基于Matlab实现多项式与插值拟合（源码+数据）.rar

%-------------------------------------------------------------------------- % 第7章 多项式与插值拟合 %-------------------------------------------------------------------------- %% examp7.1-1 多项式拟合 %--------------------散点图------------------ [Data,Textdata] = xlsread('食品零售价格.xls'); x = Data(:,1); y = Data(:,3); timestr = Textdata(3:end,2); plot(x,y,'k.','Markersize',15); set(gca,'XTick',1:2:numel(x),'XTickLabel',timestr(1:2:end)); set(gca,'XTickLabelRotation',-30); xlabel('时间(x)'); ylabel('食品零售价格分类指数'); %-------------------4阶多项式拟合-------------------- [p4,S4] = polyfit(x,y,4) r = poly2sym(p4); r = vpa(r,5) %--------------------更高阶多项式拟合--------------------- [p5,S5] = polyfit(x,y,5); S5.normr [p6,S6] = polyfit(x,y,6); S6.normr [p7,S7] = polyfit(x,y,7); S7.normr [p8,S8] = polyfit(x,y,8); S8.normr [p9,S9] = polyfit(x,y,9); S9.normr %-------------------拟合效果图---------------------- figure; plot(x,y,'k.','Markersize',15); set(gca,'XTick',1:2:numel(x),'XTickLabel',timestr(1:2:end)); set(gca,'XTickLabelRotation',-30); xlabel('时间(x)'); ylabel('食品零售价格分类指数'); hold on; yd4 = polyval(p4,x); yd6 = polyval(p6,x); yd8 = polyval(p8,x); yd9 = polyval(p9,x); plot(x,yd4,'r:+'); plot(x,yd6,'g--s'); plot(x,yd8,'b-.d'); plot(x,yd9,'m-p'); legend('原始散点','4次多项式拟合','6次多项式拟合','8次多项式拟合','9次多项式拟合') %% examp7.4-1 一维插值 x0 = [0,3,5,7,9,11,12,13,14,15]; y01 = [0,1.8,2.2,2.7,3.0,3.1,2.9,2.5,2.0,1.6]; y02 = [0,1.2,1.7,2.0,2.1,2.0,1.8,1.2,1.0,1.6]; x = 0:0.1:15; ysp1 = interp1(x0,y01,x,'spline'); ysp2 = interp1(x0,y02,x,'spline'); plot([x0,x0],[y01,y02],'o'); hold on; plot(x,ysp1,'r',x,ysp2,'r'); xlabel('X') ylabel('Y') legend('插值节点','三次样条插值','location','northwest') %% examp7.4-2 一维插值 fun = @(x)sin(pi*x/2).*(x>=-1&x<1) + x.*exp(1-x.^2).*(x>=1 | x<-1); %%----------------区间[0,1]上的三次样条插值------------------ x01 = linspace(0,1,6); y01 = fun(x01); x1 = linspace(0,1,20); pp1 = csape(x01,[1,y01,0],'complete'); y1 = fnval(pp1,x1); %%----------------区间[1,3]上的三次样条插值------------------ x02 = linspace(1,3,8); y02 = fun(x02); x2 = linspace(1,3,30); pp2 = csape(x02,[0,y02,0.01],[1,2]); y2 = fnval(pp2,x2); %%-----------------------绘图--------------------- plot([x01,x02],[y01,y02],'ko'); hold on; plot([x1,x2],fun([x1,x2]),'k','linewidth',2); plot([x1,x2],[y1,y2],'--','linewidth',2); xlabel('X'); ylabel('Y = f(x)'); legend('插值节点','原函数图像','三次样条插值'); %% examp7.4-3 二维网格节点插值 x = 100:100:500; y = 100:100:400; [X,Y] = meshgrid(x,y); Z = [450 478 624 697 636 420 478 630 712 698 400 412 598 674 680 310 334 552 626 662]; xd = 100:20:500; yd = 100:20:400; [Xd1,Yd1] = meshgrid(xd,yd); [Xd2,Yd2] = ndgrid(xd,yd); figure; % 新建图形窗口 % -------------- 调用interp2函数作三次样条插值------------------- Zd1 = interp2(X,Y,Z,Xd1,Yd1,'spline'); subplot(1,2,1); surf(Xd1,Yd1,Zd1); xlabel('X'); ylabel('Y'); zlabel('Z'); title('interp2') % ---------调用griddedInterpolant函数作三次样条插值-------------- F = griddedInterpolant({x,y},Z','spline'); Zd2 = F(Xd2,Yd2); subplot(1,2,2); surf(Xd2,Yd2,Zd2); xlabel('X'); ylabel('Y'); zlabel('Z'); title('griddedInterpolant') %% examp7.4-4 二维散乱节点插值 xyz = xlsread('cumcm2011A.xls',1,'B4:D322'); Cd = xlsread('cumcm2011A.xls',2,'C4:C322'); x = xyz(:,1); y = xyz(:,2); z = xyz(:,3); xd = linspace(min(x),max(x),60); yd = linspace(min(y),max(y),60); [Xd,Yd] = meshgrid(xd,yd); % ------------调用griddata函数作散乱节点插值--------------- Zd1 = griddata(x,y,z,Xd,Yd); Cd1 = griddata(x,y,Cd,Xd,Yd); figure; subplot(1,2,1); surf(Xd,Yd,Zd1,Cd1); shading interp; xlabel('X'); ylabel('Y'); zlabel('Z'); title('griddata'); colorbar; % ------------调用scatteredInterpolant函数作散乱节点插值------------ F1 = scatteredInterpolant(x,y,z,'linear','none'); Zd2 = F1(Xd,Yd); % 计算插值点处的海拔高度 F2 = scatteredInterpolant(x,y,Cd,'linear','none'); Cd2 = F2(Xd,Yd); subplot(1,2,2); surf(Xd,Yd,Zd2,Cd2); shading interp; xlabel('X'); ylabel('Y'); zlabel('Z');title('scatteredInterpolant'); colorbar; %% examp7.4-5 高维插值 data = xlsread('温度场.xlsx'); x = data(:,1); y = data(:,2); z = data(:,3); v = data(:,4); xi = linspace(min(x),max(x),60); yi = linspace(min(y),max(y),60); zi = linspace(min(z),max(z),60); [Xd,Yd,Zd] = meshgrid(xi,yi,zi); F = scatteredInterpolant(x,y,z,v); Vd = F(Xd,Yd,Zd); sxyz = [1:15:60,60]; % 设置切片位置 % 绘制切片图 slice(Xd,Yd,Zd,Vd,xi(sxyz),yi(sxyz),zi(sxyz)); shading interp; % 插值染色 alpha(0.5); % 设置透明度 xlabel('x');ylabel('y');zlabel('z') axis equal colorbar; % 添加颜色条 figure; MyIsosurface(Xd,Yd,Zd,Vd,800);