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trunk/src/math/Polynomial.hpp (file contents), Revision 507 by gezelter, Fri Apr 15 22:04:00 2005 UTC vs.
branches/development/src/math/Polynomial.hpp (file contents), Revision 1874 by gezelter, Wed May 15 15:09:35 2013 UTC

#	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, 234107 (2008).
39	+	* [4]  Kuang & Gezelter,  J. Chem. Phys. 133, 164101 (2010).
40	+	* [5]  Vardeman, Stocker & Gezelter, J. Chem. Theory Comput. 7, 834 (2011).
41		*/
42
43		/**
#	Line 53 | Line 54
54		#include <list>
55		#include <map>
56		#include <utility>
57	+	#include <complex>
58	+	#include "config.h"
59	+	#include "math/Eigenvalue.hpp"
60
61	<	namespace oopse {
61	>	namespace OpenMD {
62	>
63	>	template<typename Real> Real fastpow(Real x, int N) {
64	>	Real result(1); //or 1.0?
65
59	–	template<typename ElemType> ElemType pow(ElemType x, int N) {
60	–	ElemType result(1);
61	–
66		for (int i = 0; i < N; ++i) {
67		result *= x;
68		}
#	Line 70 | Line 74 | namespace oopse {
74		* @class Polynomial Polynomial.hpp "math/Polynomial.hpp"
75		* A generic Polynomial class
76		*/
77	<	template<typename ElemType>
77	>	template<typename Real>
78		class Polynomial {
79
80		public:
81	<
81	>	typedef Polynomial<Real> PolynomialType;
82		typedef int ExponentType;
83	<	typedef ElemType CoefficientType;
83	>	typedef Real CoefficientType;
84		typedef std::map<ExponentType, CoefficientType> PolynomialPairMap;
85		typedef typename PolynomialPairMap::iterator iterator;
86		typedef typename PolynomialPairMap::const_iterator const_iterator;
87	+
88	+	Polynomial() {}
89	+	Polynomial(Real v) {setCoefficient(0, v);}
90		/**
91		* Calculates the value of this Polynomial evaluated at the given x value.
92	<	* @return The value of this Polynomial evaluates at the given x value
93	<	* @param x the value of the independent variable for this Polynomial function
92	>	* @return The value of this Polynomial evaluates at the given x value
93	>	* @param x the value of the independent variable for this
94	>	* Polynomial function
95		*/
96	<	ElemType evaluate(const ElemType& x) {
97	<	ElemType result = ElemType();
96	>	Real evaluate(const Real& x) {
97	>	Real result = Real();
98		ExponentType exponent;
99		CoefficientType coefficient;
100
101		for (iterator i = polyPairMap_.begin(); i != polyPairMap_.end(); ++i) {
102		exponent = i->first;
103		coefficient = i->second;
104	<	result  += pow(x, exponent) * coefficient;
104	>	result  += fastpow(x, exponent) * coefficient;
105		}
106
107		return result;
#	Line 104 | Line 112 | namespace oopse {
112		* @return the first derivative of this polynomial
113		* @param x
114		*/
115	<	ElemType evaluateDerivative(const ElemType& x) {
116	<	ElemType result = ElemType();
115	>	Real evaluateDerivative(const Real& x) {
116	>	Real result = Real();
117		ExponentType exponent;
118		CoefficientType coefficient;
119
120		for (iterator i = polyPairMap_.begin(); i != polyPairMap_.end(); ++i) {
121		exponent = i->first;
122		coefficient = i->second;
123	<	result  += pow(x, exponent - 1) * coefficient * exponent;
123	>	result  += fastpow(x, exponent - 1) * coefficient * exponent;
124		}
125
126		return result;
127		}
128
129	+
130		/**
131	<	* Set the coefficent of the specified exponent, if the coefficient is already there, it
132	<	* will be overwritten.
131	>	* Set the coefficent of the specified exponent, if the
132	>	* coefficient is already there, it will be overwritten.
