1 |
|
/* |
2 |
< |
* Copyright (C) 2000-2004 Object Oriented Parallel Simulation Engine (OOPSE) project |
3 |
< |
* |
4 |
< |
* Contact: oopse@oopse.org |
5 |
< |
* |
6 |
< |
* This program is free software; you can redistribute it and/or |
7 |
< |
* modify it under the terms of the GNU Lesser General Public License |
8 |
< |
* as published by the Free Software Foundation; either version 2.1 |
9 |
< |
* of the License, or (at your option) any later version. |
10 |
< |
* All we ask is that proper credit is given for our work, which includes |
11 |
< |
* - but is not limited to - adding the above copyright notice to the beginning |
12 |
< |
* of your source code files, and to any copyright notice that you may distribute |
13 |
< |
* with programs based on this work. |
14 |
< |
* |
15 |
< |
* This program is distributed in the hope that it will be useful, |
16 |
< |
* but WITHOUT ANY WARRANTY; without even the implied warranty of |
17 |
< |
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
18 |
< |
* GNU Lesser General Public License for more details. |
19 |
< |
* |
20 |
< |
* You should have received a copy of the GNU Lesser General Public License |
21 |
< |
* along with this program; if not, write to the Free Software |
22 |
< |
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. |
2 |
> |
* Copyright (c) 2005 The University of Notre Dame. All Rights Reserved. |
3 |
|
* |
4 |
+ |
* The University of Notre Dame grants you ("Licensee") a |
5 |
+ |
* non-exclusive, royalty free, license to use, modify and |
6 |
+ |
* redistribute this software in source and binary code form, provided |
7 |
+ |
* that the following conditions are met: |
8 |
+ |
* |
9 |
+ |
* 1. Acknowledgement of the program authors must be made in any |
10 |
+ |
* publication of scientific results based in part on use of the |
11 |
+ |
* program. An acceptable form of acknowledgement is citation of |
12 |
+ |
* the article in which the program was described (Matthew |
13 |
+ |
* A. Meineke, Charles F. Vardeman II, Teng Lin, Christopher |
14 |
+ |
* J. Fennell and J. Daniel Gezelter, "OOPSE: An Object-Oriented |
15 |
+ |
* Parallel Simulation Engine for Molecular Dynamics," |
16 |
+ |
* J. Comput. Chem. 26, pp. 252-271 (2005)) |
17 |
+ |
* |
18 |
+ |
* 2. Redistributions of source code must retain the above copyright |
19 |
+ |
* notice, this list of conditions and the following disclaimer. |
20 |
+ |
* |
21 |
+ |
* 3. Redistributions in binary form must reproduce the above copyright |
22 |
+ |
* notice, this list of conditions and the following disclaimer in the |
23 |
+ |
* documentation and/or other materials provided with the |
24 |
+ |
* distribution. |
25 |
+ |
* |
26 |
+ |
* This software is provided "AS IS," without a warranty of any |
27 |
+ |
* kind. All express or implied conditions, representations and |
28 |
+ |
* warranties, including any implied warranty of merchantability, |
29 |
+ |
* fitness for a particular purpose or non-infringement, are hereby |
30 |
+ |
* excluded. The University of Notre Dame and its licensors shall not |
