fixed dependencies

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

@@ -0,0 +1,130 @@
+// IntegralGaussLagendre
+/*
+------------------------------------------------------
+作者   : Black Ghost
+日期   : 2018-12-12
+版本   : 0.0.0
+------------------------------------------------------
+    不超过8次的Gauss-Lagendre求积分公式
+理论：
+    对于积分
+    b
+    |f(x)dx
+    a
+
+    使用n+1次Lagendre多项式的零点作为高斯点，可获得代数
+    精度为2n+1的高斯型求积公式
+    其中区间[a, b]需要预先转换为区间[-1, 1]
+
+    参考 李信真, 车刚明, 欧阳洁, 等. 计算方法. 西北工业大学
+       出版社, 2000, pp 162-164.
+------------------------------------------------------
+输入   :
+    fun     被积分函数
+    a, b    积分区间
+    n       求积分公式次数
+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
+
+// IntegralGaussLagendre 不超过8次的Gauss-Lagendre求积分公式
+func IntegralGaussLagendre(fun func(float64) float64, a, b float64, n int) (float64, bool) {
+	/*
+		不超过8次的Gauss-Lagendre求积分公式
+		输入   :
+		    fun     被积分函数
+		    a, b    积分区间
+		    n       求积分公式次数
+		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n范围
+	if (n < 1) || (n > 8) {
+		panic("Error in goNum.IntegralGaussLagendre: n is a not correct input")
+	}
+
+	xi := [][]float64{
+		{0.0},
+		{-0.5773502692, 0.5773502692},
+		{-0.7745966692, 0.0, 0.7745966692},
+		{-0.8611363116, -0.3399810436, 0.3399810436, 0.8611363116},
+		{-0.9061798459, -0.5384693101, 0.0, 0.5384693101, 0.9061798459},
+		{-0.9324695142, -0.6612093865, -0.2386191861, 0.2386191861, 0.6612093865, 0.9324695142},
+		{-0.9491079123, -0.7415311856, -0.4058451514, 0.0, 0.4058451514, 0.7415311856, 0.9491079123},
+		{-0.9602898566, -0.7966664774, -0.5255324099, -0.1834346425, 0.1834346425, 0.5255324099, 0.7966664774, 0.9602898566},
+	}
+	Ai := [][]float64{
+		{2.0},
+		{1.0, 1.0},
+		{0.555555555555556, 0.888888888888889, 0.555555555555556},
+		{0.3478548451, 0.6521451549, 0.6521451549, 0.3478548451},
+		{0.2369268851, 0.4786286705, 0.568888889, 0.4786286705, 0.2369268851},
+		{0.1713244924, 0.3607615730, 0.4679139346, 0.4679139346, 0.3607615730, 0.1713244924},
+		{0.1294849662, 0.2797053915, 0.3818300505, 0.4179591837, 0.3818300505, 0.2797053915, 0.1294849662},
+		{0.1012285363, 0.2223810345, 0.3137066459, 0.3626837834, 0.3626837834, 0.3137066459, 0.2223810345, 0.1012285363},
+	}
+
+	//区间转换
+	c := (b - a) / 2.0
+	d := (a + b) / 2.0
+
+	switch n {
+	case 1:
+		sol := 0.0
+		for i := 0; i < len(xi[0]); i++ {
+			sol += Ai[0][i] * fun(d+c*xi[0][i])
+		}
+		return c * sol, true
+	case 2:
+		sol := 0.0
+		for i := 0; i < len(xi[1]); i++ {
+			sol += Ai[1][i] * fun(d+c*xi[1][i])
+		}
+		return c * sol, true
+	case 3:
+		sol := 0.0
+		for i := 0; i < len(xi[2]); i++ {
+			sol += Ai[2][i] * fun(d+c*xi[2][i])
+		}
+		return c * sol, true
+	case 4:
+		sol := 0.0
+		for i := 0; i < len(xi[3]); i++ {
+			sol += Ai[3][i] * fun(d+c*xi[3][i])
+		}
+		return c * sol, true
+	case 5:
+		sol := 0.0
+		for i := 0; i < len(xi[4]); i++ {
+			sol += Ai[4][i] * fun(d+c*xi[4][i])
+		}
+		return c * sol, true
+	case 6:
+		sol := 0.0
+		for i := 0; i < len(xi[5]); i++ {
+			sol += Ai[5][i] * fun(d+c*xi[5][i])
+		}
+		return c * sol, true
+	case 7:
+		sol := 0.0
+		for i := 0; i < len(xi[6]); i++ {
+			sol += Ai[6][i] * fun(d+c*xi[6][i])
+		}
+		return c * sol, true
+	case 8:
+		sol := 0.0
+		for i := 0; i < len(xi[7]); i++ {
+			sol += Ai[7][i] * fun(d+c*xi[7][i])
+		}
+		return c * sol, true
+	default:
+		return 0.0, false
+	}
+}