├── go.mod
├── Test
    └── Test.go
├── Tree.go
├── README.md
├── Node.go
└── go.sum


/go.mod:
--------------------------------------------------------------------------------
 1 | module github.com/hammamikhairi/Decision-Tree
 2 | 
 3 | go 1.19
 4 | 
 5 | require (
 6 | 	github.com/go-gota/gota v0.12.0 // indirect
 7 | 	github.com/mauricelam/genny v0.0.0-20190320071652-0800202903e5 // indirect
 8 | 	github.com/tobgu/qframe v0.3.6 // indirect
 9 | 	golang.org/x/net v0.0.0-20210423184538-5f58ad60dda6 // indirect
10 | 	gonum.org/v1/gonum v0.9.1 // indirect
11 | )
12 | 


--------------------------------------------------------------------------------
/Test/Test.go:
--------------------------------------------------------------------------------
 1 | package main
 2 | 
 3 | import (
 4 | 	"fmt"
 5 | 	"os"
 6 | 
 7 | 	DecisionTree "github.com/hammamikhairi/Decision-Tree"
 8 | 
 9 | 	"github.com/go-gota/gota/dataframe"
10 | 	"github.com/go-gota/gota/series"
11 | )
12 | 
13 | func ReadCSVToDF(path string) dataframe.DataFrame {
14 | 	csvfile, err := os.Open(path)
15 | 	if err != nil {
16 | 		panic(err)
17 | 	}
18 | 
19 | 	return dataframe.ReadCSV(csvfile)
20 | }
21 | 
22 | func test() {
23 | 
24 | 	// Load Data
25 | 	// tested on the Titanic dataset from kaggle
26 | 	// https://www.kaggle.com/competitions/titanic/data
27 | 	f := ReadCSVToDF("Data/train.csv")
28 | 
29 | 	f = f.Select([]string{"Survived", "Age", "Fare", "Pclass", "SibSp"}).Filter(
30 | 		dataframe.F{Colname: "Age", Comparator: series.GreaterEq, Comparando: 0},
31 | 		dataframe.F{Colname: "Fare", Comparator: series.GreaterEq, Comparando: 0},
32 | 		dataframe.F{Colname: "Survived", Comparator: series.GreaterEq, Comparando: 0},
33 | 		dataframe.F{Colname: "Pclass", Comparator: series.GreaterEq, Comparando: 0},
34 | 		dataframe.F{Colname: "SibSp", Comparator: series.GreaterEq, Comparando: 0},
35 | 	)
36 | 
37 | 	Y, err := f.Col("Survived").Int()
38 | 	if err != nil {
39 | 		panic(err)
40 | 	}
41 | 
42 | 	tree := DecisionTree.TreeInit(Y, f.Select([]string{"Age", "Fare", "Pclass", "SibSp"}), 100, 4)
43 | 
44 | 	tree.Sprout()
45 | 
46 | 	df := ReadCSVToDF("Data/test.csv").Select([]string{"Age", "Fare", "Pclass", "SibSp"})
47 | 
48 | 	response := tree.Predict(df)
49 | 
50 | 	res, err := ReadCSVToDF("Data/verif.csv").Col("Survived").Int()
51 | 
52 | 	if err != nil {
53 | 		panic(err)
54 | 	}
55 | 
56 | 	var total int = len(response)
57 | 	var passed int = 0
58 | 
59 | 	for index, pred := range response {
60 | 		if pred == fmt.Sprint(res[index]) {
61 | 			passed++
62 | 		} else {
63 | 			fmt.Println(pred, res[index])
64 | 		}
65 | 	}
66 | 
67 | 	fmt.Println(total, passed)
68 | 
69 | }
70 | 


--------------------------------------------------------------------------------
/Tree.go:
--------------------------------------------------------------------------------
  1 | package decisiontree
  2 | 
  3 | import (
  4 | 	"fmt"
  5 | 	"math"
  6 | 	"sort"
  7 | 
  8 | 	"github.com/go-gota/gota/dataframe"
  9 | 	"github.com/go-gota/gota/series"
 10 | )
 11 | 
 12 | type Counter map[string]int
 13 | 
 14 | // The Decision Tree
 15 | type DecisionTree struct {
 16 | 	root *node
 17 | }
 18 | 
 19 | // Initialize the Decision Tree
 20 | //
 21 | // Parameters
 22 | // ----------
 23 | // Y : []int : The target variable to predict
 24 | // X : dataframe.DataFrame <float64 & float64> : The features
