曲線擬合給定10個點擬合曲線復制即用c++

1、#include <iostream>#include <fstream>#include <string>#include<iomanip.h>#defineF1(t)(1+(t)*(t)*(2*(t)-3)#defineF2(t)(t)*(t)*(-2*(t)+3)#defineF3(t)(t)*(1+(t)*(t)-2)#defineF4(t)(t)*(t)*(t)-1)using namespace std;void tangent(double *y,double *dy,int n)/ 計算各個節(jié)點的切矢，采用自由端點條件/ 追趕法求

2、解三對角方程組int i;double *a,*b,*c,*d; a=new doublen;b=new doublen; c=new doublen;d=new doublen; / 追趕法計算系數(shù) for(i=1;i <n;i+) ai=1;b0=2;bn-1=2;for(i=1;i <n-1;i+) bi=4;for(i=0;i <n-1;i+) ci=1; d0=3*(y1-y0); dn-1=3*(yn-1-yn-2);for(i=1;i <n-1;i+) di=3*(yi+1-yi-1);/ 追趕法回代double *L,*U;L=new doublen;

3、U=new doublen;U0=b0; for(i=1;i <n;i+)Li=ai/Ui-1;Ui=bi-Li*ci-1;double *yy;yy=new doublen;yy0=d0;for(i=1;i <n;i+)yyi=di-Li*yyi-1; dyn-1=yyn-1/Un-1;for(i=n-2;i>=0;i-) dyi=(yyi-ci*dyi+1)/Ui; /delete a,b,c,d,L,U,yy;xa,int n)double spline(double *x,double *y,double *dy,double / 三次 Hermite 插值/ 數(shù)據(jù)點

4、 xn,yn, 切矢 dyn/ 返回 xa 處的插值數(shù)值/ 要求 x 嚴格遞增， x0 <=xa <=xn-1int i;for(i=0;i <n-1;i+)if(xa <=xi+1)break;double t = (xa-xi)/(xi+1-xi);return F1(t)*yi+F2(t)*yi+1+F3(t)*dyi+F4(t)*dyi+1;int main()doubles_ua,xa_ua;/A 類型循環(huán)變量doubles_ub,xa_ub;/B 類型循環(huán)變量doubles_uc,xa_uc; /C 類型循環(huán)變量doubles_a_result,xa_a_r

5、esult;/doubles_b_result,xa_b_result;/doubleaverage_s,average_xa;doubledy_ua4;doubledy_ub4;doubledy_uc4;doublex_ua4=0.000,0,0,0;doubley_ua4=0.0000,0,0,0;doublex_ub4=0.000,0,0,0;doubley_ub4=0.0000,0,0,0;double x_uc4=0.000,0,0,0;double y_uc4=0.0000,0,0,0;/DNA/double X10 0.000,7.000,11.197,17.910,28.649

6、,45.826,73.301,117.251,187.551,300.00;/double Y10 = 272,3008,5854,10287,18398,32204,56751,95727,151346,232604; /HCG/double X10 0.000,0.500,1.000,5.000,10.000,50.000,100.000,500.000,1000.000,5000.000;/double Y10 = 1477,1869,1920,4279,7010,28345,55156,245217,415291,1294682; /HSV-M/double X10 = 0.000,0

7、.500,0.645,0.832,1.073,1.385,1.786,2.304,2.973,3.835; /double Y10 = 349,4273,5487,7054,9072,11685,15043,19381,24984,32203;/Trepdouble X10 = 0.000,0.400,0.761,1.450,2.760,5.254,10.001,19.039,36.245,70.000; double Y10 = 988,2620,4889,9686,19423,39364,81962,152041,249416,398202; int n;/*string s_a;/ 用于

8、 a b c 段線string s_b;/ 用于 b c 段線string s_c;/ 用于 c 段線string s_avarage;/ 用于 b c 段線 求均值*/for(n=0;n<9;n+) /computing(X,Y ,n);int k_a,k_b,k_c;/ 插值函數(shù)調(diào)用，并把結(jié)果輸入到文件if(n = 0) cout<<n<<endl; for(k_a=0;k_a<4;k_a+)x_uak_a = Xk_a+n;y_uak_a = Yk_a+n;/ 給 x、y 賦初值。ofstream ofs_all("d:spline_all.

9、txt");/ 寫文件流 if(!ofs_all) return 10000;tangent(y_ua,dy_ua,4);for(xa_ua = X0;xa_ua <= X1;xa_ua += 0.01)s_ua=spline(x_ua,y_ua,dy_ua,xa_ua,4);/fprintf(ofs_all,"%f#%fn ",xa,s); ofs_all<<setw(15)<<xa_ua<<setw(15)<<s_ua<<endl;/ ofs_all.close();/ 寫入第一部分else i

10、f(n = 1)cout<<n<<endl; for(k_a=0;k_a<4;k_a+)x_uak_a = Xk_a; y_uak_a = Yk_a;/ 給 x、y 賦初值。 tangent(y_ua,dy_ua,4);ofstream ofs_all("d:spline_all.txt",ios_base:app);/ 寫文件流 if(!ofs_all) return 10000;for(xa_ua = X1;xa_ua <= X2;xa_ua += 0.01) s_ua=spline(x_ua,y_ua,dy_ua,xa_ua,4);

