simpson and lagranje dalambair math methods
TRANSCRIPT
Damascus University
Faculty of Information Technology Engineering
Simpson and Lagranje
Dalambair math methods
CODE:
#include<iostream>
#include<cmath>
#include"graphics.h"
using namespace std;
void simpson(double x0,double xn,int en, double f[100][100],double& sum1)
{
double h;
double* b= new double[en] ; // F( Xi)
h=(xn-x0)/en; // h
//Find points
cout<<"Now put for each point Xi .. its F(xi): \n;"
for(int i=0; i<=en;i)++
{
cout<<"F( "<<x0+(i*h;" = )"<<)
cin>>b[i;]
}
//calculate the INTEGRATION !!!!
//double sum1;
sum1=b[0]+b[en]; // sum=f0 + fn
for(int i=1; i<en; i)++
{
if(i % 2 !=0)
sum1=sum1+4*b[i;]
else
sum1=sum1+2*b[i;]
}
sum1=sum1*(h/3) ;// I= h/3 [f0 + 4f1+ 2f2 + 4f3+ 2f4+ .... +fn]
// copy to the F array
for(int i=0;i<=en;i)++
{
f[1][i]=b[i;]
f[0][i]=x0+i*h;
}
}
void fillarr(double a[][100] , int n)
{
for(int i=0; i<=1; i++) // first row X0
for(int j=0; j<=n ; j++) //second row Y0
{
if( i==0)
cout<<"X "<<j;" = "<<
else
cout<<"Y "<<j;" = "<<
cin>>a[i][j;]
}
}
double p(double a[][100],int n , double x)
{
double res,sum,temp;
sum=0;
for(int i=0; i<=n; i)++
{
res=1;
for(int j=0; j<=n ; j)++
{
if(j != i)
res=res*(x-a[0][j;)]
}
temp=1;
for(int k=0;k<=n; k)++
{
if(k!=i)
temp=temp*(a[0][i]-a[0][k;)]
}
res=res/temp ;
res=res*a[1][i]; // * (y0,y1...,
sum=sum+res;
}
return sum;
}
void print(double a[][100] , int n)
{
cout<<"P"<<n<<"(x;" =)
double temp;
for(int i=0; i<=n;i)++
{
temp=1;
for(int j=0; j<=n;j)++
{
if(j!=i)
temp=temp*(a[0][i]-a[0][j;)]
}
temp=a[1][i]/temp;
if(temp>0 && i!=0)
cout<<"+"<<temp;
else if (temp==0)
cout<<"0 ;"
else
cout<<temp;
if(temp!=0)
{
for(int k=0; k<= n ; k)++
{
if(k!= i)
{
if(a[0][k]<0)
cout<<"(x + "<<fabs(a[0][k;" )"<<)]
else if(a[0][k]>0)
cout<<"(x - "<<a[0][k;" )"<<]
else
cout<<"( x ;")
}
}
}
}
cout<<endl;
}
void get_xy(double wxb ,double wyb ,double wxt ,double wyt ,int vxt ,int vyt ,int vxb ,int
vyb ,double wx ,double wy ,int& vx, int & vy)
{
double sx,sy;
sx=abs((vxb-vxt)/(wxt-wxb;) )
sy=abs((vyb-vyt)/(wyt-wyb;) )
vx=(vxt+( wx-wxb)*sx;)
vy=(vyb-( wy-wyb)*sy;)
}
void draw_function (double a[][100] , int n )
{
// Variables for graphics
initwindow(1000, 650, "Function Ploting"); //initilize windows
int maxx=getmaxx;)(
int maxy=getmaxy;)(
double x1,x2,y1,y2;
int nx1,nx2,ny1,ny2;
double x00=-70 ,xm=70, n_graph=2000;
//domain of x [x00, xm]
double wyb=-49.8, wyt=50;
double dx; dx=abs(xm-x00)/n_graph;
x1=x00 ;
y1=p(a,n-1,x1;)
get_xy(x00,wyb,xm,wyt,0,0,maxx,maxy,x1,y1,nx1,ny1); // get x y after appropriate
coordinates
for(int i=1; i<=n_graph; i)++
{
x2=x00+(i*dx;)
y2=p(a,n-1,x2;)
get_xy(x00,wyb,xm,wyt,0,0,maxx,maxy,x2,y2,nx2,ny2;)
line(nx1,ny1,nx2,ny2;)
nx1=nx2;
ny1=ny2;
}
outtextxy(30,0,"Approximetely
Drawing");outtextxy(maxx-200,maxy-30,"Student:kinan-keshkeh ;)"
*/ draw Ordinates */ setcolor(10); line(0, maxy/ 2,maxx,maxy / 2);
line(maxx / 2,0,maxx / 2,maxy ;)
}
void main_menu(int & q)
{
cout<<"|----------------------------------------------------------------------|\n;"
cout<<"| CHOICE MENU |\n; "
cout<<"|-----|----|-----------------------------------------------------------|\n;"
cout<<"| |(1)-| (Interpolation)Lagranje Dalambair 'press (1) ' |\n;"
cout<<"| --|----|------------------------------------------- |\n;"
cout<<"| |(2)-| (Integration )Simpson 'press (2) ' |\n;"
cout<<"| --|----|------------------------------------------- |\n;"
cout<<"| |(0)-| Exit 'press (0) ' |\n ";
cout<<"| --|----|------------------------------------------- |\n;"
cin>>q;
}
void menu2(int & q1)
{
cout<<"|----------------------------------------------------------------------|\n;"
cout<<"| CHOICE MENU |\n; "
cout<<"|-----|----|-----------------------------------------------------------|\n;"
