在go语言中实现马尔科夫链预测下一状态概率的示例
Go  /  管理员 发布于 1年前   342
马尔可夫链在很多情况下都很有用,尤其是在交易中,它可以用来预测下一个趋势是看跌、看涨还是停滞。
如果你不知道这些代码想要做什么,可以自行先了解一下马尔可夫链。
第1部分示例代码 :
package main
import (
"fmt"
"strconv"
"strings"
"time"
"math/rand"
"github.com/gonum/matrix/mat64"
)
// 状态空间
var states = []string{"sleep", "icecream", "run"}
// 可能发生的事件
var transitionFromSleep = []string{
"SS",
"SR",
"SI",
}
var transitionFromRun = []string{
"RS",
"RR",
"RI",
}
var transitionFromIceCream = []string{
"IS",
"IR",
"II",
}
var transitionMatrix mat64.Matrix
func main() {
// 概率矩阵(过渡矩阵)
// 数字是凭空捏造的...
transitionMatrixString := "[0.2 0.6 0.2;0.1 0.6 0.3; 0.2 0.7 0.1]"
transitionMatrix = matrix(transitionMatrixString)
// 打印所有过渡矩阵元素
fmt.Printf("transitionMatrix :\n%v\n\n", mat64.Formatted(transitionMatrix, mat64.Prefix(""), mat64.Excerpt(0)))
// 执行简单的正确性检查。
// 所有概率之和必须为 1,因此我们有 3 行,最终结果必须等于 3。
// 结果必须等于 3
s := mat64.Sum(transitionMatrix)
s1 := fmt.Sprintf("%0.1f", s)
if s1 != "3.0" {
panic("概率总和必须等于 3,每行总和为 1。检查您的转换矩阵")
} else {
fmt.Println("过渡矩阵检查完毕,进入下一阶段!")
}
activityForecast(2)
}
func matrixByRow(a mat64.Matrix, rowNumber int) []float64 {
dst := []float64{0.0, 0.0, 0.0}
mat64.Row(dst, rowNumber, a)
return dst
}
func sampleSet(cdf []float64) int {
// https://stackoverflow.com/questions/50507513/golang-choice-number-from-slice-array-with-given-probability
rand.Seed(time.Now().UnixNano())
r := rand.Float64()
bucket := 0
for r > cdf[bucket] {
bucket++
if bucket == len(cdf) {
bucket--
break // 需要这样做来防止运行时出错:索引超出范围
}
}
return bucket
}
func activityForecast(days int) {
// 默认状态
todayActivity := "sleep"
fmt.Println("Start state : ", todayActivity)
activityList := []string{}
activityList = append(activityList, todayActivity)
i := 0
// 计算活动列表的概率
prob := 1.0
for i < days {
if todayActivity == "sleep" {
sleepNextProbabilityDistribution := matrixByRow(transitionMatrix, 0)
randomChoice := sampleSet(sleepNextProbabilityDistribution)
change := transitionFromSleep[randomChoice]
if change == "SS" {
prob = prob * 0.2
activityList = append(activityList, "sleep")
} else if change == "SR" {
prob = prob * 0.6
todayActivity = "run"
activityList = append(activityList, "run")
} else {
prob = prob * 0.2
todayActivity = "icecream"
activityList = append(activityList, "icecream")
}
} else if todayActivity == "run" {
runNextProbabilityDistribution := matrixByRow(transitionMatrix, 1)
randomChoice := sampleSet(runNextProbabilityDistribution)
change := transitionFromRun[randomChoice]
if change == "RR" {
prob = prob * 0.5
activityList = append(activityList, "run")
} else if change == "RS" {
prob = prob * 0.2
todayActivity = "sleep"
activityList = append(activityList, "sleep")
} else {
prob = prob * 0.3
todayActivity = "icecream"
activityList = append(activityList, "icecream")
}
} else {
sleepNextProbabilityDistribution := matrixByRow(transitionMatrix, 2)
randomChoice := sampleSet(sleepNextProbabilityDistribution)
change := transitionFromIceCream[randomChoice]
if change == "II" {
prob = prob * 0.1
activityList = append(activityList, "icecream")
} else if change == "IS" {
prob = prob * 0.2
todayActivity = "sleep"
activityList = append(activityList, "sleep")
} else {
prob = prob * 0.7
todayActivity = "run"
activityList = append(activityList, "run")
}
}
i = i + 1
}
fmt.Println("Possible states : ", activityList)
fmt.Println("End state after " + strconv.Itoa(days) + " days : " + todayActivity)
fmt.Println("可能的状态序列概率:", strconv.FormatFloat(prob, 'f', 6, 64))
}
// 从仿真 NumPy 创建矩阵的方法示例:https://www.zongscan.com/demo333/96244.html
// 警告:此函数不对输入字符串进行错误检查。
// 您可能需要修改该函数,以便对以下情况进行正确性检查:
// 例如只有一对 [ ]
// 所有列和行都有数字或 0
// 所有行的大小相同 [pynum 将抛出 "ValueError: Rows not the same size.]