11、 xa_a_result = xa_ua;s_a_result= s_ua;for(k_b=0;k_b<4;k_b+)x_ubk_b = Xk_b+1;y_ubk_b = Yk_b+1; tangent(y_ub,dy_ub,4);/for(xa_ub = X1;xa_ub <= X2;xa_ub += 0.01) / xa_ub = xa_ua-0.01;s_ub=spline(x_ub,y_ub,dy_ub,xa_ua,4); average_s = (s_a_result+s_ub)/2; average_xa = (xa_a_result+xa_ub)/2;ofs_all&

12、lt;<setw(15)<<average_xa<<setw(15)<<average_s<<endl;/ofs_all.close();/C x2x3else if(n = 2) cout<<n<<endl;for(k_a=0;k_a<4;k_a+)x_uak_a = Xk_a+n-2;y_uak_a = Yk_a+n-2;/ 給 x、y 賦初值。寫文件流tangent(y_ua,dy_ua,4);ofstream ofs_all("d:spline_all.txt",ios_base:a

13、pp);/ if(!ofs_all) return 10000;for(xa_ua = X2;xa_ua <= X3;xa_ua += 0.01)s_ua=spline(x_ua,y_ua,dy_ua,xa_ua,4); xa_a_result = xa_ua;s_a_result = s_ua;/bfor(k_b=0;k_b<4;k_b+)x_ubk_b = Xk_b+n-1; y_ubk_b = Yk_b+n-1;tangent(y_ub,dy_ub,4);xa_ub = xa_ua-0.01;xa_uc = xa_ub;s_ub=spline(x_ub,y_ub,dy_ub,

14、xa_ua,4); /average_s = (s_a_result+s_ub)/ 2; /average_xa = (xa_a_result+xa_ub)/ 2;/cfor(k_c=0;k_c<4;k_c+)x_uck_c = Xk_c+n;y_uck_c = Yk_c+n;tangent(y_uc,dy_uc,4); s_uc=spline(x_uc,y_uc,dy_uc,xa_ua,4); average_s = (s_a_result+s_ub+s_uc)/3; average_xa = (xa_a_result+xa_ub+xa_uc)/3;ofs_all<<set

15、w(15)<<average_xa<<setw(15)<<average_s<<endl;/ofs_all.close();else if(n = 3)cout<<n<<endl;for(k_a=0;k_a<4;k_a+)x_uak_a = Xk_a+n-2;y_uak_a = Yk_a+n-2;/ 給 x、y 賦初值。寫文件流tangent(y_ua,dy_ua,4);ofstream ofs_all("d:spline_all.txt",ios_base:app);/ if(!ofs_all)

16、 return 10000;for(xa_ua = X3;xa_ua <= X4;xa_ua += 0.01)s_ua=spline(x_ua,y_ua,dy_ua,xa_ua,4); xa_a_result = xa_ua;s_a_result = s_ua;/bfor(k_b=0;k_b<4;k_b+)x_ubk_b = Xk_b+n-1;y_ubk_b = Yk_b+n-1;tangent(y_ub,dy_ub,4);xa_ub = xa_ua-0.01;xa_uc = xa_ub;s_ub=spline(x_ub,y_ub,dy_ub,xa_ua,4); /average_

17、s = (s_a_result+s_ub)/ 2; /average_xa = (xa_a_result+xa_ub)/ 2;/cfor(k_c=0;k_c<4;k_c+)x_uck_c = Xk_c+n;y_uck_c = Yk_c+n;tangent(y_uc,dy_uc,4); s_uc=spline(x_uc,y_uc,dy_uc,xa_ua,4); average_s = (s_a_result+s_ub+s_uc)/3; average_xa = (xa_a_result+xa_ub+xa_uc)/3; ofs_all<<setw(15)<<avera

18、ge_xa<<setw(15)<<average_s<<endl;/ofs_all.close();else if(n = 4)cout<<n<<endl;for(k_a=0;k_a<4;k_a+)x_uak_a = Xk_a+n-2;y_uak_a = Yk_a+n-2;/ 給 x、y 賦初值。tangent(y_ua,dy_ua,4);ofstream ofs_all("d:spline_all.txt",ios_base:app);/ 寫文件流 if(!ofs_all) return 10000;for

19、(xa_ua = X4;xa_ua <= X5;xa_ua += 0.01)s_ua=spline(x_ua,y_ua,dy_ua,xa_ua,4);xa_a_result = xa_ua;s_a_result = s_ua;/bfor(k_b=0;k_b<4;k_b+)x_ubk_b = Xk_b+n-1;y_ubk_b = Yk_b+n-1;tangent(y_ub,dy_ub,4);xa_ub = xa_ua-0.01;xa_uc = xa_ub;s_ub=spline(x_ub,y_ub,dy_ub,xa_ua,4);/average_s = (s_a_result+s_u

