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root/OpenMD/branches/development/src/math/Polynomial.hpp

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trunk/src/math/Polynomial.hpp (file contents), Revision 385 by tim, Tue Mar 1 20:10:14 2005 UTC vs.
branches/development/src/math/Polynomial.hpp (file contents), Revision 1465 by chuckv, Fri Jul 9 23:08:25 2010 UTC

#	Line 1 | Line 1
1	<	/*
1	>	/*
2		* Copyright (c) 2005 The University of Notre Dame. All Rights Reserved.
3		*
4		* The University of Notre Dame grants you ("Licensee") a
#	Line 6 | Line 6
6		* redistribute this software in source and binary code form, provided
7		* that the following conditions are met:
8		*
9	<	* 1. Acknowledgement of the program authors must be made in any
10	<	*    publication of scientific results based in part on use of the
11	<	*    program.  An acceptable form of acknowledgement is citation of
12	<	*    the article in which the program was described (Matthew
13	<	*    A. Meineke, Charles F. Vardeman II, Teng Lin, Christopher
14	<	*    J. Fennell and J. Daniel Gezelter, "OOPSE: An Object-Oriented
15	<	*    Parallel Simulation Engine for Molecular Dynamics,"
16	<	*    J. Comput. Chem. 26, pp. 252-271 (2005))
17	<	*
18	<	* 2. Redistributions of source code must retain the above copyright
9	>	* 1. Redistributions of source code must retain the above copyright
10		*    notice, this list of conditions and the following disclaimer.
11		*
12	<	* 3. Redistributions in binary form must reproduce the above copyright
12	>	* 2. Redistributions in binary form must reproduce the above copyright
13		*    notice, this list of conditions and the following disclaimer in the
14		*    documentation and/or other materials provided with the
15		*    distribution.
#	Line 37 | Line 28
28		* arising out of the use of or inability to use software, even if the
29		* University of Notre Dame has been advised of the possibility of
30		* such damages.
31	+	*
32	+	* SUPPORT OPEN SCIENCE!  If you use OpenMD or its source code in your
33	+	* research, please cite the appropriate papers when you publish your
34	+	* work.  Good starting points are:
35	+	*
36	+	* [1]  Meineke, et al., J. Comp. Chem. 26, 252-271 (2005).
37	+	* [2]  Fennell & Gezelter, J. Chem. Phys. 124, 234104 (2006).
38	+	* [3]  Sun, Lin & Gezelter, J. Chem. Phys. 128, 24107 (2008).
39	+	* [4]  Vardeman & Gezelter, in progress (2009).
40		*/
41
42		/**
#	Line 53 | Line 53
53		#include <list>
54		#include <map>
55		#include <utility>
56	+	#include <complex>
57	+	#include "config.h"
58	+	#include "math/Eigenvalue.hpp"
59
60	<	namespace oopse {
60	>	namespace OpenMD {
61	>
62	>	template<typename Real> Real fastpow(Real x, int N) {
63	>	Real result(1); //or 1.0?
64
59	–	template<typename ElemType> ElemType pow(ElemType x, int N) {
60	–	ElemType result(1);
61	–
65		for (int i = 0; i < N; ++i) {
66	<	result *= x;
66	>	result *= x;
67		}
68
69		return result;
70	<	}
70	>	}
71
72	<	/**
73	<	* @class Polynomial Polynomial.hpp "math/Polynomial.hpp"
74	<	* A generic Polynomial class
75	<	*/
76	<	template<typename ElemType>
77	<	class Polynomial {
72	>	/**
73	>	* @class Polynomial Polynomial.hpp "math/Polynomial.hpp"
74	>	* A generic Polynomial class
75	>	*/
76	>	template<typename Real>
77	>	class Polynomial {
78
79	<	public:
80	<
81	<	typedef int ExponentType;
82	<	typedef ElemType CoefficientType;
83	<	typedef std::map<ExponentType, CoefficientType> PolynomialPairMap;
84	<	typedef typename PolynomialPairMap::iterator iterator;
85	<	typedef typename PolynomialPairMap::const_iterator const_iterator;
86	<	/**
87	<	* Calculates the value of this Polynomial evaluated at the given x value.
