| 6 |
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* 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. |
| 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 |
|
/** |
| 58 |
|
#include "config.h" |
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|
#include "math/Eigenvalue.hpp" |
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|
|
| 61 |
< |
namespace oopse { |
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> |
namespace OpenMD { |
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|
|
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template<typename Real> Real fastpow(Real x, int N) { |
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Real result(1); //or 1.0? |
| 159 |
|
* this Polynomial. |
| 160 |
|
* @return the coefficient associated with the given power for |
| 161 |
|
* this Polynomial |
| 162 |
< |
* @exponent exponent of any term in this Polynomial |
| 162 |
> |
* @param exponent exponent of any term in this Polynomial |
| 163 |
|
*/ |
| 164 |
|
Real getCoefficient(ExponentType exponent) { |
| 165 |
|
iterator i = polyPairMap_.find(exponent); |
| 273 |
|
* Returns the first derivative of this polynomial. |
| 274 |
|
* @return the first derivative of this polynomial |
| 275 |
|
*/ |
| 276 |
< |
PolynomialType & getDerivative() { |
| 277 |
< |
Polynomial<Real> p(); |
| 276 |
> |
PolynomialType* getDerivative() { |
| 277 |
> |
Polynomial<Real>* p = new Polynomial<Real>(); |
| 278 |
|
|
| 279 |
|
typename Polynomial<Real>::const_iterator i; |
| 280 |
|
ExponentType exponent; |
| 283 |
|
for (i = this->begin(); i != this->end(); ++i) { |
| 284 |
|
exponent = i->first; |
| 285 |
|
coefficient = i->second; |
| 286 |
< |
p.setCoefficient(exponent-1, coefficient * exponent); |
| 286 |
> |
p->setCoefficient(exponent-1, coefficient * exponent); |
| 287 |
|
} |
| 288 |
|
|
| 289 |
|
return p; |
| 317 |
|
|
| 318 |
|
std::vector<complex<Real> > roots; |
| 319 |
|
for (int i = 0; i < rank; i++) { |
| 320 |
< |
roots.push_back(complex(reals(i), imags(i))); |
| 320 |
> |
roots.push_back(complex<Real>(reals(i), imags(i))); |
| 321 |
|
} |
| 322 |
|
|
| 323 |
|
return roots; |
| 338 |
|
roots.push_back( -fC0 / fC1); |
| 339 |
|
return roots; |
| 340 |
|
} |
| 340 |
– |
break; |
| 341 |
|
case 2: { |
| 342 |
|
Real fC2 = getCoefficient(2); |
| 343 |
|
Real fC1 = getCoefficient(1); |
| 346 |
|
if (abs(fDiscr) <= fEpsilon) { |
| 347 |
|
fDiscr = (Real)0.0; |
| 348 |
|
} |
| 349 |
< |
|
| 349 |
> |
|
| 350 |
|
if (fDiscr < (Real)0.0) { // complex roots only |
| 351 |
|
return roots; |
| 352 |
|
} |
| 353 |
< |
|
| 353 |
> |
|
| 354 |
|
Real fTmp = ((Real)0.5)/fC2; |
| 355 |
< |
|
| 355 |
> |
|
| 356 |
|
if (fDiscr > (Real)0.0) { // 2 real roots |
| 357 |
|
fDiscr = sqrt(fDiscr); |
| 358 |
|
roots.push_back(fTmp*(-fC1 - fDiscr)); |
| 361 |
|
roots.push_back(-fTmp * fC1); // 1 real root |
| 362 |
|
} |
| 363 |
|
} |
| 364 |
< |
return roots; |
| 365 |
< |
break; |
| 366 |
< |
|
| 364 |
> |
return roots; |
| 365 |
|
case 3: { |
| 366 |
|
Real fC3 = getCoefficient(3); |
| 367 |
|
Real fC2 = getCoefficient(2); |
| 428 |
|
} |
| 429 |
|
} |
| 430 |
|
return roots; |
| 433 |
– |
break; |
| 431 |
|
case 4: { |
| 432 |
|
Real fC4 = getCoefficient(4); |
| 433 |
|
Real fC3 = getCoefficient(3); |
| 513 |
|
} |
| 514 |
|
} |
| 515 |
|
return roots; |
| 519 |
– |
break; |
| 516 |
|
default: { |
| 517 |
|
DynamicRectMatrix<Real> companion = CreateCompanion(); |
| 518 |
|
JAMA::Eigenvalue<Real> eig(companion); |
| 526 |
|
} |
| 527 |
|
} |
| 528 |
|
return roots; |
| 533 |
– |
break; |
| 529 |
|
} |
| 535 |
– |
|
| 536 |
– |
return roots; // should be empty if you got here |
| 530 |
|
} |
| 531 |
< |
|
| 531 |
> |
|
| 532 |
|
private: |
| 533 |
|
|
| 534 |
|
PolynomialPairMap polyPairMap_; |
| 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(); |
| 625 |
> |
Polynomial<Real> * getDerivative(const Polynomial<Real>& p1) { |
| 626 |
> |
Polynomial<Real> * p = new Polynomial<Real>(); |
| 627 |
|
|
| 628 |
|
typename Polynomial<Real>::const_iterator i; |
| 629 |
< |
ExponentType exponent; |
| 630 |
< |
CoefficientType coefficient; |
| 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); |
| 635 |
> |
p->setCoefficient(exponent-1, coefficient * exponent); |
| 636 |
|
} |
| 637 |
|
|
| 638 |
|
return p; |
| 668 |
|
|
| 669 |
|
typedef Polynomial<RealType> DoublePolynomial; |
| 670 |
|
|
| 671 |
< |
} //end namespace oopse |
| 671 |
> |
} //end namespace OpenMD |
| 672 |
|
#endif //MATH_POLYNOMIAL_HPP |
