homework

d/main.go

@@ -0,0 +1,23 @@
+package main
+
+import (
+	"fmt"
+)
+
+func derivative(f func(float64) float64, x, e float64) float64 {
+	return (f(x+e) - f(x-e)) / (e)
+}
+
+func gradient(f func(x float64) float64, a, x, e float64) float64 {
+	for derivative(f, x, e) > 1e-6 {
+		x -= a * derivative(f, x, e)
+	}
+	return x
+}
+
+func main() {
+	e := 1e-6
+	f := func(x float64) float64 { return x*x*x*x - 4*x*x*x + 2*x*x + 10*x + 12 }
+	min := gradient(f, 0.01, 1, e)
+	fmt.Println(min)
+}

d/main_test.go

@@ -0,0 +1,26 @@
+package main
+
+import (
+	"math"
+	"testing"
+)
+
+func TestSolveSecant(t *testing.T) {
+	for _, tc := range []struct {
+		f         func(float64) float64
+		a, x, eps float64
+		want      float64
+	}{
+		{f: func(x float64) float64 { return math.Pow(x, 3) - 2*x - 5 }, a: 0.01, x: 2, eps: 1e-3, want: 0.816},
+		{f: func(x float64) float64 { return 3*x*x*x*x - 4*x*x*x - 12*x*x - 5 }, a: 0.01, x: 1, eps: 1, want: 2},
+		{f: func(x float64) float64 { return x - 5*math.Sin(x) - 3.5 }, a: 0.09, x: 10, eps: 1e-5, want: 7.65262},
+		{f: func(x float64) float64 { return (1+x)*math.Pow(10, 3*x) - 5 }, a: 0.01, x: 0.01, eps: 1e-3, want: -1.145},
+		{f: func(x float64) float64 { return -(1+x)*math.Pow(10, (-2)*x) + 8 }, a: 0.001, x: 2, eps: 1e-3, want: -0.783},
+	} {
+		got := gradient(tc.f, tc.a, tc.x, tc.eps)
+		if math.Abs(got-tc.want) > tc.eps {
+			t.Errorf("got = %v, want = %v", got, tc.want)
+		}
+
+	}
+}

main.go

@@ -3,26 +3,48 @@ package main
 import (
 	"image"
 	"log"
+	"math"
 	"time"
 
 	"github.com/hajimehoshi/ebiten/v2"
 )
 
-func f(x float64) float64  { return x*x + 5*x - 3 }
-func df(x float64) float64 { return 2*x + 5 }
+func f(x float64) float64 { return -(1+x)*math.Pow(10, (-2)*x) + 8 }
+
+func derivative(f func(float64) float64, x, e float64) float64 {
+	return (f(x+e) - f(x-e)) / (2 * e)
+}
+
+func sign(x float64) float64 {
+	if x > 0 {
+		return 1
+	} else if x < 0 {
+		return -1
+	}
+	return 0
+}
+
+func gradientlength(a float64) float64 {
+	return a / math.Sqrt(a*a)
+}
 
 func main() {
 	ebiten.SetWindowSize(640, 480)
 	ebiten.SetWindowTitle("Gradient descent")
 
 	img := make(chan *image.RGBA, 1)
 	go func() {
+		e := 1e-6
 		p := Plot(-5, 0, 0.1, f)
 		x := 0.0
 		img <- p(x)
-		for i := 0; i < 50; i++ {
+		lr := 1e-3
+		for derivative(f, x, e) > 1e-6 {
 			time.Sleep(30 * time.Millisecond)
-			x -= df(x) * 0.1
+			// x -= lr * sign(derivative(f, x, e))
+			gradient := derivative(f, x, e)
+			normalized := (1 / gradientlength(gradient)) * gradient
+			x -= lr * sign(normalized)
 			img <- p(x)
 		}
 	}()