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/* |
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* Copyright (c) 2005 The University of Notre Dame. All Rights Reserved. |
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* |
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* The University of Notre Dame grants you ("Licensee") a |
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* non-exclusive, royalty free, license to use, modify and |
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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. 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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* 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 |
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* documentation and/or other materials provided with the |
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* distribution. |
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* |
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* This software is provided "AS IS," without a warranty of any |
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* kind. All express or implied conditions, representations and |
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* warranties, including any implied warranty of merchantability, |
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* fitness for a particular purpose or non-infringement, are hereby |
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* excluded. The University of Notre Dame and its licensors shall not |
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* be liable for any damages suffered by licensee as a result of |
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* using, modifying or distributing the software or its |
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* derivatives. In no event will the University of Notre Dame or its |
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* licensors be liable for any lost revenue, profit or data, or for |
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* direct, indirect, special, consequential, incidental or punitive |
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* damages, however caused and regardless of the theory of liability, |
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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 |
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* research, please cite the appropriate papers when you publish your |
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* work. Good starting points are: |
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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] Kuang & Gezelter, J. Chem. Phys. 133, 164101 (2010). |
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* [5] Vardeman, Stocker & Gezelter, J. Chem. Theory Comput. 7, 834 (2011). |
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*/ |
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|
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#include "math/Vector.hpp" |
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|
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#ifndef MATH_CHOLESKYDECOMPOSITION_HPP |
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#define MATH_CHOLESKYDECOMPOSITION_HPP |
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|
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using namespace std; |
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namespace OpenMD { |
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|
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template<class MatrixType> |
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void CholeskyDecomposition(MatrixType& A, MatrixType& L) { |
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|
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int n = A.getNRow(); |
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assert(n == A.getNCol() && n == L.getNRow() && n == L.getNCol()); |
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|
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bool isspd(true); |
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RealType eps = A.diagonals().abs().max() * |
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(numeric_limits<RealType>::epsilon())/100; |
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|
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|
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for(int j = 0; j < n; j++) { |
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RealType d(0.0); |
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for (int k = 0; k < j; k++) { |
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RealType s(0.0); |
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|
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for (int i = 0; i < k; i++) { |
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s += L(k,i) * L(j,i); |
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} |
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|
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// if L(k,k) != 0 |
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if (std::abs(L(k,k)) > eps) { |
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s = (A(j,k) - s) / L(k,k); |
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} else { |
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s = (A(j,k) -s); |
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isspd = false; |
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} |
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L(j,k) = s; |
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d = d + s*s; |
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|
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// this is approximately doing: isspd = isspd && ( A(k,j) == A(j,k) ) |
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isspd = isspd && (abs(A(k,j) - A(j,k)) < eps ); |
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} |
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d = A(j,j) - d; |
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isspd = isspd && (d > eps); |
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L(j,j) = sqrt(d > 0.0 ? d : 0.0); |
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for (int k = j+1; k < n; k++) { |
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L(j,k) = 0.0; |
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} |
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} |
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} |
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} |
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|
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#endif |
