fixed dependencies
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nuknal
187
vendor/github.com/nuknal/goNum/RKF45.go
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187
vendor/github.com/nuknal/goNum/RKF45.go
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// RKF45
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/*
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------------------------------------------------------
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作者 : Black Ghost
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日期 : 2018-12-19
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版本 : 0.0.0
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------------------------------------------------------
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四级五阶变步长Runge-Kutta法求解常微分方程组
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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 9.5.4.
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------------------------------------------------------
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输入 :
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fun 第i个方程(计算变量值向量, i)
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x0 初值向量，(fn+1)x1，一个x，fn个因变量
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xend 终止x
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tol 步长控制误差
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fn 方程个数
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n 最大迭代步数
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输出 :
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sol 解向量
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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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// RKF45 四级五阶变步长Runge-Kutta法求解常微分方程组
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func RKF45(fun func(Matrix, int) float64, x0 Matrix,
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xend, tol float64, fn, n int) (Matrix, bool) {
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/*
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四级五阶变步长Runge-Kutta法求解常微分方程组
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输入 :
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fun 第i个方程(计算变量值向量, i)
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x0 初值向量，(fn+1)x1，一个x，fn个因变量
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xend 终止x
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tol 步长控制误差
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fn 方程个数
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n 最大迭代步数
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输出 :
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sol 解向量
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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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//判断方程个数是否对应初值个数
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if x0.Rows != fn+1 {
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panic("Error in goNum.RKF45: Quantities of x0 and fn+1 are not equal")
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}
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//判断tol值
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if tol <= 0.0 {
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panic("Error in goNum.RKF45: tol less than or euqals to zero")
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}
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//判断xend值
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if xend <= x0.Data[0] {
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panic("Error in goNum.RKF45: xend less than or euqals to x0")
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}
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sol0 := ZeroMatrix(fn+1, n+1)
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var err bool = false
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h := 100.0 * (xend - x0.Data[0]) / float64(n) //初始步长，100倍最小步长，可修改
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//把初值赋给sol
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for i := 0; i < fn+1; i++ {
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sol0.SetMatrix(i, 0, x0.Data[i])
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}
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//nreal解矩阵实际长度
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var i, nreal int = 1, 1
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for sol0.GetFromMatrix(0, i-1) < xend { //最大迭代次数控制
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temp0 := ZeroMatrix(fn+1, 1)
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//给temp0赋i-1步值，每一步开始
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for j := 0; j < fn+1; j++ {
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temp0.Data[j] = sol0.GetFromMatrix(j, i-1)
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}
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k1 := ZeroMatrix(fn, 1)
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k2 := ZeroMatrix(fn, 1)
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k3 := ZeroMatrix(fn, 1)
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k4 := ZeroMatrix(fn, 1)
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k5 := ZeroMatrix(fn, 1)
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k6 := ZeroMatrix(fn, 1)
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//1. k1
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for j := 0; j < fn; j++ { //微分方程迭代
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k1.Data[j] = h * fun(temp0, j)
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}
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//2. k2
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temp0.Data[0] = sol0.GetFromMatrix(0, i-1) + h/4.0 //xn+h/4
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for j := 1; j < fn+1; j++ { //yn+k1/4
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temp0.Data[j] = sol0.GetFromMatrix(j, i-1) + k1.Data[j-1]/4.0
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}
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for j := 0; j < fn; j++ { //微分方程迭代
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k2.Data[j] = h * fun(temp0, j)
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}
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//3. k3
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temp0.Data[0] = sol0.GetFromMatrix(0, i-1) + 3.0*h/8.0 //xn+3h/8
