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(lèi)型的散點(diǎn)擬合無(wú)從下手伊佃，常規(guī)的方法就是嘗試各種擬合曲線窜司，然后選出最優(yōu)的，但是問(wèn)題就來(lái)了航揉，對(duì)這么多的曲線編寫(xiě)程序豈不是累死塞祈？
幸好有Matlab！幸好有cftool帅涂！
我們可以先把數(shù)據(jù)導(dǎo)入matlab议薪，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(chē)媳友，打開(kāi)Curve Fitting tool工具箱
在這里面選擇數(shù)據(jù)來(lái)源斯议，并選擇函數(shù)名稱(chēng)，即可進(jìn)行擬合醇锚，matlab會(huì)提供函數(shù)和誤差哼御。接下來(lái)選最好的函數(shù)就行了！
參考如圖：
注：工具箱提供的擬合類(lèi)型如下焊唬，進(jìn)行簡(jiǎn)要說(shuō)明恋昼，可以嘗試各種不同類(lèi)型擬合效果
- Custom Equations：用戶自定義的函數(shù)類(lèi)型
- Exponential：指數(shù)逼近，有2種類(lèi)型求晶， aexp(bx) 焰雕、 aexp(bx) + cexp(dx)
- Fourier：傅立葉逼近衷笋，有7種類(lèi)型芳杏，基礎(chǔ)型是 a0 + a1cos(xw) + b1sin(xw)
- Gaussian：高斯逼近，有8種類(lèi)型辟宗，基礎(chǔ)型是 a1*exp(-((x-b1)/c1)^2)
- Interpolant：插值逼近爵赵，有4種類(lèi)型，linear泊脐、nearest neighbor空幻、cubic spline、shape-preserving
- Polynomial：多形式逼近容客，有9種類(lèi)型秕铛，linear ~、quadratic ~缩挑、cubic ~但两、4-9th degree ~
- Power：冪逼近，有2種類(lèi)型供置，ax^b 谨湘、ax^b + c
- Rational：有理數(shù)逼近，分子、分母共有的類(lèi)型是linear ~紧阔、quadratic ~坊罢、cubic ~、4-5th degree ~擅耽；此外活孩，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：正弦曲線逼近秫筏，有8種類(lèi)型诱鞠，基礎(chǔ)型是 a1sin(b1x + c1)
Weibull：只有一種，abx(b-1)*exp(-a*xb)
參考網(wǎng)址：matlab 2011b曲線擬合工具箱cftool的使用