31 |
+ |
* be liable for any damages suffered by licensee as a result of |
32 |
+ |
* using, modifying or distributing the software or its |
33 |
+ |
* derivatives. In no event will the University of Notre Dame or its |
34 |
+ |
* licensors be liable for any lost revenue, profit or data, or for |
35 |
+ |
* direct, indirect, special, consequential, incidental or punitive |
36 |
+ |
* damages, however caused and regardless of the theory of liability, |
37 |
+ |
* arising out of the use of or inability to use software, even if the |
38 |
+ |
* University of Notre Dame has been advised of the possibility of |
39 |
+ |
* such damages. |
40 |
|
*/ |
41 |
< |
|
41 |
> |
|
42 |
|
/** |
43 |
|
* @file SquareMatrix.hpp |
44 |
|
* @author Teng Lin |
45 |
|
* @date 10/11/2004 |
46 |
|
* @version 1.0 |
47 |
|
*/ |
48 |
< |
#ifndef MATH_SQUAREMATRIX_HPP |
48 |
> |
#ifndef MATH_SQUAREMATRIX_HPP |
49 |
|
#define MATH_SQUAREMATRIX_HPP |
50 |
|
|
51 |
|
#include "math/RectMatrix.hpp" |
52 |
|
|
53 |
|
namespace oopse { |
54 |
|
|
55 |
< |
/** |
56 |
< |
* @class SquareMatrix SquareMatrix.hpp "math/SquareMatrix.hpp" |
57 |
< |
* @brief A square matrix class |
58 |
< |
* @template Real the element type |
59 |
< |
* @template Dim the dimension of the square matrix |
60 |
< |
*/ |
61 |
< |
template<typename Real, int Dim> |
62 |
< |
class SquareMatrix : public RectMatrix<Real, Dim, Dim> { |
63 |
< |
public: |
55 |
> |
/** |
56 |
> |
* @class SquareMatrix SquareMatrix.hpp "math/SquareMatrix.hpp" |
57 |
> |
* @brief A square matrix class |
58 |
> |
* @template Real the element type |
59 |
> |
* @template Dim the dimension of the square matrix |
60 |
> |
*/ |
61 |
> |
template<typename Real, int Dim> |
62 |
> |
class SquareMatrix : public RectMatrix<Real, Dim, Dim> { |
63 |
> |
public: |
64 |
> |
typedef Real ElemType; |
65 |
> |
typedef Real* ElemPoinerType; |
66 |
|
|
67 |
< |
/** default constructor */ |
68 |
< |
SquareMatrix() { |
69 |
< |
for (unsigned int i = 0; i < Dim; i++) |
70 |
< |
for (unsigned int j = 0; j < Dim; j++) |
71 |
< |
data_[i][j] = 0.0; |
72 |
< |
} |
67 |
> |
/** default constructor */ |
68 |
> |
SquareMatrix() { |
69 |
> |
for (unsigned int i = 0; i < Dim; i++) |
70 |
> |
for (unsigned int j = 0; j < Dim; j++) |
71 |
> |
this->data_[i][j] = 0.0; |
72 |
> |
} |
73 |
|
|
74 |
< |
/** copy constructor */ |
75 |
< |
SquareMatrix(const RectMatrix<Real, Dim, Dim>& m) : RectMatrix<Real, Dim, Dim>(m) { |
76 |
< |
} |
59 |
< |
|
60 |
< |
/** copy assignment operator */ |
61 |
< |
SquareMatrix<Real, Dim>& operator =(const RectMatrix<Real, Dim, Dim>& m) { |
62 |
< |
RectMatrix<Real, Dim, Dim>::operator=(m); |
63 |
< |
return *this; |
64 |
< |
} |
65 |
< |
|
66 |
< |
/** Retunrs an identity matrix*/ |
74 |
> |
/** Constructs and initializes every element of this matrix to a scalar */ |
75 |
> |
SquareMatrix(Real s) : RectMatrix<Real, Dim, Dim>(s){ |
76 |
> |
} |
77 |
|
|
78 |
< |
static SquareMatrix<Real, Dim> identity() { |
79 |
< |
SquareMatrix<Real, Dim> m; |
78 |
> |
/** Constructs and initializes from an array */ |