func matrix(str string) *mat64.Dense {
// 删除 [ 和 ]
str = strings.Replace(str, "[", "", -1)
str = strings.Replace(str, "]", "", -1)
// 计算总行数
parts := strings.SplitN(str, ";", -1)
rows := len(parts)
// 计算列总数
colSlice := strings.Fields(parts[0])
columns := len(colSlice)
// 将所有 ; 替换为空格
str = strings.Replace(str, ";", " ", -1)
// 将字符串转换为片段
// 摘自 https://www.zongscan.com/demo333/96243.html
elements := strings.Fields(str)
//为新矩阵填充数据(密集型)
data := make([]float64, rows*columns)
for i := range data {
floatValue, _ := strconv.ParseFloat(elements[i], 64)
data[i] = floatValue
}
M := mat64.NewDense(rows, columns, data)
return M
}
输出示例:
transitionMatrix :
⎡0.2 0.6 0.2⎤
⎢0.1 0.6 0.3⎥
⎣0.2 0.7 0.1⎦
过渡矩阵检查完毕,进入下一阶段!
开始状态:睡眠
可能的状态 [睡眠 运行 运行]
2 天后的结束状态:运行
可能的状态序列概率 : 0.300000
第2部分示例代码 :
package main
import (
"fmt"
"strconv"
"strings"
"time"
"math/rand"
"github.com/gonum/matrix/mat64"
)
// 状态空间
var states = []string{"sleep", "icecream", "run"}
// 可能发生的事件
var transitionFromSleep = []string{
"SS",
"SR",
"SI",
}
var transitionFromRun = []string{
"RS",
"RR",
"RI",
}
var transitionFromIceCream = []string{
"IS",
"IR",
"II",
}
var transitionMatrix mat64.Matrix
func main() {
// 概率矩阵(过渡矩阵)
// 数字是凭空捏造的...
transitionMatrixString := "[0.2 0.6 0.2;0.1 0.6 0.3; 0.2 0.7 0.1]"
transitionMatrix = matrix(transitionMatrixString)
// 打印所有过渡矩阵元素
fmt.Printf("transitionMatrix :\n%v\n\n", mat64.Formatted(transitionMatrix, mat64.Prefix(""), mat64.Excerpt(0)))
// 执行简单的正确性检查。
// 所有概率之和必须为 1,因此我们有 3 行,最终结果必须等于 3。
// 结果必须等于 3
s := mat64.Sum(transitionMatrix)
s1 := fmt.Sprintf("%0.1f", s)
if s1 != "3.0" {
panic("概率总和必须等于 3,每行总和为 1。检查您的过渡矩阵")
} else {
fmt.Println("过渡矩阵已检查完毕,进入下一阶段!")