88	<	* @return The value of this Polynomial evaluates at the given x value
89	<	* @param x the value of the independent variable for this Polynomial function
90	<	*/
91	<	ElemType evaluate(const ElemType& x) {
92	<	ElemType result = ElemType();
93	<	ExponentType exponent;
94	<	CoefficientType coefficient;
79	>	public:
80	>	typedef Polynomial<Real> PolynomialType;
81	>	typedef int ExponentType;
82	>	typedef Real CoefficientType;
83	>	typedef std::map<ExponentType, CoefficientType> PolynomialPairMap;
84	>	typedef typename PolynomialPairMap::iterator iterator;
85	>	typedef typename PolynomialPairMap::const_iterator const_iterator;
86	>
87	>	Polynomial() {}
88	>	Polynomial(Real v) {setCoefficient(0, v);}
89	>	/**
90	>	* Calculates the value of this Polynomial evaluated at the given x value.
91	>	* @return The value of this Polynomial evaluates at the given x value
92	>	* @param x the value of the independent variable for this
93	>	* Polynomial function
94	>	*/
95	>	Real evaluate(const Real& x) {
96	>	Real result = Real();
97	>	ExponentType exponent;
98	>	CoefficientType coefficient;
99
100	<	for (iterator i = polyPairMap_.begin(); i != polyPairMap_.end(); ++i) {
101	<	exponent = i->first;
102	<	coefficient = i->second;
103	<	result  += pow(x, exponent) * coefficient;
104	<	}
100	>	for (iterator i = polyPairMap_.begin(); i != polyPairMap_.end(); ++i) {
101	>	exponent = i->first;
102	>	coefficient = i->second;
103	>	result  += fastpow(x, exponent) * coefficient;
104	>	}
105
106	<	return result;
107	<	}
106	>	return result;
107	>	}
108
109	<	/**
110	<	* Returns the first derivative of this polynomial.
111	<	* @return the first derivative of this polynomial
112	<	* @param x
113	<	*/
114	<	ElemType evaluateDerivative(const ElemType& x) {
115	<	ElemType result = ElemType();
116	<	ExponentType exponent;
117	<	CoefficientType coefficient;
109	>	/**
110	>	* Returns the first derivative of this polynomial.
111	>	* @return the first derivative of this polynomial
112	>	* @param x
113	>	*/
114	>	Real evaluateDerivative(const Real& x) {
115	>	Real result = Real();
116	>	ExponentType exponent;
117	>	CoefficientType coefficient;
118
119	<	for (iterator i = polyPairMap_.begin(); i != polyPairMap_.end(); ++i) {
120	<	exponent = i->first;
121	<	coefficient = i->second;
122	<	result  += pow(x, exponent - 1) * coefficient * exponent;
123	<	}
119	>	for (iterator i = polyPairMap_.begin(); i != polyPairMap_.end(); ++i) {
120	>	exponent = i->first;
121	>	coefficient = i->second;
122	>	result  += fastpow(x, exponent - 1) * coefficient * exponent;
123	>	}
124
125	<	return result;
126	<	}
125	>	return result;
126	>	}
127
121	–	/**
122	–	* Set the coefficent of the specified exponent, if the coefficient is already there, it
123	–	* will be overwritten.
124	–	* @param exponent exponent of a term in this Polynomial
125	–	* @param coefficient multiplier of a term in this Polynomial
126	–	*/
127	–
128	–	void setCoefficient(int exponent, const ElemType& coefficient) {
129	–	polyPairMap_.insert(typename PolynomialPairMap::value_type(exponent, coefficient));
130	–	}
128
129	<	/**
130	<	* Set the coefficent of the specified exponent. If the coefficient is already there,  just add the
131	<	* new coefficient to the old one, otherwise,  just call setCoefficent
132	<	* @param exponent exponent of a term in this Polynomial
133	<	* @param coefficient multiplier of a term in this Polynomial
134	<	*/
135	<
136	<	void addCoefficient(int exponent, const ElemType& coefficient) {
137	<	iterator i = polyPairMap_.find(exponent);
129	>	/**
130	>	* Set the coefficent of the specified exponent, if the
131	>	* coefficient is already there, it will be overwritten.