cout<<"| |(1)-| calculate (Integration )Simpson 'press (1) ' |\n;"
cout<<"| --|----|------------------------------------------- |\n;"
cout<<"| |(2)-| Draw F(x) 'press (2) ' |\n;"
cout<<"| --|----|------------------------------------------- |\n;"
cout<<"| |(00)| to Main_Menu.. 'press (00) ' |\n;"
cout<<"| --|----|------------------------------------------- |\n;"
cin>>q1;
}
void menu(int & y)
{
cout<<"|----------------------------------------------------------------------|\n;"
cout<<"| CHOICE MENU |\n; "
cout<<"|-----|----|-----------------------------------------------------------|\n;"
cout<<"| |(1)-| Put the Xi / Yi 'press (1) ' |\n;"
cout<<"| --|----|------------------------------------------- |\n;"
cout<<"| |(2)-| print the Lagranj Function for this points 'press (2) ' |\n;"
cout<<"| --|----|------------------------------------------- |\n;"
cout<<"| |(3)-| Find Pn(b) 'press (3) ' |\n;"
cout<<"| --|----|------------------------------------------- |\n;"
cout<<"| |(4)-| Draw F(x) 'press (4) ' |\n;"
cout<<"| --|----|------------------------------------------- |\n;"
cout<<"| |(0)-| to Main_Menu.. 'press (0) ' |\n;"
cout<<"|-----|----|-----------------------------------------------------------|\n;"
cout<<"|----------------------------------------------------------------------|\n;"
cout<<"enter your choice ;" :
cin>>y;
}
void main)(
{
//double v1,v2; //for draw domain [v1,v2]
cout.setf(ios::fixed); // to print just 4 numbers after the Point
cout.setf(ios::showpoint;)
cout.precision(2;)
int q; main_menu(q;)
while (q!=0)
{
switch(q)
{
case 1{ :
//////////////////////////////////////////////////////Lagranj/////////////////////////////////////////////////////
int n,y; double a[100][100;]
double x;
menu(y); //Print the menu and get choice y
while (y!=0)
{
switch(y)
{
case 1 : { cout<<" How many points?? \n;"
cout<<"put the number of points : N= \n; "
cin>>n;
fillarr(a,n-1;)
menu(y ;)
break;
}
case 2{ :
cout<<"Two numbers after POINT: ex (0.00) (!!more than 2 may not
seen!!! )\n;"
print(a,n-1 ;)
menu(y ;)
break;
}
case 3{ :
cout<<"Put the X0 : f(x0)....\n"; cin>>x;
cout<<"P"<<n-1<<"("<<x<<") = "<<p(a,n-1,x)<<endl;
menu(y ;)
break;
}
case 4:
{
draw_function(a,n-1;)
menu(y ;)
break;
}
case 0 : { cout<<" :) :) End program My wishes :) :) !! \n ;"
menu(y ;)
break } ;
default:{ cout<<"Error in choice !!! \n ;"
menu(y); //Print the menu and get choice y
break} ;
// }switch
cout<<".................................... \n;"
}
main_menu(q;)
break;}//case 1
//////////////////////////////////////////////////////Simpson/////////////////////////////////////////////////////
case 2:
{
int q1; double x0,xn; int en; double sum1,sum2;
double f[100][100;]
menu2(q1;)
while (q1!=0)
{
switch(q1)
{
case 1:
{
cout<<" Put the Domain [ X0, Xn ]\n;"
cout<<" X0 = "; cin>>x0; cout<<" Xn = "; cin>>xn;
cout<<" Put the NUmber of Domains u want to Divide into
them(even) : \n"; cin>>en;
if(en %2 !=0) // en isn't Even
{
cout<<"YOUR "<<en<<" is not Even and i will calculat by
another way !! \n;"
cout<<"simpson(fo -->fn-1) + simpson(fn-1-->fn)\n;"
simpson(x0,xn-((xn-x0)/en),en-1,f,sum1); //fo -->fn-1
simpson(xn-((xn-x0)/en),xn,en-1,f,sum2); //fn-1-->fn
cout<<"The Integration fo -->fn-1 = I1 = "<<sum1<<endl;
cout<<"The Integration fn-1-->fn = I2 = "<<sum2<<endl;
cout<<"The Integration = I = "<<sum1+sum2<<endl;
}
else
{
simpson(x0,xn,en,f,sum1;)
cout<<"The Integration = I = "<<sum1<<endl;
}
menu2(q1;)
break;
}
case 2: { draw_function(f,en-1);menu2(q1); break};
case 00 : { break} ;
default:{ cout<<"Error choice!!!\n"; menu2(q1); break} ;
//}switch
}
main_menu(q;)
break;
//}case 2
case 0 :
{
cout<<":) Best wishes >>>End Program>>>>>>>>>>>>>>>> \n;"
break};
default:{ cout<<"Error In choice!!!!!!!!! \n"; main_menu(q); break } ;
}
}
//while q != 0
system("pause;)"
}