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gezelter |
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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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gezelter |
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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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tim |
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#include "math/MatVec3.h" |
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gezelter |
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/* |
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* Contains various utilities for dealing with 3x3 matrices and |
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* length 3 vectors |
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*/ |
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void identityMat3(double A[3][3]) { |
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int i; |
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for (i = 0; i < 3; i++) { |
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A[i][0] = A[i][1] = A[i][2] = 0.0; |
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A[i][i] = 1.0; |
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} |
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} |
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void swapVectors3(double v1[3], double v2[3]) { |
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int i; |
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for (i = 0; i < 3; i++) { |
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double tmp = v1[i]; |
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v1[i] = v2[i]; |
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v2[i] = tmp; |
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} |
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} |
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double normalize3(double x[3]) { |
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double den; |
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int i; |
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if ( (den = norm3(x)) != 0.0 ) { |
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for (i=0; i < 3; i++) |
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{ |
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x[i] /= den; |
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} |
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} |
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return den; |
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} |
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void matMul3(double a[3][3], double b[3][3], double c[3][3]) { |
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double r00, r01, r02, r10, r11, r12, r20, r21, r22; |
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r00 = a[0][0]*b[0][0] + a[0][1]*b[1][0] + a[0][2]*b[2][0]; |
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r01 = a[0][0]*b[0][1] + a[0][1]*b[1][1] + a[0][2]*b[2][1]; |
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r02 = a[0][0]*b[0][2] + a[0][1]*b[1][2] + a[0][2]*b[2][2]; |
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r10 = a[1][0]*b[0][0] + a[1][1]*b[1][0] + a[1][2]*b[2][0]; |
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r11 = a[1][0]*b[0][1] + a[1][1]*b[1][1] + a[1][2]*b[2][1]; |
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r12 = a[1][0]*b[0][2] + a[1][1]*b[1][2] + a[1][2]*b[2][2]; |
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r20 = a[2][0]*b[0][0] + a[2][1]*b[1][0] + a[2][2]*b[2][0]; |
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r21 = a[2][0]*b[0][1] + a[2][1]*b[1][1] + a[2][2]*b[2][1]; |
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r22 = a[2][0]*b[0][2] + a[2][1]*b[1][2] + a[2][2]*b[2][2]; |
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c[0][0] = r00; c[0][1] = r01; c[0][2] = r02; |
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c[1][0] = r10; c[1][1] = r11; c[1][2] = r12; |
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c[2][0] = r20; c[2][1] = r21; c[2][2] = r22; |
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} |
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void matVecMul3(double m[3][3], double inVec[3], double outVec[3]) { |
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double a0, a1, a2; |
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a0 = inVec[0]; a1 = inVec[1]; a2 = inVec[2]; |
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outVec[0] = m[0][0]*a0 + m[0][1]*a1 + m[0][2]*a2; |
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outVec[1] = m[1][0]*a0 + m[1][1]*a1 + m[1][2]*a2; |
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outVec[2] = m[2][0]*a0 + m[2][1]*a1 + m[2][2]*a2; |
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} |
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double matDet3(double a[3][3]) { |
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int i, j, k; |
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double determinant; |
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determinant = 0.0; |
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for(i = 0; i < 3; i++) { |
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j = (i+1)%3; |
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k = (i+2)%3; |
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determinant += a[0][i] * (a[1][j]*a[2][k] - a[1][k]*a[2][j]); |
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} |
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return determinant; |
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} |
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void invertMat3(double a[3][3], double b[3][3]) { |
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int i, j, k, l, m, n; |
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double determinant; |
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determinant = matDet3( a ); |
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if (determinant == 0.0) { |
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sprintf( painCave.errMsg, |
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"Can't invert a matrix with a zero determinant!\n"); |
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painCave.isFatal = 1; |
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simError(); |
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} |
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for (i=0; i < 3; i++) { |
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j = (i+1)%3; |
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k = (i+2)%3; |
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for(l = 0; l < 3; l++) { |
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m = (l+1)%3; |
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n = (l+2)%3; |
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b[l][i] = (a[j][m]*a[k][n] - a[j][n]*a[k][m]) / determinant; |
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} |
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} |
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} |
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void transposeMat3(double in[3][3], double out[3][3]) { |
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double temp[3][3]; |
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int i, j; |
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for (i = 0; i < 3; i++) { |
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for (j = 0; j < 3; j++) { |
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temp[j][i] = in[i][j]; |
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} |
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} |
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for (i = 0; i < 3; i++) { |
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for (j = 0; j < 3; j++) { |
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out[i][j] = temp[i][j]; |
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} |
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} |
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} |
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void printMat3(double A[3][3] ){ |
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fprintf(stderr, "[ %g, %g, %g ]\n[ %g, %g, %g ]\n[ %g, %g, %g ]\n", |
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A[0][0] , A[0][1] , A[0][2], |
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A[1][0] , A[1][1] , A[1][2], |
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A[2][0] , A[2][1] , A[2][2]) ; |
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} |
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void printMat9(double A[9] ){ |
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fprintf(stderr, "[ %g, %g, %g ]\n[ %g, %g, %g ]\n[ %g, %g, %g ]\n", |
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A[0], A[1], A[2], |
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A[3], A[4], A[5], |
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A[6], A[7], A[8]); |
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} |
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double matTrace3(double m[3][3]){ |
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double trace; |
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trace = m[0][0] + m[1][1] + m[2][2]; |
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return trace; |
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} |
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void crossProduct3(double a[3],double b[3], double out[3]){ |
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out[0] = a[1] * b[2] - a[2] * b[1]; |
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out[1] = a[2] * b[0] - a[0] * b[2] ; |
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out[2] = a[0] * b[1] - a[1] * b[0]; |
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} |
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double dotProduct3(double a[3], double b[3]){ |
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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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// 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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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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// 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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{ |
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C[i][0] = A[i][0]; |
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C[i][1] = A[i][1]; |
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C[i][2] = A[i][2]; |
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ATemp[i] = C[i]; |
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VTemp[i] = V[i]; |
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} |
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// diagonalize using Jacobi |
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JacobiN(ATemp,3,w,VTemp); |
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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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// transpose temporarily, it makes it easier to sort the eigenvectors |
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transposeMat3(V,V); |
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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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{ |
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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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{ |
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if (maxVal < (tmp = fabs(V[i][j]))) |
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{ |
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maxVal = tmp; |
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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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if (maxI != i) |
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{ |
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tmp = w[maxI]; |
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w[maxI] = w[i]; |
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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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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][1] = -V[maxI][1]; |