132	>	* @param exponent exponent of a term in this Polynomial
133	>	* @param coefficient multiplier of a term in this Polynomial
134	>	*/
135	>	void setCoefficient(int exponent, const Real& coefficient) {
136	>	polyPairMap_[exponent] = coefficient;
137	>	}
138	>
139	>	/**
140	>	* Set the coefficent of the specified exponent. If the
141	>	* coefficient is already there, just add the new coefficient to
142	>	* the old one, otherwise, just call setCoefficent
143	>	* @param exponent exponent of a term in this Polynomial
144	>	* @param coefficient multiplier of a term in this Polynomial
145	>	*/
146	>	void addCoefficient(int exponent, const Real& coefficient) {
147	>	iterator i = polyPairMap_.find(exponent);
148
149	<	if (i != end()) {
150	<	i->second += coefficient;
151	<	} else {
152	<	setCoefficient(exponent, coefficient);
153	<	}
154	<	}
149	>	if (i != end()) {
150	>	i->second += coefficient;
151	>	} else {
152	>	setCoefficient(exponent, coefficient);
153	>	}
154	>	}
155
156	<
157	<	/**
158	<	* Returns the coefficient associated with the given power for this Polynomial.
159	<	* @return the coefficient associated with the given power for this Polynomial
160	<	* @exponent exponent of any term in this Polynomial
161	<	*/
162	<	ElemType getCoefficient(ExponentType exponent) {
163	<	iterator i = polyPairMap_.find(exponent);
164	<
158	<	if (i != end()) {
159	<	return i->second;
160	<	} else {
161	<	return ElemType(0);
162	<	}
163	<	}
156	>	/**
157	>	* Returns the coefficient associated with the given power for
158	>	* this Polynomial.
159	>	* @return the coefficient associated with the given power for
160	>	* this Polynomial
161	>	* @exponent exponent of any term in this Polynomial
162	>	*/
163	>	Real getCoefficient(ExponentType exponent) {
164	>	iterator i = polyPairMap_.find(exponent);
165
166	<	iterator begin() {
167	<	return polyPairMap_.begin();
168	<	}
166	>	if (i != end()) {
167	>	return i->second;
168	>	} else {
169	>	return Real(0);
170	>	}
171	>	}
172
173	<	const_iterator begin() const{
174	<	return polyPairMap_.begin();
175	<	}
173	>	iterator begin() {
174	>	return polyPairMap_.begin();
175	>	}
176	>
177	>	const_iterator begin() const{
178	>	return polyPairMap_.begin();
179	>	}
180
181	<	iterator end() {
182	<	return polyPairMap_.end();
183	<	}
181	>	iterator end() {
182	>	return polyPairMap_.end();
183	>	}
184
185	<	const_iterator end() const{
186	<	return polyPairMap_.end();
185	>	const_iterator end() const{
186	>	return polyPairMap_.end();
187	>	}
188	>
189	>	iterator find(ExponentType exponent) {
190	>	return polyPairMap_.find(exponent);
191	>	}
192	>
193	>	size_t size() {
194	>	return polyPairMap_.size();
195	>	}
196	>
197	>	int degree() {
198	>	int deg = 0;
199	>	for (iterator i = polyPairMap_.begin(); i != polyPairMap_.end(); ++i) {
200	>	if (i->first > deg)
201	>	deg = i->first;
202	>	}
203	>	return deg;
204	>	}
205	>
206	>	PolynomialType& operator = (const PolynomialType& p) {
207	>
208	>	if (this != &p)  // protect against invalid self-assignment
209	>	{
210	>	typename Polynomial<Real>::const_iterator i;
211	>
212	>	polyPairMap_.clear();  // clear out the old map
213	>
214	>	for (i =  p.begin(); i != p.end(); ++i) {
215	>	this->setCoefficient(i->first, i->second);
216	>	}
217		}
218	+	// by convention, always return *this
219	+	return *this;
220	+	}