 25 | // maxTreeDepth : int : The maximum depth of the tree
 26 | // minDfSplit : int : The minimum number of samples to split a node
 27 | func TreeInit(Y []int, X dataframe.DataFrame, maxTreeDepth, minDfSplit int) *DecisionTree {
 28 | 	tree := &DecisionTree{
 29 | 		root: NodeInit(Y, X, 0, maxTreeDepth, minDfSplit, "ROOT"),
 30 | 	}
 31 | 	return tree
 32 | }
 33 | 
 34 | func count(Y []int) Counter {
 35 | 	counter := make(Counter)
 36 | 	for _, cont := range Y {
 37 | 		counter[fmt.Sprint(cont)]++
 38 | 	}
 39 | 
 40 | 	return counter
 41 | }
 42 | func countErr(Y []int, err error) Counter {
 43 | 	counter := make(Counter)
 44 | 	for _, cont := range Y {
 45 | 		counter[fmt.Sprint(cont)]++
 46 | 	}
 47 | 
 48 | 	return counter
 49 | }
 50 | 
 51 | func maxCount(counter Counter) string {
 52 | 
 53 | 	keys := make([]string, 0, len(counter))
 54 | 	for key := range counter {
 55 | 		keys = append(keys, key)
 56 | 	}
 57 | 
 58 | 	if len(keys) <= 1 {
 59 | 		return keys[0]
 60 | 	}
 61 | 
 62 | 	sort.SliceStable(keys, func(i, j int) bool {
 63 | 		return counter[keys[i]] > counter[keys[j]]
 64 | 	})
 65 | 
 66 | 	return keys[0]
 67 | }
 68 | 
 69 | func giniImputiry(s0, s1 int) float64 {
 70 | 
 71 | 	if s0+s1 == 0 {
 72 | 		return 0.0
 73 | 	}
 74 | 
 75 | 	prob0 := float64(s0) / float64(s0+s1)
 76 | 	prob1 := float64(s1) / float64(s0+s1)
 77 | 
 78 | 	return 1 - (math.Pow(prob0, 2) + math.Pow(prob1, 2))
 79 | 
 80 | }
 81 | func setFromList(list []string) (set []string) {
 82 | 	ks := make(map[string]bool) // map to keep track of repeats
 83 | 
 84 | 	for _, e := range list {
 85 | 		if _, v := ks[e]; !v {
 86 | 			ks[e] = true
 87 | 			set = append(set, e)
 88 | 		}
 89 | 	}
 90 | 	return
 91 | }
 92 | 
 93 | func uniqueGotaSeries(s series.Series) series.Series {
 94 | 	return series.New(setFromList(s.Records()), s.Type(), s.Name)
 95 | }
 96 | 
 97 | func meth(col []float64) []float64 {
 98 | 	var methed []float64
 99 | 	for i := 0; i < len(col)-1; i++ {
100 | 		methed = append(methed, (col[i]+col[i+1])/2)
101 | 	}
102 | 
103 | 	return methed
104 | }
105 | 
106 | // Generate tree
107 | func (tree *DecisionTree) Sprout() {
108 | 	tree.root.sprout()
109 | }
110 | 
111 | // Predict the target variable for a given set of features
112 | //
113 | // Parameters
114 | // ----------
115 | // X : dataframe.DataFrame : The features
116 | func (tree *DecisionTree) Predict(data dataframe.DataFrame) []string {
117 | 
118 | 	features := tree.root.data.features
119 | 	var predictions []string
120 | 
121 | 	x, _ := data.Dims()
122 | 	for i := 0; i < x; i++ {
123 | 		nmap := make(map[string]float64)
124 | 		for _, feature := range features {
125 | 			nmap[feature] = data.Col(feature).Elem(i).Float()
126 | 		}
127 | 		predictions = append(predictions, tree.root.predict(nmap))
128 | 	}
129 | 
130 | 	return predictions
131 | }
132 | 
133 | // Print the tree in a human readable format
134 | func (tree *DecisionTree) Print() {
135 | 	tree.root.print(1)
136 | }
137 | 


--------------------------------------------------------------------------------
/README.md:
--------------------------------------------------------------------------------
  1 | # Decision Tree
  2 | 
  3 | ## What is a Decision Tree
  4 | 
