98 lines
2.5 KiB
Go
98 lines
2.5 KiB
Go
// NLEs_SeidelIterate
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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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多元非线性方程组Seidel迭代
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理论：
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Pk = x0
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Fk = [f1, f2,..., fn]'
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|df1/dx1 df1/dx2 ... df1/dxn|
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|df2/dx1 df2/dx2 ... df2/dxn|
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Jk = |... ... ... ... |
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|dfn/dx1 dfn/dx2 ... dfn/dxn|
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Jk*dPk = -Fk
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P_(k+1) = Pk+dPk
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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 3.7
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------------------------------------------------------
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输入 :
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funs 方程组，nx1
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J Joccobi矩阵，nxn
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x0 初值x
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tol 控制误差
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n 最大迭代次数
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输出 :
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sol 解，nx1
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err 解出标志：false-未解出或达到边界；
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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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// NLEs_SeidelIterate 多元非线性方程组Seidel迭代
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func NLEs_SeidelIterate(funs, J func(Matrix) Matrix, x0 Matrix,
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tol float64, n int) (Matrix, bool) {
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/*
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多元非线性方程组Seidel迭代
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输入 :
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funs 方程组，nx1
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J Joccobi矩阵，nxn
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x0 初值x
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tol 控制误差
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n 最大迭代次数
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输出 :
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sol 解，nx1
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err 解出标志：false-未解出或达到边界；
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true-全部解出
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*/
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//判断x维数
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if x0.Columns != 1 {
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panic("Error in goNum.NLEs_SeidelIterate: x0 is not a vector")
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}
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sol := ZeroMatrix(x0.Rows, 1) //解向量
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xold := ZeroMatrix(x0.Rows, 1) //Pk
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var err bool = false
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//将x0赋予xold
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for i := 0; i < x0.Rows; i++ {
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xold.Data[i] = x0.Data[i]
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sol.Data[i] = x0.Data[i]
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}
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//循环迭代
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y := NumProductMatrix(funs(xold), -1.0)
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for i := 0; i < n; i++ {
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ja := J(xold)
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dx, dxerr := LEs_ECPE(Matrix2ToSlices(ja), y.Data)
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if dxerr != true {
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panic("Error in goNum.NLEs_SeidelIterate: Solve error")
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}
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//求解新值
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for i := 0; i < x0.Rows; i++ {
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sol.Data[i] = xold.Data[i] + dx[i]
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xold.Data[i] = sol.Data[i]
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}
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y = NumProductMatrix(funs(xold), -1.0)
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//判断误差
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maxy, _, _ := MaxAbs(y.Data)
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if math.Abs(maxy) < tol {
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err = true
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return sol, err
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}
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}
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return sol, err
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}
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