Method |
Description |
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beta ( integer $x, integer $y ) : float |
Beta function |
|
complementaryErrorFunction ( number $x ) : number |
Complementary error function (erfc)
erfc(x) ≡ 1 - erf(x) |
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confluentHypergeometric ( number $a, number $b, number $z ) : number |
Confluent Hypergeometric Function |
|
erf ( number $x ) : number |
Error function (Gauss error function)
Convenience method for errorFunction |
|
erfc ( number $x ) : number |
Complementary error function (erfc)
Convenience method for complementaryErrorFunction |
|
errorFunction ( number $x ) : number |
Error function (Gauss error function)
https://en.wikipedia.org/wiki/Error_function |
|
gamma ( number $n ) : number |
Gamma function
https://en.wikipedia.org/wiki/Gamma_function
https://en.wikipedia.org/wiki/Particular_values_of_the_Gamma_function |
|
gammaLanczos ( number $z ) : number |
Gamma function - Lanczos' approximation
https://en.wikipedia.org/wiki/Gamma_function
https://en.wikipedia.org/wiki/Lanczos_approximation |
|
gammaStirling ( number $n ) : number |
Gamma function - Stirling approximation
https://en.wikipedia.org/wiki/Gamma_function
https://en.wikipedia.org/wiki/Stirling%27s_approximation
https://www.wolframalpha.com/input/?i=Gamma(n)&lk=3 |
|
generalizedHypergeometric ( integer $p, integer $q, variadic $params ) : number |
Generalized Hypergeometric Function |
|
hypergeometric ( number $a, number $b, number $c, number $z ) : number |
Hypergeometric Function |
|
incompleteBeta ( $x, $a, $b ) : number |
Incomplete Beta Function - B(x;a,b) |
|
logistic ( number $x₀, number $L, number $k, number $x ) : float |
Logistic function (logistic sigmoid function)
A logistic function or logistic curve is a common "S" shape (sigmoid curve). |
|
lowerIncompleteGamma ( $s, $x ) : number |
Lower incomplete gamma function - γ(s, t)
https://en.wikipedia.org/wiki/Incomplete_gamma_function#Lower_incomplete_Gamma_function |
|
regularizedIncompleteBeta ( $x, $a, $b ) : number |
Regularized incomplete beta function - Iₓ(a, b) |
|
sgn ( float $x ) : integer |
Sign function (signum function) - sgn
Convenience wrapper for signum function. |
|
sigmoid ( number $t ) : float |
Sigmoid function
A sigmoid function is a mathematical function having an "S" shaped curve (sigmoid curve). |
|
signum ( float $x ) : integer |
Sign function (signum function) - sgn
Extracts the sign of a real number. |
|
softmax ( array $𝐳 ) : array |
Softmax (normalized exponential)
A generalization of the logistic function that "squashes" a K-dimensional
vector z of arbitrary real values to a K-dimensional vector σ(z) of real values
in the range (0, 1) that add up to 1. |
|
upperIncompleteGamma ( number $s, number $x ) : number |
Upper Incomplete Gamma Function - Γ(s,x)
https://en.wikipedia.org/wiki/Incomplete_gamma_function |
|
Γ ( number $n ) : number |
Gamma function convenience method |
|
γ ( $s, $x ) : number |
γ - Convenience method for lower incomplete gamma function
https://en.wikipedia.org/wiki/Incomplete_gamma_function#Lower_incomplete_Gamma_function |
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