116 lines
2.9 KiB
Go
116 lines
2.9 KiB
Go
// Muller
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/*
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------------------------------------------------------
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作者 : Black Ghost
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日期 : 2018-12-20
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版本 : 0.0.0
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------------------------------------------------------
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Muller法求解非线性方程f(x)=0的解
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理论：
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参考 John H. Mathews and Kurtis D. Fink. Numerical
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methods using MATLAB, 4th ed. Pearson
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Education, 2004. ss 2.5.2.
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------------------------------------------------------
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输入 :
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fun 求解函数
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x0 初值自变量，三个不同点，3x1
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tol 控制误差
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n 最大迭代步数
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输出 :
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sol 解
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err 解出标志：false-未解出或达到步数上限；
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true-全部解出
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------------------------------------------------------
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*/
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package goNum
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import (
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"math"
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)
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// Muller Muller法求解非线性方程f(x)=0的解
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func Muller(fun func(float64) float64, x0 Matrix, tol float64, n int) (float64, bool) {
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/*
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Muller法求解非线性方程f(x)=0的解
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输入 :
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fun 求解函数
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x0 初值自变量，三个不同点，3x1
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tol 控制误差
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n 最大迭代步数
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输出 :
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sol 解
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err 解出标志：false-未解出或达到步数上限；
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true-全部解出
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*/
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//判断tol
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if tol <= 0.0 {
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panic("Error in goNum.Muller: tol less than or euqals to zero")
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}
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var sol float64
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var err bool = false
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//x0赋给p0并计算对应的y0
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p0 := ZeroMatrix(x0.Rows, x0.Columns+1)
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x0sort, _ := MinMaxSort(x0.Data)
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for i := 0; i < x0.Rows; i++ {
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p0.SetMatrix(i, 0, x0sort[i])
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p0.SetMatrix(i, 1, fun(x0sort[i]))
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}
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//迭代计算
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for i := 0; i < n; i++ {
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//准备系数
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h0 := p0.GetFromMatrix(0, 0) - p0.GetFromMatrix(2, 0)
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h1 := p0.GetFromMatrix(1, 0) - p0.GetFromMatrix(2, 0)
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c := p0.GetFromMatrix(2, 1)
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e0 := p0.GetFromMatrix(0, 1) - c
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e1 := p0.GetFromMatrix(1, 1) - c
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b := h1*h0*h0 - h0*h1*h1
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a := (e0*h1 - e1*h0) / b
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b = (e1*h0*h0 - e0*h1*h1) / b
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//求根
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z2 := b*b - 4.0*a*c
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if z2 < 0 {
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//panic("Error in goNum.Muller: There is complex values exist")
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z2 = 0
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}
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var z float64
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if b < 0 {
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z = -2.0 * c / (b - math.Sqrt(z2))
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}
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z = -2.0 * c / (b + math.Sqrt(z2))
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z = p0.GetFromMatrix(2, 0) + z
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//判断解
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if math.Abs(fun(z)) < tol {
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err = true
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sol = z
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return sol, err
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}
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//删除离z最远的点
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dis := []float64{
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z - p0.GetFromMatrix(0, 0),
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z - p0.GetFromMatrix(1, 0),
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z - p0.GetFromMatrix(2, 0)}
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_, deli, _ := MaxAbs(dis)
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for j := 0; j < 3; j++ {
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if deli == j {
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p0.SetMatrix(j, 0, z)
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}
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}
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x0sort, _ = MinMaxSort(p0.ColumnOfMatrix(0))
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for j := 0; j < 3; j++ {
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p0.SetMatrix(j, 0, x0sort[j])
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p0.SetMatrix(j, 1, fun(x0sort[j]))
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}
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}
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err = false
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return sol, err
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}
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