Homework

main.go

@@ -1,32 +1,107 @@
 package main
 
 import (
+	"fmt"
 	"image"
 	"log"
-	"time"
+	"math/rand"
 
 	"github.com/hajimehoshi/ebiten/v2"
+	"gonum.org/v1/plot/plotter"
 )
 
-func f(x float64) float64  { return x*x + 5*x - 3 }
-func df(x float64) float64 { return 2*x + 5 }
+const (
+	screenWidth, screenHeight                     = 640, 480
+	randMin, randMax                              = -10, 10
+	epochs, lr                                    = 1000000, 0.0001
+	plotMinX, plotMaxX, plotMinY, plotMaxY        = -10, 10, -50, 100
+	inputPointsMinY, inputPointsMaxY, inputPoints = -20, 20, 10
+)
+
+// Function points are spawed along
+func f(x float64) float64 {
+	return x*x + 5*x - 3
+}
+
+// func df(f func(float64) float64) func(float64) float64 {
+// 	return func(x float64) float64 {
+// 		dx := 1e-10 // dx -> 0
+// 		return (f(x+dx) - f(x)) / dx
+// 	}
+// }
+
+// Inference for 1 argument
+func i(x, w, b float64) float64 { return w*x + b }
+
+// For all the input data
+func inference(x []float64, w, b float64) (out []float64) {
+	for _, v := range x {
+		out = append(out, i(v, w, b))
+	}
+	return
+}
+
+// func loss(y, labels []float64) float64 {
+// 	var errSum float64
+// 	for i := range labels {
+// 		errSum += math.Pow((y[i] - labels[i]), 2)
+// 	}
+// 	return errSum / float64(len(labels)) // n
+// }
+
+func gradient(xs, ys, labels []float64) (w, b float64) {
+	for i := 0; i < len(labels); i++ {
+		dif := ys[i] - labels[i]
+		w += dif * xs[i]
+		b += dif
+	}
+	n := float64(len(labels))
+	w *= 2 / n
+	b *= 2 / n
+	return
+}
+
+func train(inputs, labels []float64) (w, b float64) {
+	randFloat64 := func() float64 {
+		return randMin + rand.Float64()*(randMax-randMin)
+	}
+	w, b = randFloat64(), randFloat64()
+	var dw, db float64
+	for i := 0; i < epochs; i++ {
+		dw, db = gradient(labels, inference(inputs, w, b), inputs)
+		w -= dw * lr
+		b -= db * lr
+		fmt.Println(w, b)
+	}
+	return
+}
+
+func randPoints(f func(float64) float64, inputPointsMinY, inputPointsMaxY float64, inputPoints int) (xs, labels []float64) {
+	for i := 0; i < inputPoints; i++ {
+		x := plotMinX + (plotMaxX-plotMinX)*rand.Float64()
+		inputPointsY := inputPointsMinY + (inputPointsMaxY-inputPointsMinY)*rand.Float64()
+		xs = append(xs, x)
+		labels = append(labels, f(x)+inputPointsY)
+	}
+	return
+}
 
 func main() {
-	ebiten.SetWindowSize(640, 480)
+	ebiten.SetWindowSize(screenWidth, screenHeight)
 	ebiten.SetWindowTitle("Gradient descent")
 
 	img := make(chan *image.RGBA, 1)
-	go func() {
-		p := Plot(-5, 0, 0.1, f)
-		x := 0.0
-		img <- p(x)
-		for i := 0; i < 50; i++ {
-			time.Sleep(30 * time.Millisecond)
-			x -= df(x) * 0.1
-			img <- p(x)
-		}
-	}()
-
+	inputs, labels := randPoints(f, inputPointsMinY, inputPointsMaxY, inputPoints)
+	var points plotter.XYs
+	for i := 0; i < inputPoints; i++ {
+		points = append(points, plotter.XY{X: inputs[i], Y: labels[i]})
+	}
+	pointsScatter, _ := plotter.NewScatter(points)
+	fp := plotter.NewFunction(f)
+	w, b := train(inputs, labels)
+	fmt.Println(w, b)
+	ap := plotter.NewFunction(func(x float64) float64 { return w*x + b })
+	img <- Plot(pointsScatter, fp, ap)
 	if err := ebiten.RunGame(&App{Img: img}); err != nil {
 		log.Fatal(err)
 	}

plot.go

@@ -1,60 +1,23 @@
 package main
 
 import (
-	"fmt"
 	"image"
-	"image/color"
-	"log"
 
 	"gonum.org/v1/plot"
 	"gonum.org/v1/plot/plotter"
-	"gonum.org/v1/plot/vg"
 	"gonum.org/v1/plot/vg/draw"
 	"gonum.org/v1/plot/vg/vgimg"
 )
 
-func Plot(xmin, xmax, xstep float64, f func(float64) float64) func(x float64) *image.RGBA {
-	var pts plotter.XYs
-	for x := xmin; x <= xmax; x += xstep {
-		pts = append(pts, plotter.XY{X: x, Y: f(x)})
-	}
-	fn, err := plotter.NewLine(pts)
-	if err != nil {
-		log.Fatalf("Failed to NewLine: %v", err)
-	}
-	fn.Color = color.RGBA{B: 255, A: 255}
-	return func(x float64) *image.RGBA {
-		pts := plotter.XYs{{X: x, Y: f(x)}}
-		xScatter, err := plotter.NewScatter(pts)
-		if err != nil {
-			log.Fatalf("Failed to NewScatter: %v", err)
-		}
-		xScatter.Color = color.RGBA{R: 255, A: 255}
-
-		labels, err := plotter.NewLabels(plotter.XYLabels{
-			XYs:    pts,
-			Labels: []string{fmt.Sprintf("x = %.2f", x)},
-		})
-		labels.Offset = vg.Point{X: -10, Y: 15}
-		if err != nil {
-			log.Fatalf("Failed to NewLabels: %v", err)
-		}
-
-		p := plot.New()
-		p.Add(
-			plotter.NewGrid(),
-			fn,
-			xScatter,
-			labels,
-		)
-		p.Legend.Add("f(x)", fn)
-		p.Legend.Add("x", xScatter)
-		p.X.Label.Text = "X"
-		p.Y.Label.Text = "Y"
-
-		img := image.NewRGBA(image.Rect(0, 0, 640, 480))
-		c := vgimg.NewWith(vgimg.UseImage(img))
-		p.Draw(draw.New(c))
-		return c.Image().(*image.RGBA)
-	}
+func Plot(ps ...plot.Plotter) *image.RGBA {
+	p := plot.New()
+	p.X.Min, p.X.Max = plotMinX, plotMaxX
+	p.Y.Min, p.Y.Max = plotMinY, plotMaxY
+	p.Add(append([]plot.Plotter{
+		plotter.NewGrid(),
+	}, ps...)...)
+	img := image.NewRGBA(image.Rect(0, 0, screenWidth, screenHeight))
+	c := vgimg.NewWith(vgimg.UseImage(img))
+	p.Draw(draw.New(c))
+	return c.Image().(*image.RGBA)
 }