#include<stdio.h>

#include<conio.h>

#include<math.h>

void main(){

clrscr();

char choice='y';

int n,i,j,k;

float h[10],a,b,c,d,sum,s[10]={0},x[10],F[10],f[10],p,m[10][10]={0},temp;

printf("No of samples? ");

scanf("%d",&n);

printf("\nEnter all sample points: ");

for(i=0;i<n;i++)

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

for(i=n-1;i>0;i--){

F[i]=(f[i]-f[i-1])/(x[i]-x[i-1]);

h[i-1]=x[i]-x[i-1];

}

//*********** formation of h, s , f matrix **************//

for(i=1;i<n-1;i++){

m[i][i]=2*(h[i-1]+h[i]);

if(i!=1){

m[i][i-1]=h[i-1];

m[i-1][i]=h[i-1];

}

m[i][n-1]=6*(F[i+1]-F[i]);

}

//*********** forward elimination **************//

for(i=1;i<n-2;i++){

temp=(m[i+1][i]/m[i][i]);

for(j=1;j<=n-1;j++)

m[i+1][j]-=temp*m[i][j];

}

//*********** backward substitution *********//

for(i=n-2;i>0;i--){

sum=0;

for(j=i;j<=n-2;j++)

sum+=m[i][j]*s[j];

s[i]=(m[i][n-1]-sum)/m[i][i];

}

while(choice=='y'){

printf("\nEnter x : ");

scanf("%f",&p);

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

if(x[i]<=p&&p<=x[i+1]){

a=(s[i+1]-s[i])/(6*h[i]);

b=s[i]/2;

c=(f[i+1]-f[i])/h[i]-(2*h[i]*s[i]+s[i+1]*h[i])/6;

d=f[i];

sum=a*pow((p-x[i]),3)+b*pow((p-x[i]),2)+c*(p-x[i])+d;

}

printf("\nCoefficients of sub intervals are : %f\n%f\n%f\n%f",a,b,c,d);

printf("\nFunctional value is: %f",sum);

printf("\nContinue (y/n) ? ");

scanf("%c",&choice);

}

getch();

}

**Sample Output:**

No of samples? 5

Enter all sample points: 1 2

2 3

3 4

4 5

5 6

Enter x : 3.5

Coefficients of sub intervals are : 0.000000

0.000000

1.000000

4.000000

Functional value is: 4.500000

Continue (y/n) ?

©Dixit Bhatta 2013

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ReplyDeletewarning: unused variable ‘k’ :P

ReplyDeleteYes, when writing complex programs you can often end up with unused variables. You can remove 'k' from declaration to see how it behaves. I wrote this program long ago, so can't really remember, but if the program still works fine, there is no harm in removing 'k'.

DeleteHi, I am trying to figure out what all your variables meaning, can you help me to understand about your code, I need to know the meaning of matrix, thanks!!!

ReplyDeleteThe arrays are used to hold values of f and f(x), and intermediate values. The matrix 'm' in particular is used for holding values during elimination and substitution steps, which I think is clearly labelled in the code. You will need to revisit the theory behind Cubic-Spline interpolation to fully understand.

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