Matlab直线拟合和平面拟合.doc

利用Matlab实现直线和平面的拟合 2011-04-14 10:45:43| 分类： 算法思想 |举报|字号 订阅直线和平面拟合是很常用的两个算法，原理非常简单。但如果matlab不太熟的话，写起来也不是那么容易。搜了很久才找到这两个代码，保存之，免得日后麻烦。1、直线拟合的matlab代码% Fitting a best-fit line to data, both noisy and non-noisyx = rand(1,10);n = rand(size(x); % Noisey = 2*x + 3; % x and y satisfy y = 2*x + 3yn = y + n; % x and yn roughly satisfy yn = 2*x + 3 due to the noise% Determine coefficients for non-noisy line y=m1*x+b1Xcolv = x(:); % Make X a column vectorYcolv = y(:); % Make Y a column vectorConst = ones(size(Xcolv); % Vector of ones for constant termCoeffs = Xcolv ConstYcolv; % Find the coefficientsm1 = Coeffs(1);b1 = Coeffs(2);% To fit another function to this data, simply change the first % matrix on the line defining Coeffs% For example, this code would fit a quadratic % y = Coeffs(1)*x2+Coeffs(2)*x+Coeffs(3)% Coeffs = Xcolv.2 Xcolv ConstYcolv; % Note the . before the exponent of the first term% Plot the original points and the fitted curvefigureplot(x,y,ro)hold onx2 = 0:0.01:1;y2 = m1*x2+b1; % Evaluate fitted curve at many pointsplot(x2, y2, g-)title(sprintf(Non-noisy data: y=%f*x+%f,m1,b1)% Determine coefficients for noisy line yn=m2*x+b2Xcolv = x(:); % Make X a column vectorYncolv = yn(:); % Make Yn a column vectorConst = ones(size(Xcolv); % Vector of ones for constant termNoisyCoeffs = Xcolv ConstYncolv; % Find the coefficientsm2 = NoisyCoeffs(1);b2 = NoisyCoeffs(2);% Plot the original points and the fitted curvefigureplot(x,yn,ro)hold onx2 = 0:0.01:1;yn2 = m2*x2+b2;plot(x2, yn2, g-)title(sprintf(Noisy data: y=%f*x+%f,m2,b2)2、平面拟合matlab代码x = rand(1,10);y = rand(1,10);z = (3-2*x-5*y)/4; % Equation of the plane containing % (x,y,z) points is 2*x+5*y+4*z=3Xcolv = x(:); % Make X a column vectorYcolv = y(:); % Make Y a column vectorZcolv = z(:); % Make Z a column vectorConst = ones(size(Xcolv); % Vector of ones for constant termCoefficients = Xcolv Ycolv ConstZcolv; % Find the coefficientsXCoeff = Coefficients(1); % X coefficientYCoeff = Coefficients(2); % X coefficientCCoeff = Coefficients(3); % constant term% Using the above variables, z = XCoeff * x + YCoeff * y + CCoeffL=plot3(x,y,z,ro); % Plot the original data pointsset(L,Markersize,2*get(L,Markersize) % Making the circle markers largerset(L,Markerfacecolor,r) % Filling in the markershold onxx, yy=meshgrid(0:0.1:1,0:0.1:1); % Generating a regular grid for plottingzz = XCoeff * xx + YCoeff * yy + CCoeff;surf(xx,yy,zz) % Plotting the surfacetitle(sprintf(Plotting plane z=(%f)*x+(%f)*y+(%f),XCoeff, YCoeff, CCoeff)% By rotating the surface, you can see that the points lie on the plane% Also, if you multiply both sides of the equation in the title by 4,% you get the equation in the comment on the third line of this example如何用matlab最小二乘法进行平面拟合MATLAB软件提供了基本的曲线拟合函数的命令：多项式函数拟合： a = polyfit（xdata，ydata，n）其中n表示多项式的最高阶数，xdata，ydata 为要拟合的数据，它是用数组的方式输入。输出参数a为拟合多项式y = a1xn + + anx + an+1的系数a = a1, , an, an+1。多项式在x处的值y可用下面程序计算。y = polyval (a, x)一般的曲线拟合： p = curvefit（Funp0，xdata，ydata）其中Fun表示函数Fun (p, xdata)的M-文件，p0表示函数的初值。curvefit命令的求解问题形式是：minp sum (Fun (p, xdata)-ydata).2若要求解点x处的函数值可用程序f = Fun(p, x) 计算。例如已知函数形式 y = ae - bx + ce dx ，并且已知数据点(xi, yi), i = 1,2, n，要确定四个未知参数a, b, c, d。使用curvefit命令，数据输入xdata = x1,x2, , xn; ydata = y1,y2, , yn;初值输入p0 = a0,b0,c0,d0; 并且建立函数y = ae - bx + ce dx的M-文件（Fun.m）。若定义p1 = a, p2 = b, p3 = c, p4 = d , 则输出p = p1, p2, p3, p4。引例求解： t=1:16; %数据输入 y=4 6.4 8 8.4 9.28 9.5 9.7 9.86 10 10.2 10.32 10.42 10.5 10.55 10.58 10.6; plot(t,y,o) %画散点图 p=polyfit(t,y,2) (二次多项式拟合)计算结果： p = -0.0445 1.0711 4.3252 %二次多项式的系数从而得到某化合物的浓度y与时间t的拟合函数：y = 4.3252+1.0711t 0.0445t2对函数的精度如何检测呢？仍然以图形来检测，将散点与拟合曲线画在一个画面上。 xi=linspace(0,16,160); yi=polyval(p,xi); plot(x,y,o,xi,yi) 在MATLAB的NAG Foundation Toolbox中也有一些曲面拟合函数，如e02daf，e02cf，e02def可分别求出矩形网格点数据、散点数据的最小平方误差双三次样条曲面拟合，e02def等可求出曲面拟合的函数值。用matlab的regress命令进行平面拟合(2011-08-16 22:00:38)转载标签： 教育分类： 数学软件 以少量数据为例x = 1 5 6 3 7;y = 2 9 3 5 8;z = 4 3 5 11 6;scatter3(x,y,z,filled)hold on即可将散点绘制出来我们继续X = ones(5,1) x y; /5为size(x)b = regress(z,X) /拟合，其实是线性回归，但可以用来拟合平面。regress命令还有其它用法，但一般这样就可以满足要求了。于是显示出b = 6.5642 -0.1269 -0.0381这就表示 z = 6.5643 - 0.1269 * x - 0.0381 * y 是拟合出来的平面的方程下面把它绘制出来xfit = min(x):0.1:max(x); /注 0.1表示数据的间隔yfit = min(y):0.1:max(y);XFIT,YFIT= meshgrid (xfit,yfit); /制成网格数据ZFIT = b(1) + b(2) * XFIT + b(3) * YFIT;mesh (XFIT,YFIT,ZFIT)这样，图就出来啦%r p q就是你的x,y,zr = randi(10,20,1);p = randi(10,20,1);q = randi(10,20,1