1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
|
//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;
}
| |