}
// 保存每个活动列表
activityListSlice := [][]string{}
count := 0
numberOfIterations := 10000
// 迭代
for i := 1; i < numberOfIterations; i++ {
activityListSlice = append(activityListSlice, activityForecast(2))
}
// 查看我们收集的所有 "活动列表
//fmt.Println(activityListSlice)
// 遍历列表,以获得以状态:"运行 "结束的所有活动的计数
for _, v := range activityListSlice {
if v[2] == "run" {
count++
}
}
// 计算从状态 "睡眠 "开始到状态 "运行 "结束的概率: "睡眠 "状态,并以 "运行 "状态结束
inner := float64(count) / float64(numberOfIterations)
percentage := inner * 100.00
fmt.Printf("开始于状态 "睡眠 "并结束于状态 "睡眠 "的概率 睡眠 "状态和 "运行 "状态的概率 : %0.2f%%\n", percentage)
}
func matrixByRow(a mat64.Matrix, rowNumber int) []float64 {
dst := []float64{0.0, 0.0, 0.0}
mat64.Row(dst, rowNumber, a)
return dst
}
func sampleSet(cdf []float64) int {
// https://stackoverflow.com/questions/50507513/golang-choice-number-from-slice-array-with-given-probability
rand.Seed(time.Now().UnixNano())
r := rand.Float64()
bucket := 0
for r > cdf[bucket] {
bucket++
if bucket == len(cdf) {
bucket--
break // 需要这样做来防止运行时出错:索引超出范围
}
}
return bucket
}
func activityForecast(days int) []string {
// 默认状态
todayActivity := "sleep"
activityList := []string{}
activityList = append(activityList, todayActivity)
i := 0
// 计算活动列表的概率
prob := 1.0
for i < days {
if todayActivity == "sleep" {
sleepNextProbabilityDistribution := matrixByRow(transitionMatrix, 0)
randomChoice := sampleSet(sleepNextProbabilityDistribution)
change := transitionFromSleep[randomChoice]
if change == "SS" {
prob = prob * 0.2
activityList = append(activityList, "sleep")
} else if change == "SR" {
prob = prob * 0.6
todayActivity = "run"
activityList = append(activityList, "run")
} else {
prob = prob * 0.2
todayActivity = "icecream"
activityList = append(activityList, "icecream")
}
} else if todayActivity == "run" {
runNextProbabilityDistribution := matrixByRow(transitionMatrix, 1)
randomChoice := sampleSet(runNextProbabilityDistribution)
change := transitionFromRun[randomChoice]
if change == "RR" {
prob = prob * 0.5
activityList = append(activityList, "run")
} else if change == "RS" {
prob = prob * 0.2
todayActivity = "sleep"
activityList = append(activityList, "sleep")
} else {
prob = prob * 0.3
todayActivity = "icecream"
activityList = append(activityList, "icecream")
}
} else {
sleepNextProbabilityDistribution := matrixByRow(transitionMatrix, 2)
randomChoice := sampleSet(sleepNextProbabilityDistribution)
change := transitionFromIceCream[randomChoice]
if change == "II" {
prob = prob * 0.1
activityList = append(activityList, "icecream")
} else if change == "IS" {
prob = prob * 0.2
todayActivity = "sleep"
activityList = append(activityList, "sleep")
} else {
prob = prob * 0.7
todayActivity = "run"
activityList = append(activityList, "run")
}
}
i++
}
return activityList
}
// 从仿真 NumPy 创建矩阵的方法示例:https://www.zongscan.com/demo333/96244.html
// 警告:此函数不对输入字符串进行错误检查。
// 您可能需要修改该函数,以便对以下情况进行正确性检查:
// 例如只有一对 [ ]
// 所有列和行都有数字或 0
// 所有行的大小相同 [pynum 将抛出 "ValueError: Rows not the same size.]
func matrix(str string) *mat64.Dense {
// 删除 [ 和 ]
str = strings.Replace(str, "[", "", -1)
str = strings.Replace(str, "]", "", -1)
// 计算总行数
parts := strings.SplitN(str, ";", -1)
rows := len(parts)
// 计算列总数
colSlice := strings.Fields(parts[0])
columns := len(colSlice)
// 将所有 ; 替换为空格
str = strings.Replace(str, ";", " ", -1)
// 将字符串转换为片段
// 摘自 https://www.zongscan.com/demo333/96243.html
elements := strings.Fields(str)
// 为新矩阵填充数据(密集型)
data := make([]float64, rows*columns)
for i := range data {
floatValue, _ := strconv.ParseFloat(elements[i], 64)
data[i] = floatValue
}
M := mat64.NewDense(rows, columns, data)
return M
}
输出示例:
transitionMatrix :
⎡0.2 0.6 0.2⎤
⎢0.1 0.6 0.3⎥
⎣0.2 0.7 0.1⎦
过渡矩阵检查完毕,进入下一阶段!
开始于状态 "睡眠 "并结束于状态 "睡眠 "的概率 睡眠 "状态和 "运行 "状态的概率 : 47.54
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