src/math/RealSphericalHarmonic.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 <cmath>

#include "math/RealSphericalHarmonic.hpp"

using namespace oopse;

RealSphericalHarmonic::RealSphericalHarmonic() {
}

double RealSphericalHarmonic::getValueAt(double costheta, double phi) {
  
  double p, phase;
  
  // associated Legendre polynomial
  p = LegendreP(L,M,costheta);
 
  if (functionType == RSH_SIN) {
    phase = sin((double)M * phi);
  } else {
    phase = cos((double)M * phi);
  }
  
  return coefficient*p*phase;
  
}

//---------------------------------------------------------------------------//
//
// double LegendreP (int l, int m, double 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
//
//---------------------------------------------------------------------------//
double RealSphericalHarmonic::LegendreP (int l, int m, double 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 NAN;
  }
  
  double pmm = 1.0;
  if (m > 0) {
    double 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 {
    double pmmp1 = x * (2 * m + 1) * pmm;
    if (l == (m+1))
      return pmmp1;
    else {
      double 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;
    }
  }
}

Revision:	246
Committed:	Wed Jan 12 22:41:40 2005 UTC (20 years, 9 months ago) by gezelter
File size:	3845 byte(s)
Log Message:	merging new_design branch into OOPSE-2.0
#	Content
1	/*
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 <cmath>
44
45	#include "math/RealSphericalHarmonic.hpp"
46
47	using namespace oopse;
48
49	RealSphericalHarmonic::RealSphericalHarmonic() {
50	}
51
52	double RealSphericalHarmonic::getValueAt(double costheta, double phi) {
53
54	double p, phase;
55
56	// associated Legendre polynomial
57	p = LegendreP(L,M,costheta);
58
59	if (functionType == RSH_SIN) {
60	phase = sin((double)M * phi);
61	} else {
62	phase = cos((double)M * phi);
63	}
64
65	return coefficientpphase;
66
67	}
68
69	//---------------------------------------------------------------------------//
70	//
71	// double LegendreP (int l, int m, double x);
72	//
73	// Computes the value of the associated Legendre polynomial P_lm (x)
74	// of order l at a given point.
75	//
76	// Input:
77	// l = degree of the polynomial >= 0
78	// m = parameter satisfying 0 <= m <= l,
79	// x = point in which the computation is performed, range -1 <= x <= 1.
80	// Returns:
81	// value of the polynomial in x
82	//
83	//---------------------------------------------------------------------------//
84	double RealSphericalHarmonic::LegendreP (int l, int m, double x) {
85	// check parameters
86	if (m < 0 \|\| m > l \|\| fabs(x) > 1.0) {
87	printf("LegendreP got a bad argument: l = %d\tm = %d\tx = %lf\n", l, m, x);
88	return NAN;
89	}
90
91	double pmm = 1.0;
92	if (m > 0) {
93	double h = sqrt((1.0-x)*(1.0+x)),
94	f = 1.0;
95	for (int i = 1; i <= m; i++) {
96	pmm = -f h;
97	f += 2.0;
98	}
99	}
100	if (l == m)
101	return pmm;
102	else {
103	double pmmp1 = x * (2 * m + 1) * pmm;
104	if (l == (m+1))
105	return pmmp1;
106	else {
107	double pll = 0.0;
108	for (int ll = m+2; ll <= l; ll++) {
109	pll = (x * (2 * ll - 1) * pmmp1 - (ll + m - 1) * pmm) / (ll - m);
110	pmm = pmmp1;
111	pmmp1 = pll;
112	}
113	return pll;
114	}
115	}
116	}
117