133		* @param exponent exponent of a term in this Polynomial
134		* @param coefficient multiplier of a term in this Polynomial
135	<	*/
136	<
137	<	void setCoefficient(int exponent, const ElemType& coefficient) {
129	<	polyPairMap_.insert(typename PolynomialPairMap::value_type(exponent, coefficient));
135	>	*/
136	>	void setCoefficient(int exponent, const Real& coefficient) {
137	>	polyPairMap_[exponent] = coefficient;
138		}
139	<
139	>
140		/**
141	<	* Set the coefficent of the specified exponent. If the coefficient is already there,  just add the
142	<	* new coefficient to the old one, otherwise,  just call setCoefficent
141	>	* Set the coefficent of the specified exponent. If the
142	>	* coefficient is already there, just add the new coefficient to
143	>	* the old one, otherwise, just call setCoefficent
144		* @param exponent exponent of a term in this Polynomial
145		* @param coefficient multiplier of a term in this Polynomial
146	<	*/
147	<
139	<	void addCoefficient(int exponent, const ElemType& coefficient) {
146	>	*/
147	>	void addCoefficient(int exponent, const Real& coefficient) {
148		iterator i = polyPairMap_.find(exponent);
149
150		if (i != end()) {
#	Line 146 | Line 154 | namespace oopse {
154		}
155		}
156
149	–
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
158	>	* Returns the coefficient associated with the given power for
159	>	* this Polynomial.
160	>	* @return the coefficient associated with the given power for
161	>	* this Polynomial
162	>	* @param exponent exponent of any term in this Polynomial
163		*/
164	<	ElemType getCoefficient(ExponentType exponent) {
164	>	Real getCoefficient(ExponentType exponent) {
165		iterator i = polyPairMap_.find(exponent);
166
167		if (i != end()) {
168		return i->second;
169		} else {
170	<	return ElemType(0);
170	>	return Real(0);
171		}
172		}
173
#	Line 184 | Line 193 | namespace oopse {
193
194		size_t size() {
195		return polyPairMap_.size();
196	+	}
197	+
198	+	int degree() {
199	+	int deg = 0;
200	+	for (iterator i = polyPairMap_.begin(); i != polyPairMap_.end(); ++i) {
201	+	if (i->first > deg)
202	+	deg = i->first;
203	+	}
204	+	return deg;
205	+	}
206	+
207	+	PolynomialType& operator = (const PolynomialType& p) {
208	+
209	+	if (this != &p)  // protect against invalid self-assignment
210	+	{
211	+	typename Polynomial<Real>::const_iterator i;
212	+
213	+	polyPairMap_.clear();  // clear out the old map
214	+
215	+	for (i =  p.begin(); i != p.end(); ++i) {
216	+	this->setCoefficient(i->first, i->second);
217	+	}
218	+	}
219	+	// by convention, always return *this
220	+	return *this;
221	+	}
222	+
223	+	PolynomialType& operator += (const PolynomialType& p) {
224	+	typename Polynomial<Real>::const_iterator i;
225	+
226	+	for (i =  p.begin(); i  != p.end(); ++i) {
227	+	this->addCoefficient(i->first, i->second);
228	+	}
229	+
230	+	return *this;
231	+	}
232	+
233	+	PolynomialType& operator -= (const PolynomialType& p) {
234	+	typename Polynomial<Real>::const_iterator i;
235	+	for (i =  p.begin(); i  != p.end(); ++i) {
236	+	this->addCoefficient(i->first, -i->second);
237	+	}
238	+	return *this;
239		}
240	+
241	+	PolynomialType& operator *= (const PolynomialType& p) {
242	+	typename Polynomial<Real>::const_iterator i;
243	+	typename Polynomial<Real>::const_iterator j;
244	+	Polynomial<Real> p2(*this);
245	+
246	+	polyPairMap_.clear();  // clear out old map
247	+	for (i = p2.begin(); i !=p2.end(); ++i) {
248	+	for (j = p.begin(); j !=p.end(); ++j) {
249	+	this->addCoefficient( i->first + j->first, i->second * j->second);
250	+	}
251	+	}
252	+	return *this;
253	+	}
254	+
255	+	//PolynomialType& operator *= (const Real v)
256	+	PolynomialType& operator *= (const Real v) {
257	+	typename Polynomial<Real>::const_iterator i;
258	+	//Polynomial<Real> result;
259	+
260	+	for (i = this->begin(); i != this->end(); ++i) {
261	+	this->setCoefficient( i->first, i->second*v);
262	+	}
263	+
264	+	return *this;
265	+	}
266	+
267	+	PolynomialType& operator += (const Real v) {
268	+	this->addCoefficient( 0, v);
269	+	return *this;
270	+	}
271	+
272	+	/**
273	+	* Returns the first derivative of this polynomial.
