newton-raphson-method-sqrt.go

package main

import (
	"fmt"
)

func Iteration(x, r float64) float64 {
	//f(x)=x^2-r
	//随机取的x，算出对应的y
	y := x*x - r

	//曲线方程的导函数是曲线上某一点的切线斜率 f'(x)=2x => 切线斜率=2x
	k := 2 * x

	//这一点同时在曲线上，也同时在切线上，两线x和y一样
	//曲线当前点上的切线方程为 y切线=kx切线-b，求b
	//y=kx-b => b=kx-y
	b := k*x - y

	//当y切线为0的时候，求x切线 y=kx-b => x=(y+b)/k =y为0=> x=b/k
	tangentLintX := b / k
	return tangentLintX
}

func Sqrt(x float64) float64 {
	times := 0
	guess := x / 2
	for {
		times++
		guessThisTime := Iteration(guess, x)
		if guess == guessThisTime {
			fmt.Println(times)
			return guessThisTime
		} else {
			guess = guessThisTime
		}
	}
}

func main() {
	fmt.Println(Sqrt(5))
}