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Program to estimate value of First Derivative of the function at the given points from the given data using Backward Difference Formula , Forward diff

Posted By: Easy Tutor     Category: C++ Programming     Views: 2890

A C++ Program to estimate the value of First Derivative of the function at the given points from the given data using Backward Difference Formula and Forward Difference Formula of Order One.

Code for Program to estimate value of First Derivative of the function at the given points from the given data using Backward Difference Formula , Forward diff in C++ Programming

 # include <iostream.h>
 # include   <stdlib.h>
 # include   <string.h>
 # include    <stdio.h>
 # include    <conio.h>
 # include    <ctype.h>
 # include     <math.h>

 constint max_size=13;

 int n=0;
 int top=-1;
 int choice=0;

 longdouble h=0;
 longdouble x0=0;

 longdouble xn[max_size]={0};
 longdouble fx[max_size]={0};

 char Fx[100]={NULL};
 char Dfx[100]={NULL};
 char Stack[30][30]={NULL};
 char Postfix_expression[2][30][30]={NULL};

 void push(constchar *);
 void convert_ie_to_pe(constchar *,constint);

 constchar* pop( );
 constlongdouble evaluate_postfix_expression(constlongdouble,constint);

 void show_screen( );
 void clear_screen( );
 void get_input( );
 void estimate_dfx( );

 constint get_index(constlongdouble);

 int main( )
    {
       clrscr( );
       textmode(C4350);

       show_screen( );
       get_input( );
       estimate_dfx( );

       return 0;
     }


 /*************************************************************************///--------------------------  show_screen( )  ---------------------------///*************************************************************************/void show_screen( )
    {
       cprintf("\n********************************************************************************");
       cprintf("*************************-                             -************************");
       cprintf("*------------------------- ");

       textbackground(1);
       cprintf(" Numerical Differentiation ");
       textbackground(8);

       cprintf(" ------------------------*");
       cprintf("*-***********************-                             -**********************-*");
       cprintf("*-****************************************************************************-*");

       for(int count=0;count<42;count++)
      cprintf("*-*                                                                          *-*");

       gotoxy(1,46);
       cprintf("*-****************************************************************************-*");
       cprintf("*------------------------------------------------------------------------------*");
       cprintf("********************************************************************************");

       gotoxy(1,2);
    }

 /*************************************************************************///-------------------------  clear_screen( )  ---------------------------///*************************************************************************/void clear_screen( )
    {
       for(int count=0;count<37;count++)
      {
         gotoxy(5,8+count);
         cout<<"                                                                        ";
      }

       gotoxy(1,2);
    }

 /*************************************************************************///--------------------------  push(const char*)  ------------------------///*************************************************************************/void push(constchar* Operand)
    {
       if(top==(max_size-1))
      {
         cout<<"Error : Stack is full."<<endl;
         cout<<"\n        Press any key to exit.";

         getch( );
         exit(0);
      }

       else
      {
         top++;
         strcpy(Stack[top],Operand);
      }
    }

 /*************************************************************************///------------------------------  pop( )  -------------------------------///*************************************************************************/constchar* pop( )
    {
       char Operand[40]={NULL};

       if(top==-1)
      {
         cout<<"Error : Stack is empty."<<endl;
         cout<<"\n        Press any key to exit.";

         getch( );
         exit(0);
      }

       else
      {
         strcpy(Operand,Stack[top]);
         strset(Stack[top],NULL);
         top--;
      }

       return Operand;
    }

 /*************************************************************************///----------------  convert_ie_to_pe(const char*,const int)  ------------///*************************************************************************/void convert_ie_to_pe(constchar* Expression,constint index)
    {
       char Infix_expression[100]={NULL};
       char Symbol_scanned[30]={NULL};

       push("(");
       strcpy(Infix_expression,Expression);
       strcat(Infix_expression,"+0)");

       int flag=0;
       int count_1=0;
       int count_2=0;
       int equation_length=strlen(Infix_expression);

       if(Infix_expression[0]=='(')
      flag=1;

       do
      {
         strset(Symbol_scanned,NULL);

         if(flag==0)
        {
           int count_3=0;

           do
              {
             Symbol_scanned[count_3]=Infix_expression[count_1];

             count_1++;
             count_3++;
              }
           while(count_1<=equation_length &&
               Infix_expression[count_1]!='(' &&
                  Infix_expression[count_1]!='+' &&
                 Infix_expression[count_1]!='-' &&
                    Infix_expression[count_1]!='*' &&
                       Infix_expression[count_1]!='/' &&
                      Infix_expression[count_1]!='^' &&
                         Infix_expression[count_1]!=')');


           flag=1;
        }

         elseif(flag==1)
        {
           Symbol_scanned[0]=Infix_expression[count_1];

           count_1++;