274	+	* @return the first derivative of this polynomial
275	+	*/
276	+	PolynomialType* getDerivative() {
277	+	Polynomial<Real>* p = new Polynomial<Real>();
278	+
279	+	typename Polynomial<Real>::const_iterator i;
280	+	ExponentType exponent;
281	+	CoefficientType coefficient;
282	+
283	+	for (i =  this->begin(); i  != this->end(); ++i) {
284	+	exponent = i->first;
285	+	coefficient = i->second;
286	+	p->setCoefficient(exponent-1, coefficient * exponent);
287	+	}
288	+
289	+	return p;
290	+	}
291	+
292	+	// Creates the Companion matrix for a given polynomial
293	+	DynamicRectMatrix<Real> CreateCompanion() {
294	+	int rank = degree();
295	+	DynamicRectMatrix<Real> mat(rank, rank);
296	+	Real majorCoeff = getCoefficient(rank);
297	+	for(int i = 0; i < rank; ++i) {
298	+	for(int j = 0; j < rank; ++j) {
299	+	if(i - j == 1) {
300	+	mat(i, j) = 1;
301	+	} else if(j == rank-1) {
302	+	mat(i, j) = -1 * getCoefficient(i) / majorCoeff;
303	+	}
304	+	}
305	+	}
306	+	return mat;
307	+	}
308	+
309	+	// Find the Roots of a given polynomial
310	+	std::vector<complex<Real> > FindRoots() {
311	+	int rank = degree();
312	+	DynamicRectMatrix<Real> companion = CreateCompanion();
313	+	JAMA::Eigenvalue<Real> eig(companion);
314	+	DynamicVector<Real> reals, imags;
315	+	eig.getRealEigenvalues(reals);
316	+	eig.getImagEigenvalues(imags);
317	+
318	+	std::vector<complex<Real> > roots;
319	+	for (int i = 0; i < rank; i++) {
320	+	roots.push_back(complex<Real>(reals(i), imags(i)));
321	+	}
322	+
323	+	return roots;
324	+	}
325	+
326	+	std::vector<Real> FindRealRoots() {
327	+
328	+	const Real fEpsilon = 1.0e-8;
329	+	std::vector<Real> roots;
330	+	roots.clear();
331	+
332	+	const int deg = degree();
333	+
334	+	switch (deg) {
335	+	case 1: {
336	+	Real fC1 = getCoefficient(1);
337	+	Real fC0 = getCoefficient(0);
338	+	roots.push_back( -fC0 / fC1);
339	+	return roots;
340	+	}
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	+	case 3: {
366	+	Real fC3 = getCoefficient(3);
367	+	Real fC2 = getCoefficient(2);
368	+	Real fC1 = getCoefficient(1);
369	+	Real fC0 = getCoefficient(0);
370	+
371	+	// make polynomial monic, x^3+c2*x^2+c1*x+c0
372	+	Real fInvC3 = ((Real)1.0)/fC3;
373	+	fC0 *= fInvC3;
374	+	fC1 *= fInvC3;
375	+	fC2 *= fInvC3;
376	+
377	+	// convert to y^3+a*y+b = 0 by x = y-c2/3
378	+	const Real fThird = (Real)1.0/(Real)3.0;
379	+	const Real fTwentySeventh = (Real)1.0/(Real)27.0;
380	+	Real fOffset = fThird*fC2;
381	+	Real fA = fC1 - fC2*fOffset;
382	+	Real fB = fC0+fC2*(((Real)2.0)*fC2*fC2-((Real)9.0)*fC1)*fTwentySeventh;
383	+	Real fHalfB = ((Real)0.5)*fB;
384	+
385	+	Real fDiscr = fHalfB*fHalfB + fA*fA*fA*fTwentySeventh;
386	+	if (fabs(fDiscr) <= fEpsilon) {
387	+	fDiscr = (Real)0.0;
388	+	}
389	+
390	+	if (fDiscr > (Real)0.0) {  // 1 real, 2 complex roots
391
392	+	fDiscr = sqrt(fDiscr);
393	+	Real fTemp = -fHalfB + fDiscr;
394	+	Real root;
395	+	if (fTemp >= (Real)0.0) {
