return	double

LogGamma() public static method

Returns the natural logarithm of gamma function.

public static LogGamma ( double x ) : double
x	double
return	double

NormDistr() public static method

Return the value of the normal distribution at x (e^(-x^2)).

public static NormDistr ( double x ) : double
x	double
return	double

PoissonDistribution() public static method

Returns the sum of the first k terms of the Poisson distribution.

public static PoissonDistribution ( int k, double x ) : double
k	int	number of terms
x	double	double value
return	double

SiApprox() public static method

Approximately evaluate the sine integral at x. This approximation only converges for |x| <= 5π. The sine integral is defined as x / Si(x) = | sinc(t) dt / 0 with sinc(t) = sin(t)/t.

public static SiApprox ( double x ) : double
x	double
return	double

SineSqrd() public static method

Return the value of sin(x)^2.

public static SineSqrd ( double x ) : double
x	double
return	double

SoftMax() public static method

SoftMax is an infinitely differentiable approximation of the standard Max function (i.e. it is smooth).

public static SoftMax ( double x, double y ) : double
x	double
y	double
return	double

SoftMin() public static method

SoftMin is an infinitely differentiable approximation of the standard Min function (i.e. it is smooth).

public static SoftMin ( double x, double y ) : double
x	double
y	double
return	double

Y0() public static method

Returns the Bessel function of the second kind, of order 0 of the specified number.

public static Y0 ( double x ) : double
x	double
return	double

Y1() public static method

Returns the Bessel function of the second kind, of order 1 of the specified number.

public static Y1 ( double x ) : double
x	double
return	double

YN() public static method

Returns the Bessel function of the second kind, of order n of the specified number.

public static YN ( int n, double x ) : double
n	int
x	double
return	double