90 lines
2.5 KiB
Go
90 lines
2.5 KiB
Go
// FittingTriPoly
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/*
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------------------------------------------------------
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作者 : Black Ghost
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日期 : 2018-12-23
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版本 : 0.0.0
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------------------------------------------------------
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基于傅立叶（Fourier）级数的三角多项式拟合
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理论：
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若f(x)周期为2pi，则存在M（2M<N）阶傅立叶（Fourier）级数
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使得N+1个数据对（xi等距分布）的拟合表示为：
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a0 M
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TM(x) = --- + Sum (aj*cos(jx)+bj*sin(jx))
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2 j=1
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其中
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2 N
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aj = ---Sum yk*cos(j*xk), j=0,1,2,...,M
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N k=1
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2 N
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bj = ---Sum yk*sin(j*xk), j=1,2,...,M
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N k=1
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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 5.4.1
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------------------------------------------------------
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输入 :
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XY 数据对，nx2，x-y
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M 傅立叶级数，< N/2
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输出 :
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sol 解，(M+1)x2
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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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// FittingTriPoly 基于傅立叶（Fourier）级数的三角多项式拟合
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func FittingTriPoly(XY Matrix, M int) (Matrix, bool) {
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/*
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基于傅立叶（Fourier）级数的三角多项式拟合
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输入 :
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XY 数据对，nx2，x-y
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M 傅立叶级数，< N/2
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输出 :
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sol 解，(M+1)x2
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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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//判断维数
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if XY.Columns < 2 {
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panic("Error in goNum.FittingTriPoly: At least 2 columns of XY needed")
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}
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N := XY.Rows
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//判断M
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if float64(M) >= float64(N)/2.0 {
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panic("Error in goNum.FittingTriPoly: M is wrong")
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}
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sol := ZeroMatrix(M+1, 2) //b0=0.0
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var err bool = false
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//a0
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var a0 float64
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for k := 1; k < N; k++ {
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// a0 += XY.GetFromMatrix(k, 1) * math.Cos(0.0*XY.GetFromMatrix(k, 0))
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a0 += XY.GetFromMatrix(k, 1)
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}
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sol.SetMatrix(0, 0, 2.0*a0/float64(N))
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//aj, bj
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for j := 1; j < M+1; j++ {
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var aj, bj float64
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for k := 1; k < N; k++ {
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aj += XY.GetFromMatrix(k, 1) * math.Cos(float64(j)*XY.GetFromMatrix(k, 0))
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bj += XY.GetFromMatrix(k, 1) * math.Sin(float64(j)*XY.GetFromMatrix(k, 0))
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}
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sol.SetMatrix(j, 0, 2.0*aj/float64(N))
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sol.SetMatrix(j, 1, 2.0*bj/float64(N))
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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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