79 |
> |
SquareMatrix(Real* array) : RectMatrix<Real, Dim, Dim>(array){ |
80 |
> |
} |
81 |
> |
|
82 |
> |
|
83 |
> |
/** copy constructor */ |
84 |
> |
SquareMatrix(const RectMatrix<Real, Dim, Dim>& m) : RectMatrix<Real, Dim, Dim>(m) { |
85 |
> |
} |
86 |
|
|
87 |
< |
for (unsigned int i = 0; i < Dim; i++) |
88 |
< |
for (unsigned int j = 0; j < Dim; j++) |
89 |
< |
if (i == j) |
90 |
< |
m(i, j) = 1.0; |
91 |
< |
else |
92 |
< |
m(i, j) = 0.0; |
87 |
> |
/** copy assignment operator */ |
88 |
> |
SquareMatrix<Real, Dim>& operator =(const RectMatrix<Real, Dim, Dim>& m) { |
89 |
> |
RectMatrix<Real, Dim, Dim>::operator=(m); |
90 |
> |
return *this; |
91 |
> |
} |
92 |
> |
|
93 |
> |
/** Retunrs an identity matrix*/ |
94 |
|
|
95 |
< |
return m; |
96 |
< |
} |
95 |
> |
static SquareMatrix<Real, Dim> identity() { |
96 |
> |
SquareMatrix<Real, Dim> m; |
97 |
> |
|
98 |
> |
for (unsigned int i = 0; i < Dim; i++) |
99 |
> |
for (unsigned int j = 0; j < Dim; j++) |
100 |
> |
if (i == j) |
101 |
> |
m(i, j) = 1.0; |
102 |
> |
else |
103 |
> |
m(i, j) = 0.0; |
104 |
|
|
105 |
< |
/** |
106 |
< |
* Retunrs the inversion of this matrix. |
83 |
< |
* @todo need implementation |
84 |
< |
*/ |
85 |
< |
SquareMatrix<Real, Dim> inverse() { |
86 |
< |
SquareMatrix<Real, Dim> result; |
105 |
> |
return m; |
106 |
> |
} |
107 |
|
|
108 |
< |
return result; |
109 |
< |
} |
108 |
> |
/** |
109 |
> |
* Retunrs the inversion of this matrix. |
110 |
> |
* @todo need implementation |
111 |
> |
*/ |
112 |
> |
SquareMatrix<Real, Dim> inverse() { |
113 |
> |
SquareMatrix<Real, Dim> result; |
114 |
|
|
115 |
< |
/** |
116 |
< |
* Returns the determinant of this matrix. |
93 |
< |
* @todo need implementation |
94 |
< |
*/ |
95 |
< |
Real determinant() const { |
96 |
< |
Real det; |
97 |
< |
return det; |
98 |
< |
} |
115 |
> |
return result; |
116 |
> |
} |
117 |
|
|
118 |
< |
/** Returns the trace of this matrix. */ |
119 |
< |
Real trace() const { |
120 |
< |
Real tmp = 0; |
121 |
< |
|
122 |
< |
for (unsigned int i = 0; i < Dim ; i++) |
123 |
< |
tmp += data_[i][i]; |
118 |
> |
/** |
119 |
> |
* Returns the determinant of this matrix. |
120 |
> |
* @todo need implementation |
121 |
> |
*/ |
122 |
> |
Real determinant() const { |
123 |
> |
Real det; |
124 |
> |
return det; |
125 |
> |
} |
126 |
|
|
127 |
< |
return tmp; |
128 |
< |
} |
127 |
> |
/** Returns the trace of this matrix. */ |
128 |
> |
Real trace() const { |
129 |
> |
Real tmp = 0; |
130 |
> |
|
131 |
> |
for (unsigned int i = 0; i < Dim ; i++) |
132 |
> |
tmp += this->data_[i][i]; |
133 |
|
|
134 |
< |
/** Tests if this matrix is symmetrix. */ |
135 |
< |
bool isSymmetric() const { |
112 |
< |
for (unsigned int i = 0; i < Dim - 1; i++) |
113 |
< |
for (unsigned int j = i; j < Dim; j++) |
114 |
< |
if (fabs(data_[i][j] - data_[j][i]) > oopse::epsilon) |
115 |
< |
return false; |
116 |
< |
|
117 |
< |
return true; |
118 |
< |
} |
134 |
> |
return tmp; |
135 |
> |
} |
136 |
|
|
137 |
< |
/** Tests if this matrix is orthogonal. */ |
138 |
< |
bool isOrthogonal() { |
139 |
