github.com/gopherd/gonum@v0.0.4/mathext/internal/gonum/beta.go (about)

     1  // Copyright ©2016 The Gonum Authors. All rights reserved.
     2  // Use of this source code is governed by a BSD-style
     3  // license that can be found in the LICENSE file.
     4  
     5  package gonum
     6  
     7  import (
     8  	"math"
     9  )
    10  
    11  // Beta returns the value of the complete beta function B(a, b). It is defined as
    12  //  Γ(a)Γ(b) / Γ(a+b)
    13  // Special cases are:
    14  //  B(a,b) returns NaN if a or b is Inf
    15  //  B(a,b) returns NaN if a and b are 0
    16  //  B(a,b) returns NaN if a or b is NaN
    17  //  B(a,b) returns NaN if a or b is < 0
    18  //  B(a,b) returns +Inf if a xor b is 0.
    19  //
    20  // See http://mathworld.wolfram.com/BetaFunction.html for more detailed information.
    21  func Beta(a, b float64) float64 {
    22  	return math.Exp(Lbeta(a, b))
    23  }
    24  
    25  // Lbeta returns the natural logarithm of the complete beta function B(a,b).
    26  // Lbeta is defined as:
    27  //  Ln(Γ(a)Γ(b)/Γ(a+b))
    28  // Special cases are:
    29  //  Lbeta(a,b) returns NaN if a or b is Inf
    30  //  Lbeta(a,b) returns NaN if a and b are 0
    31  //  Lbeta(a,b) returns NaN if a or b is NaN
    32  //  Lbeta(a,b) returns NaN if a or b is < 0
    33  //  Lbeta(a,b) returns +Inf if a xor b is 0.
    34  func Lbeta(a, b float64) float64 {
    35  	switch {
    36  	case math.IsInf(a, +1) || math.IsInf(b, +1):
    37  		return math.NaN()
    38  	case a == 0 && b == 0:
    39  		return math.NaN()
    40  	case a < 0 || b < 0:
    41  		return math.NaN()
    42  	case math.IsNaN(a) || math.IsNaN(b):
    43  		return math.NaN()
    44  	case a == 0 || b == 0:
    45  		return math.Inf(+1)
    46  	}
    47  
    48  	la, _ := math.Lgamma(a)
    49  	lb, _ := math.Lgamma(b)
    50  	lab, _ := math.Lgamma(a + b)
    51  	return la + lb - lab
    52  }