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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] Vardeman & Gezelter, in progress (2009). |
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*/ |
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|
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/*========================================================================= |
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|
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Program: Visualization Toolkit |
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Module: $RCSfile: LU.hpp,v $ |
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|
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Copyright (c) 1993-2003 Ken Martin, Will Schroeder, Bill Lorensen |
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All rights reserved. |
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|
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Redistribution and use in source and binary forms, with or without |
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modification, are permitted provided that the following conditions are met: |
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|
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* Redistributions of source code must retain the above copyright notice, |
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this list of conditions and the following disclaimer. |
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|
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* Redistributions in binary form must reproduce the above copyright notice, |
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this list of conditions and the following disclaimer in the documentation |
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and/or other materials provided with the distribution. |
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|
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* Neither name of Ken Martin, Will Schroeder, or Bill Lorensen nor the names |
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of any contributors may be used to endorse or promote products derived |
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from this software without specific prior written permission. |
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|
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* Modified source versions must be plainly marked as such, and must not be |
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misrepresented as being the original software. |
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|
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THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ``AS IS'' |
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AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
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IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE |
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ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHORS OR CONTRIBUTORS BE LIABLE FOR |
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ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL |
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DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR |
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SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER |
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CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, |
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OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE |
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OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. |
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|
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=========================================================================*/ |
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#ifndef MATH_LU_HPP |
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#define MATH_LU_HPP |
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|
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#include "utils/NumericConstant.hpp" |
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|
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namespace OpenMD { |
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|
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/** |
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* Invert input square matrix A into matrix AI. |
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* @param A input square matrix |
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* @param AI output square matrix |
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* @return true if inverse is computed, otherwise return false |
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* @note A is modified during the inversion |
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*/ |
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template<class MatrixType> |
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bool invertMatrix(MatrixType& A, MatrixType& AI) |
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{ |
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typedef typename MatrixType::ElemType Real; |
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if (A.getNRow() != A.getNCol() || A.getNRow() != AI.getNRow() || A.getNCol() != AI.getNCol()) { |
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return false; |
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} |
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|
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int size = A.getNRow(); |
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int *index=NULL, iScratch[10]; |
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Real *column=NULL, dScratch[10]; |
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|
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// Check on allocation of working vectors |
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// |
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if ( size <= 10 ) { |
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index = iScratch; |
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column = dScratch; |
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} else { |
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index = new int[size]; |
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column = new Real[size]; |
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} |
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|
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bool retVal = invertMatrix(A, AI, size, index, column); |
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|
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if ( size > 10 ) { |
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delete [] index; |
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delete [] column; |
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} |
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|
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return retVal; |
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} |
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|
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/** |
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* Invert input square matrix A into matrix AI (Thread safe versions). |
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* @param A input square matrix |
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* @param AI output square matrix |
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* @param size size of the matrix and temporary arrays |
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* @param tmp1Size temporary array |
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* @param tmp2Size temporary array |
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* @return true if inverse is computed, otherwise return false |
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* @note A is modified during the inversion. |
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*/ |
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|
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template<class MatrixType> |
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bool invertMatrix(MatrixType& A , MatrixType& AI, int size, |
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int *tmp1Size, typename MatrixType::ElemPoinerType tmp2Size) |
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{ |
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if (A.getNRow() != A.getNCol() || A.getNRow() != AI.getNRow() || A.getNCol() != AI.getNCol() || A.getNRow() != size) { |
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return false; |
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} |
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|
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int i, j; |
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|
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// |
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// Factor matrix; then begin solving for inverse one column at a time. |
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// Note: tmp1Size returned value is used later, tmp2Size is just working |
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// memory whose values are not used in LUSolveLinearSystem |
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// |
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if ( LUFactorLinearSystem(A, tmp1Size, size, tmp2Size) == 0 ){ |
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return false; |
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} |
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|
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for ( j=0; j < size; j++ ) { |
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for ( i=0; i < size; i++ ) { |
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tmp2Size[i] = 0.0; |
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} |
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tmp2Size[j] = 1.0; |
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|
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LUSolveLinearSystem(A,tmp1Size,tmp2Size,size); |
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|
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for ( i=0; i < size; i++ ) { |
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AI(i, j) = tmp2Size[i]; |
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} |
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} |
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|
