Divided Difference

#include<stdio.h>
#include<malloc.h>
#include<stdlib.h>
void differenceTable(double **A,double **L,int ROW);
double result(double **A,double **L,double x,int ROW);
double factorial(int n);
FILE *fp;
int main(int argc, char *argv[])
{
double **A,*b,*xn,*xnplus1,*p,temp,x,**L,**U,lambda,error,t1=0.0;
int ROW,i,j,k=0,t=1,m=1,bo=1;
char ch;
if(argc==1)
    {
    printf("\n Enter the number of values:");
    scanf("%d",&ROW);
    printf("\n Enter the value at which value has to be aprroximated:");
    scanf("%lf",&x);
    A=(double **)malloc((ROW+1)*sizeof(double*));
    L=(double **)malloc((ROW+1)*sizeof(double*));
    U=(double **)malloc((ROW+1)*sizeof(double*));
    for(i=0;i<=ROW;i++)
        {
        A[i]=(double *)malloc((ROW+1)*sizeof(double));
        L[i]=(double *)malloc((ROW+1)*sizeof(double));
        U[i]=(double *)malloc((ROW+1)*sizeof(double));
        }
    b=(double *)malloc((ROW+1)*sizeof(double));
    p=(double *)malloc((ROW+1)*sizeof(double));
    xn=(double *)malloc((ROW+1)*sizeof(double));
    xnplus1=(double *)malloc((ROW+1)*sizeof(double));
    for(i=1;i<=ROW;i++)
        {
        printf("\n Enter the value of X[%d]:",i);
        scanf("%lf",&A[i][1]);
        }
    for(i=1;i<=ROW;i++)
        {
        printf("\n Enter the value of Y[%d]:",i);
        scanf("%lf",&A[i][2]);
        }
       
    }
else if (argc==2)
    {
    fp=fopen(argv[1],"r");
        if(fp==NULL)
            {
            printf("\n File not found, program will terminate:");
            exit(0);
            }
    fscanf(fp,"%d",&ROW);
    fscanf(fp,"%lf",&x);
    A=(double **)malloc((ROW+1)*sizeof(double*));
    L=(double **)malloc((ROW+1)*sizeof(double*));
    U=(double **)malloc((ROW+1)*sizeof(double*));
    for(i=0;i<=ROW;i++)
        {
        A[i]=(double *)malloc((ROW+1)*sizeof(double));
        L[i]=(double *)malloc((ROW+1)*sizeof(double));
        U[i]=(double *)malloc((ROW+1)*sizeof(double));
        }
    b=(double *)malloc((ROW+1)*sizeof(double));
    p=(double *)malloc((ROW+1)*sizeof(double));
    xn=(double *)malloc((ROW+1)*sizeof(double));
    xnplus1=(double *)malloc((ROW+1)*sizeof(double));
   
    while(!feof(fp))
    {
    for(i=1;i<=ROW;i++)
    {
        for(j=1;j<=2;j++)
        {
        fscanf(fp,"%lf ",&A[i][j]);
        }
       
    }
    }
    fclose(fp);
    }
    else
    {
    printf("\n Invalid Arguments,program will terminate:\n");
    exit(0);
    }
printf("\n         X          Y");
printf("\n------------------------------------------------------------------\n");
for(i=1;i<=ROW;i++)
    {
    for(j=1;j<=2;j++)
        {
       
        U[i][j]=A[i][j];
        printf("   %+lf",U[i][j]);
        }
    printf("\n");
    }
for(i=1;i<=ROW-1;i++)
    {
    for(j=ROW-i,t=1;j>=1;j--,t++)
        {
        L[t][i]=(U[t+1][2]-U[t][2])/(A[t+1+k][1]-A[t][1]);
        //printf("\n (%d,%d)------>%lf",t-1,t+1-1+k,L[t][i]);
        }
    for(t=1;t<=ROW-i;t++)
        U[t][2]=L[t][i];
    //printf("\n>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>");
    k++;
    }   
differenceTable(A,L,ROW);
printf("\n Value at %+lf by Divied Difference Interpolation formula is %+lf\n",x,result(A,L,x,ROW));
return 0;
}
double result(double **A,double **L,double x,int ROW)
{
int i,j;
double value=0,tmp=1.0;
for(i=0;i<ROW;i++)
{
    if(i==0)
        value +=A[1][2];
    else
    {
    for(j=1;j<=i;j++)
        tmp=tmp*(x-A[j][1]);
    tmp = tmp/factorial(i);
    tmp = tmp*L[1][i];
    value +=tmp;
    }
    if(i==0)
    printf("%2.2lf ",A[1][2]);
    else
    printf("%2.2lf ",L[1][i]);
    tmp=1.0;
}
return value;
}
double factorial(int n)
{
 if(n<=1)
     return 1;
 else
     return n*factorial(n-1);
}
void differenceTable(double **A,double **L,int ROW)
{
int **position,*ap,j,m,i;
position=(int **)malloc((ROW+1)*sizeof(int*));
ap=(int *)malloc((ROW+1)*sizeof(int));
for(i=0;i<=ROW;i++)
    position[i]=(int *)malloc((ROW+1)*sizeof(int));
int an,tmp;
tmp=ROW;
for(i=1;i<=ROW;i++)
    {
    an=1+(i-1)*2;
    ap[i]=an;
    for(j=1;j<=tmp;j++)
        {
        position[i][j]=an+(j-1)*4;
        }
    tmp--;
    }
tmp=ROW;
tmp=ROW+(ROW-1)*3;
int *match,tmp1,l,*pos,flag,z,k;
match=(int *)malloc((ROW+1)*sizeof(int));
pos=(int *)malloc((ROW+1)*sizeof(int));
for(i=0;i<=ROW;i++)
    {
    match[i]=0;
    pos[i]=0;
    }

printf("\n-------------------------------------Divided Difference Table----------------------------------\n");
printf("\n X        Y");
for(i=1;i<=ROW-1;i++)
    printf("                D^%d",i);
printf("\n----------------------------------------------------------------------------------------------\n");
for(i=1;i<=tmp;i++)
{
tmp1=ROW;

    for(l=1;l<=ROW;l++)
    {
    flag=0;
    for(m=1;m<=tmp1;m++)
        {
        if(i==position[l][m])
            {
            flag=1;
            match[l]=1;
            pos[m]=position[l][m];
            break;
            }
        } //inner for
    if(flag==1)
    {
    for(k=1;k<=ROW;k++)
        {
    if(match[k]==0)
    {
        printf("");
    }
    else
        {
        if(k==1)
            //printf("(%d,%d)+(%d,%d)|%d",(position[l][m]/4)+1,k,(position[l][m]/4)+1,k+1,i);
            printf("%+2.4lf\t %+2.4lf",A[(position[l][m]/4)+1][k],A[(position[l][m]/4)+1][k+1]);
        else
            {
            z=(position[l][m]-ap[k])/4+1;
            //printf("\t\t(%d,%d)|%d",z,k-1,i);
            printf("\t\t\t%+lf",L[z][k-1]);
            }
       
        }
        } //end of k-loop
           
    } //end of flag==1
   
    else
        {printf(" ");}
    tmp1--;
    for(k=0;k<=ROW;k++)
    {
    pos[k]=0;
    match[k]=0;
    }
    }
   
printf("\n");
}
printf("\n----------------------------------------------------------------------------------------------\n");
}