Coding Fever: Program to estimate the value of First Derivative of the function at the given points from the given data using Central Difference Formula

# include <iostream.h>
# include <stdlib.h>
# include <string.h>
# include <stdio.h>
# include <conio.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 = 3 | max. n = 12 ]";

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

cin>>n;

if(n<3 || 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<3 || 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<<"Centeral Difference Formula of Order 2 :";

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

gotoxy(8,13);
cout<<"f'(x) ÷ [f(x+h)-f(x-h)]/2h";

gotoxy(6,17);
cout<<"Estimation of f'(x) :";

gotoxy(6,18);
cout<<"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ";

char Choice=NULL;

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

int error_flag=0;

do
{
Choice=NULL;

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

gotoxy(10,20);
cout<<"Enter the value of x = ";

cin>>x;

if(x<=xn[0] || x>=xn[(n-1)])
{
error_flag=1;

gotoxy(10,23);
cout<<"Error: Please enter x greater than x(0) and less than x(n).";
}

else
{
int index=0;

index=get_index(x);

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

dfx=((fxph-fxmh)/(2*h));

gotoxy(10,23);
cout<<"The estimated value of f'("<<x<<") ÷ "<<dfx;
}

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

gotoxy(10,25);
cout<<"The Actual value of f'("<<x<<") = "<<actual_dfx;

gotoxy(10,28);
cout<<"Absolute Error = E(abs) = "<<fabs((actual_dfx-dfx));
}

gotoxy(15,42);
cout<<"Press <Esc> to exit or any other key to continue...";

Choice=getch( );

if(int(Choice)!=27)
{
gotoxy(10,20);
cout<<" ";

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

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

gotoxy(10,28);
cout<<" ";

gotoxy(15,42);
cout<<" ";
}

elseif(int(Choice)==27)
exit(0);
}
while(1);
}

Coding Fever

Program to estimate the value of First Derivative of the function at the given points from the given data using Central Difference Formula

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