221
222	<	iterator find(ExponentType exponent) {
223	<	return polyPairMap_.find(exponent);
222	>	PolynomialType& operator += (const PolynomialType& p) {
223	>	typename Polynomial<Real>::const_iterator i;
224	>
225	>	for (i =  p.begin(); i  != p.end(); ++i) {
226	>	this->addCoefficient(i->first, i->second);
227	>	}
228	>
229	>	return *this;
230	>	}
231	>
232	>	PolynomialType& operator -= (const PolynomialType& p) {
233	>	typename Polynomial<Real>::const_iterator i;
234	>	for (i =  p.begin(); i  != p.end(); ++i) {
235	>	this->addCoefficient(i->first, -i->second);
236	>	}
237	>	return *this;
238	>	}
239	>
240	>	PolynomialType& operator *= (const PolynomialType& p) {
241	>	typename Polynomial<Real>::const_iterator i;
242	>	typename Polynomial<Real>::const_iterator j;
243	>	Polynomial<Real> p2(*this);
244	>
245	>	polyPairMap_.clear();  // clear out old map
246	>	for (i = p2.begin(); i !=p2.end(); ++i) {
247	>	for (j = p.begin(); j !=p.end(); ++j) {
248	>	this->addCoefficient( i->first + j->first, i->second * j->second);
249		}
250	+	}
251	+	return *this;
252	+	}
253
254	<	size_t size() {
255	<	return polyPairMap_.size();
254	>	//PolynomialType& operator *= (const Real v)
255	>	PolynomialType& operator *= (const Real v) {
256	>	typename Polynomial<Real>::const_iterator i;
257	>	//Polynomial<Real> result;
258	>
259	>	for (i = this->begin(); i != this->end(); ++i) {
260	>	this->setCoefficient( i->first, i->second*v);
261	>	}
262	>
263	>	return *this;
264	>	}
265	>
266	>	PolynomialType& operator += (const Real v) {
267	>	this->addCoefficient( 0, v);
268	>	return *this;
269	>	}
270	>
271	>	/**
272	>	* Returns the first derivative of this polynomial.
273	>	* @return the first derivative of this polynomial
274	>	*/
275	>	PolynomialType & getDerivative() {
276	>	Polynomial<Real> p();
277	>
278	>	typename Polynomial<Real>::const_iterator i;
279	>	ExponentType exponent;
280	>	CoefficientType coefficient;
281	>
282	>	for (i =  this->begin(); i  != this->end(); ++i) {
283	>	exponent = i->first;
284	>	coefficient = i->second;
285	>	p.setCoefficient(exponent-1, coefficient * exponent);
286	>	}
287	>
288	>	return p;
289	>	}
290	>
291	>	// Creates the Companion matrix for a given polynomial
292	>	DynamicRectMatrix<Real> CreateCompanion() {
293	>	int rank = degree();
294	>	DynamicRectMatrix<Real> mat(rank, rank);
295	>	Real majorCoeff = getCoefficient(rank);
296	>	for(int i = 0; i < rank; ++i) {
297	>	for(int j = 0; j < rank; ++j) {
298	>	if(i - j == 1) {
299	>	mat(i, j) = 1;
300	>	} else if(j == rank-1) {
301	>	mat(i, j) = -1 * getCoefficient(i) / majorCoeff;
302	>	}
303		}
304	<
305	<	private:
306	<
307	<	PolynomialPairMap polyPairMap_;
308	<	};
304	>	}
305	>	return mat;
306	>	}
307	>
308	>	// Find the Roots of a given polynomial
309	>	std::vector<complex<Real> > FindRoots() {
310	>	int rank = degree();
311	>	DynamicRectMatrix<Real> companion = CreateCompanion();
312	>	JAMA::Eigenvalue<Real> eig(companion);
313	>	DynamicVector<Real> reals, imags;
314	>	eig.getRealEigenvalues(reals);
315	>	eig.getImagEigenvalues(imags);
316	>
317	>	std::vector<complex<Real> > roots;
318	>	for (int i = 0; i < rank; i++) {
319	>	roots.push_back(complex<Real>(reals(i), imags(i)));
320	>	}
321
322	+	return roots;
323	+	}
324
325	<	/**
326	<	* Generates and returns the product of two given Polynomials.
