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;
  
  // associated Legendre polynomial
  p = Ptilde(L, M, costheta);
  ComplexType phase(0.0, (RealType)M * phi);    

  return exp(phase) * (ComplexType)p;
  
}
//
// Routine to calculate the associated Legendre polynomials for m>=0
//
RealType SphericalHarmonic::LegendreP(int l,int m, RealType x) {

  RealType temp1, temp2, temp3, temp4, result;
  RealType temp5;
  int i, ll;
  
  if (fabs(x) > 1.0) {
    printf("LegendreP: x out of range: l = %d\tm = %d\tx = %lf\n", l, m, x);
    return std::numeric_limits <RealType>:: quiet_NaN();
  }
  
  if (m>l) {
    printf("LegendreP: m > l: l = %d\tm = %d\tx = %lf\n", l, m, x);
    return std::numeric_limits <RealType>:: quiet_NaN();
  }
    
  if (m<0) { 
    printf("LegendreP: m < 0: l = %d\tm = %d\tx = %lf\n", l, m, x);
    return std::numeric_limits <RealType>:: quiet_NaN();
  } else {
    temp3=1.0;
    
    if (m>0) {
      temp1=sqrt(1.0-pow(x,2));
      temp5 = 1.0;
      for (i=1;i<=m;++i) {
        temp3 *= -temp5*temp1;
        temp5 += 2.0;
      }
    }
    if (l==m) {
      result = temp3;
    } else {
      temp4=x*(2.*m+1.)*temp3;
      if (l==(m+1)) {
        result = temp4;
      } else {
        for (ll=(m+2);ll<=l;++ll) {
          temp2 = (x*(2.*ll-1.)*temp4-(ll+m-1.)*temp3)/(RealType)(ll-m);
          temp3=temp4;
          temp4=temp2;
        }
        result = temp2;
      }
    }
  }
  return result;
}


//
// 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)*LegendreP(l,-m,x);
    result = mpow(-m)*Fact(l+m)/Fact(l-m)*LegendreP(l, -m, x);
  }
  result *=mpow(m);
  return result;
}
//
// Routine to calculate the normalized associated Legendre polynomials...
//
RealType SphericalHarmonic::Ptilde(int l,int m, RealType x){

