fixed dependencies

vendor/github.com/nuknal/goNum/Muller.go

@@ -0,0 +1,115 @@
+// Muller
+/*
+------------------------------------------------------
+作者   : Black Ghost
+日期   : 2018-12-20
+版本   : 0.0.0
+------------------------------------------------------
+    Muller法求解非线性方程f(x)=0的解
+理论：
+
+    参考 John H. Mathews and Kurtis D. Fink. Numerical
+         methods using MATLAB, 4th ed. Pearson
+         Education, 2004. ss 2.5.2.
+------------------------------------------------------
+输入   :
+    fun     求解函数
+    x0      初值自变量，三个不同点，3x1
+    tol     控制误差
+    n       最大迭代步数
+输出   :
+    sol     解
+    err     解出标志：false-未解出或达到步数上限；
+                     true-全部解出
+------------------------------------------------------
+*/
+
+package goNum
+
+import (
+	"math"
+)
+
+// Muller Muller法求解非线性方程f(x)=0的解
+func Muller(fun func(float64) float64, x0 Matrix, tol float64, n int) (float64, bool) {
+	/*
+	   Muller法求解非线性方程f(x)=0的解
+	   输入   :
+	       fun     求解函数
+	       x0      初值自变量，三个不同点，3x1
+	       tol     控制误差
+	       n       最大迭代步数
+	   输出   :
+	       sol     解
+	       err     解出标志：false-未解出或达到步数上限；
+	                        true-全部解出
+	*/
+	//判断tol
+	if tol <= 0.0 {
+		panic("Error in goNum.Muller: tol less than or euqals to zero")
+	}
+
+	var sol float64
+	var err bool = false
+
+	//x0赋给p0并计算对应的y0
+	p0 := ZeroMatrix(x0.Rows, x0.Columns+1)
+	x0sort, _ := MinMaxSort(x0.Data)
+	for i := 0; i < x0.Rows; i++ {
+		p0.SetMatrix(i, 0, x0sort[i])
+		p0.SetMatrix(i, 1, fun(x0sort[i]))
+	}
+
+	//迭代计算
+	for i := 0; i < n; i++ {
+		//准备系数
+		h0 := p0.GetFromMatrix(0, 0) - p0.GetFromMatrix(2, 0)
+		h1 := p0.GetFromMatrix(1, 0) - p0.GetFromMatrix(2, 0)
+		c := p0.GetFromMatrix(2, 1)
+		e0 := p0.GetFromMatrix(0, 1) - c
+		e1 := p0.GetFromMatrix(1, 1) - c
+		b := h1*h0*h0 - h0*h1*h1
+		a := (e0*h1 - e1*h0) / b
+		b = (e1*h0*h0 - e0*h1*h1) / b
+		//求根
+		z2 := b*b - 4.0*a*c
+		if z2 < 0 {
+			//panic("Error in goNum.Muller: There is complex values exist")
+			z2 = 0
+		}
+
+		var z float64
+		if b < 0 {
+			z = -2.0 * c / (b - math.Sqrt(z2))
+		}
+		z = -2.0 * c / (b + math.Sqrt(z2))
+		z = p0.GetFromMatrix(2, 0) + z
+
+		//判断解
+		if math.Abs(fun(z)) < tol {
+			err = true
+			sol = z
+			return sol, err
+		}
+
+		//删除离z最远的点
+		dis := []float64{
+			z - p0.GetFromMatrix(0, 0),
+			z - p0.GetFromMatrix(1, 0),
+			z - p0.GetFromMatrix(2, 0)}
+		_, deli, _ := MaxAbs(dis)
+		for j := 0; j < 3; j++ {
+			if deli == j {
+				p0.SetMatrix(j, 0, z)
+			}
+		}
+		x0sort, _ = MinMaxSort(p0.ColumnOfMatrix(0))
+		for j := 0; j < 3; j++ {
+			p0.SetMatrix(j, 0, x0sort[j])
+			p0.SetMatrix(j, 1, fun(x0sort[j]))
+		}
+	}
+
+	err = false
+	return sol, err
+}