           if(Infix_expression[count_1]!='(' &&
             Infix_expression[count_1]!='^' &&
                Infix_expression[count_1]!='*' &&
                   Infix_expression[count_1]!='/' &&
                  Infix_expression[count_1]!='+' &&
                     Infix_expression[count_1]!='-' &&
                    Infix_expression[count_1]!=')')
              flag=0;

           if(Infix_expression[count_1-1]=='(' &&
               (Infix_expression[count_1]=='-' ||
                 Infix_expression[count_1]=='+'))
              flag=0;
        }

         if(strcmp(Symbol_scanned,"(")==0)
        push("(");

         elseif(strcmp(Symbol_scanned,")")==0)
        {
           while(strcmp(Stack[top],"(")!=0)
              {
             strcpy(Postfix_expression[index][count_2],pop( ));

             count_2++;
              }

           pop( );
        }

         elseif(strcmp(Symbol_scanned,"^")==0 ||
               strcmp(Symbol_scanned,"+")==0 ||
                 strcmp(Symbol_scanned,"-")==0 ||
                       strcmp(Symbol_scanned,"*")==0 ||
                         strcmp(Symbol_scanned,"/")==0)
        {
           if(strcmp(Symbol_scanned,"^")==0)
              {  }

           elseif(strcmp(Symbol_scanned,"*")==0 ||
                          strcmp(Symbol_scanned,"/")==0)
              {
             while(strcmp(Stack[top],"^")==0 ||
                     strcmp(Stack[top],"*")==0 ||
                       strcmp(Stack[top],"/")==0)
                {
                   strcpy(Postfix_expression[index][count_2],pop( ));

                   count_2++;
                }
              }

           elseif(strcmp(Symbol_scanned,"+")==0 ||
                    strcmp(Symbol_scanned,"-")==0)
              {
             while(strcmp(Stack[top],"(")!=0)
                {
                   strcpy(Postfix_expression[index][count_2],pop( ));

                   count_2++;
                }
              }

           push(Symbol_scanned);
        }

         else
        {
           strcat(Postfix_expression[index][count_2],Symbol_scanned);

           count_2++;
        }
      }
       while(strcmp(Stack[top],NULL)!=0);

       strcat(Postfix_expression[index][count_2],"=");
       count_2++;
    }

 /*************************************************************************///-----  evaluate_postfix_expression(const long double,const int)  ------///*************************************************************************/constlongdouble evaluate_postfix_expression(
                    constlongdouble x,constint index)
    {
       longdouble function_value=0;

       int count_1=-1;

       char Symbol_scanned[30]={NULL};

       do
      {
         count_1++;

         strcpy(Symbol_scanned,Postfix_expression[index][count_1]);

         if(strcmp(Symbol_scanned,"^")==0 ||
              strcmp(Symbol_scanned,"*")==0 ||
                strcmp(Symbol_scanned,"/")==0 ||
                  strcmp(Symbol_scanned,"+")==0 ||
                    strcmp(Symbol_scanned,"-")==0)

        {
           char Result[30]={NULL};
           char Operand[2][30]={NULL};

           strcpy(Operand[0],pop( ));
           strcpy(Operand[1],pop( ));

           longdouble operand[2]={0};
           longdouble result=0;

           char *endptr;

           for(int count_2=0;count_2<2;count_2++)
              {
             int flag=0;

             if(Operand[count_2][0]=='-')
                {
                   int length=strlen(Operand[count_2]);

                   for(int count_3=0;count_3<(length-1);count_3++)
                  Operand[count_2][count_3]=Operand[count_2][(count_3+1)];

                   Operand[count_2][count_3]=NULL;

                   flag=1;
                }

             if(strcmp(Operand[count_2],"x")==0)
                operand[count_2]=x;

             elseif(strcmp(Operand[count_2],"e")==0)
                operand[count_2]=2.718282;

             elseif(strcmp(Operand[count_2],"sinx")==0)
                operand[count_2]=sinl(x);

             elseif(strcmp(Operand[count_2],"cosx")==0)
                operand[count_2]=cosl(x);

             elseif(strcmp(Operand[count_2],"tanx")==0)
                operand[count_2]=tanl(x);

             elseif(strcmp(Operand[count_2],"lnx")==0)
                operand[count_2]=logl(x);

             elseif(strcmp(Operand[count_2],"logx")==0)
                operand[count_2]=log10l(x);

             else
                operand[count_2]=strtod(Operand[count_2],&endptr);

             if(flag)
                operand[count_2]*=-1;
              }

           switch(Symbol_scanned[0])
              {
             case'^' : result=powl(operand[1],operand[0]);
                    break;

             case'*' : result=operand[1]*operand[0];
                    break;

             case'/' : result=operand[1]/operand[0];
                    break;

             case'+' : result=operand[1]+operand[0];
                    break;