327	<	* @return A Polynomial containing the product of the two given Polynomial parameters
328	<	*/
329	<	template<typename ElemType>
330	<	Polynomial<ElemType> operator *(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
331	<	typename Polynomial<ElemType>::const_iterator i;
332	<	typename Polynomial<ElemType>::const_iterator j;
333	<	Polynomial<ElemType> p;
325	>	std::vector<Real> FindRealRoots() {
326	>
327	>	const Real fEpsilon = 1.0e-8;
328	>	std::vector<Real> roots;
329	>	roots.clear();
330	>
331	>	const int deg = degree();
332	>
333	>	switch (deg) {
334	>	case 1: {
335	>	Real fC1 = getCoefficient(1);
336	>	Real fC0 = getCoefficient(0);
337	>	roots.push_back( -fC0 / fC1);
338	>	return roots;
339	>	}
340	>	break;
341	>	case 2: {
342	>	Real fC2 = getCoefficient(2);
343	>	Real fC1 = getCoefficient(1);
344	>	Real fC0 = getCoefficient(0);
345	>	Real fDiscr = fC1*fC1 - 4.0*fC0*fC2;
346	>	if (abs(fDiscr) <= fEpsilon) {
347	>	fDiscr = (Real)0.0;
348	>	}
349	>
350	>	if (fDiscr < (Real)0.0) {  // complex roots only
351	>	return roots;
352	>	}
353	>
354	>	Real fTmp = ((Real)0.5)/fC2;
355	>
356	>	if (fDiscr > (Real)0.0) { // 2 real roots
357	>	fDiscr = sqrt(fDiscr);
358	>	roots.push_back(fTmp*(-fC1 - fDiscr));
359	>	roots.push_back(fTmp*(-fC1 + fDiscr));
360	>	} else {
361	>	roots.push_back(-fTmp * fC1);  // 1 real root
362	>	}
363	>	}
364	>	return roots;
365	>	break;
366	>
367	>	case 3: {
368	>	Real fC3 = getCoefficient(3);
369	>	Real fC2 = getCoefficient(2);
370	>	Real fC1 = getCoefficient(1);
371	>	Real fC0 = getCoefficient(0);
372	>
373	>	// make polynomial monic, x^3+c2*x^2+c1*x+c0
374	>	Real fInvC3 = ((Real)1.0)/fC3;
375	>	fC0 *= fInvC3;
376	>	fC1 *= fInvC3;
377	>	fC2 *= fInvC3;
378	>
379	>	// convert to y^3+a*y+b = 0 by x = y-c2/3
380	>	const Real fThird = (Real)1.0/(Real)3.0;
381	>	const Real fTwentySeventh = (Real)1.0/(Real)27.0;
382	>	Real fOffset = fThird*fC2;
383	>	Real fA = fC1 - fC2*fOffset;
384	>	Real fB = fC0+fC2*(((Real)2.0)*fC2*fC2-((Real)9.0)*fC1)*fTwentySeventh;
385	>	Real fHalfB = ((Real)0.5)*fB;
386	>
387	>	Real fDiscr = fHalfB*fHalfB + fA*fA*fA*fTwentySeventh;
388	>	if (fabs(fDiscr) <= fEpsilon) {
389	>	fDiscr = (Real)0.0;
390	>	}
391	>
392	>	if (fDiscr > (Real)0.0) {  // 1 real, 2 complex roots
393	>
394	>	fDiscr = sqrt(fDiscr);
395	>	Real fTemp = -fHalfB + fDiscr;
396	>	Real root;
397	>	if (fTemp >= (Real)0.0) {
398	>	root = pow(fTemp,fThird);
399	>	} else {
400	>	root = -pow(-fTemp,fThird);
401	>	}
402	>	fTemp = -fHalfB - fDiscr;
403	>	if ( fTemp >= (Real)0.0 ) {
404	>	root += pow(fTemp,fThird);
405	>	} else {
406	>	root -= pow(-fTemp,fThird);
407	>	}
408	>	root -= fOffset;
409	>
410	>	roots.push_back(root);
411	>	} else if (fDiscr < (Real)0.0) {
412	>	const Real fSqrt3 = sqrt((Real)3.0);
413	>	Real fDist = sqrt(-fThird*fA);
414	>	Real fAngle = fThird*atan2(sqrt(-fDiscr), -fHalfB);
