標題: matlab中實現(xiàn)最小二乘擬合函數(shù)曲線 [打印本頁]
作者: tjoey1991    時間: 2017-7-2 20:34
標題: matlab中實現(xiàn)最小二乘擬合函數(shù)曲線
通過矩陣計算的方式實現(xiàn)用最小二乘法擬合高次函數(shù)曲線

matlab源程序如下:
  1. clc;
  2. clear;
  3. close all;
  4. %% 取樣并代入曲線

  6. x_all = 0:0.01:1.81;
  7. [y_truth_all,y_all]=unknown_model1(x_all);

  9. N = length(x_all);

  11. %用前半段取樣點訓練并顯示理想值
  12. x = x_all(1:N/2);
  13. y = y_all(1:N/2);
  14. y_truth = y_truth_all(1:N/2);

  16. plot(x,y_truth,'g-x','LineWidth',1.5);
  17. hold on;
  18. plot(x,y,'m-x','LineWidth',1.5);
  19. legend('model truth','observation');
  20. title('training');

  22. %% 二階曲線擬合
  23. X = [x.^2;x;ones(1,length(x))]';
  24. Y = y';
  25. lambda1 = (X'*X)\X'*Y;
  26. % evaluate the esimated model
  27. ye1 = X*lambda1;
  28. hold on;
  29. plot(x,ye1,'c-o','LineWidth',1.5);
  30. legend('model truth','observation', 'order-2 poly fitting');
  31. %% 四階曲線擬合
  32. X = [x.^4;x.^3;x.^2;x;ones(1,length(x))]';
  33. Y = y';
  34. lambda2 = (X'*X)\X'*Y;
  35. % evaluate the esimated model
  36. ye2 = X*lambda2;
  37. hold on;
  38. plot(x,ye2,'r-o','LineWidth',1.5);
  39. legend('model truth','observation', 'order-2 poly fitting','order-4 poly fitting');

  41. %% 八階曲線擬合
  42. X = [x.^8;x.^7;x.^6;x.^5;x.^4;x.^3;x.^2;x;ones(1,length(x))]';
  43. Y = y';
  44. lambda3 = (X'*X)\X'*Y
  45. % evaluate the esimated model
  46. ye3 = X*lambda3;
  47. a=ye3'-y;
  48. a1=20*log10(a);
  49. hold on;
  50. plot(x,ye3,'b-o','LineWidth',1.5);
  51. xlabel('Fs');
  52. ylabel('幅頻值');
  53. legend('model truth','observation', 'order-2 poly fitting','order-4 poly fitting','order-8 poly fitting');
  54. %擬合的1/sinc曲線與理想曲線的誤差范圍
  55. figure;
  56. plot(x,-20*log10(y./abs(a)));
  57. xlabel('Fs');
  58. ylabel('1/sinc擬合誤差(dB)');
  59. title('1/sinc擬合誤差');
  60. %% 補償后的誤差
  61. b=ye3'.*sinc(x);
  62. figure;
  63. subplot(2,1,1);
  64. plot(x,sinc(x),x,b);
  65. xlabel('Fs');
  66. ylabel('幅頻');
  67. title('補償后對比');
  68. subplot(2,1,2);
  69. plot(x,-20*log10(1./(1-b)));
  70. xlabel('Fs');
  71. ylabel('補償后的誤差(dB)');
  72. title('補償后的誤差');
  73. %% show future trends

  75. %X = [x_all;ones(1,length(x_all))]';
  76. %ye1 = X*lambda1;
  77. %X = [x_all.^3;x_all.^2;x_all;ones(1,length(x_all))]';
  78. %ye2 = X*lambda2;
  79. %X = [x_all.^5;x_all.^4;x_all.^3;x_all.^2;x_all;ones(1,length(x_all))]';
  80. %ye3 = X*lambda3;
  81. %figure;
  82. %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);
  83. %legend('model truth','observation', 'order-1 poly fitting','order-3 poly fitting', 'order-5 poly fitting');
  84. %title('testing');
  85. …………限于本文篇幅 余下代碼請從51黑下載附件…………
復制代碼

所有資料51hei提供下載:
demo_experiment1.zip (933 Bytes, 下載次數(shù): 11)






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