src/math/SphericalHarmonic.cpp

/*
 * Copyright (c) 2005 The University of Notre Dame. All Rights Reserved.
 *
 * The University of Notre Dame grants you ("Licensee") a
 * non-exclusive, royalty free, license to use, modify and
 * redistribute this software in source and binary code form, provided
 * that the following conditions are met:
 *
 * 1. Acknowledgement of the program authors must be made in any
 *    publication of scientific results based in part on use of the
 *    program.  An acceptable form of acknowledgement is citation of
 *    the article in which the program was described (Matthew
 *    A. Meineke, Charles F. Vardeman II, Teng Lin, Christopher
 *    J. Fennell and J. Daniel Gezelter, "OOPSE: An Object-Oriented
 *    Parallel Simulation Engine for Molecular Dynamics,"
 *    J. Comput. Chem. 26, pp. 252-271 (2005))
 *
 * 2. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 *
 * 3. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the
 *    distribution.
 *
 * This software is provided "AS IS," without a warranty of any
 * kind. All express or implied conditions, representations and
 * warranties, including any implied warranty of merchantability,
 * fitness for a particular purpose or non-infringement, are hereby
 * excluded.  The University of Notre Dame and its licensors shall not
 * be liable for any damages suffered by licensee as a result of
 * using, modifying or distributing the software or its
 * derivatives. In no event will the University of Notre Dame or its
 * licensors be liable for any lost revenue, profit or data, or for
 * direct, indirect, special, consequential, incidental or punitive
 * damages, however caused and regardless of the theory of liability,
 * arising out of the use of or inability to use software, even if the
 * University of Notre Dame has been advised of the possibility of
 * such damages.
 */
 
#include <stdio.h>
#include <limits>
#include "math/SphericalHarmonic.hpp"
#include "utils/simError.h"

using namespace oopse;

SphericalHarmonic::SphericalHarmonic() {
}

ComplexType SphericalHarmonic::getValueAt(RealType costheta, RealType phi) {
  
  RealType p;
  ComplexType phase;
  ComplexType I(0.0, 1.0);
  
  // associated Legendre polynomial
  p = Legendre(L, M, costheta);
 
  phase = exp(I * (ComplexType)M * (ComplexType)phi);
    
  return coefficient * phase * (ComplexType)p;
  
}

//---------------------------------------------------------------------------//
//
// RealType LegendreP (int l, int m, RealType x);
//
// Computes the value of the associated Legendre polynomial P_lm (x)
// of order l at a given point.
//
// Input:
//   l  = degree of the polynomial  >= 0
//   m  = parameter satisfying 0 <= m <= l,
//   x  = point in which the computation is performed, range -1 <= x <= 1.
// Returns:
//   value of the polynomial in x
//
//---------------------------------------------------------------------------//
RealType SphericalHarmonic::LegendreP (int l, int m, RealType x) {
  // check parameters
  if (m < 0 || m > l || fabs(x) > 1.0) {
    printf("LegendreP got a bad argument: l = %d\tm = %d\tx = %lf\n", l, m, x);
    return std::numeric_limits <RealType>:: quiet_NaN();
  }
  
  RealType pmm = 1.0;
  if (m > 0) {
    RealType h = sqrt((1.0-x)*(1.0+x)),
      f = 1.0;
    for (int i = 1; i <= m; i++) {
      pmm *= -f * h;
      f += 2.0;
    }
  }
  if (l == m)
    return pmm;
  else {
    RealType pmmp1 = x * (2 * m + 1) * pmm;
    if (l == (m+1))
      return pmmp1;
    else {
      RealType pll = 0.0;
      for (int ll = m+2; ll <= l; ll++) {
        pll = (x * (2 * ll - 1) * pmmp1 - (ll + m - 1) * pmm) / (ll - m);
        pmm = pmmp1;
        pmmp1 = pll;
      }
      return pll;
    }
  }
}

