| 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). |
| 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 "math/Vector.hpp" |
| 44 |
+ |
|
| 45 |
|
#ifndef MATH_CHOLESKYDECOMPOSITION_HPP |
| 46 |
|
#define MATH_CHOLESKYDECOMPOSITION_HPP |
| 47 |
|
|
| 48 |
+ |
using namespace std; |
| 49 |
|
namespace OpenMD { |
| 50 |
< |
template<class MatrixType> |
| 51 |
< |
int CholeskyDecomposition(MatrixType& A, MatrixType& L) { |
| 50 |
> |
|
| 51 |
> |
template<class MatrixType> |
| 52 |
> |
void CholeskyDecomposition(MatrixType& A, MatrixType& L) { |
| 53 |
> |
|
| 54 |
|
int n = A.getNRow(); |
| 55 |
< |
assert(n == A.getNCol() && n == L.getNRow()&& n==L.getNCol()); |
| 56 |
< |
for(int i = 0; i < n; ++i) { |
| 57 |
< |
RealType sum1 = 0; |
| 58 |
< |
for (int k = 0; k < i -1; ++k) { |
| 59 |
< |
sum1 +=L(i,k)*L(i,k); |
| 55 |
> |
assert(n == A.getNCol() && n == L.getNRow() && n == L.getNCol()); |
| 56 |
> |
|
| 57 |
> |
bool isspd(true); |
| 58 |
> |
RealType eps = A.diagonals().abs().max() * |
| 59 |
> |
(numeric_limits<RealType>::epsilon())/100; |
| 60 |
> |
|
| 61 |
> |
|
| 62 |
> |
for(int j = 0; j < n; j++) { |
| 63 |
> |
RealType d(0.0); |
| 64 |
> |
for (int k = 0; k < j; k++) { |
| 65 |
> |
RealType s(0.0); |
| 66 |
> |
|
| 67 |
> |
for (int i = 0; i < k; i++) { |
| 68 |
> |
s += L(k,i) * L(j,i); |
| 69 |
|
} |
| 70 |
< |
L(i, i) = sqrt(A(i, i) - sum1); |
| 71 |
< |
for (int j = i+1; j < n; ++j) { |
| 72 |
< |
RealType sum2 = 0; |
| 73 |
< |
for (int k = 0; k < i-1; ++k) { |
| 74 |
< |
sum2 += L(j ,k)*L(i, k); |
| 75 |
< |
} |
| 76 |
< |
L(j, i) = (A(j, i) - sum2) /L(i,i); |
| 70 |
> |
|
| 71 |
> |
// if L(k,k) != 0 |
| 72 |
> |
if (std::abs(L(k,k)) > eps) { |
| 73 |
> |
s = (A(j,k) - s) / L(k,k); |
| 74 |
> |
} else { |
| 75 |
> |
s = (A(j,k) -s); |
| 76 |
> |
isspd = false; |
| 77 |
|
} |
| 78 |
+ |
L(j,k) = s; |
| 79 |
+ |
d = d + s*s; |
| 80 |
+ |
|
| 81 |
+ |
// this is approximately doing: isspd = isspd && ( A(k,j) == A(j,k) ) |
| 82 |
+ |
isspd = isspd && (abs(A(k,j) - A(j,k)) < eps ); |
| 83 |
+ |
} |
| 84 |
+ |
d = A(j,j) - d; |
| 85 |
+ |
isspd = isspd && (d > eps); |
| 86 |
+ |
L(j,j) = sqrt(d > 0.0 ? d : 0.0); |
| 87 |
+ |
for (int k = j+1; k < n; k++) { |
| 88 |
+ |
L(j,k) = 0.0; |
| 89 |
+ |
} |
| 90 |
|
} |
| 91 |
< |
|
| 64 |
< |
return 0; |
| 65 |
< |
|
| 91 |
> |
} |
| 92 |
|
} |
| 93 |
|
|
| 68 |
– |
|
| 69 |
– |
} |
| 70 |
– |
|
| 94 |
|
#endif |