20、b)/ 2;/average_xa = (xa_a_result+xa_ub)/ 2;/cfor(k_c=0;k_c<4;k_c+)x_uck_c = Xk_c+n;y_uck_c = Yk_c+n;tangent(y_uc,dy_uc,4); s_uc=spline(x_uc,y_uc,dy_uc,xa_ua,4); average_s = (s_a_result+s_ub+s_uc)/3;average_xa = (xa_a_result+xa_ub+xa_uc)/3;ofs_all<<setw(15)<<average_xa<<setw(15)&

21、lt;<average_s<<endl;/ofs_all.close();else if(n = 5)cout<<n<<endl;for(k_a=0;k_a<4;k_a+)x_uak_a = Xk_a+n-2;y_uak_a = Yk_a+n-2;/ 給 x、y 賦初值。tangent(y_ua,dy_ua,4);ofstream ofs_all("d:spline_all.txt",ios_base:app);/ 寫文件流 if(!ofs_all) return 10000;for(xa_ua = X5;xa_ua <

22、= X6;xa_ua += 0.01)s_ua=spline(x_ua,y_ua,dy_ua,xa_ua,4);xa_a_result = xa_ua;s_a_result = s_ua;/bfor(k_b=0;k_b<4;k_b+)x_ubk_b = Xk_b+n-1;y_ubk_b = Yk_b+n-1;tangent(y_ub,dy_ub,4);xa_ub = xa_ua-0.01;xa_uc = xa_ub;s_ub=spline(x_ub,y_ub,dy_ub,xa_ua,4);/average_s = (s_a_result+s_ub)/ 2;/average_xa = (x

23、a_a_result+xa_ub)/ 2;/cfor(k_c=0;k_c<4;k_c+)x_uck_c = Xk_c+n;y_uck_c = Yk_c+n;tangent(y_uc,dy_uc,4); s_uc=spline(x_uc,y_uc,dy_uc,xa_ua,4); average_s = (s_a_result+s_ub+s_uc)/3;average_xa = (xa_a_result+xa_ub+xa_uc)/3;ofs_all<<setw(15)<<average_xa<<setw(15)<<average_s<&l

24、t;endl;/ofs_all.close();else if(n = 6)cout<<n<<endl;for(k_a=0;k_a<4;k_a+)x_uak_a = Xk_a+n-2;y_uak_a = Yk_a+n-2;/ 給 x、y 賦初值。tangent(y_ua,dy_ua,4);ofstream ofs_all("d:spline_all.txt",ios_base:app);/ 寫文件流 if(!ofs_all) return 10000;for(xa_ua = X6;xa_ua <= X7;xa_ua += 0.01)s_u

25、a=spline(x_ua,y_ua,dy_ua,xa_ua,4);xa_a_result = xa_ua;s_a_result = s_ua;/bfor(k_b=0;k_b<4;k_b+)x_ubk_b = Xk_b+n-1;y_ubk_b = Yk_b+n-1;tangent(y_ub,dy_ub,4);xa_ub = xa_ua-0.01;xa_uc = xa_ub;s_ub=spline(x_ub,y_ub,dy_ub,xa_ua,4);/average_s = (s_a_result+s_ub)/ 2;/average_xa = (xa_a_result+xa_ub)/ 2;/

26、cfor(k_c=0;k_c<4;k_c+)x_uck_c = Xk_c+n;y_uck_c = Yk_c+n;tangent(y_uc,dy_uc,4); s_uc=spline(x_uc,y_uc,dy_uc,xa_ua,4); average_s = (s_a_result+s_ub+s_uc)/3;average_xa = (xa_a_result+xa_ub+xa_uc)/3;ofs_all<<setw(15)<<average_xa<<setw(15)<<average_s<<endl;/ofs_all.close(

27、);else if(n = 7)cout<<n<<endl;for(k_a=0;k_a<4;k_a+)x_uak_a = Xk_a+n-2;y_uak_a = Yk_a+n-2;/ 給 x、y 賦初值。tangent(y_ua,dy_ua,4);ofstream ofs_all("d:spline_all.txt",ios_base:app);/ 寫文件流 if(!ofs_all) return 10000;for(xa_ua = X7;xa_ua <= X8;xa_ua += 0.01)s_ua=spline(x_ua,y_ua,dy_

28、ua,xa_ua,4);xa_a_result = xa_ua;s_a_result= s_ua;for(k_b=0;k_b<4;k_b+)x_ubk_b = Xk_b+n-1; y_ubk_b = Yk_b+n-1;tangent(y_ub,dy_ub,4);/for(xa_ub = X1;xa_ub <= X2;xa_ub += 0.01)/xa_ub = xa_ua-0.01; s_ub=spline(x_ub,y_ub,dy_ub,xa_ua,4);average_s = (s_a_result+s_ub)/2;average_xa = (xa_a_result+xa_ub

29、)/2;ofs_all<<setw(15)<<average_xa<<setw(15)<<average_s<<endl;/ofs_all.close();else if(n =8)cout<<n<<endl;for(k_a=0;k_a<4;k_a+)x_uak_a = Xk_a+n-2;y_uak_a = Yk_a+n-2;/ 給 x、y 賦初值。ofstream ofs_all("d:spline_all.txt",ios_base:app);if(!ofs_all) return 10000;tangent(