             case'-' : result=operand[1]-operand[0];
                    break;
              }

           gcvt(result,25,Result);

           push(Result);
        }

         elseif(strcmp(Symbol_scanned,"=")!=0)
        push(Symbol_scanned);
      }
       while(strcmp(Symbol_scanned,"=")!=0);

       char Function_value[30]={NULL};
       char *endptr;

       strcpy(Function_value,pop( ));
       function_value=strtod(Function_value,&endptr);

       return function_value;
    }

 /*************************************************************************///-----------------------------  get_input( )  --------------------------///*************************************************************************/void get_input( )
    {
       do
      {
         clear_screen( );

         gotoxy(6,9);
         cout<<"Number of Distinct Data Points :";

         gotoxy(6,10);
         cout<<"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ";

         gotoxy(27,13);
         cout<<"[ min. n = 2  |  max. n = 12 ]";

         gotoxy(6,12);
         cout<<"Enter the max. number of distinct data points = n = ";

         cin>>n;

         if(n<2 || n>12)
        {
           gotoxy(12,25);
           cout<<"Error : Wrong Input. Press <Esc> to exit or any other key";

           gotoxy(12,26);
           cout<<"        to try again.";

           n=int(getche( ));

           if(n==27)
              exit(0);
        }
      }
       while(n<2 || n>12);

       gotoxy(6,16);
       cout<<"Enter the value of x0 = ";

       cin>>x0;

       gotoxy(6,18);
       cout<<"Enter the value of h = ";

       cin>>h;

       gotoxy(6,24);
       cout<<"Input Mode :";

       gotoxy(6,25);
       cout<<"ÍÍÍÍÍÍÍÍÍÍÍÍ";

       gotoxy(8,28);
       cout<<"Press : ";

       gotoxy(10,30);
       cout<<"- 'Y' or <Enter> to enter function";

       gotoxy(10,32);
       cout<<"- 'N' or <Any other key> to enter values of the function";

       gotoxy(8,35);
       cout<<"Enter your choice : ";

       char Choice=NULL;

       Choice=getch( );

       if(Choice=='y' || Choice=='Y' || int(Choice)==13)
      {
         choice=1;

         gotoxy(28,35);
         cout<<"Y";
      }

       else
      {
         gotoxy(28,35);
         cout<<"N";
      }

       gotoxy(25,43);
       cout<<"Press any key to continue...";

       getch( );

       if(choice)
      {
         clear_screen( );

         gotoxy(6,11);
         cout<<"Non-Linear Function :";

         gotoxy(6,12);
         cout<<"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ";

         gotoxy(6,37);
         cout<<"Note : Write the function with proper Braces ( ) e.g; 2x+3 as (2*x)+3";

         gotoxy(6,40);
         cout<<"Available Operators  :  ^ (raised to power) , * , / , + , -";

         gotoxy(6,42);
         cout<<"Available Operands   :  x , e , sinx , cosx , tanx , lnx , logx ,";

         gotoxy(6,44);
         cout<<"                        n = any number";

         gotoxy(6,14);
         cout<<"Enter the Function : f(x) = ";

         cin>>Fx;

         gotoxy(6,17);
         cout<<"Enter the Differential Function : f'(x) = ";

         cin>>Dfx;

         convert_ie_to_pe(Fx,0);
         convert_ie_to_pe(Dfx,1);
      }

       clear_screen( );

       gotoxy(6,9);
       cout<<"Data Points & Values of Function :";

       gotoxy(6,10);
       cout<<"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ";

       gotoxy(25,12);
       cout<<"ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿";

       gotoxy(25,13);
       cout<<"³       x       ³     f(x)      ³";

       gotoxy(25,14);
       cout<<"ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÅÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´";

       gotoxy(25,15);
       cout<<"³               ³               ³";

       for(int count_1=0;count_1<n;count_1++)
      {
         gotoxy(25,(wherey( )+1));
         cout<<"³               ³               ³";

         gotoxy(25,(wherey( )+1));
         cout<<"³               ³               ³";
      }

       gotoxy(25,(wherey( )+1));
       cout<<"ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ";

       xn[0]=x0;

       for(int count_2=0;count_2<(n-1);count_2++)
      xn[(count_2+1)]=(xn[count_2]+h);

       gotoxy(25,16);

       for(int count_3=0;count_3<n;count_3++)
      {
         gotoxy(27,wherey( ));
         cout<<xn[count_3];

         if(choice)
        {
           fx[count_3]=evaluate_postfix_expression(xn[count_3],0);

           gotoxy(43,wherey( ));
           cout<<fx[count_3];
        }

         else
        {
           gotoxy(43,wherey( ));
           cin>>fx[count_3];
        }

         if(choice)
        gotoxy(25,(wherey( )+2));

