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* redistribute this software in source and binary code form, provided |
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* that the following conditions are met: |
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* |
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* 1. Acknowledgement of the program authors must be made in any |
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* publication of scientific results based in part on use of the |
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* program. An acceptable form of acknowledgement is citation of |
| 12 |
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* the article in which the program was described (Matthew |
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* A. Meineke, Charles F. Vardeman II, Teng Lin, Christopher |
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* J. Fennell and J. Daniel Gezelter, "OOPSE: An Object-Oriented |
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* Parallel Simulation Engine for Molecular Dynamics," |
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< |
* J. Comput. Chem. 26, pp. 252-271 (2005)) |
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* |
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* 2. Redistributions of source code must retain the above copyright |
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> |
* 1. Redistributions of source code must retain the above copyright |
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|
* notice, this list of conditions and the following disclaimer. |
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|
* |
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* 3. Redistributions in binary form must reproduce the above copyright |
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> |
* 2. Redistributions in binary form must reproduce the above copyright |
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* notice, this list of conditions and the following disclaimer in the |
| 14 |
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* documentation and/or other materials provided with the |
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* distribution. |
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* arising out of the use of or inability to use software, even if the |
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* University of Notre Dame has been advised of the possibility of |
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* such damages. |
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* |
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* SUPPORT OPEN SCIENCE! If you use OpenMD or its source code in your |
| 33 |
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* research, please cite the appropriate papers when you publish your |
| 34 |
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* work. Good starting points are: |
| 35 |
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* |
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+ |
* [1] Meineke, et al., J. Comp. Chem. 26, 252-271 (2005). |
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+ |
* [2] Fennell & Gezelter, J. Chem. Phys. 124, 234104 (2006). |
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+ |
* [3] Sun, Lin & Gezelter, J. Chem. Phys. 128, 24107 (2008). |
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* [4] Vardeman & Gezelter, in progress (2009). |
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*/ |
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|
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#include <stdio.h> |
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#include <cmath> |
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#include <limits> |
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#include "math/SphericalHarmonic.hpp" |
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#include "utils/simError.h" |
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|
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using namespace oopse; |
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using namespace OpenMD; |
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|
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SphericalHarmonic::SphericalHarmonic() { |
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} |
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ComplexType SphericalHarmonic::getValueAt(RealType costheta, RealType phi) { |
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|
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RealType p; |
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ComplexType phase; |
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ComplexType I(0.0, 1.0); |
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|
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// associated Legendre polynomial |
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p = Legendre(L, M, costheta); |
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|
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phase = exp(I * (ComplexType)M * (ComplexType)phi); |
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|
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return coefficient * phase * (ComplexType)p; |
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> |
p = Ptilde(L, M, costheta); |
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ComplexType phase(0.0, (RealType)M * phi); |
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|
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return exp(phase) * (ComplexType)p; |
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|
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} |
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– |
|
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– |
//---------------------------------------------------------------------------// |
