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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. 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 |
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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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* 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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* 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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#include <stdio.h> |
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#include <math.h> |
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#include <stdlib.h> |
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return a[0]*b[0] + a[1]*b[1]+ a[2]*b[2]; |
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} |
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|
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//---------------------------------------------------------------------------- |
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// Extract the eigenvalues and eigenvectors from a 3x3 matrix. |
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// The eigenvectors (the columns of V) will be normalized. |
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// The eigenvectors are aligned optimally with the x, y, and z |
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// axes respectively. |
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/*----------------------------------------------------------------------------*/ |
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/* Extract the eigenvalues and eigenvectors from a 3x3 matrix.*/ |
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/* The eigenvectors (the columns of V) will be normalized. */ |
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/* The eigenvectors are aligned optimally with the x, y, and z*/ |
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/* axes respectively.*/ |
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|
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void diagonalize3x3(const double A[3][3], double w[3], double V[3][3]) { |
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int i,j,k,maxI; |
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double tmp, maxVal; |
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|
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// do the matrix[3][3] to **matrix conversion for Jacobi |
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/* do the matrix[3][3] to **matrix conversion for Jacobi*/ |
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double C[3][3]; |
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double *ATemp[3],*VTemp[3]; |
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for (i = 0; i < 3; i++) |
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VTemp[i] = V[i]; |
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} |
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|
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// diagonalize using Jacobi |
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/* diagonalize using Jacobi*/ |
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JacobiN(ATemp,3,w,VTemp); |
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|
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// if all the eigenvalues are the same, return identity matrix |
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/* if all the eigenvalues are the same, return identity matrix*/ |
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if (w[0] == w[1] && w[0] == w[2]) |
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{ |
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identityMat3(V); |
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return; |
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} |
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|
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// transpose temporarily, it makes it easier to sort the eigenvectors |
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/* transpose temporarily, it makes it easier to sort the eigenvectors*/ |
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transposeMat3(V,V); |
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|
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// if two eigenvalues are the same, re-orthogonalize to optimally line |
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// up the eigenvectors with the x, y, and z axes |
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/* if two eigenvalues are the same, re-orthogonalize to optimally line*/ |
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/* up the eigenvectors with the x, y, and z axes*/ |
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for (i = 0; i < 3; i++) |
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{ |
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if (w[(i+1)%3] == w[(i+2)%3]) // two eigenvalues are the same |
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if (w[(i+1)%3] == w[(i+2)%3]) /* two eigenvalues are the same*/ |
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{ |
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// find maximum element of the independant eigenvector |
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/* find maximum element of the independant eigenvector*/ |
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maxVal = fabs(V[i][0]); |
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maxI = 0; |
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for (j = 1; j < 3; j++) |
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maxI = j; |
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} |
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} |
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// swap the eigenvector into its proper position |
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/* swap the eigenvector into its proper position*/ |
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if (maxI != i) |
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{ |
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tmp = w[maxI]; |
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w[i] = tmp; |
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swapVectors3(V[i],V[maxI]); |
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} |
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// maximum element of eigenvector should be positive |
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/* maximum element of eigenvector should be positive*/ |
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if (V[maxI][maxI] < 0) |
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{ |
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V[maxI][0] = -V[maxI][0]; |
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V[maxI][2] = -V[maxI][2]; |
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} |
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|
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// re-orthogonalize the other two eigenvectors |
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/* re-orthogonalize the other two eigenvectors*/ |
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j = (maxI+1)%3; |
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k = (maxI+2)%3; |
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normalize3(V[k]); |
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crossProduct3(V[k],V[maxI],V[j]); |
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|
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// transpose vectors back to columns |
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/* transpose vectors back to columns*/ |
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transposeMat3(V,V); |
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return; |
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} |
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} |
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|
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// the three eigenvalues are different, just sort the eigenvectors |
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// to align them with the x, y, and z axes |
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/* the three eigenvalues are different, just sort the eigenvectors*/ |
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/* to align them with the x, y, and z axes*/ |
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|
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// find the vector with the largest x element, make that vector |
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// the first vector |
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/* find the vector with the largest x element, make that vector*/ |
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/* the first vector*/ |
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maxVal = fabs(V[0][0]); |
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maxI = 0; |
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for (i = 1; i < 3; i++) |
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maxI = i; |
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} |
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} |
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// swap eigenvalue and eigenvector |
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/* swap eigenvalue and eigenvector*/ |
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if (maxI != 0) |
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{ |
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tmp = w[maxI]; |
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w[0] = tmp; |
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swapVectors3(V[maxI],V[0]); |
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} |
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// do the same for the y element |
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/* do the same for the y element*/ |
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if (fabs(V[1][1]) < fabs(V[2][1])) |
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{ |
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tmp = w[2]; |
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swapVectors3(V[2],V[1]); |
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} |
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|
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// ensure that the sign of the eigenvectors is correct |
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/* ensure that the sign of the eigenvectors is correct*/ |
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for (i = 0; i < 2; i++) |
