Matlab直線擬合和平面擬合

1、利用 Matlab 實現(xiàn)直線和平面的擬合2011-04-14 10:45:43| 分類： 算法思想 |舉報|字號 訂閱 直線和平面擬合是很常用的兩個算法，原理非常簡單。但如果 matlab 不太熟的 話，寫起來也不是那么容易。搜了很久才找到這兩個代碼，保存之，免得日后麻 煩。1、直線擬合的 matlab 代碼% 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 =

2、 y + n; % x and yn roughly satisfy yn = 2*x + 3 due to the noise % Determine coefficients for non-noisy line y=m1*x+b1 Xcolv = x(:); % Make X a column vector Ycolv = y(:); % Make Y a column vectorConst = ones(size(Xcolv); % Vector of ones for constant termCoeffs = Xcolv ConstYcolv; % Find the coeffi

3、cients m1 = 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)*xA2+Coeffs (2) *x+Coeffs(3)% Coeffs = Xcolv.A2 Xcolv Con stYcolv;% Note the .a before the exp onent of

4、 the first term% Plot the original points and the fitted curve figure plot(x,y,'ro') hold onx2 = 0:0.01:1;y2 = m1*x2+b1; % Evaluate fitted curve at many points plot(x2, y2, 'g-') title(sprintf('Non-noisy data: y=%f*x+%f',m1,b1) % Determine coefficients for noisy line yn=m2*x+

5、b2 Xcolv = x(:); % Make X a column vector Yncolv = yn(:); % Make Yn a column vectorConst = ones(size(Xcolv); % Vector of ones for constant term NoisyCoeffs = Xcolv ConstYncolv; % Find the coefficients m2 = NoisyCoeffs(1);b2 = NoisyCoeffs(2);% Plot the original points and the fitted curve figureplot(

6、x,yn,'ro') hold on x2 = 0:0.01:1;yn2 = m2*x2+b2; plot(x2, yn2, 'g-') title(sprintf('Noisy data: y=%f*x+%f',m2,b2)2、平面擬合 matlab 代碼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 colum

7、n vector Ycolv = y(:); % Make Y a column vector Zcolv = z(:); % Make Z a column vectorConst = ones(size(Xcolv); % Vector of ones for constant term Coefficients = Xcolv Ycolv ConstZcolv; % Find the coefficients XCoeff = Coefficients(1); % X coefficientYCoeff = Coefficients(2); % X coefficient CCoeff

8、= Coefficients(3); % constant term% Using the above variables, z = XCoeff * x + YCoeff * y + CCoeff L=plot3(x,y,z,'ro'); % Plot the original data points set(L,'Markersize',2*get(L,'Markersize') % Making the circle markers larger set(L,'Markerfacecolor','r') %

9、Filling in the markers hold onxx, yy=meshgrid(0:0.1:1,0:0.1:1); % Generating a regular grid for plotting zz = XCoeff * xx + YCoeff * yy + CCoeff;surf(xx,yy,zz) % Plotting the surface title(sprintf('Plotting plane z=(%f)*x+(%f)*y+(%f)',XCoeff, YCoeff, CCoeff) % By rotating the surface, you ca

10、n 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 最小二乘法進行平面擬合MATLAB 軟件提供了基本的曲線擬合函數(shù)的命令： 多項式函數(shù)擬合： a = polyfit (xdata，ydata， n) 其中n表示多項式的最高階數(shù)，xdata, ydata為要擬合的數(shù)據(jù)，它

11、是用數(shù)組的方 式輸入。輸出參數(shù)a為擬合多項式y(tǒng) = a1xn + ax + an+i的系數(shù)a =，,用 an+1 。多項式在x處的值y可用下面程序計算。y = polyval (a, x)一般的曲線擬合： p = curvefit(Fun'0，pxdata， ydata)其中Fun表示函數(shù)Fun (p, xdata)的 M-文件，p0表示函數(shù)的初值。curvefit命令的 求解問題形式是：min p sum (F un (p, xdata)-ydata).A2若要求解點 x 處的函數(shù)值可用程序 f = Fun(p, x) 計算。例如已知函數(shù)形式 y = ae - bx + ce -dx

12、，并且已知數(shù)據(jù)點(xi, yi), i = 1,2,n要確定四個未知參數(shù) a, b, c, d。使用 curvefit 命令，數(shù)據(jù)輸入 xdata = x1,x2,xn; ydata = y1,y2,初值輸n;入 p0 = aO,bO,cO,dO;并且建立函數(shù) y = ae - bx + ce -dx 的 M-文件(Fun.m)。若 定義 p1 = a, p2 = b, p3 = c, p4 = d , 則輸出 p = p1, p2, p3, p4。引例求解：t=1:16; % 數(shù)據(jù)輸入y=4 6.4 8 8.4 9.28 9.5 9.7 9.86 1O 1O.2 1O.32 1O.42 1O

13、.5 1O.55 1O.58 1O.6;plot(t,y,'o') %畫散點圖p=polyfit(t,y,2) (二次多項式擬合 )計算結(jié)果：p = -O.O4451.O7114.3252%二次多項式的系數(shù)從而得到某化合物的濃度y與時間t的擬合函數(shù)：y = 4.3252+1.O711t -O.O445t2對函數(shù)的精度如何檢測呢？仍然以圖形來檢測， 將散點與擬合曲線畫在一個畫面 上。xi=linspace(O,16,16O);yi=polyval(p,xi); plot(x,y,'o',xi,yi) 在MATLAB的NAG Foundation Toolbox中也

14、有一些曲面擬合函數(shù)，如e02daf,eO2cf， eO2def 可分別求出矩形網(wǎng)格點數(shù)據(jù)、散點數(shù)據(jù)的最小平方誤差雙三次樣 條曲面擬合，e02def等可求出曲面擬合的函數(shù)值。用matlab的regress命令進行平面擬合2011-08-16 22:00:38)專載標簽:分類:數(shù)學(xué)軟件教育以少量數(shù)據(jù)為例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即可將散點繪制出來我們繼續(xù)X = ones(5,1) x y; 5 為 size(x)b = regress(

15、z,X) /擬合，其實是線性回歸，但可以用來擬合平面。regress命令還有其它用法, 但一般這樣就可以滿足要求了。于是顯示出6.5642-0.1269-0.0381這就表示 z = 6.5643 - 0.1269 * x - 0.0381 * y 是擬合出來的平面的方程 下面把它繪制出來xfit = min(x):0.1:max(x);注 0.1 表示數(shù)據(jù)的間隔yfit = mi n(y):0.1:max(y);XFIT,YFIT= meshgrid (xfit,yfit); /制成網(wǎng)格數(shù)據(jù)ZFIT = b(1) + b(2) * XFIT + b(3) * YFIT;mesh (XFIT,YFIT,ZFIT)這樣，圖就出來啦%r p q就是你的x,y,z r = ran di(10,20,1);p = ran di(10,20,1);q = ran di(10,20,1);b = re