83 lines
2.2 KiB
Go
83 lines
2.2 KiB
Go
// FittingLSQ
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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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线性最小二乘拟合
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理论：
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设对N个数据对的线性拟合表示为
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y = Ax + B
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N N N
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A*Sum xi^2 + B*Sum xi = Sum xiyi
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i=1 i=1 i=1
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N N
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A*Sum xi + NB = Sum yi
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i=1 i=1
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解此二元线性方程组即可得A、B
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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 5.1
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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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输出 :
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sol 解，2x1
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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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// FittingLSQ 线性最小二乘拟合
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func FittingLSQ(XY Matrix) (Matrix, bool) {
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/*
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线性最小二乘拟合
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输入 :
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XY 数据对，nx2，x-y
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输出 :
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sol 解，2x1
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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XY的维数
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if XY.Columns < 2 {
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panic("Error in goNum.FittingLSQ: At least 2 columns of XY needed")
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}
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sol := ZeroMatrix(2, 1)
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AS := ZeroMatrix(2, 2)
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BS := ZeroMatrix(2, 1)
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var err bool = false
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var sx2, sx, sxy, sy float64
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n := XY.Rows
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//求累加和
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for i := 0; i < n; i++ {
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sx2 += XY.GetFromMatrix(i, 0) * XY.GetFromMatrix(i, 0)
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sx += XY.GetFromMatrix(i, 0)
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sxy += XY.GetFromMatrix(i, 0) * XY.GetFromMatrix(i, 1)
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sy += XY.GetFromMatrix(i, 1)
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}
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AS.SetMatrix(0, 0, sx2)
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AS.SetMatrix(0, 1, sx)
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AS.SetMatrix(1, 0, sx)
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AS.SetMatrix(1, 1, float64(n))
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BS.SetMatrix(0, 0, sxy)
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BS.SetMatrix(1, 0, sy)
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//解二元线性方程组
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soltemp, errtemp := LEs_ECPE(Matrix2ToSlices(AS), Matrix1ToSlices(BS))
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if errtemp != true {
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panic("Error in goNum.FittingLSQ: Solve error")
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}
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sol.SetMatrix(0, 0, soltemp[1])
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sol.SetMatrix(1, 0, soltemp[0])
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err = true
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return sol, err
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}
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