76 lines
1.7 KiB
Go
76 lines
1.7 KiB
Go
// Copyright 2009 The Go Authors. All rights reserved.
|
|
// Use of this source code is governed by a BSD-style
|
|
// license that can be found in the LICENSE file.
|
|
|
|
// W.Hormann, G.Derflinger:
|
|
// "Rejection-Inversion to Generate Variates
|
|
// from Monotone Discrete Distributions"
|
|
// http://eeyore.wu-wien.ac.at/papers/96-04-04.wh-der.ps.gz
|
|
|
|
package rand
|
|
|
|
import "math"
|
|
|
|
// A Zipf generates Zipf distributed variates.
|
|
type Zipf struct {
|
|
r *Rand
|
|
imax float64
|
|
v float64
|
|
q float64
|
|
s float64
|
|
oneminusQ float64
|
|
oneminusQinv float64
|
|
hxm float64
|
|
hx0minusHxm float64
|
|
}
|
|
|
|
func (z *Zipf) h(x float64) float64 {
|
|
return math.Exp(z.oneminusQ*math.Log(z.v+x)) * z.oneminusQinv
|
|
}
|
|
|
|
func (z *Zipf) hinv(x float64) float64 {
|
|
return math.Exp(z.oneminusQinv*math.Log(z.oneminusQ*x)) - z.v
|
|
}
|
|
|
|
// NewZipf returns a Zipf generating variates p(k) on [0, imax]
|
|
// proportional to (v+k)**(-s) where s>1 and k>=0, and v>=1.
|
|
func NewZipf(r *Rand, s float64, v float64, imax uint64) *Zipf {
|
|
z := new(Zipf)
|
|
if s <= 1.0 || v < 1 {
|
|
return nil
|
|
}
|
|
z.r = r
|
|
z.imax = float64(imax)
|
|
z.v = v
|
|
z.q = s
|
|
z.oneminusQ = 1.0 - z.q
|
|
z.oneminusQinv = 1.0 / z.oneminusQ
|
|
z.hxm = z.h(z.imax + 0.5)
|
|
z.hx0minusHxm = z.h(0.5) - math.Exp(math.Log(z.v)*(-z.q)) - z.hxm
|
|
z.s = 1 - z.hinv(z.h(1.5)-math.Exp(-z.q*math.Log(z.v+1.0)))
|
|
return z
|
|
}
|
|
|
|
// Uint64 returns a value drawn from the Zipf distribution described
|
|
// by the Zipf object.
|
|
func (z *Zipf) Uint64() uint64 {
|
|
if z == nil {
|
|
panic("rand: nil Zipf")
|
|
}
|
|
k := 0.0
|
|
|
|
for {
|
|
r := z.r.Float64() // r on [0,1]
|
|
ur := z.hxm + r*z.hx0minusHxm
|
|
x := z.hinv(ur)
|
|
k = math.Floor(x + 0.5)
|
|
if k-x <= z.s {
|
|
break
|
|
}
|
|
if ur >= z.h(k+0.5)-math.Exp(-math.Log(k+z.v)*z.q) {
|
|
break
|
|
}
|
|
}
|
|
return uint64(k)
|
|
}
|