用C語言實現(xiàn)的曲線擬合的最小二乘法

11實驗名稱：曲線擬合的最小二乘法實驗?zāi)康牧私馇€擬合的最小二乘法實驗類型設(shè)計型實驗環(huán)境WindowsXPTC實驗內(nèi)容相關(guān)知識：已知C[a,b]中函數(shù)f(x)的一組實驗數(shù)據(jù)(x,y)(i=0,l,…,m),其中y=f(x)。iiii設(shè)9?(x)(j二0,1,…,n;n<m)是C[a,b]上線性無關(guān)函數(shù)族。在=span{^(x),p(x),…,p(x)}中j01n找函數(shù)f(x)曲線擬合的最小二乘解S*(x)=￡a9(x)，其法方程(組)為:jjj=0￡(p,p)a=d(k=0,1,…,n)kjjkj=o其中,x)9(x)9(x)其中,ijikii=0k=0,l,…，n瓦x)f(x)9(x)三dk=0,l,…，nTOC\o"1-5"\h\ziikiki=0特別是，求函數(shù)f(x)曲線擬合的線性最小二乘解S*(x)=ax+b的計算公式為:(區(qū)x2)(區(qū)y)-(區(qū)x)(￡xy)iiiiib=i=0(m+1)區(qū)x2-(￡x)2iii=0i=0(m(m+1)區(qū)xyii-(區(qū)x)(￡y)ii-(m+1)—x-(m+1)—x)2ix2-(遲i數(shù)據(jù)結(jié)構(gòu)：兩個一維數(shù)組或一個二維數(shù)組算法設(shè)計：(略)實驗用例：已知函數(shù)y=f(x)的一張表:x0102030405060708090y6867.166.465.664.661.861.060.860.460試驗要求：利用曲線擬合的線性最小二乘法求被逼近函數(shù)f(x)在點x=55處的近似值，并畫出實驗數(shù)據(jù)和直線。編寫代碼：#include<stdio.h>#include<stdlib.h>#include<graphics.h>doubleqiuhel(doublea[10][2],intp){inti;doubley;y=0；for(i=0;i<10;i++)y=y+a[i][p];returny;}doubleqiuhe2(doublea[10][2],intp){inti;doubley=0;for(i=0;i<10;i++)y=y+a[i][0]*a[i][p];returny;}doublenihe(doublea[10][2],doublex){doublea1,b,y;a1=(10*qiuhe2(a,l)—qiuhel(a,0)*qiuhel(a,l))/(l0*qiuhe2(a,0)—qiuhel(a,0)*qiuhe1(a,0));b=(qiuhe2(a,0)*qiuhel(a,l)-qiuhel(a,0)*qiuhe2(a,l))/(lO*qiuhe2(a,0)-qiuhel(a,0)*qiuhel(a,0));y=a1*x+b;returny;}intmain(){doublea[10][2]={0,6&10,67.1,20,66.4,30,65.6,40,64.6,50,61.&60,61.0,70,60.8,80,60.4,90,60};doublex,x1,q=1;charc[12];inti;longn;intarw[6]={515,235,520,240,515,245};intarw1[6]={315,45,320,40,325,45};intgdriver=IBM8514;intgmode=IBM8514HI;initgraph(&gdriver,&gmode,"c:\\TC20\\BGI");cleardevice();printf("inputx:\n");scanf("%lf"，&x);printf("%f\n",nihe(a,x));n=nihe(a,x)*1000000+1;c[0]='y';c[1]='=';c[4]='.';for(i=10;i>1;i—){if(i!=4){c[i]=n%10+48;n二n/10;}c[ll]='\O';x1=x;setbkcolor(7);setcolor(14);setlinestyle(0,0,3);drawpoly(3,arw);drawpoly(3,arwl);line(120,240,520,240);line(320,40,320,440);x=0;setcolor(2);setlinestyle(O,O,l);line((0+320),(int)(240-nihe(a,0)*q),(90+320),(int)(240-nihe(a,90)*q));setcolor(3);outtextxy(320,30,"Y");outtextxy(310,245,"0");outtextxy(525,240,"X");outtextxy((xl+330),((240-nihe(a,xl))-10),c);settextstyle(4,0,4);outtextxy(450,400,"Nihe...");for(i=0;i<=9;i++)putpixel((a[i][0]+320),(240-a[i][l]*q),ll);setcolor(4);setlinestyle(l,0,l);line((xl+320),((240-nihe(a,x1)*q)-