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# Program to estimate the Integral value of a given function using Gussian Quadrature Rule

Posted By: Easy Tutor     Category: C++ Programming     Views: 3463

## Code for Program to estimate the Integral value of a given function using Gussian Quadrature Rule in C++ Programming

```/*************************************************************************//*************************************************************************       A C++ Program to estimate the Integral value of a given function       using Gussian Quadrature Rule.  *************************************************************************//*************************************************************************/

# 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;

longdouble a=-1;
longdouble b=1;
longdouble two_point_result=0;
longdouble three_point_result=0;

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

/*************************************************************************//*************************************************************************///------------------------  Funcion Prototypes  -------------------------///*************************************************************************//*************************************************************************/void push(constchar *);
void convert_ie_to_pe(constchar *);

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

void show_screen( );
void clear_screen( );
void get_input( );
void change_limits( );
void show_result( );

/*************************************************************************//*************************************************************************///------------------------------  main( )  ------------------------------///*************************************************************************//*************************************************************************/int main( )
{
clrscr( );
textmode(C4350);

show_screen( );
get_input( );
show_result( );

getch( );
return 0;
}

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

textbackground(1);
cprintf(" Numerical Integration ");
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*)  ------------------///*************************************************************************/void convert_ie_to_pe(constchar* Expression)
{
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[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[count_2],pop( ));

count_2++;
}
}

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

count_2++;
}
}

push(Symbol_scanned);
}

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

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

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

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

int count_1=-1;

char Symbol_scanned[30]={NULL};

do
{
count_1++;

strcpy(Symbol_scanned,Postfix_expression[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( )
{
clear_screen( );

gotoxy(6,10);
cout<<"Non-Linear Function :";

gotoxy(6,11);
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;

convert_ie_to_pe(Fx);
}

{
longdouble temp_1=0;
longdouble temp_2=0;
longdouble temp_3=0;

temp_1=evaluate_postfix_expression((-sqrtl(0.6)));
temp_1*=(0.555555556);

temp_2=evaluate_postfix_expression(0);
temp_2*=(0.888888889);

temp_3=evaluate_postfix_expression(sqrtl(0.6));
temp_3*=(0.555555556);

three_point_result=(temp_1+temp_2+temp_3);

temp_1=0;
temp_2=0;

temp_1=evaluate_postfix_expression((-1/sqrtl(3)));
temp_2=evaluate_postfix_expression((1/sqrtl(3)));

two_point_result=(temp_1+temp_2);
}

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

gotoxy(6,9);

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

gotoxy(24,12);
cout<<" 1ô";

gotoxy(6,13);
cout<<"Two Point Rule:     ³f(x)dx ÷ f(-1/û3)+f(1/û3)";

gotoxy(24,14);
cout<<"-1õ";

gotoxy(24,16);
cout<<" 1ô";

gotoxy(6,17);
cout<<"Three Point Rule:   ³f(x)dx ÷ (5/9)f(-û(3/5))+(8/9)f(0)+(5/9)f(û(3/5))";

gotoxy(24,18);
cout<<"-1õ";

gotoxy(6,22);
cout<<"              1ô";

gotoxy(6,24);
cout<<"             -1õ";

gotoxy(6,23);
cout<<"Estimation of  ³f(x)dx :";

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

gotoxy(8,27);
cout<<"Estimated Integral Value (using 2-Point Rule) = "<<two_point_result;

gotoxy(8,29);
cout<<"Estimated Integral Value (using 3-Point Rule) = "<<three_point_result;

gotoxy(1,2);
}
```
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