Exboost.Math (ExBoost v0.3.9)

Summary

Functions

beta(a, b, z)

Provides the incomplete beta-function.

betac(a, b, z)

Provides the complementary incomplete beta-function.

digamma(z)

Provides the digamma function.

gamma_p(a, z)

Provides the regularized lower incomplete gamma function.

gamma_p_inv(a, p)

Implements the inverse of the regularized incomplete gamma function.

ibeta(a, b, z)

Provides the normalised incomplete beta-function.

ibetac(a, b, z)

Provides the complementary normalised incomplete beta-function.

init()

lgamma(z)

Provides the log gamma function.

tgamma(z)

Provides the gamma function.

tgamma_lower(a, z)

Provides the non-regularized lower incomplete gamma function.

Functions

beta(a, b, z)

@spec beta(a :: float(), b :: float(), z :: float()) :: float()

Provides the incomplete beta-function.

Examples

iex> Exboost.Math.beta(1.0,1.0,1.0)
1.0

betac(a, b, z)

@spec betac(a :: float(), b :: float(), z :: float()) :: float()

Provides the complementary incomplete beta-function.

Examples

iex> Exboost.Math.betac(1.0,1.0,1.0)
0.0

digamma(z)

@spec digamma(z :: float()) :: float()

Provides the digamma function.

Examples

iex> Exboost.Math.digamma(1.5)
0.03648997397857652

gamma_p(a, z)

@spec gamma_p(a :: float(), z :: float()) :: float()

Provides the regularized lower incomplete gamma function.

Examples

iex> Exboost.Math.gamma_p(0.234,2.3)
0.9891753004794075

iex> Exboost.Math.gamma_p(5.0,0.0)
0.0

gamma_p_inv(a, p)

@spec gamma_p_inv(a :: float(), p :: float()) :: float()

Implements the inverse of the regularized incomplete gamma function.

Examples:

iex> Exboost.Math.gamma_p_inv(0.234,0.9891753004794075) |> Float.round(6)
2.3

iex> Exboost.Math.gamma_p_inv(5.0,0.0)
0.0

ibeta(a, b, z)

@spec ibeta(a :: float(), b :: float(), z :: float()) :: float()

Provides the normalised incomplete beta-function.

Examples

iex> Exboost.Math.ibeta(4.0,2.0,0.5)
0.1875

ibetac(a, b, z)

@spec ibetac(a :: float(), b :: float(), z :: float()) :: float()

Provides the complementary normalised incomplete beta-function.

Examples

iex> Exboost.Math.ibetac(1.0,1.0,1.0)
0.0

init()

lgamma(z)

@spec lgamma(z :: float()) :: float()

Provides the log gamma function.

Examples

iex> Exboost.Math.lgamma(2.0)
0.0

tgamma(z)

@spec tgamma(z :: float()) :: float()

Provides the gamma function.

Examples

iex> Exboost.Math.tgamma(1.5)
0.8862269254527579

iex> Exboost.Math.tgamma(3.0)
2.0

tgamma_lower(a, z)

@spec tgamma_lower(a :: float(), z :: float()) :: float()

Provides the non-regularized lower incomplete gamma function.

Examples

iex> Exboost.Math.tgamma_lower(0.234,2.3)
3.846147673628932

iex> Exboost.Math.tgamma_lower(5.0,0.0)
0.0