matlab中实现最小二乘拟合函数曲线.zip.zip

clc; clear; close all; %% 取样并代入曲线 x_all = 0:0.01:1.81; [y_truth_all,y_all]=unknown_model1(x_all); N = length(x_all); %用前半段取样点训练并显示理想值 x = x_all(1:N/2); y = y_all(1:N/2); y_truth = y_truth_all(1:N/2); plot(x,y_truth,'g-x','LineWidth',1.5); hold on; plot(x,y,'m-x','LineWidth',1.5); legend('model truth','observation'); title('training'); %% 二阶曲线拟合 X = [x.^2;x;ones(1,length(x))]'; Y = y'; lambda1 = (X'*X)\X'*Y; % evaluate the esimated model ye1 = X*lambda1; hold on; plot(x,ye1,'c-o','LineWidth',1.5); legend('model truth','observation', 'order-2 poly fitting'); %% 四阶曲线拟合 X = [x.^4;x.^3;x.^2;x;ones(1,length(x))]'; Y = y'; lambda2 = (X'*X)\X'*Y; % evaluate the esimated model ye2 = X*lambda2; hold on; plot(x,ye2,'r-o','LineWidth',1.5); legend('model truth','observation', 'order-2 poly fitting','order-4 poly fitting'); %% 八阶曲线拟合 X = [x.^8;x.^7;x.^6;x.^5;x.^4;x.^3;x.^2;x;ones(1,length(x))]'; Y = y'; lambda3 = (X'*X)\X'*Y % evaluate the esimated model ye3 = X*lambda3; a=ye3'-y; a1=20*log10(a); hold on; plot(x,ye3,'b-o','LineWidth',1.5); xlabel('Fs'); ylabel('幅频值'); legend('model truth','observation', 'order-2 poly fitting','order-4 poly fitting','order-8 poly fitting'); %拟合的1/sinc曲线与理想曲线的误差范围 figure; plot(x,-20*log10(y./abs(a))); xlabel('Fs'); ylabel('1/sinc拟合误差(dB)'); title('1/sinc拟合误差'); %% 补偿后的误差 b=ye3'.*sinc(x); figure; subplot(2,1,1); plot(x,sinc(x),x,b); xlabel('Fs'); ylabel('幅频'); title('补偿后对比'); subplot(2,1,2); plot(x,-20*log10(1./(1-b))); xlabel('Fs'); ylabel('补偿后的误差(dB)'); title('补偿后的误差'); %% show future trends %X = [x_all;ones(1,length(x_all))]'; %ye1 = X*lambda1; %X = [x_all.^3;x_all.^2;x_all;ones(1,length(x_all))]'; %ye2 = X*lambda2; %X = [x_all.^5;x_all.^4;x_all.^3;x_all.^2;x_all;ones(1,length(x_all))]'; %ye3 = X*lambda3; %figure; %plot(x_all,y_truth_all,'g-x',x_all,y_all,'m-x',x_all,ye1,'c-o',x_all,ye2,'r-o',x_all,ye3,'b-o','LineWidth',1.5); %legend('model truth','observation', 'order-1 poly fitting','order-3 poly fitting', 'order-5 poly fitting'); %title('testing');