         else
        gotoxy(25,(wherey( )+1));
      }

       gotoxy(25,43);
       cout<<"Press any key to continue...";

       getch( );
    }

 /*************************************************************************///-------------------  get_index(const long double)  --------------------///*************************************************************************/constint get_index(constlongdouble x)
    {
       for(int count=0;count<n;count++)
      {
         if(xn[count]==x)
        break;
      }

       return count;
    }

 /*************************************************************************///----------------------------  estimate_dfx( )  ------------------------///*************************************************************************/void estimate_dfx( )
    {
       clear_screen( );

       gotoxy(6,9);
       cout<<"Difference Formulas of Order 1 :";

       gotoxy(6,10);
       cout<<"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ";

       gotoxy(8,12);
       cout<<"Backward Difference Formula :  f'(x) ÷ [f(x)-f(x-h)]/h";

       gotoxy(8,14);
       cout<<"Forward Difference Formula  :  f'(x) ÷ [f(x+h)-f(x)]/h";

       gotoxy(6,18);
       cout<<"Estimation of First Derivative - f'(x) :";

       gotoxy(6,19);
       cout<<"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ";

       char Choice=NULL;

       longdouble x=0;
       longdouble dfx=0;
       longdouble actual_dfx=0;

       do
      {
         Choice=NULL;

         gotoxy(8,21);
         cout<<"Press :";

         gotoxy(10,23);
         cout<<"<B> to estimate f'(x) using Backward Difference Formula";

         gotoxy(10,25);
         cout<<"<F> to estimate f'(x) using Forward Difference Formula";

         gotoxy(10,27);
         cout<<"<E> to exit";

         do
        {
           gotoxy(8,30);
           cout<<"Enter your choice : ";

           Choice=getche( );
           Choice=toupper(Choice);

           if(Choice=='B' || Choice=='F' || Choice=='E')
              break;

           else
              {
             gotoxy(18,35);
             cout<<"Wrong Choice. Please select a valid Choice.";

             gotoxy(25,37);
             cout<<"Press any Key to continue...";

             getch( );

             gotoxy(18,35);
             cout<<"                                           ";

             gotoxy(25,37);
             cout<<"                                           ";

             gotoxy(8,30);
             cout<<"                                          ";
              }
        }
         while(1);

         if(Choice=='E')
        exit(0);

         gotoxy(8,21);
         cout<<"                                                       ";

         gotoxy(10,23);
         cout<<"                                                       ";

         gotoxy(10,25);
         cout<<"                                                       ";

         gotoxy(10,27);
         cout<<"                                                       ";

         gotoxy(8,30);
         cout<<"                                                       ";

         Input_x_again:

         x=0;
         dfx=0;
         actual_dfx=0;

         gotoxy(10,21);
         cout<<"Enter the value of x = ";

         cin>>x;

         if(x>=xn[0] && x<=xn[(n-2)] && Choice=='B')
        {
           int index=0;

           index=get_index(x);

           longdouble fxph=::fx[(index+1)];
           longdouble fx=::fx[index];

           dfx=((fxph-fx)/h);
        }

         elseif(x>=xn[1] && x<=xn[(n-1)] && Choice=='F')
        {
           int index=0;

           index=get_index(x);

           longdouble fx=::fx[index];
           longdouble fxmh=::fx[(index-1)];

           dfx=((fx-fxmh)/h);
        }

         else
        {
           gotoxy(8,25);
           cout<<"Error: Please enter the valid value of x for the selected formula.";

           gotoxy(15,27);
           cout<<"Press any Key to enter the value of x again...";

           getch( );

           gotoxy(8,25);
           cout<<"                                                                  ";

           gotoxy(15,27);
           cout<<"                                                 ";

           gotoxy(10,21);
           cout<<"                                                 ";

           goto Input_x_again;
        }

         gotoxy(10,25);
         cout<<"The estimated value of f'("<<x<<")  ÷  "<<dfx;

         if(choice)
        {
           actual_dfx=evaluate_postfix_expression(x,1);

           gotoxy(10,27);
           cout<<"The Actual value of f'("<<x<<")  =  "<<actual_dfx;

           gotoxy(10,31);
           cout<<"Absolute Error = E(abs) =  "<<fabs((actual_dfx-dfx));
        }

         gotoxy(25,42);
         cout<<"Press any other key to continue...";

         getch( );

         gotoxy(10,21);
         cout<<"                                                    ";

         gotoxy(10,25);
         cout<<"                                                    ";

         gotoxy(10,27);
         cout<<"                                                    ";

         gotoxy(10,31);
         cout<<"                                                    ";

         gotoxy(25,42);
         cout<<"                                                    ";
      }
       while(1);
    }
  
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Easy Tutor author of Program to estimate value of First Derivative of the function at the given points from the given data using Backward Difference Formula , Forward diff is from United States. Easy Tutor says

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