有時(shí)候我們需要對(duì)一些散點(diǎn)進(jìn)行擬合，但是經(jīng)常會(huì)發(fā)現(xiàn)對(duì)于未知曲線類型的散點(diǎn)擬合無從下手，常規(guī)的方法就是嘗試各種擬合曲線，然后選出最優(yōu)的，但是問題就來了，對(duì)這么多的曲線編寫程序豈不是累死？

幸好有Matlab！幸好有cftool！

我們可以先把數(shù)據(jù)導(dǎo)入matlab，如：

x = [8.8,9.4,9.6,7.8,8.5,6.2,11,12.5,12.8,13.4,11,12.1,10.8,10.1,13,12,10.6,10,10.8,12.6,12,13,11.7,17.4,17.2,15.2,14,15.1,14.6,14,17.4,16.2,15.4,14,20.5,19.2,20,18,20,19.5,19.8,19.7,19.7,21.6,24.6,22,22,25,24.8,27,28.5,29.2,27.3,31,31,39]
y = [0.0296,0.035,0.04,0.022,0.036,0.0153,0.0534,0.1064,0.1133,0.122,0.076,0.1082,0.0704,0.0484,0.0926,0.108,0.0458,0.0391,0.0642,0.0981,0.0886,0.077,0.0914,0.1053,0.196,0.1637,0.112,0.1449,0.153,0.1181,0.1913,0.2268,0.1537,0.1024,0.277,0.2974,0.2664,0.1784,0.3014,0.2075,0.2724,0.2899,0.256,0.2493,0.4486,0.3494,0.2536,0.498,0.4839,0.4605,0.7285,0.8039,0.6058,0.8141,0.7751,1.3157]

輸入cftool，回車，打開Curve Fitting tool工具箱

在這里面選擇數(shù)據(jù)來源，并選擇函數(shù)名稱，即可進(jìn)行擬合，matlab會(huì)提供函數(shù)和誤差。接下來選最好的函數(shù)就行了！

參考如圖：

注：工具箱提供的擬合類型如下，進(jìn)行簡(jiǎn)要說明，可以嘗試各種不同類型擬合效果

• Custom Equations：用戶自定義的函數(shù)類型
• Exponential：指數(shù)逼近，有2種類型， aexp(bx) 、 aexp(bx) + cexp(dx)
• Fourier：傅立葉逼近，有7種類型，基礎(chǔ)型是 a0 + a1cos(xw) + b1sin(xw)
• Gaussian：高斯逼近，有8種類型，基礎(chǔ)型是 a1*exp(-((x-b1)/c1)^2)
• Interpolant：插值逼近，有4種類型，linear、nearest neighbor、cubic spline、shape-preserving
• Polynomial：多形式逼近，有9種類型，linear ~、quadratic ~、cubic ~、4-9th degree ~
• Power：冪逼近，有2種類型，ax^b 、ax^b + c
• Rational：有理數(shù)逼近，分子、分母共有的類型是linear ~、quadratic ~、cubic ~、4-5th degree ~；此外，分子還包括constant型
• Smoothing Spline：平滑逼近（翻譯的不大恰當(dāng)，不好意思）
• Sum of Sin Functions：正弦曲線逼近，有8種類型，基礎(chǔ)型是 a1sin(b1x + c1)
  Weibull：只有一種，abx^{(b-1)*exp(-a*x}b)

參考網(wǎng)址：matlab 2011b曲線擬合工具箱cftool的使用