Exchangerate

common/logistic/logistic.go

@@ -0,0 +1,194 @@
+package logistic
+
+import (
+	"fmt"
+	"math/big"
+
+	"github.com/dominant-strategies/go-quai/common"
+	"github.com/dominant-strategies/go-quai/common/math"
+	"gonum.org/v1/plot"
+	"gonum.org/v1/plot/plotter"
+	"gonum.org/v1/plot/vg"
+)
+
+var (
+	c_learningRate = big.NewFloat(0.001)
+	c_epochLength  = 100000
+)
+
+// LogisticRegression represents a logistic regression model.
+type LogisticRegression struct {
+	beta0 *big.Float // Model bias (intercept)
+	beta1 *big.Float // Model weight (slope)
+}
+
+// NewLogisticRegression initializes a new LogisticRegression model.
+func NewLogisticRegression() *LogisticRegression {
+	return &LogisticRegression{
+		beta0: big.NewFloat(0.1),
+		beta1: big.NewFloat(0.000081),
+	}
+}
+
+// sigmoid computes the sigmoid function.
+func sigmoid(z *big.Float) *big.Float {
+	// Compute exp(-z)
+	negZ := new(big.Float).Neg(z)
+	expNegZ := math.EToTheX(negZ)
+
+	// Compute 1 + exp(-z)
+	denom := new(big.Float).Add(new(big.Float).SetInt(common.Big1), expNegZ)
+
+	// Compute 1 / (1 + exp(-z))
+	result := new(big.Float).Quo(new(big.Float).SetInt(common.Big1), denom)
+
+	return result
+}
+
+// Predict computes the probability that the input belongs to class 1.
+func (lr *LogisticRegression) Predict(x *big.Float) *big.Float {
+	// z = beta0 + beta1 * x
+	beta1x := new(big.Float).Mul(lr.beta1, x)
+	z := new(big.Float).Add(lr.beta0, beta1x)
+
+	// Apply sigmoid function
+	return sigmoid(z)
+}
+
+// PredictLabel predicts the class label (0 or 1) for the input.
+func (lr *LogisticRegression) PredictLabel(x *big.Float) int {
+	prob := lr.Predict(x)
+	cmp := prob.Cmp(big.NewFloat(0.5))
+	if cmp >= 0 {
+		return 1
+	}
+	return 0
+}
+
+// Train trains the logistic regression model using gradient descent.
+func (lr *LogisticRegression) Train(x []*big.Int, y []*big.Int) {
+	nSamples := len(y)
+
+	var xfloat, yfloat []*big.Float
+	for i := 0; i < nSamples; i++ {
+		xfloat = append(xfloat, new(big.Float).SetInt(x[i]))
+		yfloat = append(yfloat, new(big.Float).SetInt(y[i]))
+	}
+
+	for epoch := 0; epoch < c_epochLength; epoch++ {
+		// Initialize gradients
+		dw := new(big.Float).SetInt(common.Big0)
+		db := new(big.Float).SetInt(common.Big0)
+
+		// Compute gradients
+		for i := 0; i < nSamples; i++ {
+			xi := xfloat[i]
+			yi := yfloat[i]
+			pred := lr.Predict(xi)
+			error := new(big.Float).Sub(pred, yi)
+			dwTerm := new(big.Float).Mul(error, xi)
+			dw.Add(dw, dwTerm)
+			db.Add(db, error)
+		}
+
+		nSamplesFloat := new(big.Float).SetInt(big.NewInt(int64(nSamples))) //big.NewFloat(float64(nSamples))
+
+		// Compute gradient averages
+		dw.Quo(dw, nSamplesFloat)
