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//Project 1
#include "stdafx.h"
#include <iostream>
#include <vector>
#include <string>
using namespace std;
//#include <ginac/ginac.h>
//using namespace GiNaC;
//Poly class definition
class poly{
public:
poly();
poly(unsigned int);
poly(string, unsigned int);
poly(string, unsigned int, double[]);
poly(const poly&);
poly(vector<double> &coeffs);
//Two ways of setting polynomials
void setPoly(double);
void setPoly(double[]);
double getcoeff(double n);
//vector<double> getAllCoeff();
void printPoly();
double eval(double);
//First, second derivative and first integral estimation
double Fderiv(double);
double Sderiv(double);
double Fintegral(double, double);
double Rroot(double);
poly add(poly &poly1, poly &poly2);
private:
string name;
int order;
vector<double>coeff;
};
//*************** Poly class constructors definiation*************\\
//default constructors
poly::poly() {
order = 0;
coeff.push_back(0);
}
//overloaded constructor with given poly order
poly::poly(unsigned int n) {
order = n;
}
//overloaded constructor with given poly name and order
poly::poly(string p, unsigned int n) {
name = p;
order = n;
}
//overloaded constructor with given poly name, order, and coefficients
poly::poly(string p, unsigned int n, double c[]) {
name = p;
order = n;
for (unsigned int i = 0; i <= n; i++)
coeff.push_back(c[i]); //notice that the array c has n+1 elements
}
poly::poly(const poly& p) { //copy constructor
name = p.name;
order = p.order;
for (unsigned int i = 0; i <= order; i++)
coeff.push_back(p.coeff[i]);
}
//set function used to set the coeff one at time
void poly::setPoly(double x) {
//coeff.push_back(x);
if (order == 0)
coeff.pop_back();
coeff.push_back(x);
order++;
}
//set function used to set all coeff using array
void poly::setPoly(double c[]) {
for (unsigned int i = 0; i <= order; i++)
coeff.push_back(c[i]);
}
poly::poly(vector<double> &coeffs) {
for (unsigned int i = 0; i <= order; i++)
coeff.push_back(coeffs[i]);
}
//printPoly function to print polynomial in nreadable format
void poly::printPoly() {
/*unsigned int i = 0;
cout << "Polynomial Name: " << name << endl;
cout << "Order: " << n << endl;
//for (unsigned int i = 0; i <= order; i++)
for (; n >= 0; i++, n--)
if (n == 0)
cout << coeff[i] << endl;
else if (n>=1)
cout << "Coefficients are: ";
cout << coeff[i] << "*x^"<<n<<"+";
*/
cout << "Polynomial Name: " << name << endl;
cout << "Order: " << order << endl;
cout << "Coefficients are: ";
for (unsigned int i = 0; i <= order; i++)
cout << coeff[i] << " ";
cout << endl;
}
//polynomial evaluation using Horner's Factorization
double poly::eval(double x) {
double ans = 0.0;
for (unsigned int i = 0; i <= order; i++)
ans = ans * x + coeff[i];
return ans;
}
//getfoeff function read a spicified coefficient value
double poly::getcoeff(double n) {
return coeff[n];
}
//returns all coeff of poly
/*
vector<double> poly::getAllCoeff() {
return coeff;
}*/
//integNT function for numerical integral estimate using the trapezoidal rule or Simpson's 1/3 rule
double poly::Fintegral(double a, double b) {
int n = 200; // assume 200 panels
double h = (b - a) / n;
double t = eval(a) + eval(b);
double sum = 0;
for (int i = 1; i<n; i++)
sum += eval(a + i*h);
return (h / 2)*(t + 2 * sum);
}
double poly::Sderiv(double x) {
double h = 1.0e-2;
double d1, d2, d3; //ans;
d1 = eval(x + h);
d2 = 2*eval(x);
d3 = eval(x - h);
return (d1 - d2 +d3) / (h * h);
}
//First derivative numerical estimate
double poly::Fderiv(double x) {
double h = 1.0e-2;
double d1, d2; //ans
d1 = eval(x + h);
d2 = eval(x - h);
return (d1 - d2) / (2 * h);
}
double poly::Rroot(double x) {
return 0;
}
poly poly::add(poly &poly1, poly &poly2) {
vector<double> temp1;
if (poly1.order > poly2.order)
{
for (int i = 0; i < poly2.order; i++)
{
temp1[i] = poly1.getcoeff(i) + poly2.getcoeff(i);
}
poly temp0(temp1);
return temp0;
}
else if (poly1.order < poly2.order)
{
for (int i = 0; i < poly1.order; i++)
{
temp1[i] = poly1.getcoeff(i) + poly2.getcoeff(i);
}
poly temp0(temp1);
return temp0;
}
}
int _tmain(int argc, _TCHAR* argv[])
{
double cq[]={1,2,5,1};
poly q("poly", 3, cq);
double cr[] = { 1,6,11,6 };
poly r( "poly", 3, cr);
cout <<"Coefficient at 1: "<< r.getcoeff(1) << endl;
r.setPoly(1);
r.printPoly();
cout << "poly evaluated at 1: " << r.eval(1) << endl;
cout << "poly evaluated at 5: " << r.eval(5) << endl;
cout << "poly evaluated at -2: " << r.eval(-2.0) << endl;
cout << r.Fintegral(0, 3) << endl; // estimate the integral from 0 to 3 using Trap rule
cout << "Estimate first derivative of polynomial at: "<< r.Fderiv(3) << endl;
cout << "Estimate second derivative of polynomial at: " << r.Sderiv(3) << endl;
d.add(r, q);
return 0;
}
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