415	>	Real fCos = cos(fAngle);
416	>	Real fSin = sin(fAngle);
417	>	roots.push_back(((Real)2.0)*fDist*fCos-fOffset);
418	>	roots.push_back(-fDist*(fCos+fSqrt3*fSin)-fOffset);
419	>	roots.push_back(-fDist*(fCos-fSqrt3*fSin)-fOffset);
420	>	} else {
421	>	Real fTemp;
422	>	if (fHalfB >= (Real)0.0) {
423	>	fTemp = -pow(fHalfB,fThird);
424	>	} else {
425	>	fTemp = pow(-fHalfB,fThird);
426	>	}
427	>	roots.push_back(((Real)2.0)*fTemp-fOffset);
428	>	roots.push_back(-fTemp-fOffset);
429	>	roots.push_back(-fTemp-fOffset);
430	>	}
431	>	}
432	>	return roots;
433	>	break;
434	>	case 4: {
435	>	Real fC4 = getCoefficient(4);
436	>	Real fC3 = getCoefficient(3);
437	>	Real fC2 = getCoefficient(2);
438	>	Real fC1 = getCoefficient(1);
439	>	Real fC0 = getCoefficient(0);
440	>
441	>	// make polynomial monic, x^4+c3*x^3+c2*x^2+c1*x+c0
442	>	Real fInvC4 = ((Real)1.0)/fC4;
443	>	fC0 *= fInvC4;
444	>	fC1 *= fInvC4;
445	>	fC2 *= fInvC4;
446	>	fC3 *= fInvC4;
447	>
448	>	// reduction to resolvent cubic polynomial y^3+r2*y^2+r1*y+r0 = 0
449	>	Real fR0 = -fC3*fC3*fC0 + ((Real)4.0)*fC2*fC0 - fC1*fC1;
450	>	Real fR1 = fC3*fC1 - ((Real)4.0)*fC0;
451	>	Real fR2 = -fC2;
452	>	Polynomial<Real> tempCubic;
453	>	tempCubic.setCoefficient(0, fR0);
454	>	tempCubic.setCoefficient(1, fR1);
455	>	tempCubic.setCoefficient(2, fR2);
456	>	tempCubic.setCoefficient(3, 1.0);
457	>	std::vector<Real> cubeRoots = tempCubic.FindRealRoots(); // always
458	>	// produces
459	>	// at
460	>	// least
461	>	// one
462	>	// root
463	>	Real fY = cubeRoots[0];
464	>
465	>	Real fDiscr = ((Real)0.25)*fC3*fC3 - fC2 + fY;
466	>	if (fabs(fDiscr) <= fEpsilon) {
467	>	fDiscr = (Real)0.0;
468	>	}
469	>
470	>	if (fDiscr > (Real)0.0) {
471	>	Real fR = sqrt(fDiscr);
472	>	Real fT1 = ((Real)0.75)*fC3*fC3 - fR*fR - ((Real)2.0)*fC2;
473	>	Real fT2 = (((Real)4.0)*fC3*fC2 - ((Real)8.0)*fC1 - fC3*fC3*fC3) /
474	>	(((Real)4.0)*fR);
475	>
476	>	Real fTplus = fT1+fT2;
477	>	Real fTminus = fT1-fT2;
478	>	if (fabs(fTplus) <= fEpsilon) {
479	>	fTplus = (Real)0.0;
480	>	}
481	>	if (fabs(fTminus) <= fEpsilon) {
482	>	fTminus = (Real)0.0;
483	>	}
484	>
485	>	if (fTplus >= (Real)0.0) {
486	>	Real fD = sqrt(fTplus);
487	>	roots.push_back(-((Real)0.25)*fC3+((Real)0.5)*(fR+fD));
488	>	roots.push_back(-((Real)0.25)*fC3+((Real)0.5)*(fR-fD));
489	>	}
490	>	if (fTminus >= (Real)0.0) {
491	>	Real fE = sqrt(fTminus);
492	>	roots.push_back(-((Real)0.25)*fC3+((Real)0.5)*(fE-fR));
493	>	roots.push_back(-((Real)0.25)*fC3-((Real)0.5)*(fE+fR));
494	>	}
495	>	} else if (fDiscr < (Real)0.0) {
496	>	//roots.clear();
497	>	} else {
498	>	Real fT2 = fY*fY-((Real)4.0)*fC0;
499	>	if (fT2 >= -fEpsilon) {
500	>	if (fT2 < (Real)0.0) { // round to zero
501	>	fT2 = (Real)0.0;
502	>	}
503	>	fT2 = ((Real)2.0)*sqrt(fT2);
504	>	Real fT1 = ((Real)0.75)*fC3*fC3 - ((Real)2.0)*fC2;
505	>	if (fT1+fT2 >= fEpsilon) {
506	>	Real fD = sqrt(fT1+fT2);