< |
SquareMatrix<Real, Dim> tmp; |
137 |
> |
/** Tests if this matrix is symmetrix. */ |
138 |
> |
bool isSymmetric() const { |
139 |
> |
for (unsigned int i = 0; i < Dim - 1; i++) |
140 |
> |
for (unsigned int j = i; j < Dim; j++) |
141 |
> |
if (fabs(this->data_[i][j] - this->data_[j][i]) > oopse::epsilon) |
142 |
> |
return false; |
143 |
> |
|
144 |
> |
return true; |
145 |
> |
} |
146 |
|
|
147 |
< |
tmp = *this * transpose(); |
147 |
> |
/** Tests if this matrix is orthogonal. */ |
148 |
> |
bool isOrthogonal() { |
149 |
> |
SquareMatrix<Real, Dim> tmp; |
150 |
|
|
151 |
< |
return tmp.isDiagonal(); |
127 |
< |
} |
151 |
> |
tmp = *this * transpose(); |
152 |
|
|
153 |
< |
/** Tests if this matrix is diagonal. */ |
154 |
< |
bool isDiagonal() const { |
155 |
< |
for (unsigned int i = 0; i < Dim ; i++) |
156 |
< |
for (unsigned int j = 0; j < Dim; j++) |
157 |
< |
if (i !=j && fabs(data_[i][j]) > oopse::epsilon) |
158 |
< |
return false; |
153 |
> |
return tmp.isDiagonal(); |
154 |
> |
} |
155 |
> |
|
156 |
> |
/** Tests if this matrix is diagonal. */ |
157 |
> |
bool isDiagonal() const { |
158 |
> |
for (unsigned int i = 0; i < Dim ; i++) |
159 |
> |
for (unsigned int j = 0; j < Dim; j++) |
160 |
> |
if (i !=j && fabs(this->data_[i][j]) > oopse::epsilon) |
161 |
> |
return false; |
162 |
> |
|
163 |
> |
return true; |
164 |
> |
} |
165 |
> |
|
166 |
> |
/** Tests if this matrix is the unit matrix. */ |
167 |
> |
bool isUnitMatrix() const { |
168 |
> |
if (!isDiagonal()) |
169 |
> |
return false; |
170 |
> |
|
171 |
> |
for (unsigned int i = 0; i < Dim ; i++) |
172 |
> |
if (fabs(this->data_[i][i] - 1) > oopse::epsilon) |
173 |
> |
return false; |
174 |
|
|
175 |
< |
return true; |
176 |
< |
} |
175 |
> |
return true; |
176 |
> |
} |
177 |
|
|
178 |
< |
/** Tests if this matrix is the unit matrix. */ |
179 |
< |
bool isUnitMatrix() const { |
180 |
< |
if (!isDiagonal()) |
142 |
< |
return false; |
143 |
< |
|
144 |
< |
for (unsigned int i = 0; i < Dim ; i++) |
145 |
< |
if (fabs(data_[i][i] - 1) > oopse::epsilon) |
146 |
< |
return false; |
178 |
> |
/** Return the transpose of this matrix */ |
179 |
> |
SquareMatrix<Real, Dim> transpose() const{ |
180 |
> |
SquareMatrix<Real, Dim> result; |
181 |
|
|
182 |
< |
return true; |
183 |
< |
} |
182 |
> |
for (unsigned int i = 0; i < Dim; i++) |
183 |
> |
for (unsigned int j = 0; j < Dim; j++) |
184 |
> |
result(j, i) = this->data_[i][j]; |
185 |
|
|
186 |
< |
/** @todo need implementation */ |
187 |
< |
void diagonalize() { |
188 |
< |
//jacobi(m, eigenValues, ortMat); |
189 |
< |
} |
186 |
> |
return result; |
187 |
> |
} |
188 |
> |
|
189 |
> |
/** @todo need implementation */ |
190 |
> |
void diagonalize() { |
191 |
> |
//jacobi(m, eigenValues, ortMat); |
192 |
> |
} |
193 |
|
|
194 |
< |
/** |
195 |
< |
* Jacobi iteration routines for computing eigenvalues/eigenvectors of |
196 |
< |
* real symmetric matrix |
197 |
< |
* |
198 |
< |
* @return true if success, otherwise return false |
199 |
< |
* @param a symmetric matrix whose eigenvectors are to be computed. On return, the matrix is |