396	+	root = pow(fTemp,fThird);
397	+	} else {
398	+	root = -pow(-fTemp,fThird);
399	+	}
400	+	fTemp = -fHalfB - fDiscr;
401	+	if ( fTemp >= (Real)0.0 ) {
402	+	root += pow(fTemp,fThird);
403	+	} else {
404	+	root -= pow(-fTemp,fThird);
405	+	}
406	+	root -= fOffset;
407	+
408	+	roots.push_back(root);
409	+	} else if (fDiscr < (Real)0.0) {
410	+	const Real fSqrt3 = sqrt((Real)3.0);
411	+	Real fDist = sqrt(-fThird*fA);
412	+	Real fAngle = fThird*atan2(sqrt(-fDiscr), -fHalfB);
413	+	Real fCos = cos(fAngle);
414	+	Real fSin = sin(fAngle);
415	+	roots.push_back(((Real)2.0)*fDist*fCos-fOffset);
416	+	roots.push_back(-fDist*(fCos+fSqrt3*fSin)-fOffset);
417	+	roots.push_back(-fDist*(fCos-fSqrt3*fSin)-fOffset);
418	+	} else {
419	+	Real fTemp;
420	+	if (fHalfB >= (Real)0.0) {
421	+	fTemp = -pow(fHalfB,fThird);
422	+	} else {
423	+	fTemp = pow(-fHalfB,fThird);
424	+	}
425	+	roots.push_back(((Real)2.0)*fTemp-fOffset);
426	+	roots.push_back(-fTemp-fOffset);
427	+	roots.push_back(-fTemp-fOffset);
428	+	}
429	+	}
430	+	return roots;
431	+	case 4: {
432	+	Real fC4 = getCoefficient(4);
433	+	Real fC3 = getCoefficient(3);
434	+	Real fC2 = getCoefficient(2);
435	+	Real fC1 = getCoefficient(1);
436	+	Real fC0 = getCoefficient(0);
437	+
438	+	// make polynomial monic, x^4+c3*x^3+c2*x^2+c1*x+c0
439	+	Real fInvC4 = ((Real)1.0)/fC4;
440	+	fC0 *= fInvC4;
441	+	fC1 *= fInvC4;
442	+	fC2 *= fInvC4;
443	+	fC3 *= fInvC4;
444	+
445	+	// reduction to resolvent cubic polynomial y^3+r2*y^2+r1*y+r0 = 0
446	+	Real fR0 = -fC3*fC3*fC0 + ((Real)4.0)*fC2*fC0 - fC1*fC1;
447	+	Real fR1 = fC3*fC1 - ((Real)4.0)*fC0;
448	+	Real fR2 = -fC2;
449	+	Polynomial<Real> tempCubic;
450	+	tempCubic.setCoefficient(0, fR0);
451	+	tempCubic.setCoefficient(1, fR1);
452	+	tempCubic.setCoefficient(2, fR2);
453	+	tempCubic.setCoefficient(3, 1.0);
454	+	std::vector<Real> cubeRoots = tempCubic.FindRealRoots(); // always
455	+	// produces
456	+	// at
457	+	// least
458	+	// one
459	+	// root
460	+	Real fY = cubeRoots[0];
461	+
462	+	Real fDiscr = ((Real)0.25)*fC3*fC3 - fC2 + fY;
463	+	if (fabs(fDiscr) <= fEpsilon) {
464	+	fDiscr = (Real)0.0;
465	+	}
466	+
467	+	if (fDiscr > (Real)0.0) {
468	+	Real fR = sqrt(fDiscr);
469	+	Real fT1 = ((Real)0.75)*fC3*fC3 - fR*fR - ((Real)2.0)*fC2;
470	+	Real fT2 = (((Real)4.0)*fC3*fC2 - ((Real)8.0)*fC1 - fC3*fC3*fC3) /
471	+	(((Real)4.0)*fR);
472	+
473	+	Real fTplus = fT1+fT2;
474	+	Real fTminus = fT1-fT2;
475	+	if (fabs(fTplus) <= fEpsilon) {
476	+	fTplus = (Real)0.0;
477	+	}
478	+	if (fabs(fTminus) <= fEpsilon) {
479	+	fTminus = (Real)0.0;
480	+	}
481	+
482	+	if (fTplus >= (Real)0.0) {
483	+	Real fD = sqrt(fTplus);
484	+	roots.push_back(-((Real)0.25)*fC3+((Real)0.5)*(fR+fD));
485	+	roots.push_back(-((Real)0.25)*fC3+((Real)0.5)*(fR-fD));
486	+	}
487	+	if (fTminus >= (Real)0.0) {
488	+	Real fE = sqrt(fTminus);
489	+	roots.push_back(-((Real)0.25)*fC3+((Real)0.5)*(fE-fR));