  5 | Decision Tree is the most powerful and popular tool for classification and prediction. A Decision tree is a flowchart-like tree structure, where each internal node denotes a test on an attribute, each branch represents an outcome of the test, and each leaf node (terminal node) holds a class label. ( sited from [here](https://www.geeksforgeeks.org/decision-tree/) )
  6 | 
  7 | <p align="center">
  8 |   <img src="https://forum.huawei.com/enterprise/en/data/attachment/forum/202103/24/190400o09x7rhnnhy2yon7.png?1.png" alt="Decision Tree"/>
  9 | </p>
 10 | 
 11 | ## Usage
 12 | 
 13 | ```go
 14 | 
 15 | package main
 16 | 
 17 | import (
 18 |   "fmt"
 19 |   "os"
 20 | 
 21 |   DecisionTree "github.com/hammamikhairi/Decision-Tree"
 22 | 
 23 |   "github.com/go-gota/gota/dataframe"
 24 |   "github.com/go-gota/gota/series"
 25 | )
 26 | 
 27 | func main() {
 28 | 
 29 |   // Load data
 30 |   // tested on the Titanic dataset from kaggle
 31 | 	// https://www.kaggle.com/competitions/titanic/data
 32 |   csvfile, err := os.Open("Data/train.csv")
 33 |   if err != nil {
 34 |     panic(err)
 35 |   }
 36 | 
 37 |   // convert data into a dataframe
 38 |   f := dataframe.ReadCSV(csvfile)
 39 | 
 40 |   // chose the column to train on
 41 |   Y, err := f.Col("Survived").Int()
 42 |   if err != nil {
 43 |     panic(err)
 44 |   }
 45 | 
 46 |   // initialize Decision Tree
 47 |   tree := DecisionTree.TreeInit(Y, f.Select([]string{"Age", "Fare"}), 10, 20)
 48 | 
 49 |   // generate Tree
 50 |   tree.Sprout()
 51 | 
 52 |   // print Tree
 53 |   tree.Print()
 54 | 
 55 |   // Root
 56 |   //    | GINI impurity :  0.48238903404499056
 57 |   //    | Class distribution : {0: 424, 1: 290}
 58 |   //    | Predicted class :  0
 59 |   // --- Split rule :  Fare <= 52.277100000000004
 60 |   //       | GINI impurity :  0.4448243103771814
 61 |   //       | Class distribution : {0: 389, 1: 195}
 62 |   //       | Predicted class :  0
 63 |   // ---------- Split rule :  Fare <= 10.48125
 64 |   //              | GINI impurity :  0.31596085502704785
 65 |   //              | Class distribution : {0: 192, 1: 47}
 66 |   //              | Predicted class :  0
 67 |   // ---------- Split rule :  Fare > 10.48125
 68 |   //              | GINI impurity :  0.48991388363789123
 69 |   //              | Class distribution : {0: 197, 1: 148}
 70 |   //              | Predicted class :  0
 71 |   // --- Split rule :  Fare > 52.277100000000004
 72 |   //       | GINI impurity :  0.39349112426035515
 73 |   //       | Class distribution : {0: 35, 1: 95}
 74 |   //       | Predicted class :  1
 75 |   // ---------- Split rule :  Age <= 63.5
 76 |   //              | GINI impurity :  0.37696075392150785
 77 |   //              | Class distribution : {0: 32, 1: 95}
 78 |   //              | Predicted class :  1
 79 |   // ---------- Split rule :  Age > 63.5
 80 |   //              | GINI impurity :  0
 81 |   //              | Class distribution : {0: 3, 1: 0}
 82 |   //              | Predicted class :  0
 83 | 
 84 | 
 85 |   // prepare a dataframe for prediction
 86 |   df := dataframe.New(
 87 |     series.New([]string{"20", "15"}, series.String, "Age"),
 88 |     series.New([]float64{53.025, 14.0}, series.Float, "Fare"),
 89 |   )
 90 | 
 91 |   // predict
 92 |   fmt.Println(tree.Predict(df)) // -> [1, 0]
 93 | 
 94 | }
 95 | ```
 96 | 
 97 | ## Installation
 98 | 
 99 | ```bash
100 | go get github.com/hammamikhairi/Decision-Tree
101 | ```
102 | 
103 | ## LFSA 88
104 | 
105 | This project is a part of [LFSA 88](https://github.com/hammamikhairi/LFSA-88).