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return true; |
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} |
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|
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/** |
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* Factor linear equations Ax = b using LU decompostion A = LU where L is |
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* lower triangular matrix and U is upper triangular matrix. |
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* @param A input square matrix |
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* @param index pivot indices |
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* @param size size of the matrix and temporary arrays |
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* @param tmpSize temporary array |
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* @return true if inverse is computed, otherwise return false |
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* @note A is modified during the inversion. |
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*/ |
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template<class MatrixType> |
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int LUFactorLinearSystem(MatrixType& A, int *index, int size, |
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typename MatrixType::ElemPoinerType tmpSize) |
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{ |
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typedef typename MatrixType::ElemType Real; |
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int i, j, k; |
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int maxI = 0; |
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Real largest, temp1, temp2, sum; |
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|
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// |
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// Loop over rows to get implicit scaling information |
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// |
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for ( i = 0; i < size; i++ ) { |
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for ( largest = 0.0, j = 0; j < size; j++ ) { |
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if ( (temp2 = fabs(A(i, j))) > largest ) { |
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largest = temp2; |
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} |
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} |
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|
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if ( largest == 0.0 ) { |
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//vtkGenericWarningMacro(<<"Unable to factor linear system"); |
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return 0; |
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} |
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tmpSize[i] = 1.0 / largest; |
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} |
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// |
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// Loop over all columns using Crout's method |
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// |
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for ( j = 0; j < size; j++ ) { |
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for (i = 0; i < j; i++) { |
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sum = A(i, j); |
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for ( k = 0; k < i; k++ ) { |
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sum -= A(i, k) * A(k, j); |
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} |
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A(i, j) = sum; |
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} |
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// |
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// Begin search for largest pivot element |
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// |
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for ( largest = 0.0, i = j; i < size; i++ ) { |
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sum = A(i, j); |
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for ( k = 0; k < j; k++ ) { |
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sum -= A(i, k) * A(k, j); |
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} |
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A(i, j) = sum; |
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|
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if ( (temp1 = tmpSize[i]*fabs(sum)) >= largest ) { |
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largest = temp1; |
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maxI = i; |
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} |
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} |
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// |
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// Check for row interchange |
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// |
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if ( j != maxI ) { |
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for ( k = 0; k < size; k++ ) { |
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temp1 = A(maxI, k); |
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A(maxI, k) = A(j, k); |
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A(j, k) = temp1; |
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} |
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tmpSize[maxI] = tmpSize[j]; |
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} |
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// |
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// Divide by pivot element and perform elimination |
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// |
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index[j] = maxI; |
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|
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if ( fabs(A(j, j)) <= OpenMD::NumericConstant::epsilon ) { |
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//vtkGenericWarningMacro(<<"Unable to factor linear system"); |
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return false; |
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} |
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|
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if ( j != (size-1) ) { |
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temp1 = 1.0 / A(j, j); |
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for ( i = j + 1; i < size; i++ ) { |
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A(i, j) *= temp1; |
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} |
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} |
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} |
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|
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return 1; |
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} |
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|
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/** |
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* Solve linear equations Ax = b using LU decompostion A = LU where L is |
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* lower triangular matrix and U is upper triangular matrix. |
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* @param A input square matrix |
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* @param index pivot indices |
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* @param size size of the matrix and temporary arrays |
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* @param tmpSize temporary array |
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* @return true if inverse is computed, otherwise return false |
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* @note A=LU and index[] are generated from method LUFactorLinearSystem). |
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* Also, solution vector is written directly over input load vector. |
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*/ |
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template<class MatrixType> |
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void LUSolveLinearSystem(MatrixType& A, int *index, |
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typename MatrixType::ElemPoinerType x, int size) |
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{ |
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typedef typename MatrixType::ElemType Real; |
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int i, j, ii, idx; |
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Real sum; |
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// |
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// Proceed with forward and backsubstitution for L and U |
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// matrices. First, forward substitution. |
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// |
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for ( ii = -1, i = 0; i < size; i++ ) { |
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idx = index[i]; |
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sum = x[idx]; |
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x[idx] = x[i]; |
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|
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if ( ii >= 0 ) { |
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for ( j = ii; j <= (i-1); j++ ) { |
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sum -= A(i, j)*x[j]; |
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} |
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} else if (sum) { |
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ii = i; |
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} |
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|
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x[i] = sum; |
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} |
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// |
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// Now, back substitution |
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// |
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for ( i = size-1; i >= 0; i-- ) { |
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sum = x[i]; |
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for ( j = i + 1; j < size; j++ ) { |
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sum -= A(i, j)*x[j]; |
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} |
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x[i] = sum / A(i, i); |
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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 |
