 ROOT   Reference Guide Polynomial.h
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1// @(#)root/mathmore:$Id$
2// Authors: L. Moneta, A. Zsenei 08/2005
3
4 /**********************************************************************
5 * *
6 * Copyright (c) 2004 ROOT Foundation, CERN/PH-SFT *
7 * *
8 * This library is free software; you can redistribute it and/or *
9 * modify it under the terms of the GNU General Public License *
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11 * of the License, or (at your option) any later version. *
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13 * This library is distributed in the hope that it will be useful, *
14 * but WITHOUT ANY WARRANTY; without even the implied warranty of *
15 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
16 * General Public License for more details. *
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18 * You should have received a copy of the GNU General Public License *
19 * along with this library (see file COPYING); if not, write *
20 * to the Free Software Foundation, Inc., 59 Temple Place, Suite *
21 * 330, Boston, MA 02111-1307 USA, or contact the author. *
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23 **********************************************************************/
24
25// Header file for class Polynomial
26//
27// Created by: Lorenzo Moneta at Wed Nov 10 17:46:19 2004
28//
29// Last update: Wed Nov 10 17:46:19 2004
30//
31#ifndef ROOT_Math_Polynomial
32#define ROOT_Math_Polynomial
33
34#include <complex>
35
36#include "Math/ParamFunction.h"
37
38// #ifdef _WIN32
39// #pragma warning(disable : 4250)
40// #endif
41
42namespace ROOT {
43namespace Math {
44
45//_____________________________________________________________________________________
46 /**
47 Parametric Function class describing polynomials of order n.
48
49 <em>P(x) = p + p*x + p*x**2 + ....... + p[n]*x**n</em>
50
51 The class implements also the derivatives, \a dP(x)/dx and the \a dP(x)/dp[i].
52
53 The class provides also the method to find the roots of the polynomial.
54 It uses analytical methods up to quartic polynomials.
55
56 Implements both the Parameteric function interface and the gradient interface
57 since it provides the analytical gradient with respect to x
58
59
60 @ingroup ParamFunc
61 */
62
65{
66
67
68public:
69
71 /**
72 Construct a Polynomial function of order n.
73 The number of Parameters is n+1.
74 */
75
76 Polynomial(unsigned int n = 0);
77
78 /**
79 Construct a Polynomial of degree 1 : a*x + b
80 */
81 Polynomial(double a, double b);
82
83 /**
84 Construct a Polynomial of degree 2 : a*x**2 + b*x + c
85 */
86 Polynomial(double a, double b, double c);
87
88 /**
89 Construct a Polynomial of degree 3 : a*x**3 + b*x**2 + c*x + d
90 */
91 Polynomial(double a, double b, double c, double d);
92
93 /**
94 Construct a Polynomial of degree 4 : a*x**4 + b*x**3 + c*x**2 + dx + e
95 */
96 Polynomial(double a, double b, double c, double d, double e);
97
98
99 virtual ~Polynomial() {}
100
101 // use default copy-ctor and assignment operators
102
103
104
105// using ParamFunction::operator();
106
107
108 /**
109 Find the polynomial roots.
110 For n <= 4, the roots are found analytically while for larger order an iterative numerical method is used
111 The numerical method used is from GSL (see <A HREF="http://www.gnu.org/software/gsl/manual/gsl-ref_6.html#SEC53" )
112 */
113 const std::vector<std::complex <double> > & FindRoots();