106 | 


--------------------------------------------------------------------------------
/Node.go:
--------------------------------------------------------------------------------
  1 | package decisiontree
  2 | 
  3 | import (
  4 | 	"fmt"
  5 | 	"strconv"
  6 | 	"strings"
  7 | 
  8 | 	"github.com/go-gota/gota/dataframe"
  9 | 	"github.com/go-gota/gota/series"
 10 | )
 11 | 
 12 | type Data struct {
 13 | 	rule         string
 14 | 	features     []string
 15 | 	counts       map[string]int
 16 | 	giniImpurity float64
 17 | 	yhat         string
 18 | 	nb           int
 19 | }
 20 | 
 21 | type node struct {
 22 | 	Y           []int
 23 | 	X           dataframe.DataFrame
 24 | 	bestFeature string
 25 | 	bestValue   string
 26 | 	depth       int
 27 | 	maxDepth    int
 28 | 	minDfSplit  int
 29 | 	data        *Data
 30 | 	left        *node
 31 | 	right       *node
 32 | }
 33 | 
 34 | func NodeInit(Y []int, X dataframe.DataFrame, depth, maxDepth, minDfSplit int, rule string) *node {
 35 | 
 36 | 	if len(Y) == 0 {
 37 | 		return nil
 38 | 	}
 39 | 
 40 | 	genCount := count(Y)
 41 | 	var nd *node = &node{
 42 | 		Y:          Y,
 43 | 		X:          X,
 44 | 		depth:      depth,
 45 | 		maxDepth:   maxDepth,
 46 | 		minDfSplit: minDfSplit,
 47 | 		data: &Data{
 48 | 			rule:         rule,
 49 | 			features:     X.Names(),
 50 | 			counts:       genCount,
 51 | 			giniImpurity: giniImputiry(genCount["0"], genCount["1"]),
 52 | 			yhat:         maxCount(genCount),
 53 | 			nb:           len(Y),
 54 | 		},
 55 | 		left:        nil,
 56 | 		right:       nil,
 57 | 		bestFeature: "",
 58 | 		bestValue:   "",
 59 | 	}
 60 | 
 61 | 	return nd
 62 | }
 63 | 
 64 | func (nd *node) split() (string, string) {
 65 | 	df := nd.X.Copy().Mutate(
 66 | 		series.New(nd.Y, series.Int, "Y"),
 67 | 	)
 68 | 
 69 | 	giniBase := nd.data.giniImpurity
 70 | 	maxGain := 0.0
 71 | 	bestFeature := ""
 72 | 	bestValue := ""
 73 | 
 74 | 	for _, feature := range nd.data.features {
 75 | 		sorted := df.Arrange(
 76 | 			dataframe.Sort(feature),
 77 | 		)
 78 | 		xmeans := meth(uniqueGotaSeries(sorted.Col(feature)).Float())
 79 | 
 80 | 		for _, val := range xmeans {
 81 | 			leftCounts := countErr(
 82 | 				sorted.Filter(
 83 | 					dataframe.F{Colname: feature, Comparator: series.Less, Comparando: val},
 84 | 				).Col("Y").Int(),
 85 | 			)
 86 | 			rightCounts := countErr(
 87 | 				sorted.Filter(
 88 | 					dataframe.F{Colname: feature, Comparator: series.GreaterEq, Comparando: val},
 89 | 				).Col("Y").Int(),
 90 | 			)
 91 | 
 92 | 			s0Left, s1Left, s0Right, s1Right := leftCounts["0"], leftCounts["1"], rightCounts["0"], rightCounts["1"]
 93 | 
 94 | 			totalLeft := s0Left + s1Left
 95 | 			totalRight := s0Right + s1Right
 96 | 
 97 | 			weightLeft := float64(totalLeft) / float64(totalLeft+totalRight)
 98 | 			weightRight := float64(totalRight) / float64(totalLeft+totalRight)
 99 | 
