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]  Vardeman & Gezelter, in progress (2009).                        
 */
 
#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:	1390
Committed:	Wed Nov 25 20:02:06 2009 UTC (15 years, 5 months ago) by gezelter
File size:	3987 byte(s)
Log Message:	Almost all of the changes necessary to create OpenMD out of our old project (OOPSE-4)
#	User	Rev	Content
1	gezelter	507	/*
2	gezelter	246	* 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	gezelter	1390	* 1. Redistributions of source code must retain the above copyright
10	gezelter	246	* notice, this list of conditions and the following disclaimer.
11			*
12	gezelter	1390	* 2. Redistributions in binary form must reproduce the above copyright
13	gezelter	246	* 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	gezelter	1390	*
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] Vardeman & Gezelter, in progress (2009).
40	gezelter	246	*/
41
42	gezelter	98	#include <stdio.h>
43			#include <cmath>
44	chuckv	526	#include <limits>
45	gezelter	98	#include "math/RealSphericalHarmonic.hpp"
46
47	gezelter	1390	using namespace OpenMD;
48	gezelter	98
49			RealSphericalHarmonic::RealSphericalHarmonic() {
50			}
51
52	tim	963	RealType RealSphericalHarmonic::getValueAt(RealType costheta, RealType phi) {
53	gezelter	98
54	tim	963	RealType p, phase;
55	gezelter	98
56			// associated Legendre polynomial
57			p = LegendreP(L,M,costheta);
58	chrisfen	195
59	gezelter	158	if (functionType == RSH_SIN) {
60	tim	963	phase = sin((RealType)M * phi);
61	gezelter	98	} else {
62	tim	963	phase = cos((RealType)M * phi);
63	gezelter	98	}
64
65			return coefficientpphase;
66
67			}
68
69			//---------------------------------------------------------------------------//
70			//
71	tim	963	// RealType LegendreP (int l, int m, RealType x);
72	gezelter	98	//
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	tim	963	RealType RealSphericalHarmonic::LegendreP (int l, int m, RealType x) {
85	gezelter	98	// 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	chuckv	526	// return NAN;
89	tim	963	return std::numeric_limits <RealType>:: quiet_NaN();
90	gezelter	98	}
91
92	tim	963	RealType pmm = 1.0;
93	gezelter	98	if (m > 0) {
94	tim	963	RealType h = sqrt((1.0-x)*(1.0+x)),
95	gezelter	98	f = 1.0;
96			for (int i = 1; i <= m; i++) {
97			pmm = -f h;
98			f += 2.0;
99			}
100			}
101			if (l == m)
102			return pmm;
103			else {
104	tim	963	RealType pmmp1 = x * (2 * m + 1) * pmm;
105	gezelter	98	if (l == (m+1))
106			return pmmp1;
107			else {
108	tim	963	RealType pll = 0.0;
109	gezelter	98	for (int ll = m+2; ll <= l; ll++) {
110			pll = (x * (2 * ll - 1) * pmmp1 - (ll + m - 1) * pmm) / (ll - m);
111			pmm = pmmp1;
112			pmmp1 = pll;
113			}
114			return pll;
115			}
116			}
117			}
118