Curve Fitting

► Algorithm Of Different Numerical Curve Fitting Methods Including
line fitting and parabola fitting:-


1. Line Fitting

Linefitting(a)
{
Here a[] is a structure array to hold the points of the coordinate axes.
  
  for(i=0 to i<n0)
    {
    xi=xi+a[i].x
    yi=yi+a[i].y
    xi2=xi2+(a[i].x)*(a[i].x)
    xyi=xyi+(a[i].x)*(a[i].y)
    }
      b[0][0]=xi2
      b[0][1]=xi
      b[0][2]=xyi
      b[1][0]=xi
      b[1][1]=n0
      b[1][2]=yi        //Creates the required coordinate matrix coordinate matrix
      Gauss(b,2) //It calls to the Gauss function to solve the coordinate matrix                 
  }
   

2.Parabola fitting

parabolafit(a)
{
Here a[] is a structure array to hold the points of the coordinate axes.
And b[][] is the required co-ordinate matrix to solve which is to be calculated
by this algorithm.

yi=xyi=x2yi=0
for(i=0 to 4)
 xi[i]=0


for(i=0 to n0)
 {
 xi[0]=xi[0]+a[i].x
 yi=yi+a[i].y
 xi[3]=xi[3]+(a[i].x)*(a[i].x)*(a[i].x)*(a[i].x)
 xi[2]=xi[2]+(a[i].x)*(a[i].x)*(a[i].x)
 xi[1]=xi[1]+(a[i].x)*(a[i].x)
 xyi=xyi+(a[i].x)*(a[i].y)
 x2yi=x2yi+(a[i].x)*(a[i].x)*(a[i].y)
 }

for(i=0 to 3)
 for(j=0 to 4)
  {                                       
  if(j=3)
   { 
   if(i≠0)
    b[i][j]=(i=1)?xyi:yi   //adjusting value of the
                                                         b[][] matrix
   else
    b[i][j]=x2yi
   continue
   }
  else if(j=2 && i=2)
   {
   b[i][j]=n0
   continue
   }
  b[i][j]=xi[(4-i-j)-1]      //sending the b[][] matrix to gauss elimination
                                            fn for solving it. 

  }

          gauss(b,3)

}
 




C Program For Curve Fitting

Source Code:

#include<stdio.h>
#include<conio.h>


struct coordinate
 {
 int x,y;
 };

int n0,i;
float x[5];

void gauss(float **a,int n)
{
int row,col,k,j;
float m,sum;


for(k=0;k<n-1;k++)

 {
 for(row=k+1;row<n;row++)
  {
  m=a[row][k]/a[k][k];
  for(col=0;col<=n;col++)
   {
   a[row][col]=a[row][col]-m*a[k][col];
   }
  }
 }

x[n-1]=a[n-1][n]/a[n-1][n-1];

for(i=n-2;i>=0;i--)
 {
 sum=0;
 for(j=i+1;j<n;j++)
  {
  sum=sum+a[i][j]*x[j];
  }
 x[i]=(a[i][n]-sum)/a[i][i];
 }
if(n==2)
 printf("\n\nRequired straight line:-\n\ty=(%g)x+(%g)",x[0],x[1]);
else
 printf("\n\nRequired Parabola:-\n\ty=(%g)x^2+(%g)x+(%g)",x[0],x[1],x[2]);

}

void linef(struct coordinate *a)
{
float **b,xi,xi2,yi,xyi;
int j;

xi=xi2=yi=xyi=0;

b=(float **)malloc(sizeof(float *)*2);

for(i=0;i<2;i++)
 {
 b[i]=(float *)malloc(sizeof(float )*(3));
 }

for(i=0;i<n0;i++)
 {
 xi=xi+a[i].x;
 yi=yi+a[i].y;
 xi2=xi2+(a[i].x)*(a[i].x);
 xyi=xyi+(a[i].x)*(a[i].y);
 }

b[0][0]=xi2;
b[0][1]=xi;
b[0][2]=xyi;
b[1][0]=xi;
b[1][1]=n0;
b[1][2]=yi;

printf("\nRequired matrix to solve ");
for(i=0;i<2;i++)
 {
 printf("\n");
 for(j=0;j<3;j++)
  printf("\t%g",b[i][j]);
 }

gauss(b,2);
}

void parabola(struct coordinate *a)
{
float **b,xi[4],yi,xyi,x2yi;
int j;

yi=xyi=x2yi=0;
for(i=0;i<4;i++)
 xi[i]=0;

b=(float **)malloc(sizeof(float *)*3);

for(i=0;i<3;i++)
 {
 b[i]=(float *)malloc(sizeof(float )*(4));
 }

for(i=0;i<n0;i++)
 {
 xi[0]=xi[0]+a[i].x;
 yi=yi+a[i].y;
 xi[3]=xi[3]+(a[i].x)*(a[i].x)*(a[i].x)*(a[i].x);
 xi[2]=xi[2]+(a[i].x)*(a[i].x)*(a[i].x);
 xi[1]=xi[1]+(a[i].x)*(a[i].x);
 xyi=xyi+(a[i].x)*(a[i].y);
 x2yi=x2yi+(a[i].x)*(a[i].x)*(a[i].y);
 }

for(i=0;i<3;i++)
 for(j=0;j<4;j++)
  {
  if(j==3)
   {
   if(i!=0)
    b[i][j]=(i==1)?xyi:yi;
   else
    b[i][j]=x2yi;
   continue;
   }
  else if(j==2 && i==2)
   {
   b[i][j]=n0;
   continue;
   }
  b[i][j]=xi[(4-i-j)-1];

  }

printf("\nRequired matrix to solve ");
for(i=0;i<3;i++)
 {
 printf("\n");
 for(j=0;j<4;j++)
  printf("\t%g",b[i][j]);
 }
gauss(b,3);

}

void main()
{
int ch;
struct coordinate *a;

clrscr();
printf("\nWhich type of curve fitting is to be done.?\n1.Line Fitting\n2.Parabola Fitting
\n\nYours choice ");
scanf("%d",&ch);
printf("\nEnter the no. of co-ordinates you will insert ");
scanf("%d",&n0);

a=(struct coordinate *)malloc(sizeof(struct coordinate)*n0);

for(i=0;i<n0;i++)
 {
 printf("Enter co-ordinate %d ",i+1);
 scanf("%d %d",&a[i].x,&a[i].y);
 }

switch(ch)
 {
 case 1: linef(a);
  break;
 case 2: parabola(a);
  break;
 default:printf("\nThis wasn't a valid choice.. :(")
 }

getch();
}