/*************************************************************************//************************************************************************* 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 apply_gaussian_quadrature_rule( );
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);
}
/*************************************************************************///----------------- apply_gaussian_quadrature_rule( ) -----------------///*************************************************************************/void apply_gaussian_quadrature_rule( )
{
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);
cout<<"Gaussian Quadrature Rule:";
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";
apply_gaussian_quadrature_rule( );
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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