//
// Routine to calculate the associated Legendre polynomials for all m...
//
RealType SphericalHarmonic::Legendre(int l, int m, RealType x)  {
  RealType result;
  if ( m>l || m <-l ) {
    printf("Legendre got a bad argument: l = %d\tm = %d\tx = %lf\n", l, m, x);
    return std::numeric_limits <RealType>:: quiet_NaN();
  } else if (m >= 0) {
    result = LegendreP(l,m,x);
  } else {
    result = mpow(-m)*Fact(l+m)/Fact(l-m)*LegendreP(l, -m, x);
  }
  result *=mpow(m);
  return result;
}
//
// mpow returns (-1)**m
//
RealType SphericalHarmonic::mpow(int m) {
  int result;
  if (m<0) m=-m;   
  if (m & 0x1) result = -1;
  else result = 1;
  return result;
}
//
// factorial_list is a lookup table for n!
//
static RealType factorial_list[171]=
   {1.,1.,2.,6.,24.,120.,720.,5040.,40320.,362880.,3.6288e6,3.99168e7,4.790016e8,6.2270208e9,
   8.71782912e10,1.307674368e12,2.0922789888e13,3.55687428096e14,6.402373705728e15,
   1.21645100408832e17,
   2.43290200817664e18,5.109094217170944e19,1.1240007277776077e21,2.585201673888498e22,
   6.204484017332394e23,1.5511210043330986e25,4.0329146112660565e26,1.0888869450418352e28,
   3.0488834461171387e29,8.841761993739702e30,2.6525285981219107e32,8.222838654177922e33,
   2.631308369336935e35,8.683317618811886e36,2.9523279903960416e38,1.0333147966386145e40,
   3.7199332678990125e41,1.3763753091226346e43,5.230226174666011e44,2.0397882081197444e46,
   8.159152832478977e47,3.345252661316381e49,1.40500611775288e51,6.041526306337383e52,
   2.658271574788449e54,1.1962222086548019e56,5.502622159812089e57,2.5862324151116818e59,
   1.2413915592536073e61,6.082818640342675e62,3.0414093201713376e64,1.5511187532873822e66,
   8.065817517094388e67,4.2748832840600255e69,2.308436973392414e71,1.2696403353658276e73,
   7.109985878048635e74,4.0526919504877214e76,2.3505613312828785e78,1.3868311854568984e80,
   8.32098711274139e81,5.075802138772248e83,3.146997326038794e85,1.98260831540444e87,
   1.2688693218588417e89,8.247650592082472e90,5.443449390774431e92,3.647111091818868e94,
   2.4800355424368305e96,1.711224524281413e98,1.1978571669969892e100,8.504785885678623e101,
   6.1234458376886085e103,4.4701154615126844e105,3.307885441519386e107,2.48091408113954e109,
   1.8854947016660504e111,1.4518309202828587e113,1.1324281178206297e115,8.946182130782976e116,
   7.156945704626381e118,5.797126020747368e120,4.753643337012842e122,3.945523969720659e124,
   3.314240134565353e126,2.81710411438055e128,2.4227095383672734e130,2.107757298379528e132,
   1.8548264225739844e134,1.650795516090846e136,1.4857159644817615e138,1.352001527678403e140,
   1.2438414054641308e142,1.1567725070816416e144,1.087366156656743e146,1.032997848823906e148,
   9.916779348709496e149,9.619275968248212e151,9.426890448883248e153,9.332621544394415e155,
   9.332621544394415e157,9.42594775983836e159,9.614466715035127e161,9.90290071648618e163,
   1.0299016745145628e166,1.081396758240291e168,1.1462805637347084e170,1.226520203196138e172,
   1.324641819451829e174,1.4438595832024937e176,1.588245541522743e178,1.7629525510902446e180,
   1.974506857221074e182,2.2311927486598138e184,2.5435597334721877e186,2.925093693493016e188,
   3.393108684451898e190,3.969937160808721e192,4.684525849754291e194,5.574585761207606e196,
   6.689502913449127e198,8.094298525273444e200,9.875044200833601e202,1.214630436702533e205,
   1.506141741511141e207,1.882677176888926e209,2.372173242880047e211,3.0126600184576594e213,
   3.856204823625804e215,4.974504222477287e217,6.466855489220474e219,8.47158069087882e221,
   1.1182486511960043e224,1.4872707060906857e226,1.9929427461615188e228,2.6904727073180504e230,
   3.659042881952549e232,5.012888748274992e234,6.917786472619489e236,9.615723196941089e238,
   1.3462012475717526e241,1.898143759076171e243,2.695364137888163e245,3.854370717180073e247,
   5.5502938327393044e249,8.047926057471992e251,1.1749972043909107e254,1.727245890454639e256,
   2.5563239178728654e258,3.80892263763057e260,5.713383956445855e262,8.62720977423324e264,
   1.3113358856834524e267,2.0063439050956823e269,3.0897696138473508e271,4.789142901463394e273,
   7.471062926282894e275,1.1729568794264145e278,1.853271869493735e280,2.9467022724950384e282,
   4.7147236359920616e284,7.590705053947219e286,1.2296942187394494e289,2.0044015765453026e291,
   3.287218585534296e293,5.423910666131589e295,9.003691705778438e297,1.503616514864999e300,
   2.5260757449731984e302,4.269068009004705e304,7.257415615307999e306};
   