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V[maxI][2] = -V[maxI][2]; |
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} |
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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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V[j][0] = 0.0; |
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V[j][1] = 0.0; |
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V[j][2] = 0.0; |
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V[j][j] = 1.0; |
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crossProduct3(V[maxI],V[j],V[k]); |
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normalize3(V[k]); |
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crossProduct3(V[k],V[maxI],V[j]); |
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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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// 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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// 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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{ |
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if (maxVal < (tmp = fabs(V[i][0]))) |
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{ |
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maxVal = tmp; |
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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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if (maxI != 0) |
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{ |
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tmp = w[maxI]; |
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w[maxI] = w[0]; |
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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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if (fabs(V[1][1]) < fabs(V[2][1])) |
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{ |
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tmp = w[2]; |
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w[2] = w[1]; |
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w[1] = tmp; |
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swapVectors3(V[2],V[1]); |
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} |
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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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{ |
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V[i][0] = -V[i][0]; |
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V[i][1] = -V[i][1]; |
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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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if (matDet3(V) < 0) |
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{ |
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V[2][0] = -V[2][0]; |
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V[2][1] = -V[2][1]; |
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V[2][2] = -V[2][2]; |
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} |
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// transpose the eigenvectors back again |
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transposeMat3(V,V); |
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} |
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#define MAT_ROTATE(a,i,j,k,l) g=a[i][j];h=a[k][l];a[i][j]=g-s*(h+g*tau); a[k][l]=h+s*(g-h*tau); |
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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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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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int ceil_half_n; |
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double tresh, theta, tau, t, sm, s, h, g, c, tmp; |
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double bspace[4], zspace[4]; |
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double *b = bspace; |
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double *z = zspace; |
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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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// 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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{ |
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v[ip][iq] = 0.0; |
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} |
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v[ip][ip] = 1.0; |
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} |
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for (ip=0; ip<n; ip++) |
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{ |
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b[ip] = w[ip] = a[ip][ip]; |
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z[ip] = 0.0; |
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} |
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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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for (ip=0; ip<n-1; ip++) |
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{ |
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for (iq=ip+1; iq<n; iq++) |
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{ |
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sm += fabs(a[ip][iq]); |
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} |
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} |
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if (sm == 0.0) |
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{ |
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break; |
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} |
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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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else |
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{ |
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tresh = 0.0; |
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} |
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for (ip=0; ip<n-1; ip++) |
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{ |
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for (iq=ip+1; iq<n; iq++) |
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{ |
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g = 100.0*fabs(a[ip][iq]); |
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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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a[ip][iq] = 0.0; |
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} |
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else if (fabs(a[ip][iq]) > tresh) |
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{ |
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h = w[iq] - w[ip]; |
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if ( (fabs(h)+g) == fabs(h)) |
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{ |
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t = (a[ip][iq]) / h; |
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} |
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else |
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{ |
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theta = 0.5*h / (a[ip][iq]); |
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t = 1.0 / (fabs(theta)+sqrt(1.0+theta*theta)); |
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if (theta < 0.0) |
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{ |
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t = -t; |
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} |
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} |
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c = 1.0 / sqrt(1+t*t); |
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s = t*c; |
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tau = s/(1.0+c); |
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h = t*a[ip][iq]; |
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z[ip] -= h; |
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z[iq] += h; |
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w[ip] -= h; |
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w[iq] += h; |
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a[ip][iq]=0.0; |
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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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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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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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for (j=0; j<n; j++) |
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{ |
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MAT_ROTATE(v,j,ip,j,iq) |
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} |
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} |
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} |
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} |
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for (ip=0; ip<n; ip++) |
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{ |
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b[ip] += z[ip]; |
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w[ip] = b[ip]; |
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z[ip] = 0.0; |
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} |
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} |
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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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"Jacobi: Error extracting eigenfunctions!\n"); |
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painCave.isFatal = 1; |
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simError(); |
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return 0; |
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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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{ |
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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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{ |
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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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if (k != j) |
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{ |
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w[k] = w[j]; |
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w[j] = tmp; |
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for (i=0; i<n; i++) |
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{ |
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tmp = v[i][j]; |
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v[i][j] = v[i][k]; |
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v[i][k] = tmp; |
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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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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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for (numPos=0, i=0; i<n; i++) |
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{ |
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if ( v[i][j] >= 0.0 ) |
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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_half_n) |
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{ |
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for(i=0; i<n; i++) |
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{ |
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v[i][j] *= -1.0; |
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} |
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} |
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} |
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if (n > 4) |
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{ |
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free(b); |
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free(z); |
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} |
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return 1; |
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} |
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#undef MAT_ROTATE |
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#undef MAX_ROTATIONS |