100 | 			wGINI := weightLeft*giniImputiry(s0Left, s1Left) + weightRight*giniImputiry(s0Right, s1Right)
101 | 
102 | 			GINIgain := giniBase - wGINI
103 | 
104 | 			if GINIgain >= maxGain {
105 | 				bestFeature = feature
106 | 				bestValue = fmt.Sprint(val)
107 | 
108 | 				maxGain = GINIgain
109 | 			}
110 | 		}
111 | 	}
112 | 
113 | 	return bestFeature, bestValue
114 | }
115 | 
116 | func (nd *node) sprout() {
117 | 
118 | 	if nd.depth < nd.maxDepth && nd.data.nb >= nd.minDfSplit {
119 | 		bestFeature, bestValue := nd.split()
120 | 		nd.bestFeature = bestFeature
121 | 		nd.bestValue = bestValue
122 | 		df := nd.X.Mutate(
123 | 			series.New(nd.Y, series.Int, "Y"),
124 | 		)
125 | 
126 | 		if bestFeature == "" {
127 | 			panic("bestFeature")
128 | 		}
129 | 
130 | 		leftDf, rightDf := df.Filter(
131 | 			dataframe.F{Colname: bestFeature, Comparator: series.LessEq, Comparando: bestValue},
132 | 		).Copy(), df.Filter(
133 | 			dataframe.F{Colname: bestFeature, Comparator: series.Greater, Comparando: bestValue},
134 | 		).Copy()
135 | 		// NodeInit(Y []int, X dataframe.DataFrame, maxDepth, minDfSplit int)
136 | 		leftY, lerr := leftDf.Col("Y").Int()
137 | 		rightY, rerr := rightDf.Col("Y").Int()
138 | 		if lerr != nil || rerr != nil {
139 | 			panic(lerr)
140 | 		}
141 | 		nd.left = NodeInit(
142 | 			leftY,
143 | 			leftDf,
144 | 			nd.depth+1,
145 | 			nd.maxDepth,
146 | 			nd.minDfSplit,
147 | 			fmt.Sprintf("%s <= %s", bestFeature, bestValue),
148 | 		)
149 | 		if nd.left != nil {
150 | 			nd.left.sprout()
151 | 		}
152 | 
153 | 		nd.right = NodeInit(
154 | 			rightY,
155 | 			rightDf,
156 | 			nd.depth+1,
157 | 			nd.maxDepth,
158 | 			nd.minDfSplit,
159 | 			fmt.Sprintf("%s > %s", bestFeature, bestValue),
160 | 		)
161 | 		if nd.right != nil {
162 | 			nd.right.sprout()
163 | 		}
164 | 
165 | 	}
166 | }
167 | 
168 | func (nd *node) print(padding int) {
169 | 	spaces := strings.Repeat("-", padding*nd.depth)
170 | 	fmt.Print(spaces)
171 | 	if nd.data.rule == "ROOT" {
172 | 		fmt.Println("Root")
173 | 	} else {
174 | 		fmt.Println(" Split rule : ", nd.data.rule)
175 | 	}
176 | 	fmt.Print(strings.Repeat(" ", padding*nd.depth))
177 | 	fmt.Println("   | GINI impurity : ", nd.data.giniImpurity)
178 | 	fmt.Print(strings.Repeat(" ", padding*nd.depth))
179 | 	fmt.Printf("   | Class distribution : {0: %d, 1: %d}\n", nd.data.counts["0"], nd.data.counts["1"])
180 | 	fmt.Print(strings.Repeat(" ", padding*nd.depth))
181 | 	fmt.Println("   | Predicted class : ", nd.data.yhat)
182 | 
183 | 	if nd.left != nil {
184 | 		nd.left.print(padding + 2)
185 | 	}
186 | 
187 | 	if nd.right != nil {
188 | 		nd.right.print(padding + 2)
189 | 	}
190 | }
191 | 
192 | func (nd *node) predict(to map[string]float64) string {
193 | 
194 | 	if nd.left == nil && nd.right == nil {
195 | 		return nd.data.yhat
196 | 	}
197 | 
198 | 	parsed, err := strconv.ParseFloat(nd.bestValue, 64)
199 | 	if err != nil {