507	>	roots.push_back( -((Real)0.25)*fC3+((Real)0.5)*fD);
508	>	roots.push_back( -((Real)0.25)*fC3-((Real)0.5)*fD);
509	>	}
510	>	if (fT1-fT2 >= fEpsilon) {
511	>	Real fE = sqrt(fT1-fT2);
512	>	roots.push_back( -((Real)0.25)*fC3+((Real)0.5)*fE);
513	>	roots.push_back( -((Real)0.25)*fC3-((Real)0.5)*fE);
514	>	}
515	>	}
516	>	}
517	>	}
518	>	return roots;
519	>	break;
520	>	default: {
521	>	DynamicRectMatrix<Real> companion = CreateCompanion();
522	>	JAMA::Eigenvalue<Real> eig(companion);
523	>	DynamicVector<Real> reals, imags;
524	>	eig.getRealEigenvalues(reals);
525	>	eig.getImagEigenvalues(imags);
526	>
527	>	for (int i = 0; i < deg; i++) {
528	>	if (fabs(imags(i)) < fEpsilon)
529	>	roots.push_back(reals(i));
530	>	}
531	>	}
532	>	return roots;
533	>	break;
534	>	}
535	>
536	>	return roots; // should be empty if you got here
537	>	}
538	>
539	>	private:
540	>
541	>	PolynomialPairMap polyPairMap_;
542	>	};
543	>
544	>
545	>	/**
546	>	* Generates and returns the product of two given Polynomials.
547	>	* @return A Polynomial containing the product of the two given Polynomial parameters
548	>	*/
549	>	template<typename Real>
550	>	Polynomial<Real> operator *(const Polynomial<Real>& p1, const Polynomial<Real>& p2) {
551	>	typename Polynomial<Real>::const_iterator i;
552	>	typename Polynomial<Real>::const_iterator j;
553	>	Polynomial<Real> p;
554
555		for (i = p1.begin(); i !=p1.end(); ++i) {
556	<	for (j = p2.begin(); j !=p2.end(); ++j) {
557	<	p.addCoefficient( i->first + j->first, i->second * j->second);
558	<	}
556	>	for (j = p2.begin(); j !=p2.end(); ++j) {
557	>	p.addCoefficient( i->first + j->first, i->second * j->second);
558	>	}
559		}
560
561		return p;
562	<	}
562	>	}
563
564	<	/**
565	<	* Generates and returns the sum of two given Polynomials.
566	<	* @param p1 the first polynomial
567	<	* @param p2 the second polynomial
568	<	*/
569	<	template<typename ElemType>
570	<	Polynomial<ElemType> operator +(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
571	<	Polynomial<ElemType> p(p1);
564	>	template<typename Real>
565	>	Polynomial<Real> operator *(const Polynomial<Real>& p, const Real v) {
566	>	typename Polynomial<Real>::const_iterator i;
567	>	Polynomial<Real> result;
568	>
569	>	for (i = p.begin(); i !=p.end(); ++i) {
570	>	result.setCoefficient( i->first , i->second * v);
571	>	}
572
573	<	typename Polynomial<ElemType>::const_iterator i;
573	>	return result;
574	>	}
575
576	+	template<typename Real>
577	+	Polynomial<Real> operator *( const Real v, const Polynomial<Real>& p) {
578	+	typename Polynomial<Real>::const_iterator i;
579	+	Polynomial<Real> result;
580	+
581	+	for (i = p.begin(); i !=p.end(); ++i) {
582	+	result.setCoefficient( i->first , i->second * v);
583	+	}
584	+
585	+	return result;
586	+	}
587	+
588	+	/**
589	+	* Generates and returns the sum of two given Polynomials.
