summaryrefslogtreecommitdiff
path: root/src/pkg/math/rand/zipf.go
blob: 8db2c6f5bffe2db7f5dafcc8dc119932dd487ab9 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
// 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)
}