//
// Routine to return the factorial of j
// 
RealType SphericalHarmonic::Fact(int j) {
  if (j <= 170 && j>=0) return factorial_list[j];
  
  sprintf( painCave.errMsg,
           "Fact(j) for j >= 171\n");
  painCave.isFatal = 0;
  simError();
  return 0.;
}
Revision:	3010
Committed:	Wed Sep 20 22:16:23 2006 UTC (17 years, 9 months ago) by gezelter
File size:	8611 byte(s)
Log Message:	added SphericalHarmonics, fixed a few problems with BondOrderParameter
#	User	Rev	Content
1	gezelter	3010	/*
2			* Copyright (c) 2005 The University of Notre Dame. All Rights Reserved.
3			*
4			* The University of Notre Dame grants you ("Licensee") a
5			* non-exclusive, royalty free, license to use, modify and
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
19			* notice, this list of conditions and the following disclaimer.
20			*
21			* 3. Redistributions in binary form must reproduce the above copyright
22			* notice, this list of conditions and the following disclaimer in the
23			* documentation and/or other materials provided with the
24			* distribution.
25			*
26			* This software is provided "AS IS," without a warranty of any
27			* kind. All express or implied conditions, representations and
28			* warranties, including any implied warranty of merchantability,
29			* fitness for a particular purpose or non-infringement, are hereby
30			* excluded. The University of Notre Dame and its licensors shall not
31			* be liable for any damages suffered by licensee as a result of
32			* using, modifying or distributing the software or its
33			* derivatives. In no event will the University of Notre Dame or its
34			* licensors be liable for any lost revenue, profit or data, or for
35			* direct, indirect, special, consequential, incidental or punitive
36			* damages, however caused and regardless of the theory of liability,
37			* arising out of the use of or inability to use software, even if the
38			* University of Notre Dame has been advised of the possibility of
39			* such damages.
40			*/
41
42			#include <stdio.h>
43			#include <limits>
44			#include "math/SphericalHarmonic.hpp"
45			#include "utils/simError.h"
46
47			using namespace oopse;
48
49			SphericalHarmonic::SphericalHarmonic() {
50			}
51
52			ComplexType SphericalHarmonic::getValueAt(RealType costheta, RealType phi) {
53
54			RealType p;
55			ComplexType phase;
56			ComplexType I(0.0, 1.0);
57
58			// associated Legendre polynomial
59			p = Legendre(L, M, costheta);
60
61			phase = exp(I * (ComplexType)M * (ComplexType)phi);
62
63			return coefficient * phase * (ComplexType)p;
64
65			}
66
67			//---------------------------------------------------------------------------//
68			//
69			// RealType LegendreP (int l, int m, RealType x);
70			//
71			// Computes the value of the associated Legendre polynomial P_lm (x)
72			// of order l at a given point.
73			//
74			// Input:
75			// l = degree of the polynomial >= 0
76			// m = parameter satisfying 0 <= m <= l,
77			// x = point in which the computation is performed, range -1 <= x <= 1.