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// |
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// RealType LegendreP (int l, int m, RealType x); |
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// Routine to calculate the associated Legendre polynomials for m>=0 |
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// |
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// Computes the value of the associated Legendre polynomial P_lm (x) |
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// of order l at a given point. |
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// |
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// Input: |
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// l = degree of the polynomial >= 0 |
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// m = parameter satisfying 0 <= m <= l, |
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// x = point in which the computation is performed, range -1 <= x <= 1. |
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// Returns: |
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// value of the polynomial in x |
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// |
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//---------------------------------------------------------------------------// |
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RealType SphericalHarmonic::LegendreP (int l, int m, RealType x) { |
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// check parameters |
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if (m < 0 || m > l || fabs(x) > 1.0) { |
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printf("LegendreP got a bad argument: l = %d\tm = %d\tx = %lf\n", l, m, x); |
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> |
RealType SphericalHarmonic::LegendreP(int l,int m, RealType x) { |
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> |
|
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> |
RealType temp1, temp2, temp3, temp4, result; |
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> |
RealType temp5; |
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> |
int i, ll; |
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> |
|
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> |
if (fabs(x) > 1.0) { |
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> |
printf("LegendreP: x out of range: l = %d\tm = %d\tx = %lf\n", l, m, x); |
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return std::numeric_limits <RealType>:: quiet_NaN(); |
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} |
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|
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< |
RealType pmm = 1.0; |
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< |
if (m > 0) { |
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< |
RealType h = sqrt((1.0-x)*(1.0+x)), |
| 92 |
< |
f = 1.0; |
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< |
for (int i = 1; i <= m; i++) { |
| 94 |
< |
pmm *= -f * h; |
| 95 |
< |
f += 2.0; |
| 96 |
< |
} |
| 78 |
> |
if (m>l) { |
| 79 |
> |
printf("LegendreP: m > l: l = %d\tm = %d\tx = %lf\n", l, m, x); |
| 80 |
> |
return std::numeric_limits <RealType>:: quiet_NaN(); |
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|
} |
| 82 |
< |
if (l == m) |
| 83 |
< |
return pmm; |
| 84 |
< |
else { |
| 85 |
< |
RealType pmmp1 = x * (2 * m + 1) * pmm; |
| 86 |
< |
if (l == (m+1)) |
| 87 |
< |
return pmmp1; |
| 88 |
< |
else { |
| 89 |
< |
RealType pll = 0.0; |
| 90 |
< |
for (int ll = m+2; ll <= l; ll++) { |
| 91 |
< |
pll = (x * (2 * ll - 1) * pmmp1 - (ll + m - 1) * pmm) / (ll - m); |
| 92 |
< |
pmm = pmmp1; |
| 93 |
< |
pmmp1 = pll; |
| 82 |
> |
|
| 83 |
> |
if (m<0) { |
| 84 |
> |
printf("LegendreP: m < 0: l = %d\tm = %d\tx = %lf\n", l, m, x); |
| 85 |
> |
return std::numeric_limits <RealType>:: quiet_NaN(); |
| 86 |
> |
} else { |
| 87 |
> |
temp3=1.0; |
| 88 |
> |
|
| 89 |
> |
if (m>0) { |
| 90 |
> |
temp1=sqrt(1.0-pow(x,2)); |
| 91 |
> |
temp5 = 1.0; |
| 92 |
> |
for (i=1;i<=m;++i) { |
| 93 |
> |
temp3 *= -temp5*temp1; |
| 94 |
> |
temp5 += 2.0; |
| 95 |
|
} |
| 111 |
– |
return pll; |
| 96 |
|
} |
| 97 |
+ |
if (l==m) { |
| 98 |
+ |
result = temp3; |
| 99 |
+ |
} else { |
| 100 |
+ |
temp4=x*(2.*m+1.)*temp3; |
| 101 |
+ |
if (l==(m+1)) { |
| 102 |
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result = temp4; |
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+ |
} else { |
| 104 |
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for (ll=(m+2);ll<=l;++ll) { |
| 105 |
+ |
temp2 = (x*(2.*ll-1.)*temp4-(ll+m-1.)*temp3)/(RealType)(ll-m); |
| 106 |
+ |
temp3=temp4; |
| 107 |
+ |
temp4=temp2; |
| 108 |
+ |
} |
| 109 |
+ |
result = temp2; |
| 110 |
+ |
} |
| 111 |
+ |
} |
| 112 |
|
} |
| 113 |
+ |
return result; |
| 114 |
|
} |
| 115 |
|
|
| 116 |
+ |
|
| 117 |
|
// |
| 118 |
|
// Routine to calculate the associated Legendre polynomials for all m... |
| 119 |
|
// |
| 125 |
|
} else if (m >= 0) { |
| 126 |
|
result = LegendreP(l,m,x); |
| 127 |
|
} else { |
| 128 |
+ |
//result = mpow(-m)*LegendreP(l,-m,x); |
| 129 |
|
result = mpow(-m)*Fact(l+m)/Fact(l-m)*LegendreP(l, -m, x); |
| 130 |
|
} |
| 131 |
|
result *=mpow(m); |
| 132 |
|
return result; |
| 133 |
|
} |
| 134 |
|
// |
| 135 |
+ |
// Routine to calculate the normalized associated Legendre polynomials... |
| 136 |
+ |
// |
| 137 |
+ |
RealType SphericalHarmonic::Ptilde(int l,int m, RealType x){ |
| 138 |
+ |
|
| 139 |
+ |
RealType result; |
| 140 |
+ |
if (m>l || m<-l) { |
| 141 |
+ |
result = 0.; |
| 142 |
+ |
} else { |
| 143 |
+ |
RealType y=(RealType)(2.*l+1.)*Fact(l-m)/Fact(l+m); |
| 144 |
+ |
result = mpow(m) * sqrt(y) * Legendre(l,m,x) / sqrt(4.0*M_PI); |
| 145 |
+ |
} |
| 146 |
+ |
return result; |
| 147 |
+ |
} |
| 148 |
+ |
// |
| 149 |
|
// mpow returns (-1)**m |
| 150 |
|
// |
| 151 |
|
RealType SphericalHarmonic::mpow(int m) { |
