Curvefitting

Source Code:

/*      The following C program implements Curve Fitting by the Method of Least

Squares for some given tabular values. The tabular values (abscissa and

ordinate) are read as input.         */

 

#include<stdio.h>

#include<conio.h>

#include<math.h>

#define max 10

#define minvalue 0.0005

void main()

{

 int degree, count, i,j,k, noofequations, temp;

 float xtable[max][max], ytable[max][max], augmentedmatrix[max][max], temporary, r, solutions[max];

 printf("\n How many points are to be entered:-");

 scanf("%d",&count);

 printf("\n Enter x & y values in tabular format:-\n");

 for(i=0; i<count; i++)

  for(j=0; j<=1; j++)

            if(j%2==0)

             scanf("%f",&xtable[i][1]);

   else

             scanf("%f",&ytable[i][0]);

 printf("\n Degree of polynomial that is to be fitted:-  ");

 scanf("%d",&degree);

/* Constructing table with powers of x */

 for(i=0; i<count; i++)

  for(j=2; j<=2*degree; j++)

   xtable[i][j]=pow(xtable[i][1],j);

/* Constructing table with combined terms of x and y */

 for(i=0; i<count; i++)

   

for(j=1; j<=degree; j++)

   ytable[i][j]=ytable[i][0]*xtable[i][j];

/* Calculating sum */

 for(j=0;j<=2*degree;j++)

 {

  xtable[count][j]=ytable[count][j]=0;

  for(i=0;i<count;i++)

  {

  if(j!=0)

            xtable[count][j]+=xtable[i][j];

  if(j<=degree)

   ytable[count][j]+=ytable[i][j];

  }

 }

/* printing tables */

 printf("\n\nTABLE WITH POWERS OF X \n");

 for(i=0;i<count;i++)

 {

  printf("\n ");

  for(j=1;j<=2*degree;j++)

   printf("%.3f  ",xtable[i][j]);

 }

 printf("\n\n        TABLE WITH X-Y TERMS \n");

 for(i=0;i<count;i++)

 {

  printf("\n ");

  for(j=0;j<=degree;j++)

   printf("%.3f  ",ytable[i][j]);

 }

 /* Using GAUSS-JORDAN METHOD OF ELIMINATION

      to find solutions of simultaneous equations */

 noofequations=degree+1;

 xtable[count][0]=count;

/* storing augmented co-efficient matrix as a matrix of dimension

   (noofequations)x(noofequations+1) in 2D array */

 for(i=0;i<noofequations;i++)

 {

  for(j=i,k=0;j<i+noofequations;j++)

   augmentedmatrix[i][k++]=xtable[count][j];

  augmentedmatrix[i][k]=ytable[count][i];

 }

 /* converting augmented matrix into upper triangular form */

 for(j=0; j<noofequations; j++)

 {

  temp=j;

 /* finding maximum coefficient of X_j in last (noofequations-j) equations */

  for(i=j+1; i<noofequations; i++)

            if(augmentedmatrix[i][j]>augmentedmatrix[temp][j])

                        temp=i;

  if(fabs(augmentedmatrix[temp][j])<minvalue)

             {

              printf("\n Coefficients are too small to deal with !!!");

              goto end;

             }

 /* swapping row which has maximum coefficient of X_j */

  if(temp!=j)

            for(k=0; k<=noofequations; k++)

            {

            temporary=augmentedmatrix[j][k] ;

            augmentedmatrix[j][k]=augmentedmatrix[temp][k] ;

            augmentedmatrix[temp][k]=temporary ;

            }

/* performing row operations to form required diagonal matrix */

  for(i=0; i<noofequations; i++)

            if(i!=j)

            {

            r=augmentedmatrix[i][j];

for(k=0; k<=noofequations; k++)

              augmentedmatrix[i][k]-=(augmentedmatrix[j][k]/augmentedmatrix[j][j])*r ;

            }

 }

  /* storing solutions */

 for(i=0;i<noofequations; i++)

  solutions[i]=augmentedmatrix[i][noofequations]/augmentedmatrix[i][i] ;

 /* printing solutions */

 printf("\n\n\n Polynomial to be fitted is :- \n");

 for(i=0; i<noofequations; i++)

  if(i>1)

            printf("(%f)*x^%d + ",solutions[i],i);

  else if(i==1)

            printf("(%f)*x + ",solutions[1]);

  else

            printf(" %f + ",solutions[0]);

 end: getch() ;

}

Output:

Fitting the following tabular values by a 2^nd degree polynomial:

x	-2	-1	0	1	2
y	-9	-4	1	6	10