200 | 		panic(err)
201 | 	}
202 | 
203 | 	if to[nd.bestFeature] <= parsed {
204 | 		return nd.left.predict(to)
205 | 	} else {
206 | 		return nd.right.predict(to)
207 | 	}
208 | 
209 | }
210 | 


--------------------------------------------------------------------------------
/go.sum:
--------------------------------------------------------------------------------
 1 | dmitri.shuralyov.com/gpu/mtl v0.0.0-20190408044501-666a987793e9/go.mod h1:H6x//7gZCb22OMCxBHrMx7a5I7Hp++hsVxbQ4BYO7hU=
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 7 | github.com/fogleman/gg v1.2.1-0.20190220221249-0403632d5b90/go.mod h1:R/bRT+9gY/C5z7JzPU0zXsXHKM4/ayA+zqcVNZzPa1k=
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10 | github.com/go-fonts/latin-modern v0.2.0/go.mod h1:rQVLdDMK+mK1xscDwsqM5J8U2jrRa3T0ecnM9pNujks=
11 | github.com/go-fonts/liberation v0.1.1/go.mod h1:K6qoJYypsmfVjWg8KOVDQhLc8UDgIK2HYqyqAO9z7GY=
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14 | github.com/go-gl/glfw v0.0.0-20180426074136-46a8d530c326/go.mod h1:vR7hzQXu2zJy9AVAgeJqvqgH9Q5CA+iKCZ2gyEVpxRU=
15 | github.com/go-gl/glfw v0.0.0-20190409004039-e6da0acd62b1/go.mod h1:vR7hzQXu2zJy9AVAgeJqvqgH9Q5CA+iKCZ2gyEVpxRU=
16 | github.com/go-gota/gota v0.12.0 h1:T5BDg1hTf5fZ/CO+T/N0E+DDqUhvoKBl+UVckgcAAQg=
17 | github.com/go-gota/gota v0.12.0/go.mod h1:UT+NsWpZC/FhaOyWb9Hui0jXg0Iq8e/YugZHTbyW/34=
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19 | github.com/golang/freetype v0.0.0-20170609003504-e2365dfdc4a0/go.mod h1:E/TSTwGwJL78qG/PmXZO1EjYhfJinVAhrmmHX6Z8B9k=
20 | github.com/jung-kurt/gofpdf v1.0.0/go.mod h1:7Id9E/uU8ce6rXgefFLlgrJj/GYY22cpxn+r32jIOes=
21 | github.com/jung-kurt/gofpdf v1.0.3-0.20190309125859-24315acbbda5/go.mod h1:7Id9E/uU8ce6rXgefFLlgrJj/GYY22cpxn+r32jIOes=
22 | github.com/llgcode/draw2d v0.0.0-20180817132918-587a55234ca2/go.mod h1:mVa0dA29Db2S4LVqDYLlsePDzRJLDfdhVZiI15uY0FA=
23 | github.com/llgcode/ps v0.0.0-20150911083025-f1443b32eedb/go.mod h1:1l8ky+Ew27CMX29uG+a2hNOKpeNYEQjjtiALiBlFQbY=
24 | github.com/mauricelam/genny v0.0.0-20190320071652-0800202903e5 h1:PnFl95tWh3j7c5DebZG/TGsBJvbnHvPjK4lzltouI4Y=
25 | github.com/mauricelam/genny v0.0.0-20190320071652-0800202903e5/go.mod h1:i2AazGGunAlAR5u0zXGYVmIT7nnwE6j9lwKSMx7N6ko=
26 | github.com/phpdave11/gofpdf v1.4.2/go.mod h1:zpO6xFn9yxo3YLyMvW8HcKWVdbNqgIfOOp2dXMnm1mY=
27 | github.com/phpdave11/gofpdi v1.0.12/go.mod h1:vBmVV0Do6hSBHC8uKUQ71JGW+ZGQq74llk/7bXwjDoI=
28 | github.com/pkg/errors v0.8.1/go.mod h1:bwawxfHBFNV+L2hUp1rHADufV3IMtnDRdf1r5NINEl0=
29 | github.com/pkg/errors v0.9.1/go.mod h1:bwawxfHBFNV+L2hUp1rHADufV3IMtnDRdf1r5NINEl0=
30 | github.com/pmezard/go-difflib v1.0.0/go.mod h1:iKH77koFhYxTK1pcRnkKkqfTogsbg7gZNVY4sRDYZ/4=
31 | github.com/ruudk/golang-pdf417 v0.0.0-20181029194003-1af4ab5afa58/go.mod h1:6lfFZQK844Gfx8o5WFuvpxWRwnSoipWe/p622j1v06w=
32 | github.com/stretchr/objx v0.1.0/go.mod h1:HFkY916IF+rwdDfMAkV7OtwuqBVzrE8GR6GFx+wExME=