590	+	* @param p1 the first polynomial
591	+	* @param p2 the second polynomial
592	+	*/
593	+	template<typename Real>
594	+	Polynomial<Real> operator +(const Polynomial<Real>& p1, const Polynomial<Real>& p2) {
595	+	Polynomial<Real> p(p1);
596	+
597	+	typename Polynomial<Real>::const_iterator i;
598	+
599		for (i =  p2.begin(); i  != p2.end(); ++i) {
600	<	p.addCoefficient(i->first, i->second);
600	>	p.addCoefficient(i->first, i->second);
601		}
602
603		return p;
604
605	<	}
605	>	}
606
607	<	/**
608	<	* Generates and returns the difference of two given Polynomials.
609	<	* @return
610	<	* @param p1 the first polynomial
611	<	* @param p2 the second polynomial
612	<	*/
613	<	template<typename ElemType>
614	<	Polynomial<ElemType> operator -(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
615	<	Polynomial<ElemType> p(p1);
607	>	/**
608	>	* Generates and returns the difference of two given Polynomials.
609	>	* @return
610	>	* @param p1 the first polynomial
611	>	* @param p2 the second polynomial
612	>	*/
613	>	template<typename Real>
614	>	Polynomial<Real> operator -(const Polynomial<Real>& p1, const Polynomial<Real>& p2) {
615	>	Polynomial<Real> p(p1);
616
617	<	typename Polynomial<ElemType>::const_iterator i;
617	>	typename Polynomial<Real>::const_iterator i;
618
619		for (i =  p2.begin(); i  != p2.end(); ++i) {
620	<	p.addCoefficient(i->first, -i->second);
620	>	p.addCoefficient(i->first, -i->second);
621		}
622
623		return p;
624
625	<	}
625	>	}
626
627	<	/**
628	<	* Tests if two polynomial have the same exponents
629	<	* @return true if these all of the exponents in these Polynomial are identical
630	<	* @param p1 the first polynomial
631	<	* @param p2 the second polynomial
632	<	* @note this function does not compare the coefficient
633	<	*/
634	<	template<typename ElemType>
635	<	bool equal(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
627	>	/**
628	>	* Returns the first derivative of this polynomial.
629	>	* @return the first derivative of this polynomial
630	>	*/
631	>	template<typename Real>
632	>	Polynomial<Real> getDerivative(const Polynomial<Real>& p1) {
633	>	Polynomial<Real> p();
634	>
635	>	typename Polynomial<Real>::const_iterator i;
636	>	int exponent;
637	>	Real coefficient;
638	>
639	>	for (i =  p1.begin(); i  != p1.end(); ++i) {
640	>	exponent = i->first;
641	>	coefficient = i->second;
642	>	p.setCoefficient(exponent-1, coefficient * exponent);
643	>	}
644	>
645	>	return p;
646	>	}
647
648	<	typename Polynomial<ElemType>::const_iterator i;
649	<	typename Polynomial<ElemType>::const_iterator j;
648	>	/**
649	>	* Tests if two polynomial have the same exponents
650	>	* @return true if all of the exponents in these Polynomial are identical
651	>	* @param p1 the first polynomial
652	>	* @param p2 the second polynomial
653	>	* @note this function does not compare the coefficient
654	>	*/
655	>	template<typename Real>
656	>	bool equal(const Polynomial<Real>& p1, const Polynomial<Real>& p2) {
657
658	+	typename Polynomial<Real>::const_iterator i;
659	+	typename Polynomial<Real>::const_iterator j;
660	+
661		if (p1.size() != p2.size() ) {
662	<	return false;
662	>	return false;
663		}
664
665		for (i =  p1.begin(), j = p2.begin(); i  != p1.end() && j != p2.end(); ++i, ++j) {
666	<	if (i->first != j->first) {
667	<	return false;
668	<	}
666	>	if (i->first != j->first) {
667	>	return false;
668	>	}
669		}
670
671		return true;
672	<	}
672	>	}
673
279	–	typedef Polynomial<double> DoublePolynomial;
674
675	<	} //end namespace oopse
675	>
676	>	typedef Polynomial<RealType> DoublePolynomial;
677	>
678	>	} //end namespace OpenMD
679		#endif //MATH_POLYNOMIAL_HPP

Comparing:
trunk/src/math/Polynomial.hpp (property svn:keywords), Revision 385 by tim, Tue Mar 1 20:10:14 2005 UTC vs.
branches/development/src/math/Polynomial.hpp (property svn:keywords), Revision 1465 by chuckv, Fri Jul 9 23:08:25 2010 UTC

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