200 |
< |
* overwritten |
201 |
< |
* @param w will contain the eigenvalues of the matrix On return of this function |
202 |
< |
* @param v the columns of this matrix will contain the eigenvectors. The eigenvectors are |
203 |
< |
* normalized and mutually orthogonal. |
204 |
< |
*/ |
205 |
< |
|
206 |
< |
static int jacobi(SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& d, |
207 |
< |
SquareMatrix<Real, Dim>& v); |
208 |
< |
};//end SquareMatrix |
194 |
> |
/** |
195 |
> |
* Jacobi iteration routines for computing eigenvalues/eigenvectors of |
196 |
> |
* real symmetric matrix |
197 |
> |
* |
198 |
> |
* @return true if success, otherwise return false |
199 |
> |
* @param a symmetric matrix whose eigenvectors are to be computed. On return, the matrix is |
200 |
> |
* overwritten |
201 |
> |
* @param w will contain the eigenvalues of the matrix On return of this function |
202 |
> |
* @param v the columns of this matrix will contain the eigenvectors. The eigenvectors are |
203 |
> |
* normalized and mutually orthogonal. |
204 |
> |
*/ |
205 |
> |
|
206 |
> |
static int jacobi(SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& d, |
207 |
> |
SquareMatrix<Real, Dim>& v); |
208 |
> |
};//end SquareMatrix |
209 |
|
|
210 |
|
|
211 |
< |
/*========================================================================= |
211 |
> |
/*========================================================================= |
212 |
|
|
213 |
|
Program: Visualization Toolkit |
214 |
|
Module: $RCSfile: SquareMatrix.hpp,v $ |
217 |
|
All rights reserved. |
218 |
|
See Copyright.txt or http://www.kitware.com/Copyright.htm for details. |
219 |
|
|
220 |
< |
This software is distributed WITHOUT ANY WARRANTY; without even |
221 |
< |
the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR |
222 |
< |
PURPOSE. See the above copyright notice for more information. |
220 |
> |
This software is distributed WITHOUT ANY WARRANTY; without even |
221 |
> |
the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR |
222 |
> |
PURPOSE. See the above copyright notice for more information. |
223 |
|
|
224 |
< |
=========================================================================*/ |
224 |
> |
=========================================================================*/ |
225 |
|
|
226 |
< |
#define VTK_ROTATE(a,i,j,k,l) g=a(i, j);h=a(k, l);a(i, j)=g-s*(h+g*tau);\ |
227 |
< |
a(k, l)=h+s*(g-h*tau) |
226 |
> |
#define VTK_ROTATE(a,i,j,k,l) g=a(i, j);h=a(k, l);a(i, j)=g-s*(h+g*tau); \ |
227 |
> |
a(k, l)=h+s*(g-h*tau) |
228 |
|
|
229 |
|
#define VTK_MAX_ROTATIONS 20 |
230 |
|
|
231 |
< |
// Jacobi iteration for the solution of eigenvectors/eigenvalues of a nxn |
232 |
< |
// real symmetric matrix. Square nxn matrix a; size of matrix in n; |
233 |
< |
// output eigenvalues in w; and output eigenvectors in v. Resulting |
234 |
< |
// eigenvalues/vectors are sorted in decreasing order; eigenvectors are |
235 |
< |
// normalized. |
236 |
< |
template<typename Real, int Dim> |
237 |
< |