33 | github.com/stretchr/testify v1.2.2/go.mod h1:a8OnRcib4nhh0OaRAV+Yts87kKdq0PP7pXfy6kDkUVs=
34 | github.com/stretchr/testify v1.3.0/go.mod h1:M5WIy9Dh21IEIfnGCwXGc5bZfKNJtfHm1UVUgZn+9EI=
35 | github.com/tobgu/qframe v0.3.6 h1:WAoXQA10dyKDMk8ioCz4tHOba8pDGBgfngeI7pKNWok=
36 | github.com/tobgu/qframe v0.3.6/go.mod h1:2Xb/8FU39symTNTNAwsfdf6NGBExauEc4CxgGOmoUMk=
37 | golang.org/x/crypto v0.0.0-20190308221718-c2843e01d9a2/go.mod h1:djNgcEr1/C05ACkg1iLfiJU5Ep61QUkGW8qpdssI0+w=
38 | golang.org/x/crypto v0.0.0-20190510104115-cbcb75029529/go.mod h1:yigFU9vqHzYiE8UmvKecakEJjdnWj3jj499lnFckfCI=
39 | golang.org/x/exp v0.0.0-20180321215751-8460e604b9de/go.mod h1:CJ0aWSM057203Lf6IL+f9T1iT9GByDxfZKAQTCR3kQA=
40 | golang.org/x/exp v0.0.0-20180807140117-3d87b88a115f/go.mod h1:CJ0aWSM057203Lf6IL+f9T1iT9GByDxfZKAQTCR3kQA=
41 | golang.org/x/exp v0.0.0-20190125153040-c74c464bbbf2/go.mod h1:CJ0aWSM057203Lf6IL+f9T1iT9GByDxfZKAQTCR3kQA=
42 | golang.org/x/exp v0.0.0-20190306152737-a1d7652674e8/go.mod h1:CJ0aWSM057203Lf6IL+f9T1iT9GByDxfZKAQTCR3kQA=
43 | golang.org/x/exp v0.0.0-20191002040644-a1355ae1e2c3/go.mod h1:NOZ3BPKG0ec/BKJQgnvsSFpcKLM5xXVWnvZS97DWHgE=
44 | golang.org/x/image v0.0.0-20180708004352-c73c2afc3b81/go.mod h1:ux5Hcp/YLpHSI86hEcLt0YII63i6oz57MZXIpbrjZUs=
45 | golang.org/x/image v0.0.0-20190227222117-0694c2d4d067/go.mod h1:kZ7UVZpmo3dzQBMxlp+ypCbDeSB+sBbTgSJuh5dn5js=
46 | golang.org/x/image v0.0.0-20190802002840-cff245a6509b/go.mod h1:FeLwcggjj3mMvU+oOTbSwawSJRM1uh48EjtB4UJZlP0=
47 | golang.org/x/image v0.0.0-20190910094157-69e4b8554b2a/go.mod h1:FeLwcggjj3mMvU+oOTbSwawSJRM1uh48EjtB4UJZlP0=
48 | golang.org/x/image v0.0.0-20200119044424-58c23975cae1/go.mod h1:FeLwcggjj3mMvU+oOTbSwawSJRM1uh48EjtB4UJZlP0=
49 | golang.org/x/image v0.0.0-20200430140353-33d19683fad8/go.mod h1:FeLwcggjj3mMvU+oOTbSwawSJRM1uh48EjtB4UJZlP0=
50 | golang.org/x/image v0.0.0-20200618115811-c13761719519/go.mod h1:FeLwcggjj3mMvU+oOTbSwawSJRM1uh48EjtB4UJZlP0=
51 | golang.org/x/image v0.0.0-20201208152932-35266b937fa6/go.mod h1:FeLwcggjj3mMvU+oOTbSwawSJRM1uh48EjtB4UJZlP0=
52 | golang.org/x/image v0.0.0-20210216034530-4410531fe030/go.mod h1:FeLwcggjj3mMvU+oOTbSwawSJRM1uh48EjtB4UJZlP0=
53 | golang.org/x/mobile v0.0.0-20190719004257-d2bd2a29d028/go.mod h1:E/iHnbuqvinMTCcRqshq8CkpyQDoeVncDDYHnLhea+o=
54 | golang.org/x/mod v0.1.0/go.mod h1:0QHyrYULN0/3qlju5TqG8bIK38QM8yzMo5ekMj3DlcY=
55 | golang.org/x/net v0.0.0-20190311183353-d8887717615a/go.mod h1:t9HGtf8HONx5eT2rtn7q6eTqICYqUVnKs3thJo3Qplg=
56 | golang.org/x/net v0.0.0-20190404232315-eb5bcb51f2a3/go.mod h1:t9HGtf8HONx5eT2rtn7q6eTqICYqUVnKs3thJo3Qplg=
57 | golang.org/x/net v0.0.0-20190620200207-3b0461eec859/go.mod h1:z5CRVTTTmAJ677TzLLGU+0bjPO0LkuOLi4/5GtJWs/s=
58 | golang.org/x/net v0.0.0-20210423184538-5f58ad60dda6 h1:0PC75Fz/kyMGhL0e1QnypqK2kQMqKt9csD1GnMJR+Zk=
59 | golang.org/x/net v0.0.0-20210423184538-5f58ad60dda6/go.mod h1:OJAsFXCWl8Ukc7SiCT/9KSuxbyM7479/AVlXFRxuMCk=