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{ |
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if (V[i][i] < 0) |
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V[i][2] = -V[i][2]; |
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} |
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} |
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// set sign of final eigenvector to ensure that determinant is positive |
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/* set sign of final eigenvector to ensure that determinant is positive*/ |
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if (matDet3(V) < 0) |
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{ |
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V[2][0] = -V[2][0]; |
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V[2][2] = -V[2][2]; |
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} |
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|
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// transpose the eigenvectors back again |
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/* transpose the eigenvectors back again*/ |
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transposeMat3(V,V); |
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} |
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|
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#define MAX_ROTATIONS 20 |
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// Jacobi iteration for the solution of eigenvectors/eigenvalues of a nxn |
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// real symmetric matrix. Square nxn matrix a; size of matrix in n; |
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// output eigenvalues in w; and output eigenvectors in v. Resulting |
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// eigenvalues/vectors are sorted in decreasing order; eigenvectors are |
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// normalized. |
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/* Jacobi iteration for the solution of eigenvectors/eigenvalues of a nxn*/ |
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/* real symmetric matrix. Square nxn matrix a; size of matrix in n;*/ |
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/* output eigenvalues in w; and output eigenvectors in v. Resulting*/ |
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/* eigenvalues/vectors are sorted in decreasing order; eigenvectors are*/ |
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/* normalized.*/ |
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int JacobiN(double **a, int n, double *w, double **v) { |
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int i, j, k, iq, ip, numPos; |
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double *z = zspace; |
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|
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// only allocate memory if the matrix is large |
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/* only allocate memory if the matrix is large*/ |
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if (n > 4) |
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{ |
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b = (double *) calloc(n, sizeof(double)); |
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z = (double *) calloc(n, sizeof(double)); |
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} |
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|
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// initialize |
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/* initialize*/ |
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for (ip=0; ip<n; ip++) |
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{ |
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for (iq=0; iq<n; iq++) |
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z[ip] = 0.0; |
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} |
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// begin rotation sequence |
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/* begin rotation sequence*/ |
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for (i=0; i<MAX_ROTATIONS; i++) |
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{ |
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sm = 0.0; |
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break; |
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} |
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if (i < 3) // first 3 sweeps |
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if (i < 3) /* first 3 sweeps*/ |
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{ |
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tresh = 0.2*sm/(n*n); |
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} |
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{ |
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g = 100.0*fabs(a[ip][iq]); |
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|
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// after 4 sweeps |
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/* after 4 sweeps*/ |
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if (i > 3 && (fabs(w[ip])+g) == fabs(w[ip]) |
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&& (fabs(w[iq])+g) == fabs(w[iq])) |
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{ |
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w[iq] += h; |
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a[ip][iq]=0.0; |
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|
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// ip already shifted left by 1 unit |
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/* ip already shifted left by 1 unit*/ |
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for (j = 0;j <= ip-1;j++) |
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{ |
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MAT_ROTATE(a,j,ip,j,iq) |
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} |
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// ip and iq already shifted left by 1 unit |
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/* ip and iq already shifted left by 1 unit*/ |
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for (j = ip+1;j <= iq-1;j++) |
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{ |
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MAT_ROTATE(a,ip,j,j,iq) |
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} |
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// iq already shifted left by 1 unit |
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/* iq already shifted left by 1 unit*/ |
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for (j=iq+1; j<n; j++) |
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{ |
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MAT_ROTATE(a,ip,j,iq,j) |
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} |
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} |
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|
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//// this is NEVER called |
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/*// this is NEVER called*/ |
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if ( i >= MAX_ROTATIONS ) |
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{ |
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sprintf( painCave.errMsg, |
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return 0; |
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} |
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|
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// sort eigenfunctions these changes do not affect accuracy |
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for (j=0; j<n-1; j++) // boundary incorrect |
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/* sort eigenfunctions these changes do not affect accuracy */ |
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for (j=0; j<n-1; j++) /* boundary incorrect*/ |
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{ |
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k = j; |
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tmp = w[k]; |
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for (i=j+1; i<n; i++) // boundary incorrect, shifted already |
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for (i=j+1; i<n; i++) /* boundary incorrect, shifted already*/ |
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{ |
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if (w[i] >= tmp) // why exchage if same? |
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if (w[i] >= tmp) /* why exchage if same?*/ |
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{ |
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k = i; |
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tmp = w[k]; |
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} |
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} |
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} |
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// insure eigenvector consistency (i.e., Jacobi can compute vectors that |
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// are negative of one another (.707,.707,0) and (-.707,-.707,0). This can |
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// reek havoc in hyperstreamline/other stuff. We will select the most |
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// positive eigenvector. |
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/* insure eigenvector consistency (i.e., Jacobi can compute vectors that*/ |
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/* are negative of one another (.707,.707,0) and (-.707,-.707,0). This can*/ |
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/* reek havoc in hyperstreamline/other stuff. We will select the most*/ |
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/* positive eigenvector.*/ |
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ceil_half_n = (n >> 1) + (n & 1); |
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for (j=0; j<n; j++) |
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{ |
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numPos++; |
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} |
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} |
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// if ( numPos < ceil(double(n)/double(2.0)) ) |
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/* if ( numPos < ceil(double(n)/double(2.0)) )*/ |
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if ( numPos < ceil_half_n) |
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{ |
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for(i=0; i<n; i++) |
