Newtons divided difference interpolation formula implementation using perl language

#-Newtons divided difference interpolation formula implementation using perl language-----

=comment

    -----Input Instruction------

    Enter the number of records

    Now enter the value of x and corresponding y

    Finally enter the value of x for finding y.

=cut

    #-------------main code start---------

   

  print "\Enter how many record you to enter : ";

  $n = <>;

  $k = 0;

  print "Enter the value of x with corresponding y : \n";

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

  {

   $x[$i] = <>; # Input x[]

   $y[$k][$i]= <>; # Input y[]

  }

  print "\n\nEnter X for finding f(x): ";

  $p = <>;

 

  # Mechanism for difference table-----------

  for($i=1;$i<$n;$i++)

  {

    $k=$i;

    for($j=0;$j<($n-$i);$j++)

    {

     $y[$i][$j]=($y[$i-1][$j+1]-$y[$i-1][$j])/($x[$k]-$x[$j]);

     $k++;

    }

  }

  # Print difference table-----------

print "\n\n--------------------------------Difference table for Newtons Divided Formula Formula--------------------------------------\n";

print "------------------------------------------------------------------------------------------------------------------------------------------\n";

print "     X\t\t";

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

    print "Y($i)\t\t";

}

print "\n------------------------------------------------------------------------------------------------------------------------------------------\n";


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

  {

    printf("\n %.4lf\t",$x[$i]);

    for($j=0;$j<($n-$i);$j++)

    {

     printf("           %.3lf             ",$y[$j][$i]);

    }

   print "\n";

  }


  $i=0;

  do

  {

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

    $k=1;

    }

   else{

    $i++;

    }

  }while($k != 1);

 

  $f=$i;

  $sum=0;

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

  {

   $k=$f;

   $temp=1;

   for($j=0;$j<$i;$j++)

   {

    $temp = $temp * ($p - $x[$k]);

    $k++;

   }

    $sum = $sum + ($temp*($y[$i][$f]));

  }

  printf("\n\nFinal answer f(%.2f) = %f\n\n",$p,$sum);

  print "-------------THANK YOU------------\n";

 

=comment

--------------Input example-----------

    5

    0 1

    1 3

    3 49

    4 129

    7 813

    .3

    Ans : (0.30) = 1.831000

=cut