60 | golang.org/x/sync v0.0.0-20190423024810-112230192c58/go.mod h1:RxMgew5VJxzue5/jJTE5uejpjVlOe/izrB70Jof72aM=
61 | golang.org/x/sys v0.0.0-20190215142949-d0b11bdaac8a/go.mod h1:STP8DvDyc/dI5b8T5hshtkjS+E42TnysNCUPdjciGhY=
62 | golang.org/x/sys v0.0.0-20190312061237-fead79001313/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs=
63 | golang.org/x/sys v0.0.0-20190412213103-97732733099d/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs=
64 | golang.org/x/sys v0.0.0-20201119102817-f84b799fce68/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs=
65 | golang.org/x/sys v0.0.0-20210304124612-50617c2ba197/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs=
66 | golang.org/x/sys v0.0.0-20210423082822-04245dca01da/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs=
67 | golang.org/x/term v0.0.0-20201126162022-7de9c90e9dd1/go.mod h1:bj7SfCRtBDWHUb9snDiAeCFNEtKQo2Wmx5Cou7ajbmo=
68 | golang.org/x/text v0.3.0/go.mod h1:NqM8EUOU14njkJ3fqMW+pc6Ldnwhi/IjpwHt7yyuwOQ=
69 | golang.org/x/text v0.3.5/go.mod h1:5Zoc/QRtKVWzQhOtBMvqHzDpF6irO9z98xDceosuGiQ=
70 | golang.org/x/text v0.3.6/go.mod h1:5Zoc/QRtKVWzQhOtBMvqHzDpF6irO9z98xDceosuGiQ=
71 | golang.org/x/tools v0.0.0-20180525024113-a5b4c53f6e8b/go.mod h1:n7NCudcB/nEzxVGmLbDWY5pfWTLqBcC2KZ6jyYvM4mQ=
72 | golang.org/x/tools v0.0.0-20180917221912-90fa682c2a6e/go.mod h1:n7NCudcB/nEzxVGmLbDWY5pfWTLqBcC2KZ6jyYvM4mQ=
73 | golang.org/x/tools v0.0.0-20190206041539-40960b6deb8e/go.mod h1:n7NCudcB/nEzxVGmLbDWY5pfWTLqBcC2KZ6jyYvM4mQ=
74 | golang.org/x/tools v0.0.0-20190319232107-3f1ed9edd1b4/go.mod h1:LCzVGOaR6xXOjkQ3onu1FJEFr0SW1gC7cKk1uF8kGRs=
75 | golang.org/x/tools v0.0.0-20190927191325-030b2cf1153e/go.mod h1:b+2E5dAYhXwXZwtnZ6UAqBI28+e2cm9otk0dWdXHAEo=
76 | golang.org/x/xerrors v0.0.0-20190717185122-a985d3407aa7/go.mod h1:I/5z698sn9Ka8TeJc9MKroUUfqBBauWjQqLJ2OPfmY0=
77 | gonum.org/v1/gonum v0.0.0-20180816165407-929014505bf4/go.mod h1:Y+Yx5eoAFn32cQvJDxZx5Dpnq+c3wtXuadVZAcxbbBo=
78 | gonum.org/v1/gonum v0.8.2/go.mod h1:oe/vMfY3deqTw+1EZJhuvEW2iwGF1bW9wwu7XCu0+v0=
79 | gonum.org/v1/gonum v0.9.1 h1:HCWmqqNoELL0RAQeKBXWtkp04mGk8koafcB4He6+uhc=
80 | gonum.org/v1/gonum v0.9.1/go.mod h1:TZumC3NeyVQskjXqmyWt4S3bINhy7B4eYwW69EbyX+0=
81 | gonum.org/v1/netlib v0.0.0-20180816165226-ebcc3d2662d3/go.mod h1:wa6Ws7BG/ESfp6dHfk7C6KdzKA7wR7u/rKwOGE66zvw=
82 | gonum.org/v1/netlib v0.0.0-20190313105609-8cb42192e0e0/go.mod h1:wa6Ws7BG/ESfp6dHfk7C6KdzKA7wR7u/rKwOGE66zvw=
83 | gonum.org/v1/plot v0.0.0-20180905080458-5f3c436ce602/go.mod h1:VIQWjXleEHakKVLjfhAAXUy3mq0NuXvobpOBf0ZBZro=
84 | gonum.org/v1/plot v0.0.0-20190515093506-e2840ee46a6b/go.mod h1:Wt8AAjI+ypCyYX3nZBvf6cAIx93T+c/OS2HFAYskSZc=
85 | gonum.org/v1/plot v0.9.0/go.mod h1:3Pcqqmp6RHvJI72kgb8fThyUnav364FOsdDo2aGW5lY=
86 | rsc.io/pdf v0.1.1/go.mod h1:n8OzWcQ6Sp37PL01nO98y4iUCRdTGarVfzxY20ICaU4=
87 | 


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