求：分段函数最小二乘拟和软件包

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求：分段函数最小二乘拟和软件包！

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关键词：分段函数 最小二乘 软件包 函数 分段 软件包 最小二乘

R语言里面，用nls()非线性最小二乘，就在自带的stats包里面。下面是一个例子——
m.lrp <- nls(y ~ f.lrp(x, a, b, t.x), data = test, start = list(a = 0, b = 0.1,
    t.x = 50), trace = T, control = list(warnOnly = T, minFactor = 1/2048))
## 32.74 :   0.0  0.1 50.0
## 7.352 :   2.16251  0.04619 59.34899
## 1.25 :   2.16251  0.04619 70.24081
## 1.116 :   2.15689  0.04639 72.09071
## 1.116 :   2.15689  0.04639 72.08250
summary(m.lrp)
##
## Formula: y ~ f.lrp(x, a, b, t.x)
##
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)   
## a    2.15689    0.06562    32.9   <2e-16 ***
## b    0.04639    0.00157    29.6   <2e-16 ***
## t.x 72.08250    1.76996    40.7   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.176 on 36 degrees of freedom
##
## Number of iterations to convergence: 4
## Achieved convergence tolerance: 3.63e-09
画图来看看拟合的可靠性：
plot(test$y ~ test$x, main = "Linear response and plateau yield response", xlab = "Fertilizer added",
    ylab = "Crop yield")
(max.yield <- a.0 + b.0 * t.x.0)
## [1] 5.5
lines(x = c(0, t.x.0, 120), y = c(a.0, max.yield, max.yield), lty = 2, col = "blue")
abline(v = t.x.0, lty = 3, col = "blue")
abline(h = max.yield, lty = 3, col = "blue")
(max.yield <- coefficients(m.lrp)["a"] + coefficients(m.lrp)["b"] * coefficients(m.lrp)["t.x"])
##     a
## 5.501
lines(x = c(0, coefficients(m.lrp)["t.x"], 120), y = c(coefficients(m.lrp)["a"],
    max.yield, max.yield), lty = 1)
abline(v = coefficients(m.lrp)["t.x"], lty = 4)
abline(h = max.yield, lty = 4)
text(120, 4, "known true model", col = "blue", pos = 2)
text(120, 3.5, "fitted model", col = "black", pos = 2)
Python的话，可以用scipy扩展库的leastsq函数。下面是一个例子——
import numpy as np
from scipy.optimize import leastsq
def residuals(p, x, y):
    temp = np.array([0,0,0,0,0,0],dtype=float)
    for i in range(0, len(x)):
        temp = fun(x, p)
    return temp - y


r = leastsq(residuals, [1, 1], args=(x, y))