78			// Returns:
79			// value of the polynomial in x
80			//
81			//---------------------------------------------------------------------------//
82			RealType SphericalHarmonic::LegendreP (int l, int m, RealType x) {
83			// check parameters
84			if (m < 0 \|\| m > l \|\| fabs(x) > 1.0) {
85			printf("LegendreP got a bad argument: l = %d\tm = %d\tx = %lf\n", l, m, x);
86			return std::numeric_limits <RealType>:: quiet_NaN();
87			}
88
89			RealType pmm = 1.0;
90			if (m > 0) {
91			RealType h = sqrt((1.0-x)*(1.0+x)),
92			f = 1.0;
93			for (int i = 1; i <= m; i++) {
94			pmm = -f h;
95			f += 2.0;
96			}
97			}
98			if (l == m)
99			return pmm;
100			else {
101			RealType pmmp1 = x * (2 * m + 1) * pmm;
102			if (l == (m+1))
103			return pmmp1;
104			else {
105			RealType pll = 0.0;
106			for (int ll = m+2; ll <= l; ll++) {
107			pll = (x * (2 * ll - 1) * pmmp1 - (ll + m - 1) * pmm) / (ll - m);
108			pmm = pmmp1;
109			pmmp1 = pll;
110			}
111			return pll;
112			}
113			}
114			}
115
116			//
117			// Routine to calculate the associated Legendre polynomials for all m...
118			//
119			RealType SphericalHarmonic::Legendre(int l, int m, RealType x) {
120			RealType result;
121			if ( m>l \|\| m <-l ) {
122			printf("Legendre got a bad argument: l = %d\tm = %d\tx = %lf\n", l, m, x);
123			return std::numeric_limits <RealType>:: quiet_NaN();
124			} else if (m >= 0) {
125			result = LegendreP(l,m,x);
126			} else {
127			result = mpow(-m)Fact(l+m)/Fact(l-m)LegendreP(l, -m, x);
128			}
129			result *=mpow(m);
130			return result;
131			}
132			//
133			// mpow returns (-1)**m
134			//
135			RealType SphericalHarmonic::mpow(int m) {
136			int result;
137			if (m<0) m=-m;
138			if (m & 0x1) result = -1;
139			else result = 1;
140			return result;
141			}
142			//
143			// factorial_list is a lookup table for n!
144			//
145			static RealType factorial_list[171]=
146			{1.,1.,2.,6.,24.,120.,720.,5040.,40320.,362880.,3.6288e6,3.99168e7,4.790016e8,6.2270208e9,
147			8.71782912e10,1.307674368e12,2.0922789888e13,3.55687428096e14,6.402373705728e15,
148			1.21645100408832e17,
149			2.43290200817664e18,5.109094217170944e19,1.1240007277776077e21,2.585201673888498e22,
150			6.204484017332394e23,1.5511210043330986e25,4.0329146112660565e26,1.0888869450418352e28,
151			3.0488834461171387e29,8.841761993739702e30,2.6525285981219107e32,8.222838654177922e33,
152			2.631308369336935e35,8.683317618811886e36,2.9523279903960416e38,1.0333147966386145e40,
153			3.7199332678990125e41,1.3763753091226346e43,5.230226174666011e44,2.0397882081197444e46,
154			8.159152832478977e47,3.345252661316381e49,1.40500611775288e51,6.041526306337383e52,
155			2.658271574788449e54,1.1962222086548019e56,5.502622159812089e57,2.5862324151116818e59,
156			1.2413915592536073e61,6.082818640342675e62,3.0414093201713376e64,1.5511187532873822e66,
157			8.065817517094388e67,4.2748832840600255e69,2.308436973392414e71,1.2696403353658276e73,