int SquareMatrix<Real, Dim>::jacobi(SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& w, |
238 |
< |
SquareMatrix<Real, Dim>& v) { |
239 |
< |
const int n = Dim; |
240 |
< |
int i, j, k, iq, ip, numPos; |
241 |
< |
Real tresh, theta, tau, t, sm, s, h, g, c, tmp; |
242 |
< |
Real bspace[4], zspace[4]; |
243 |
< |
Real *b = bspace; |
244 |
< |
Real *z = zspace; |
231 |
> |
// Jacobi iteration for the solution of eigenvectors/eigenvalues of a nxn |
232 |
> |
// real symmetric matrix. Square nxn matrix a; size of matrix in n; |
233 |
> |
// output eigenvalues in w; and output eigenvectors in v. Resulting |
234 |
> |
// eigenvalues/vectors are sorted in decreasing order; eigenvectors are |
235 |
> |
// normalized. |
236 |
> |
template<typename Real, int Dim> |
237 |
> |
int SquareMatrix<Real, Dim>::jacobi(SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& w, |
238 |
> |
SquareMatrix<Real, Dim>& v) { |
239 |
> |
const int n = Dim; |
240 |
> |
int i, j, k, iq, ip, numPos; |
241 |
> |
Real tresh, theta, tau, t, sm, s, h, g, c, tmp; |
242 |
> |
Real bspace[4], zspace[4]; |
243 |
> |
Real *b = bspace; |
244 |
> |
Real *z = zspace; |
245 |
|
|
246 |
< |
// only allocate memory if the matrix is large |
247 |
< |
if (n > 4) |
248 |
< |
{ |
249 |
< |
b = new Real[n]; |
250 |
< |
z = new Real[n]; |
213 |
< |
} |
246 |
> |
// only allocate memory if the matrix is large |
247 |
> |
if (n > 4) { |
248 |
> |
b = new Real[n]; |
249 |
> |
z = new Real[n]; |
250 |
> |
} |
251 |
|
|
252 |
< |
// initialize |
253 |
< |
for (ip=0; ip<n; ip++) |
254 |
< |
{ |
255 |
< |
for (iq=0; iq<n; iq++) |
256 |
< |
{ |
257 |
< |
v(ip, iq) = 0.0; |
258 |
< |
} |
259 |
< |
v(ip, ip) = 1.0; |
260 |
< |
} |
261 |
< |
for (ip=0; ip<n; ip++) |
262 |
< |
{ |
226 |
< |
b[ip] = w[ip] = a(ip, ip); |
227 |
< |
z[ip] = 0.0; |
228 |
< |
} |
252 |
> |
// initialize |
253 |
> |
for (ip=0; ip<n; ip++) { |
254 |
> |
for (iq=0; iq<n; iq++) { |
255 |
> |
v(ip, iq) = 0.0; |
256 |
> |
} |
257 |
> |
v(ip, ip) = 1.0; |
258 |
> |
} |
259 |
> |
for (ip=0; ip<n; ip++) { |
260 |
> |
b[ip] = w[ip] = a(ip, ip); |
261 |
> |
z[ip] = 0.0; |
262 |
> |
} |
263 |
|
|
264 |
< |
// begin rotation sequence |
265 |
< |
for (i=0; i<VTK_MAX_ROTATIONS; i++) |
266 |
< |
{ |
267 |
< |
sm = 0.0; |
268 |
< |
for (ip=0; ip<n-1; ip++) |
269 |
< |
{ |
270 |
< |
for (iq=ip+1; iq<n; iq++) |
271 |
< |
{ |
272 |
< |
sm += fabs(a(ip, iq)); |
273 |
< |
} |
274 |
< |
} |
241 |
< |
if (sm == 0.0) |
242 |
< |
{ |
243 |
< |
break; |
244 |
< |
} |
264 |
> |
// begin rotation sequence |
265 |
> |
for (i=0; i<VTK_MAX_ROTATIONS; i++) { |
266 |
> |
sm = 0.0; |
267 |
> |
for (ip=0; ip<n-1; ip++) { |
268 |
> |
for (iq=ip+1; iq<n; iq++) { |
269 |
> |
sm += fabs(a(ip, iq)); |
270 |
> |
} |
271 |
> |
} |
272 |
> |
if (sm == 0.0) { |
273 |
> |
break; |
274 |
> |
} |
275 |
|
|
276 |
< |
if (i < 3) // first 3 sweeps |
277 |
< |
{ |
278 |
< |
tresh = 0.2*sm/(n*n); |
279 |
< |
} |
280 |
< |
else |
251 |
< |
{ |
252 |
< |
tresh = 0.0; |
253 |
< |
} |
276 |
> |
if (i < 3) { // first 3 sweeps |
277 |
> |
tresh = 0.2*sm/(n*n); |
278 |
> |
} else { |
