用正交多项式作最小二乘拟合的java实现（转）

?

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195

import java.util.Scanner;       public class Least_square_fit {               public static double Least_square_method(int n,int m,double X[],double Y[],double A[],double err[],double sum[],double my_sum,double bel[],double alp[]){         double S1[]=new double[m+1];//S1存放前一次多项式的值，范围为S1[0]~S1[m]         double S0[]=new double[m+1];//S0存放前两次多项式的值，范围为S0[0]~S0[m]         double SS[]=new double[m+1];//用于交换         double AU=0,AL=0,alp_L=0,alp_U=0,bel_U=0,bel_L=0;//AU为计算A的分子，AL为计算A的分母，alp_L、alp_U分别为计算alpha的分母和分子，alp_L_bel为计算belta的分母         double sum_temp[]=new double[m+1];///////////         double error=0;//误差的平方和         my_sum=0;         double my_sumtemp=0;         boolean flag=true;         /*计算A[0],alp[1]*/         for(int i=0;i<=m;i++)         {             AU+=Y[i];             AL++;             alp_L++;             alp_U+=X[i];             S0[i]=1;         }         A[0]=AU/AL;         bel_L=AL;         alp[1]=alp_U/alp_L;         my_sum+=A[0]*1;         for(int i=0;i<=m;i++){             sum[i]+=A[0]*1;//////////////////         }                               /*计算A[1],alp[2],bel[1]*/         AU=0;AL=0;alp_L=0;alp_U=0;bel_U=0;//变量清零         double temp=0;         for(int i=0;i<=m;i++)         {             temp=(X[i]-alp[1]);             S1[i]=temp;             AU+=Y[i]*temp;             AL+=temp*temp;             alp_U+=X[i]*temp*temp;         }         alp_L=AL;         A[1]=AU/AL;         alp[2]=alp_U/alp_L;         bel_U=AL;         bel[1]=bel_U/bel_L;         my_sum+=A[1]*(X[1]-alp[1]);         for(int i=0;i<=m;i++){         sum[i]+=A[1]*(X[i]-alp[1]);///////////         }                    /*递推计算A[2]~A[n-1],alp[3]~alp[n],bel[2]~bel[n-1]*/         for(int j=3;j<=n;j++){             AU=0;AL=0;alp_L=0;alp_U=0;bel_U=0;bel_L=0;//每次计算变量清零             for(int ii=0;ii<=m;ii++){                 SS[ii]=S1[ii];             }             for(int i=0;i<=m;i++){                 sum_temp[i]=(X[i]-alp[j-1])*S1[0]-bel[j-2]*S0[0];///////////////////             }             for(int i=0;i<=m;i++){                 if(flag){                     my_sumtemp=(X[1]-alp[j-1])*S1[0]-bel[j-2]*S0[0];                 }                                                       bel_L=bel_L+S1[i]*S1[i];                 S1[i]=(X[i]-alp[j-1])*S1[i]-bel[j-2]*S0[i];                 alp_L=alp_L+S1[i]*S1[i];                 alp_U=alp_U+X[i]*S1[i]*S1[i];                 S0[i]=SS[i];                 AU=AU+Y[i]*S1[i];                 flag=false;             }             flag=true;             bel_U=alp_L;             AL=alp_L;             alp[j]=alp_U/alp_L;             bel[j-1]=bel_U/bel_L;             A[j-1]=AU/AL;             my_sum+=A[j-1]*my_sumtemp;             for(int i=0;i<=m;i++)             {                 sum[i]+=A[j-1]*sum_temp[i];             }                               }         /*计算A[n]*/         AU=0;AL=0;alp_L=0;alp_U=0;bel_U=0;bel_L=0;//变量清零         for(int ii=0;ii<=m;ii++){             SS[ii]=S1[ii];         }         flag=true;         for(int i=0;i<=m;i++){             sum_temp[i]=(X[i]-alp[n])*S1[0]-bel[n-1]*S0[0];         }         for(int i=0;i<=m;i++){             if(flag){                 my_sumtemp=(X[1]-alp[n])*S1[0]-bel[n-1]*S0[0];             }                                               S1[i]=(X[i]-alp[n])*S1[i]-bel[n-1]*S0[i];             AL=AL+S1[i]*S1[i];             S0[i]=SS[i];             AU=AU+Y[i]*S1[i];             flag=false;         }         A[n]=AU/AL;         my_sum+=A[n]*my_sumtemp;         for(int i=0;i<=m;i++){             sum[i]+=A[n]*sum_temp[i];         }                    /*返回误差的平方和*/         for(int i=0;i<=m;i++)         {             err[i]=sum[i]-Y[i];             error+=err[i]*err[i];         }                    return error;     }        public static void main(String[] args) {         Scanner scan=new Scanner(System.in);         System.out.println("输入多项式次数：");         int n=scan.nextInt();         System.out.println("输入数据点个数：");         int mm=scan.nextInt();         int m=mm-1;//为方便观察使用m         double bel[]=new double[n];//系数belta从bel[1]~bel[n-1]         double alp[]=new double[n+1];//系数alpha从alpha[1]~alpha[n]         double X[]=new double[m+1];//X存放mm个数据点横坐标值，范围为X[0]~X[m]         double Y[]=new double[m+1];//Y存放mm个数据点纵坐标值，范围为Y[0]~Y[m]         double A[]=new double[n+1];//A存放多项式系数，范围A[0]~A[n]         double error;//误差平方和         double err[]=new double[m+1];//记录个点误差         double sum[]=new double[m+1];//记录个点拟合值         double my_sum=0;                           System.out.println("输入X:");         for(int i=0;i<=m;i++){             X[i]=scan.nextDouble();         }         System.out.println("输入Y:");         for(int i=0;i<=m;i++){             Y[i]=scan.nextDouble();         }                    error=Least_square_method(n, m, X, Y,A,err,sum,my_sum,bel,alp);         System.out.println("多项式系数分别为：");//输出多项式系数         for(int i=0;i<=n;i++){             System.out.print("A["+i+"]="+A[i]+" ");         }         System.out.println();         System.out.println("alpha为：");//输出系数alpha         for(int i=1;i<=n;i++){             System.out.print("alp["+i+"]="+alp[i]+" ");         }         System.out.println();         System.out.println("belta为：");//输出系数belta         for(int i=1;i<=n-1;i++){             System.out.print("bel["+i+"]="+bel[i]+" ");         }         System.out.println();                           /*输出误差相关*/         System.out.println("各点拟合值为：");         for(int i=0;i<=m;i++)         {             System.out.println(sum[i]+" ");         }         System.out.println();         System.out.println("各点误差为：");         for(int i=1;i<=m;i++){             System.out.print(err[i]+" ");         }         System.out.println();         System.out.println("误差平方和为：");         System.out.println(error);                    System.out.println("my_Sum:"+my_sum);                   }    }

http://www.oschina.net/code/snippet_574827_43214