+		db.Quo(db, nSamplesFloat)
+
+		// Update weight: beta1 = beta1 - LearningRate * dw
+		lrUpdateW := new(big.Float).Mul(c_learningRate, dw)
+		lr.beta1.Sub(lr.beta1, lrUpdateW)
+
+		// Update bias: beta0 = beta0 - LearningRate * db
+		lrUpdateB := new(big.Float).Mul(c_learningRate, db)
+		lr.beta0.Sub(lr.beta0, lrUpdateB)
+	}
+}
+
+// Beta0 returns the model's bias (intercept) term.
+func (lr *LogisticRegression) Beta0() *big.Float {
+	return new(big.Float).Set(lr.beta0)
+}
+
+// Beta1 returns the model's weight (slope) term.
+func (lr *LogisticRegression) Beta1() *big.Float {
+	return new(big.Float).Set(lr.beta1)
+}
+
+// BigBeta0 returns the model's bias (intercept) term.
+func (lr *LogisticRegression) BigBeta0() *big.Int {
+	bigBeta := new(big.Float).Mul(lr.beta0, new(big.Float).SetInt(common.Big2e64))
+	bigBetaInt, _ := bigBeta.Int(nil)
+	return bigBetaInt
+}
+
+// BigBeta1 returns the model's weight (slope) term.
+func (lr *LogisticRegression) BigBeta1() *big.Int {
+	bigBeta := new(big.Float).Mul(lr.beta1, new(big.Float).SetInt(common.Big2e64))
+	bigBetaInt, _ := bigBeta.Int(nil)
+	return bigBetaInt
+}
+
+// Plot the given trained logistic regression values with Beta0 and Beta1
+func (lr *LogisticRegression) PlotSigmoid(xValues, yValues []float64) error {
+	// Create a new plot
+	p := plot.New()
+
+	beta0, _ := lr.beta0.Float64()
+	beta1, _ := lr.beta1.Float64()
+
+	p.Title.Text = fmt.Sprintf("Sigmoid Function: Beta0=%.10f, Beta1=%.10f", beta0, beta1)
+	p.X.Label.Text = "x"
+	p.Y.Label.Text = "sigmoid(x)"
+
+	plotValues := make(plotter.XYs, 0)
+	for i := range xValues {
+		value := plotter.XY{xValues[i], yValues[i]}
+		plotValues = append(plotValues, value)
+	}
+
+	// Create a line plotter with x and y values
+	line, err := plotter.NewLine(plotValues)
+	if err != nil {
+		return err
+	}
+
+	// Add the line to the plot
+	p.Add(line)
+
+	// Create the function to be plotted
+	sigmoidFunc := plotter.NewFunction(func(x float64) float64 {
+		result := lr.Predict(big.NewFloat(x))
+		resultF, _ := result.Float64()
+		return resultF
+	})
+
+	// Set the style for the function line
+	sigmoidFunc.Color = plotter.DefaultLineStyle.Color
+	sigmoidFunc.Width = vg.Points(2)
+
+	// Set the range for x-axis values
+	// Find the min and max in the xValues
+	xMin := float64(math.MaxInt64)
+	xMax := float64(0)
+	for _, x := range xValues {
+		if x < xMin {
+			xMin = x
+		} else if x > xMax {
+			xMax = x
+		}
+	}
+	sigmoidFunc.XMin = xMin
+	sigmoidFunc.XMax = xMax
+
+	p.Add(sigmoidFunc)
+
+	// Save the plot as a PNG image
+	if err := p.Save(6*vg.Inch, 4*vg.Inch, "sigmoid.png"); err != nil {
+		return err
+	}
+
+	return nil
+}