114
115
116 /**
117 Find the only the real polynomial roots.
118 For n <= 4, the roots are found analytically while for larger order an iterative numerical method is used
119 The numerical method used is from GSL (see <A HREF="http://www.gnu.org/software/gsl/manual/gsl-ref_6.html#SEC53" )
120 */
121 std::vector<double > FindRealRoots();
122
123
124 /**
125 Find the polynomial roots using always an iterative numerical methods
126 The numerical method used is from GSL (see <A HREF="http://www.gnu.org/software/gsl/manual/gsl-ref_6.html#SEC53" )
127 */
128 const std::vector<std::complex <double> > & FindNumRoots();
129
130 /**
131 Order of Polynomial
132 */
133 unsigned int Order() const { return fOrder; }
134
135
136 IGenFunction * Clone() const;
137
138 /**
139 Optimized method to evaluate at the same time the function value and derivative at a point x.
140 Implement the interface specified bby ROOT::Math::IGradientOneDim.
141 In the case of polynomial there is no advantage to compute both at the same time
142 */
143 void FdF (double x, double & f, double & df) const {
144 f = (*this)(x);
145 df = Derivative(x);
146 }
147
148
149private:
150
151 double DoEvalPar ( double x, const double * p ) const ;
152
153 double DoDerivative (double x) const ;
154
155 double DoParameterDerivative(double x, const double * p, unsigned int ipar) const;
156
157
158 // cache order = number of params - 1)
159 unsigned int fOrder;
160
161 // cache Parameters for Gradient
162 mutable std::vector<double> fDerived_params;
163
164 // roots
165
166 std::vector< std::complex < double > > fRoots;
167
168};
169
170} // namespace Math
171} // namespace ROOT
172
173
174#endif /* ROOT_Math_Polynomial */
#define d(i)
Definition: RSha256.hxx:102
#define b(i)
Definition: RSha256.hxx:100
#define f(i)
Definition: RSha256.hxx:104
#define c(i)
Definition: RSha256.hxx:101
#define e(i)
Definition: RSha256.hxx:103
Interface (abstract class) for generic functions objects of one-dimension Provides a method to evalua...
Definition: IFunction.h:135
Specialized Gradient interface(abstract class) for one dimensional functions It provides a method to ...
Definition: IFunction.h:247
double Derivative(double x) const
Return the derivative of the function at a point x Use the private method DoDerivative.
Definition: IFunction.h:258
Base template class for all Parametric Functions.
Definition: ParamFunction.h:67
Parametric Function class describing polynomials of order n.
Definition: Polynomial.h:65
IGenFunction * Clone() const
Clone a function.
Definition: Polynomial.cxx:144
void FdF(double x, double &f, double &df) const
Optimized method to evaluate at the same time the function value and derivative at a point x.
Definition: Polynomial.h:143
double DoDerivative(double x) const
function to evaluate the derivative with respect each coordinate.
Definition: Polynomial.cxx:128
const std::vector< std::complex< double > > & FindRoots()
Find the polynomial roots.
Definition: Polynomial.cxx:152
std::vector< std::complex< double > > fRoots
Definition: Polynomial.h:166
Polynomial(unsigned int n=0)
Construct a Polynomial function of order n.
Definition: Polynomial.cxx:50
unsigned int fOrder
Definition: Polynomial.h:159
Definition: Polynomial.h:70
unsigned int Order() const
Order of Polynomial.
Definition: Polynomial.h:133
double DoParameterDerivative(double x, const double *p, unsigned int ipar) const
Evaluate the gradient, to be implemented by the derived classes.
Definition: Polynomial.cxx:137
double DoEvalPar(double x, const double *p) const
Implementation of the evaluation function using the x value and the parameters.
Definition: Polynomial.cxx:120
std::vector< double > FindRealRoots()
Find the only the real polynomial roots.
Definition: Polynomial.cxx:238
const std::vector< std::complex< double > > & FindNumRoots()
Find the polynomial roots using always an iterative numerical methods The numerical method used is fr...
Definition: Polynomial.cxx:248
std::vector< double > fDerived_params
Definition: Polynomial.h:162
Double_t x[n]
Definition: legend1.C:17
const Int_t n
Definition: legend1.C:16
Namespace for new Math classes and functions.
VSD Structures.
Definition: StringConv.hxx:21
auto * a
Definition: textangle.C:12