158			7.109985878048635e74,4.0526919504877214e76,2.3505613312828785e78,1.3868311854568984e80,
159			8.32098711274139e81,5.075802138772248e83,3.146997326038794e85,1.98260831540444e87,
160			1.2688693218588417e89,8.247650592082472e90,5.443449390774431e92,3.647111091818868e94,
161			2.4800355424368305e96,1.711224524281413e98,1.1978571669969892e100,8.504785885678623e101,
162			6.1234458376886085e103,4.4701154615126844e105,3.307885441519386e107,2.48091408113954e109,
163			1.8854947016660504e111,1.4518309202828587e113,1.1324281178206297e115,8.946182130782976e116,
164			7.156945704626381e118,5.797126020747368e120,4.753643337012842e122,3.945523969720659e124,
165			3.314240134565353e126,2.81710411438055e128,2.4227095383672734e130,2.107757298379528e132,
166			1.8548264225739844e134,1.650795516090846e136,1.4857159644817615e138,1.352001527678403e140,
167			1.2438414054641308e142,1.1567725070816416e144,1.087366156656743e146,1.032997848823906e148,
168			9.916779348709496e149,9.619275968248212e151,9.426890448883248e153,9.332621544394415e155,
169			9.332621544394415e157,9.42594775983836e159,9.614466715035127e161,9.90290071648618e163,
170			1.0299016745145628e166,1.081396758240291e168,1.1462805637347084e170,1.226520203196138e172,
171			1.324641819451829e174,1.4438595832024937e176,1.588245541522743e178,1.7629525510902446e180,
172			1.974506857221074e182,2.2311927486598138e184,2.5435597334721877e186,2.925093693493016e188,
173			3.393108684451898e190,3.969937160808721e192,4.684525849754291e194,5.574585761207606e196,
174			6.689502913449127e198,8.094298525273444e200,9.875044200833601e202,1.214630436702533e205,
175			1.506141741511141e207,1.882677176888926e209,2.372173242880047e211,3.0126600184576594e213,
176			3.856204823625804e215,4.974504222477287e217,6.466855489220474e219,8.47158069087882e221,
177			1.1182486511960043e224,1.4872707060906857e226,1.9929427461615188e228,2.6904727073180504e230,
178			3.659042881952549e232,5.012888748274992e234,6.917786472619489e236,9.615723196941089e238,
179			1.3462012475717526e241,1.898143759076171e243,2.695364137888163e245,3.854370717180073e247,
180			5.5502938327393044e249,8.047926057471992e251,1.1749972043909107e254,1.727245890454639e256,
181			2.5563239178728654e258,3.80892263763057e260,5.713383956445855e262,8.62720977423324e264,
182			1.3113358856834524e267,2.0063439050956823e269,3.0897696138473508e271,4.789142901463394e273,
183			7.471062926282894e275,1.1729568794264145e278,1.853271869493735e280,2.9467022724950384e282,
184			4.7147236359920616e284,7.590705053947219e286,1.2296942187394494e289,2.0044015765453026e291,
185			3.287218585534296e293,5.423910666131589e295,9.003691705778438e297,1.503616514864999e300,
186			2.5260757449731984e302,4.269068009004705e304,7.257415615307999e306};
187
188			//
189			// Routine to return the factorial of j
190			//
191			RealType SphericalHarmonic::Fact(int j) {
192			if (j <= 170 && j>=0) return factorial_list[j];
193
194			sprintf( painCave.errMsg,
195			"Fact(j) for j >= 171\n");
196			painCave.isFatal = 0;
197			simError();
198			return 0.;
199			}