common/logistic/logistic_test.go

@@ -0,0 +1,32 @@
+package logistic
+
+import (
+	"fmt"
+	"math/big"
+	"testing"
+)
+
+func TestLogistic(t *testing.T) {
+	r := NewLogisticRegression()
+
+	X := []*big.Float{big.NewFloat(1), big.NewFloat(2), big.NewFloat(3), big.NewFloat(4), big.NewFloat(10), big.NewFloat(11), big.NewFloat(12), big.NewFloat(13)}
+	Y := []*big.Float{big.NewFloat(0), big.NewFloat(0), big.NewFloat(0), big.NewFloat(0), big.NewFloat(1), big.NewFloat(1), big.NewFloat(1), big.NewFloat(1)}
+
+	r.Train(X, Y)
+
+	fmt.Println("Beta0/1 after training", r.Beta0(), r.Beta1())
+
+	xValues := make([]float64, 0)
+	for _, x := range X {
+		xF, _ := x.Float64()
+		xValues = append(xValues, xF)
+	}
+
+	yValues := make([]float64, 0)
+	for _, y := range Y {
+		yF, _ := y.Float64()
+		yValues = append(yValues, yF)
+	}
+
+	r.PlotSigmoid(xValues, yValues)
+}

common/math/big.go

@@ -292,3 +292,70 @@ func TwoToTheX(x *big.Float) *big.Float {
 
 	return result
 }
+
+// EToTheX computes the expression 1 + x + (1/2)*x^2 + (1/6)*x^3 + (1/24)*x^4 + (1/120)*x^5 + (1/720)*x^6 + (1/5040)*x^7
+func EToTheX(x *big.Float) *big.Float {
+	// Set the desired precision
+	prec := uint(16) // You can adjust the precision as needed
+
+	// Initialize constants with the specified precision
+	one := new(big.Float).SetPrec(prec).SetFloat64(1.0)
+	half := new(big.Float).SetPrec(prec).SetFloat64(0.5)
+	oneSixth := new(big.Float).SetPrec(prec).Quo(
+		new(big.Float).SetPrec(prec).SetFloat64(1.0),
+		new(big.Float).SetPrec(prec).SetFloat64(6.0),
+	)
+	oneTwentyFourth := new(big.Float).SetPrec(prec).Quo(
+		new(big.Float).SetPrec(prec).SetFloat64(1.0),
+		new(big.Float).SetPrec(prec).SetFloat64(24.0),
+	)
+	oneOneTwentieth := new(big.Float).SetPrec(prec).Quo(
+		new(big.Float).SetPrec(prec).SetFloat64(1.0),
+		new(big.Float).SetPrec(prec).SetFloat64(120.0),
+	)
+	oneOneSevenTwentieth := new(big.Float).SetPrec(prec).Quo(
+		new(big.Float).SetPrec(prec).SetFloat64(1.0),
+		new(big.Float).SetPrec(prec).SetFloat64(720.0),
+	)
+	oneFiveThousandFourtieth := new(big.Float).SetPrec(prec).Quo(
+		new(big.Float).SetPrec(prec).SetFloat64(1.0),
+		new(big.Float).SetPrec(prec).SetFloat64(5040.0),
+	)
+
+	// Compute x^2
+	x2 := new(big.Float).SetPrec(prec).Mul(x, x)
+
+	// Compute x^3
+	x3 := new(big.Float).SetPrec(prec).Mul(x2, x)
+
+	// Compute x^4
+	x4 := new(big.Float).SetPrec(prec).Mul(x3, x)
+
+	// Compute x^5
+	x5 := new(big.Float).SetPrec(prec).Mul(x4, x)
+
+	// Compute x^6
+	x6 := new(big.Float).SetPrec(prec).Mul(x5, x)
+
+	// Compute x^7
+	x7 := new(big.Float).SetPrec(prec).Mul(x6, x)
+
+	// Compute terms
+	term2 := new(big.Float).SetPrec(prec).Mul(half, x2)                     // 0.5 * x^2
+	term3 := new(big.Float).SetPrec(prec).Mul(oneSixth, x3)                 // (1/6) * x^3
+	term4 := new(big.Float).SetPrec(prec).Mul(oneTwentyFourth, x4)          // (1/24) * x^4
+	term5 := new(big.Float).SetPrec(prec).Mul(oneOneTwentieth, x5)          // (1/120) * x^5
+	term6 := new(big.Float).SetPrec(prec).Mul(oneOneSevenTwentieth, x6)     // (1/720) * x^6
+	term7 := new(big.Float).SetPrec(prec).Mul(oneFiveThousandFourtieth, x7) // (1/5040) * x^7
+
+	// Sum up the terms: result = 1 + x + term2 + term3 + term4
+	result := new(big.Float).SetPrec(prec).Add(one, x) // result = 1 + x
+	result.Add(result, term2)                          // result += term2
+	result.Add(result, term3)                          // result += term3
+	result.Add(result, term4)                          // result += term4
+	result.Add(result, term5)                          // result += term5
+	result.Add(result, term6)                          // result += term6
+	result.Add(result, term7)                          // result += term7
+
+	return result
+}

common/math/big_test.go

@@ -384,3 +384,53 @@ func TestTwoToTheX(t *testing.T) {
 		}
 	}
 }
+
+func TestEtoTheX(t *testing.T) {
+	tests := []struct {
+		x      *big.Float
+		actual *big.Float
+	}{
+		{
+			x:      big.NewFloat(1.625),
+			actual: big.NewFloat(5.0784190371800815),
+		},
+		{
+			x:      big.NewFloat(0.765),
+			actual: big.NewFloat(2.1489943746552203),
+		},
+		{
+			x:      big.NewFloat(1.685),
+			actual: big.NewFloat(5.392450932349507),
+		},
+		{
+			x:      big.NewFloat(2.0),
+			actual: big.NewFloat(7.38905609893065),
+		},
+		{
+			x:      big.NewFloat(-1.25),
+			actual: big.NewFloat(0.2865047968601901),
+		},
+		{
+			x:      big.NewFloat(5.5),
+			actual: big.NewFloat(244.69193226422038),
+		},
+		{
+			x:      big.NewFloat(-0.00000045456),
+			actual: big.NewFloat(0.9999999999),
+		},
+		{
+			x:      big.NewFloat(0.0),
+			actual: big.NewFloat(1.0), // e^0 = 1
+		},
+	}
+
+	for _, test := range tests {
+		result := EToTheX(test.x)
+		lowerBound := new(big.Float).Mul(test.actual, big.NewFloat(0.98))
+		upperBound := new(big.Float).Mul(test.actual, big.NewFloat(1.02))
+
+		if result.Cmp(lowerBound) < 0 || result.Cmp(upperBound) > 0 {
+			t.Errorf("TwoToTheX(%s) = %g, want %g within 3%%", test.x.Text('f', -1), result, test.actual)
+		}
+	}
+}