曲线拟合算法

1、Illi线拟介算法实现序号大类拟合方法公式A1Lin ear Regressi on Models 线性回归模型Linear Fit苴线拟合y=a + bx1Quadratic Fit 二次多项式拟合y = a + bx+ ex24n degree Polynomial Fitn次多项式拟合y = a + hx+ ex2 + dx3 + .2Exponential Family 指数类Exponential Fit 指数模型bxy= ae5Modified Exp on ential 修正指数模型h y aex6Logarithm Fit 对数拟合y=a + hln(x)2Reciprocal

2、 Logarithm Fit 倒数对数拟合_ 1a + bln(x)3Vapor Pressure Model 蒸汽床力模型+c llX-t)y = e x3Power Family 幕函数类Power Fit 幕函数拟合b y= ax7Modified Power 修正幕函数y = abx8Shifted Power Fit 变形幕函数模型y= a(x-b)cGeometric Fit 儿何拟合y = axbK16Modified Geometric Fit 改进的儿何拟合by = axx17Root Fit 根模型iy = abx11Hoerl Model霍尔模型y = abxxcModi

3、fied Hoerl Model 修正霍尔模型1y= abxxcIlli线拟介克法实现4Yield-Density Models 产量密度模型类Reciprocal Model 倒数/互惠模型1y *>ax+ b10Reciprocal Quadratic 二次倒数模型1y =a + bx+ ex214Bleasdale ModelBleasdale 模型Jy = (a + bx) cHarris Model 哈里斯模型1y =a + bh205Growth Family 成长类Exponential Association 22参数指数协调模型y = a(l_ 严)Exponentia

4、l Association 33参数指数协调模型y= a(b - ecx)Saturation Growth-Rate Model 饱和生长速率模型axP+ X156Sigmoidal Familys形增长模型类Gompertz Model 龚帕斯模型y-ae18Logistic Model 逻辑斯蒂模型' l + L12Richards Model 理査徳斯模型ayi(1 +严yMMF Model四参数增长模型ah + cxd y b+r13Weibull Model威布尔模型y = a-b严'197Miscellaneous Family 其它五花八门的类型Sinusoid

5、al Fit 正弦拟合y = a + bcos(cx+ d)Gaussian Model 高斯模型r.L”y = ae 2cZHyperbolic Fit 双曲线拟合b y=a + X9Heat Capacity Model 热容量模型y = a + bx + 二ATRational Function有理函数模型a + bx y ="1 + cx+ dx1以上7人类33种拟合方法，已经完成其中的20种,另外还有三次样条曲线拟合算法在保疗检验领域 的实际应用模块（以上算法实现,大部分己经用于包括时间分辨荧光免疫分析的临床）.E-mail: chiangpiong Mobile:1338

6、0263090QQ:348732824曲线拟介笄法实现拟合效果举例对照:有以下9组数据:123456789X91421284257637079y8.9310.818.5922.3339.3556.1161.7364.6267.08分别用CurveExpert和本人的算法拟化对比结果如下:拟合方法公式CurveExpert 1.3本人的拟合1Linear Fit 直线拟合y = a + bxa =-0. 59207151 b = 0. 92654998 r=0. 991842abr-0. 59207150. 92655000. 9918422Quadratic Fit 二次多项式拟 合y = a

7、 + bx+ ex2a=-4. 8737009 b=l. 217389 c=-0. 0033690953 r=0. 99378911a b c r-4. 87370091.2173890-0. 00336910. 9937893Logarithm Fit 对数拟合y = a + bn(x)a=-67. 55423 b 二30. 153799 r=0. 96374692a b r-67. 554230130. 15379860. 9637484Power Fit 幕函数拟合y = axba=0. 92722069b=0. 99705555r=0. 99175975abr0. 82513131.0

8、2423620. 9915895Gompertz Model 龚帕斯模型y = aea=82. 832151 b=l. 2237139 c=0. 037074938 r=0. 99765283ab c r85. 73835241.16167390. 03393150. 9974146Logistic Model 逻供斯蒂模世ay 71+b严a=72. 462262b=13. 709324 c=0. 067359152r=0. 99913297abc r73. 075849913. 31593550. 06572330. 9990977MMF Model 四参数增长模 型ab + cxd y - t d b+ xa二3. 922614 b=1468. 6098 c=112. 70352 d=l. 7671789 r=0. 99666044abcdr6 10673352058. 8546662104. 85920601.87590110. 9970308Weibull Model 威布尔模型y = a-bec'da=70. 292195b=62. 136784 c=0. 00011004468 d=2. 3512073r=0. 99909479a b c d r68. 495277359. 08013180. 00004342. 601