490	+	roots.push_back(-((Real)0.25)*fC3-((Real)0.5)*(fE+fR));
491	+	}
492	+	} else if (fDiscr < (Real)0.0) {
493	+	//roots.clear();
494	+	} else {
495	+	Real fT2 = fY*fY-((Real)4.0)*fC0;
496	+	if (fT2 >= -fEpsilon) {
497	+	if (fT2 < (Real)0.0) { // round to zero
498	+	fT2 = (Real)0.0;
499	+	}
500	+	fT2 = ((Real)2.0)*sqrt(fT2);
501	+	Real fT1 = ((Real)0.75)*fC3*fC3 - ((Real)2.0)*fC2;
502	+	if (fT1+fT2 >= fEpsilon) {
503	+	Real fD = sqrt(fT1+fT2);
504	+	roots.push_back( -((Real)0.25)*fC3+((Real)0.5)*fD);
505	+	roots.push_back( -((Real)0.25)*fC3-((Real)0.5)*fD);
506	+	}
507	+	if (fT1-fT2 >= fEpsilon) {
508	+	Real fE = sqrt(fT1-fT2);
509	+	roots.push_back( -((Real)0.25)*fC3+((Real)0.5)*fE);
510	+	roots.push_back( -((Real)0.25)*fC3-((Real)0.5)*fE);
511	+	}
512	+	}
513	+	}
514	+	}
515	+	return roots;
516	+	default: {
517	+	DynamicRectMatrix<Real> companion = CreateCompanion();
518	+	JAMA::Eigenvalue<Real> eig(companion);
519	+	DynamicVector<Real> reals, imags;
520	+	eig.getRealEigenvalues(reals);
521	+	eig.getImagEigenvalues(imags);
522	+
523	+	for (int i = 0; i < deg; i++) {
524	+	if (fabs(imags(i)) < fEpsilon)
525	+	roots.push_back(reals(i));
526	+	}
527	+	}
528	+	return roots;
529	+	}
530	+	}
531	+
532		private:
533
534		PolynomialPairMap polyPairMap_;
535		};
536
537	<
537	>
538		/**
539		* Generates and returns the product of two given Polynomials.
540		* @return A Polynomial containing the product of the two given Polynomial parameters
541		*/
542	<	template<typename ElemType>
543	<	Polynomial<ElemType> operator *(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
544	<	typename Polynomial<ElemType>::const_iterator i;
545	<	typename Polynomial<ElemType>::const_iterator j;
546	<	Polynomial<ElemType> p;
542	>	template<typename Real>
543	>	Polynomial<Real> operator *(const Polynomial<Real>& p1, const Polynomial<Real>& p2) {
544	>	typename Polynomial<Real>::const_iterator i;
545	>	typename Polynomial<Real>::const_iterator j;
546	>	Polynomial<Real> p;
547
548		for (i = p1.begin(); i !=p1.end(); ++i) {
549		for (j = p2.begin(); j !=p2.end(); ++j) {
#	Line 211 | Line 554 | namespace oopse {
554		return p;
555		}
556
557	+	template<typename Real>
558	+	Polynomial<Real> operator *(const Polynomial<Real>& p, const Real v) {
559	+	typename Polynomial<Real>::const_iterator i;
560	+	Polynomial<Real> result;
561	+
562	+	for (i = p.begin(); i !=p.end(); ++i) {
563	+	result.setCoefficient( i->first , i->second * v);
564	+	}
565	+
566	+	return result;
567	+	}
568	+
569	+	template<typename Real>
570	+	Polynomial<Real> operator *( const Real v, const Polynomial<Real>& p) {
571	+	typename Polynomial<Real>::const_iterator i;
572	+	Polynomial<Real> result;
573	+
574	+	for (i = p.begin(); i !=p.end(); ++i) {
575	+	result.setCoefficient( i->first , i->second * v);
576	+	}
577	+
578	+	return result;
579	+	}
580	+
581		/**
582		* Generates and returns the sum of two given Polynomials.
