Name | Description | Type | Package | Framework |
Beta | The beta function defined as: B(x,y) = frac{Gamma(x)Gamma(y)}{Gamma(x+y)}= int_0^1t^{x-1}(1-t)^{y-1},dt, x > 0, y > 0 | Class | com.numericalmethod.suanshu.analysis.function.special.beta | SuanShu |
|
BetaRegularized | The Regularized Incomplete Beta function is defined as: I_x(p,q) = frac{B(x;,p,q)}{B(p,q)} = frac{1}{B(p,q)} int_0^x t^{p-1},(1-t)^{q-1},dt, p > 0, q > 0 | Class | com.numericalmethod.suanshu.analysis.function.special.beta | SuanShu |
|
BetaRegularizedInverse | The inverse of the Regularized Incomplete Beta function is defined at: x = I^{-1}_{(p,q)}(u), 0 le u le 1 | Class | com.numericalmethod.suanshu.analysis.function.special.beta | SuanShu |
|
CumulativeNormalHastings | Hastings algorithm is faster but less accurate way to compute the cumulative standard Normal. | Class | com.numericalmethod.suanshu.analysis.function.special.gaussian | SuanShu |
|
CumulativeNormalInverse | The inverse of the cumulative standard Normal distribution function is defined as: This implementation uses the Beasley-Springer-Moro algorithm. | Class | com.numericalmethod.suanshu.analysis.function.special.gaussian | SuanShu |
|
CumulativeNormalMarsaglia | Marsaglia is about 3 times slower but is more accurate to compute the cumulative standard Normal. | Class | com.numericalmethod.suanshu.analysis.function.special.gaussian | SuanShu |
|
Digamma | The digamma function is defined as the logarithmic derivative of the gamma function. | Class | com.numericalmethod.suanshu.analysis.function.special.gamma | SuanShu |
|
Erf | The Error function is defined as: operatorname{erf}(x) = frac{2}{sqrt{pi}}int_{0}^x e^{-t^2} dt | Class | com.numericalmethod.suanshu.analysis.function.special.gaussian | SuanShu |
|
Erfc | This complementary Error function is defined as: operatorname{erfc}(x) | Class | com.numericalmethod.suanshu.analysis.function.special.gaussian | SuanShu |
|
ErfInverse | The inverse of the Error function is defined as: operatorname{erf}^{-1}(x) | Class | com.numericalmethod.suanshu.analysis.function.special.gaussian | SuanShu |
|
Gamma | The Gamma function is an extension of the factorial function to real and complex numbers, with its argument shifted down by 1. | Interface | com.numericalmethod.suanshu.analysis.function.special.gamma | SuanShu |
|
GammaGergoNemes | The Gergo Nemes' algorithm is very simple and quick to compute the Gamma function, if accuracy is not critical. | Class | com.numericalmethod.suanshu.analysis.function.special.gamma | SuanShu |
|
GammaLanczos | Lanczos approximation provides a way to compute the Gamma function such that the accuracy can be made arbitrarily precise. | Class | com.numericalmethod.suanshu.analysis.function.special.gamma | SuanShu |
|
GammaLanczosQuick | Lanczos approximation, computations are done in double. | Class | com.numericalmethod.suanshu.analysis.function.special.gamma | SuanShu |
|
GammaLowerIncomplete | The Lower Incomplete Gamma function is defined as: gamma(s,x) = int_0^x t^{s-1},e^{-t},{
m d}t = P(s,x)Gamma(s) | Class | com.numericalmethod.suanshu.analysis.function.special.gamma | SuanShu |
|
GammaRegularizedP | The Regularized Incomplete Gamma P function is defined as: P(s,x) = frac{gamma(s,x)}{Gamma(s)} = 1 - Q(s,x), s geq 0, x geq 0 | Class | com.numericalmethod.suanshu.analysis.function.special.gamma | SuanShu |
|
GammaRegularizedPInverse | The inverse of the Regularized Incomplete Gamma P function is defined as: x = P^{-1}(s,u), 0 geq u geq 1 | Class | com.numericalmethod.suanshu.analysis.function.special.gamma | SuanShu |
|
GammaRegularizedQ | The Regularized Incomplete Gamma Q function is defined as: Q(s,x)=frac{Gamma(s,x)}{Gamma(s)}=1-P(s,x), s geq 0, x geq 0 | Class | com.numericalmethod.suanshu.analysis.function.special.gamma | SuanShu |
|
GammaUpperIncomplete | The Upper Incomplete Gamma function is defined as: Gamma(s,x) = int_x^{infty} t^{s-1},e^{-t},{
m d}t = Q(s,x) imes Gamma(s) | Class | com.numericalmethod.suanshu.analysis.function.special.gamma | SuanShu |
|
Gaussian | The Gaussian function is defined as: f(x) = a e^{- { frac{(x-b)^2 }{ 2 c^2} } } | Class | com.numericalmethod.suanshu.analysis.function.special.gaussian | SuanShu |
|
Lanczos | The Lanczos approximation is a method for computing the Gamma function numerically, published by Cornelius Lanczos in 1964. | Class | com.numericalmethod.suanshu.analysis.function.special.gamma | SuanShu |
|
LogBeta | This class represents the log of Beta function log(B(x, y)). | Class | com.numericalmethod.suanshu.analysis.function.special.beta | SuanShu |
|
LogGamma | The log-Gamma function, (log (Gamma(z))), for positive real numbers, is the log of the Gamma function. | Class | com.numericalmethod.suanshu.analysis.function.special.gamma | SuanShu |
|
LogGamma .Method | the available methods to compute (log (Gamma(z)))Lanczos approximation. | Class | com.numericalmethod.suanshu.analysis.function.special.gamma | SuanShu |
|
MultinomialBetaFunction | A multinomial Beta function is defined as: frac{prod_{i=1}^K Gamma(alpha_i)}{Gammaleft(sum_{i=1}^K | Class | com.numericalmethod.suanshu.analysis.function.special.beta | SuanShu |
|
Rastrigin | The Rastrigin function is a non-convex function used as a performance test problem for optimization algorithms. | Class | com.numericalmethod.suanshu.analysis.function.special | SuanShu |
|
StandardCumulativeNormal | The cumulative Normal distribution function describes the probability of a Normal random variable falling in the interval ((-infty, x]). | Interface | com.numericalmethod.suanshu.analysis.function.special.gaussian | SuanShu |
|
Trigamma | The trigamma function is defined as the logarithmic derivative of the digamma function. | Class | com.numericalmethod.suanshu.analysis.function.special.gamma | SuanShu |