113 lines
2.7 KiB
Go
113 lines
2.7 KiB
Go
package main
|
|
|
|
import "fmt"
|
|
import "math"
|
|
import rand "math/rand/v2"
|
|
|
|
var r = rand.New(rand.NewPCG(1, 2))
|
|
|
|
// https://pkg.go.dev/math/rand/v2
|
|
|
|
func sample_unit_uniform() float64 {
|
|
return r.Float64()
|
|
}
|
|
|
|
func sample_unit_normal() float64 {
|
|
return r.NormFloat64()
|
|
}
|
|
|
|
func sample_uniform(start float64, end float64) float64 {
|
|
return sample_unit_uniform()*(end-start) + start
|
|
}
|
|
|
|
func sample_normal(mean float64, sigma float64) float64 {
|
|
return mean + sample_unit_normal()*sigma
|
|
}
|
|
|
|
func sample_lognormal(logmean float64, logstd float64) float64 {
|
|
return (math.Exp(sample_normal(logmean, logstd)))
|
|
}
|
|
|
|
func sample_normal_from_90_ci(low float64, high float64) float64 {
|
|
var normal90 float64 = 1.6448536269514727
|
|
var mean float64 = (high + low) / 2.0
|
|
var std float64 = (high - low) / (2.0 * normal90)
|
|
return sample_normal(mean, std)
|
|
|
|
}
|
|
|
|
func sample_to(low float64, high float64) float64 {
|
|
// Given a (positive) 90% confidence interval,
|
|
// returns a sample from a lognorma with a matching 90% c.i.
|
|
// Key idea: If we want a lognormal with 90% confidence interval [a, b]
|
|
// we need but get a normal with 90% confidence interval [log(a), log(b)].
|
|
// Then see code for sample_normal_from_90_ci
|
|
var loglow float64 = math.Log(low)
|
|
var loghigh float64 = math.Log(high)
|
|
return math.Exp(sample_normal_from_90_ci(loglow, loghigh))
|
|
}
|
|
|
|
type func64 func() float64
|
|
|
|
func sample_mixture(fs []func64, weights []float64) float64 {
|
|
|
|
fmt.Println("weights initially: ", weights)
|
|
var sum_weights float64 = 0
|
|
for _, weight := range weights {
|
|
sum_weights += weight
|
|
}
|
|
|
|
var total float64 = 0
|
|
var cumsummed_normalized_weights = append([]float64(nil), weights...)
|
|
for i, weight := range weights {
|
|
total += weight / sum_weights
|
|
cumsummed_normalized_weights[i] = total
|
|
}
|
|
|
|
var result float64
|
|
var flag int = 0
|
|
var p float64 = r.Float64()
|
|
|
|
for i, cnw := range cumsummed_normalized_weights {
|
|
if p < cnw {
|
|
result = fs[i]()
|
|
flag = 1
|
|
break
|
|
}
|
|
}
|
|
fmt.Println(cumsummed_normalized_weights)
|
|
|
|
if flag == 0 {
|
|
result = fs[len(fs)-1]()
|
|
}
|
|
return result
|
|
// return weights[0]
|
|
|
|
}
|
|
|
|
func main() {
|
|
|
|
sample_0 := func() float64 { return 0 }
|
|
sample_1 := func() float64 { return 1 }
|
|
sample_few := func() float64 { return sample_to(1, 3) }
|
|
sample_many := func() float64 { return sample_to(2, 10) }
|
|
fs := [4](func64){sample_0, sample_1, sample_few, sample_many}
|
|
|
|
var p_a float64 = 0.8
|
|
var p_b float64 = 0.5
|
|
var p_c float64 = p_a * p_b
|
|
ws := [4](float64){1 - p_c, p_c / 2, p_c / 4, p_c / 4}
|
|
fmt.Println("weights #1", ws)
|
|
|
|
var n_samples int = 1_000_000
|
|
var avg float64 = 0
|
|
for i := 0; i < n_samples; i++ {
|
|
x := sample_mixture(fs[0:], ws[0:])
|
|
fmt.Printf("%v\n", x)
|
|
avg += x
|
|
}
|
|
avg = avg / float64(n_samples)
|
|
fmt.Printf("Average: %v\n", avg)
|
|
|
|
}
|