583		* @param p1 the first polynomial
584		* @param p2 the second polynomial
585		*/
586	<	template<typename ElemType>
587	<	Polynomial<ElemType> operator +(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
588	<	Polynomial<ElemType> p(p1);
586	>	template<typename Real>
587	>	Polynomial<Real> operator +(const Polynomial<Real>& p1, const Polynomial<Real>& p2) {
588	>	Polynomial<Real> p(p1);
589
590	<	typename Polynomial<ElemType>::const_iterator i;
590	>	typename Polynomial<Real>::const_iterator i;
591
592		for (i =  p2.begin(); i  != p2.end(); ++i) {
593		p.addCoefficient(i->first, i->second);
#	Line 236 | Line 603 | namespace oopse {
603		* @param p1 the first polynomial
604		* @param p2 the second polynomial
605		*/
606	<	template<typename ElemType>
607	<	Polynomial<ElemType> operator -(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
608	<	Polynomial<ElemType> p(p1);
606	>	template<typename Real>
607	>	Polynomial<Real> operator -(const Polynomial<Real>& p1, const Polynomial<Real>& p2) {
608	>	Polynomial<Real> p(p1);
609
610	<	typename Polynomial<ElemType>::const_iterator i;
610	>	typename Polynomial<Real>::const_iterator i;
611
612		for (i =  p2.begin(); i  != p2.end(); ++i) {
613		p.addCoefficient(i->first, -i->second);
#	Line 251 | Line 618 | namespace oopse {
618		}
619
620		/**
621	+	* Returns the first derivative of this polynomial.
622	+	* @return the first derivative of this polynomial
623	+	*/
624	+	template<typename Real>
625	+	Polynomial<Real> * getDerivative(const Polynomial<Real>& p1) {
626	+	Polynomial<Real> * p = new Polynomial<Real>();
627	+
628	+	typename Polynomial<Real>::const_iterator i;
629	+	int exponent;
630	+	Real coefficient;
631	+
632	+	for (i =  p1.begin(); i  != p1.end(); ++i) {
633	+	exponent = i->first;
634	+	coefficient = i->second;
635	+	p->setCoefficient(exponent-1, coefficient * exponent);
636	+	}
637	+
638	+	return p;
639	+	}
640	+
641	+	/**
642		* Tests if two polynomial have the same exponents
643	<	* @return true if these all of the exponents in these Polynomial are identical
643	>	* @return true if all of the exponents in these Polynomial are identical
644		* @param p1 the first polynomial
645		* @param p2 the second polynomial
646		* @note this function does not compare the coefficient
647		*/
648	<	template<typename ElemType>
649	<	bool equal(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
648	>	template<typename Real>
649	>	bool equal(const Polynomial<Real>& p1, const Polynomial<Real>& p2) {
650
651	<	typename Polynomial<ElemType>::const_iterator i;
652	<	typename Polynomial<ElemType>::const_iterator j;
651	>	typename Polynomial<Real>::const_iterator i;
652	>	typename Polynomial<Real>::const_iterator j;
653
654		if (p1.size() != p2.size() ) {
655		return false;
#	Line 276 | Line 664 | namespace oopse {
664		return true;
665		}
666
279	–	typedef Polynomial<double> DoublePolynomial;
667
668	<	} //end namespace oopse
668	>
669	>	typedef Polynomial<RealType> DoublePolynomial;
670	>
671	>	} //end namespace OpenMD
672		#endif //MATH_POLYNOMIAL_HPP

Comparing:
trunk/src/math/Polynomial.hpp (property svn:keywords), Revision 507 by gezelter, Fri Apr 15 22:04:00 2005 UTC vs.
branches/development/src/math/Polynomial.hpp (property svn:keywords), Revision 1874 by gezelter, Wed May 15 15:09:35 2013 UTC

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