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. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 *
 * 2. 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.
 *
 * SUPPORT OPEN SCIENCE!  If you use OpenMD or its source code in your
 * research, please cite the appropriate papers when you publish your
 * work.  Good starting points are:
 *                                                                      
 * [1]  Meineke, et al., J. Comp. Chem. 26, 252-271 (2005).             
 * [2]  Fennell & Gezelter, J. Chem. Phys. 124, 234104 (2006).          
 * [3]  Sun, Lin & Gezelter, J. Chem. Phys. 128, 24107 (2008).          
 * [4]  Kuang & Gezelter,  J. Chem. Phys. 133, 164101 (2010).
 * [5]  Vardeman, Stocker & Gezelter, J. Chem. Theory Comput. 7, 834 (2011).
 */
 
#include <stdio.h>
#include <cmath>
#include <limits>
#include "math/RealSphericalHarmonic.hpp"

using namespace OpenMD;

RealSphericalHarmonic::RealSphericalHarmonic() {
}

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

//---------------------------------------------------------------------------//
//
// 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 RealSphericalHarmonic::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 NAN;
        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;
    }
  }
}

Revision:	1665
Committed:	Tue Nov 22 20:38:56 2011 UTC (13 years, 5 months ago) by gezelter
File size:	4053 byte(s)
Log Message:	updated copyright notices
#	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. Redistributions of source code must retain the above copyright
10	* notice, this list of conditions and the following disclaimer.
11	*
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.
16	*
17	* This software is provided "AS IS," without a warranty of any
18	* kind. All express or implied conditions, representations and
19	* warranties, including any implied warranty of merchantability,
20	* fitness for a particular purpose or non-infringement, are hereby
21	* excluded. The University of Notre Dame and its licensors shall not
22	* be liable for any damages suffered by licensee as a result of
23	* using, modifying or distributing the software or its
24	* derivatives. In no event will the University of Notre Dame or its
25	* licensors be liable for any lost revenue, profit or data, or for
26	* direct, indirect, special, consequential, incidental or punitive
27	* damages, however caused and regardless of the theory of liability,
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, 24107 (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	#include <stdio.h>
44	#include <cmath>
45	#include <limits>
46	#include "math/RealSphericalHarmonic.hpp"
47
48	using namespace OpenMD;
49
50	RealSphericalHarmonic::RealSphericalHarmonic() {
51	}
52
53	RealType RealSphericalHarmonic::getValueAt(RealType costheta, RealType phi) {
54
55	RealType p, phase;
56
57	// associated Legendre polynomial
58	p = LegendreP(L,M,costheta);
59
60	if (functionType == RSH_SIN) {
61	phase = sin((RealType)M * phi);
62	} else {
63	phase = cos((RealType)M * phi);
64	}
65
66	return coefficientpphase;
67
68	}
69
70	//---------------------------------------------------------------------------//
71	//
72	// RealType LegendreP (int l, int m, RealType x);
73	//
74	// Computes the value of the associated Legendre polynomial P_lm (x)
75	// of order l at a given point.
76	//
77	// Input:
78	// l = degree of the polynomial >= 0
79	// m = parameter satisfying 0 <= m <= l,
80	// x = point in which the computation is performed, range -1 <= x <= 1.
81	// Returns:
82	// value of the polynomial in x
83	//
84	//---------------------------------------------------------------------------//
85	RealType RealSphericalHarmonic::LegendreP (int l, int m, RealType x) {
86	// check parameters
87	if (m < 0 \|\| m > l \|\| fabs(x) > 1.0) {
88	printf("LegendreP got a bad argument: l = %d\tm = %d\tx = %lf\n", l, m, x);
89	// return NAN;
90	return std::numeric_limits <RealType>:: quiet_NaN();
91	}
92
93	RealType pmm = 1.0;
94	if (m > 0) {
95	RealType h = sqrt((1.0-x)*(1.0+x)),
96	f = 1.0;
97	for (int i = 1; i <= m; i++) {
98	pmm = -f h;
99	f += 2.0;
100	}
101	}
102	if (l == m)
103	return pmm;
104	else {
105	RealType pmmp1 = x * (2 * m + 1) * pmm;
106	if (l == (m+1))
107	return pmmp1;
108	else {
109	RealType pll = 0.0;
110	for (int ll = m+2; ll <= l; ll++) {
111	pll = (x * (2 * ll - 1) * pmmp1 - (ll + m - 1) * pmm) / (ll - m);
112	pmm = pmmp1;
113	pmmp1 = pll;
114	}
115	return pll;
116	}
117	}
118	}
119