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for j := 1; j < fn+1; j++ { //yn+3k1/32+9k2/32
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temp0.Data[j] = sol0.GetFromMatrix(j, i-1) + 3.0*k1.Data[j-1]/32.0 +
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9.0*k2.Data[j-1]/32.0
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}
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for j := 0; j < fn; j++ { //微分方程迭代
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k3.Data[j] = h * fun(temp0, j)
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}
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//4. k4
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temp0.Data[0] = sol0.GetFromMatrix(0, i-1) + 12.0*h/13.0 //xn+12h/13
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for j := 1; j < fn+1; j++ { //yn+1932k1/2197-7200k2/2197+7296k3/2197
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temp0.Data[j] = sol0.GetFromMatrix(j, i-1) + 1932.0*k1.Data[j-1]/2197.0 -
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7200.0*k2.Data[j-1]/2197.0 + 7296.0*k3.Data[j-1]/2197.0
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}
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for j := 0; j < fn; j++ { //微分方程迭代
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k4.Data[j] = h * fun(temp0, j)
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}
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//5. k5
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temp0.Data[0] = sol0.GetFromMatrix(0, i-1) + h //xn+h
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for j := 1; j < fn+1; j++ { //yn+439k1/216-8k2+3680k3/513-845k4/4104
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temp0.Data[j] = sol0.GetFromMatrix(j, i-1) + 439.0*k1.Data[j-1]/216.0 -
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8.0*k2.Data[j-1] + 3680.0*k3.Data[j-1]/513.0 - 845.0*k4.Data[j-1]/4104.0
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}
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for j := 0; j < fn; j++ { //微分方程迭代
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k5.Data[j] = h * fun(temp0, j)
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}
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//6. k6
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temp0.Data[0] = sol0.GetFromMatrix(0, i-1) + h/2.0 //xn+h/2
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for j := 1; j < fn+1; j++ { //yn-8k1/27+2k2-3544k3/2565+1859k4/4104-11k5/40
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temp0.Data[j] = sol0.GetFromMatrix(j, i-1) - 8.0*k1.Data[j-1]/27.0 +
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2.0*k2.Data[j-1] - 3544.0*k3.Data[j-1]/2565.0 + 1859.0*k4.Data[j-1]/4104.0 -
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11.0*k5.Data[j-1]/40.0
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}
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for j := 0; j < fn; j++ { //微分方程迭代
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k6.Data[j] = h * fun(temp0, j)
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}
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//误差与步长
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errtemp := ZeroMatrix(fn, 1) //=ABS(z_(k+1)-y_(k+1))
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for j := 1; j < fn+1; j++ {
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errtemp.Data[j-1] = k1.Data[j-1]/360.0 - 128.0*k3.Data[j-1]/4275.0 -
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2197.0*k4.Data[j-1]/75240.0 + k5.Data[j-1]/50.0 + 2.0*k6.Data[j-1]/55.0
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}
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errtemp0, _, _ := MaxAbs(errtemp.Data)
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//正常推进
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if math.Abs(errtemp0) < tol {
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//i步值
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sol0.SetMatrix(0, i, sol0.GetFromMatrix(0, i-1)+h) //xi
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for j := 1; j < fn+1; j++ {
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soltemp1 := 25.0*k1.Data[j-1]/216.0 + 1408.0*k3.Data[j-1]/2565.0 +
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2197.0*k4.Data[j-1]/4104.0 - k5.Data[j-1]/5.0
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soltemp1 = sol0.GetFromMatrix(j, i-1) + soltemp1
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sol0.SetMatrix(j, i, soltemp1)
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}
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i++
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nreal = i
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continue
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}
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//最大步数强边界
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if i >= n {
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break
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}
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//变步长
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scale := tol * h / (2.0 * math.Abs(errtemp0))
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scale = math.Pow(scale, 0.25)
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if scale < 0.75 {
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h = h / 2.0
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} else if scale > 1.5 {
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h = h * 2.0
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}
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}
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//解矩阵缩减
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sol := ZeroMatrix(fn+1, nreal)
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for j := 0; j < nreal; j++ {
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for k := 0; k < fn+1; k++ {
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sol.SetMatrix(k, j, sol0.GetFromMatrix(k, j))
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}
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}
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err = true
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return sol, err
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}
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