  RealType result;
  if (m>l || m<-l) {
    result = 0.;
  } else {
    RealType y=(RealType)(2.*l+1.)*Fact(l-m)/Fact(l+m);
    result = sqrt(y) * Legendre(l,m,x);
  }
  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:	3011
Committed:	Thu Sep 21 14:45:08 2006 UTC (17 years, 9 months ago) by gezelter
File size:	8802 byte(s)
Log Message:	Bugfixes in BondOrderParameter and SphericalHarmonic
#	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
56			// associated Legendre polynomial
57	gezelter	3011	p = Ptilde(L, M, costheta);
58			ComplexType phase(0.0, (RealType)M * phi);
59
60			return exp(phase) * (ComplexType)p;
61	gezelter	3010
62			}
63			//
64	gezelter	3011	// Routine to calculate the associated Legendre polynomials for m>=0
65	gezelter	3010	//
66	gezelter	3011	RealType SphericalHarmonic::LegendreP(int l,int m, RealType x) {
67
68			RealType temp1, temp2, temp3, temp4, result;
69			RealType temp5;
70			int i, ll;
71
72			if (fabs(x) > 1.0) {
73			printf("LegendreP: x out of range: l = %d\tm = %d\tx = %lf\n", l, m, x);
74	gezelter	3010	return std::numeric_limits <RealType>:: quiet_NaN();
75			}
76
77	gezelter	3011	if (m>l) {
78			printf("LegendreP: m > l: l = %d\tm = %d\tx = %lf\n", l, m, x);
79			return std::numeric_limits <RealType>:: quiet_NaN();
80	gezelter	3010	}
81	gezelter	3011
82			if (m<0) {
83			printf("LegendreP: m < 0: l = %d\tm = %d\tx = %lf\n", l, m, x);
84			return std::numeric_limits <RealType>:: quiet_NaN();
85			} else {
86			temp3=1.0;
87
88			if (m>0) {
89			temp1=sqrt(1.0-pow(x,2));
90			temp5 = 1.0;
91			for (i=1;i<=m;++i) {
92			temp3 = -temp5temp1;
93			temp5 += 2.0;
94	gezelter	3010	}
95			}
96	gezelter	3011	if (l==m) {
97			result = temp3;
98			} else {
99			temp4=x(2.m+1.)*temp3;
100			if (l==(m+1)) {
101			result = temp4;
102			} else {
103			for (ll=(m+2);ll<=l;++ll) {
104			temp2 = (x(2.ll-1.)temp4-(ll+m-1.)temp3)/(RealType)(ll-m);
105			temp3=temp4;
106			temp4=temp2;
107			}
108			result = temp2;
109			}
110			}
111	gezelter	3010	}
112	gezelter	3011	return result;
113	gezelter	3010	}
114
115	gezelter	3011
116	gezelter	3010	//
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	gezelter	3011	//result = mpow(-m)*LegendreP(l,-m,x);
128	gezelter	3010	result = mpow(-m)Fact(l+m)/Fact(l-m)LegendreP(l, -m, x);
129			}
130			result *=mpow(m);
131			return result;
132			}
133			//
134	gezelter	3011	// Routine to calculate the normalized associated Legendre polynomials...
135			//
136			RealType SphericalHarmonic::Ptilde(int l,int m, RealType x){
137
138			RealType result;
139			if (m>l \|\| m<-l) {
140			result = 0.;
141			} else {
142			RealType y=(RealType)(2.l+1.)Fact(l-m)/Fact(l+m);
143			result = sqrt(y) * Legendre(l,m,x);
144			}
145			return result;
146			}
147			//
148	gezelter	3010	// mpow returns (-1)**m
149			//
150			RealType SphericalHarmonic::mpow(int m) {
151			int result;
152			if (m<0) m=-m;
153			if (m & 0x1) result = -1;
154			else result = 1;
155			return result;
156			}
157			//
158			// factorial_list is a lookup table for n!
159			//
160			static RealType factorial_list[171]=
161			{1.,1.,2.,6.,24.,120.,720.,5040.,40320.,362880.,3.6288e6,3.99168e7,4.790016e8,6.2270208e9,
162			8.71782912e10,1.307674368e12,2.0922789888e13,3.55687428096e14,6.402373705728e15,
163			1.21645100408832e17,
164			2.43290200817664e18,5.109094217170944e19,1.1240007277776077e21,2.585201673888498e22,
165			6.204484017332394e23,1.5511210043330986e25,4.0329146112660565e26,1.0888869450418352e28,
166			3.0488834461171387e29,8.841761993739702e30,2.6525285981219107e32,8.222838654177922e33,
167			2.631308369336935e35,8.683317618811886e36,2.9523279903960416e38,1.0333147966386145e40,
168			3.7199332678990125e41,1.3763753091226346e43,5.230226174666011e44,2.0397882081197444e46,
169			8.159152832478977e47,3.345252661316381e49,1.40500611775288e51,6.041526306337383e52,
170			2.658271574788449e54,1.1962222086548019e56,5.502622159812089e57,2.5862324151116818e59,
171			1.2413915592536073e61,6.082818640342675e62,3.0414093201713376e64,1.5511187532873822e66,
172			8.065817517094388e67,4.2748832840600255e69,2.308436973392414e71,1.2696403353658276e73,
173			7.109985878048635e74,4.0526919504877214e76,2.3505613312828785e78,1.3868311854568984e80,
174			8.32098711274139e81,5.075802138772248e83,3.146997326038794e85,1.98260831540444e87,
175			1.2688693218588417e89,8.247650592082472e90,5.443449390774431e92,3.647111091818868e94,
176			2.4800355424368305e96,1.711224524281413e98,1.1978571669969892e100,8.504785885678623e101,
177			6.1234458376886085e103,4.4701154615126844e105,3.307885441519386e107,2.48091408113954e109,
178			1.8854947016660504e111,1.4518309202828587e113,1.1324281178206297e115,8.946182130782976e116,
179			7.156945704626381e118,5.797126020747368e120,4.753643337012842e122,3.945523969720659e124,
180			3.314240134565353e126,2.81710411438055e128,2.4227095383672734e130,2.107757298379528e132,
181			1.8548264225739844e134,1.650795516090846e136,1.4857159644817615e138,1.352001527678403e140,
182			1.2438414054641308e142,1.1567725070816416e144,1.087366156656743e146,1.032997848823906e148,
183			9.916779348709496e149,9.619275968248212e151,9.426890448883248e153,9.332621544394415e155,
184			9.332621544394415e157,9.42594775983836e159,9.614466715035127e161,9.90290071648618e163,
185			1.0299016745145628e166,1.081396758240291e168,1.1462805637347084e170,1.226520203196138e172,
186			1.324641819451829e174,1.4438595832024937e176,1.588245541522743e178,1.7629525510902446e180,
187			1.974506857221074e182,2.2311927486598138e184,2.5435597334721877e186,2.925093693493016e188,
188			3.393108684451898e190,3.969937160808721e192,4.684525849754291e194,5.574585761207606e196,
189			6.689502913449127e198,8.094298525273444e200,9.875044200833601e202,1.214630436702533e205,
190			1.506141741511141e207,1.882677176888926e209,2.372173242880047e211,3.0126600184576594e213,
191			3.856204823625804e215,4.974504222477287e217,6.466855489220474e219,8.47158069087882e221,
192			1.1182486511960043e224,1.4872707060906857e226,1.9929427461615188e228,2.6904727073180504e230,
193			3.659042881952549e232,5.012888748274992e234,6.917786472619489e236,9.615723196941089e238,
194			1.3462012475717526e241,1.898143759076171e243,2.695364137888163e245,3.854370717180073e247,
195			5.5502938327393044e249,8.047926057471992e251,1.1749972043909107e254,1.727245890454639e256,
196			2.5563239178728654e258,3.80892263763057e260,5.713383956445855e262,8.62720977423324e264,
197			1.3113358856834524e267,2.0063439050956823e269,3.0897696138473508e271,4.789142901463394e273,
198			7.471062926282894e275,1.1729568794264145e278,1.853271869493735e280,2.9467022724950384e282,
199			4.7147236359920616e284,7.590705053947219e286,1.2296942187394494e289,2.0044015765453026e291,
200			3.287218585534296e293,5.423910666131589e295,9.003691705778438e297,1.503616514864999e300,
201			2.5260757449731984e302,4.269068009004705e304,7.257415615307999e306};
202
203			//
204			// Routine to return the factorial of j
205			//
206			RealType SphericalHarmonic::Fact(int j) {
207			if (j <= 170 && j>=0) return factorial_list[j];
208
209			sprintf( painCave.errMsg,
210			"Fact(j) for j >= 171\n");
211			painCave.isFatal = 0;
212			simError();
213			return 0.;
214			}