279 |
> |
tresh = 0.0; |
280 |
> |
} |
281 |
|
|
282 |
< |
for (ip=0; ip<n-1; ip++) |
283 |
< |
{ |
284 |
< |
for (iq=ip+1; iq<n; iq++) |
258 |
< |
{ |
259 |
< |
g = 100.0*fabs(a(ip, iq)); |
282 |
> |
for (ip=0; ip<n-1; ip++) { |
283 |
> |
for (iq=ip+1; iq<n; iq++) { |
284 |
> |
g = 100.0*fabs(a(ip, iq)); |
285 |
|
|
286 |
< |
// after 4 sweeps |
287 |
< |
if (i > 3 && (fabs(w[ip])+g) == fabs(w[ip]) |
288 |
< |
&& (fabs(w[iq])+g) == fabs(w[iq])) |
289 |
< |
{ |
290 |
< |
a(ip, iq) = 0.0; |
291 |
< |
} |
292 |
< |
else if (fabs(a(ip, iq)) > tresh) |
293 |
< |
{ |
294 |
< |
h = w[iq] - w[ip]; |
295 |
< |
if ( (fabs(h)+g) == fabs(h)) |
296 |
< |
{ |
297 |
< |
t = (a(ip, iq)) / h; |
298 |
< |
} |
299 |
< |
else |
300 |
< |
{ |
301 |
< |
theta = 0.5*h / (a(ip, iq)); |
302 |
< |
t = 1.0 / (fabs(theta)+sqrt(1.0+theta*theta)); |
303 |
< |
if (theta < 0.0) |
304 |
< |
{ |
305 |
< |
t = -t; |
306 |
< |
} |
307 |
< |
} |
308 |
< |
c = 1.0 / sqrt(1+t*t); |
309 |
< |
s = t*c; |
285 |
< |
tau = s/(1.0+c); |
286 |
< |
h = t*a(ip, iq); |
287 |
< |
z[ip] -= h; |
288 |
< |
z[iq] += h; |
289 |
< |
w[ip] -= h; |
290 |
< |
w[iq] += h; |
291 |
< |
a(ip, iq)=0.0; |
286 |
> |
// after 4 sweeps |
287 |
> |
if (i > 3 && (fabs(w[ip])+g) == fabs(w[ip]) |
288 |
> |
&& (fabs(w[iq])+g) == fabs(w[iq])) { |
289 |
> |
a(ip, iq) = 0.0; |
290 |
> |
} else if (fabs(a(ip, iq)) > tresh) { |
291 |
> |
h = w[iq] - w[ip]; |
292 |
> |
if ( (fabs(h)+g) == fabs(h)) { |
293 |
> |
t = (a(ip, iq)) / h; |
294 |
> |
} else { |
295 |
> |
theta = 0.5*h / (a(ip, iq)); |
296 |
> |
t = 1.0 / (fabs(theta)+sqrt(1.0+theta*theta)); |
297 |
> |
if (theta < 0.0) { |
298 |
> |
t = -t; |
299 |
> |
} |
300 |
> |
} |
301 |
> |
c = 1.0 / sqrt(1+t*t); |
302 |
> |
s = t*c; |
303 |
> |
tau = s/(1.0+c); |
304 |
> |
h = t*a(ip, iq); |
305 |
> |
z[ip] -= h; |
306 |
> |
z[iq] += h; |
307 |
> |
w[ip] -= h; |
308 |
> |
w[iq] += h; |
309 |
> |
a(ip, iq)=0.0; |
310 |
|
|
311 |
< |
// ip already shifted left by 1 unit |
312 |
< |
for (j = 0;j <= ip-1;j++) |
313 |
< |
{ |
314 |
< |
VTK_ROTATE(a,j,ip,j,iq); |
315 |
< |
} |
316 |
< |
// ip and iq already shifted left by 1 unit |
317 |
< |
for (j = ip+1;j <= iq-1;j++) |
318 |
< |
{ |
319 |
< |
VTK_ROTATE(a,ip,j,j,iq); |
320 |
< |
} |
321 |
< |
// iq already shifted left by 1 unit |
322 |
< |
for (j=iq+1; j<n; j++) |
323 |
< |
{ |
324 |
< |
VTK_ROTATE(a,ip,j,iq,j); |
325 |
< |
} |
326 |
< |
for (j=0; j<n; j++) |
327 |
< |
{ |
328 |
< |
VTK_ROTATE(v,j,ip,j,iq); |
311 |
< |
} |
312 |
< |
} |
313 |
< |
} |
314 |
< |
} |
311 |
> |
// ip already shifted left by 1 unit |
312 |
> |
for (j = 0;j <= ip-1;j++) { |
313 |
> |
VTK_ROTATE(a,j,ip,j,iq); |
314 |
> |
} |
315 |
> |
// ip and iq already shifted left by 1 unit |
316 |
> |
for (j = ip+1;j <= iq-1;j++) { |
317 |
> |
VTK_ROTATE(a,ip,j,j,iq); |
318 |
> |
} |
319 |
> |
// iq already shifted left by 1 unit |
320 |
> |
for (j=iq+1; j<n; j++) { |
321 |
> |
VTK_ROTATE(a,ip,j,iq,j); |
322 |
> |
} |
323 |
> |
for (j=0; j<n; j++) { |
324 |
> |
VTK_ROTATE(v,j,ip,j,iq); |
325 |
> |
} |
326 |
> |
} |
327 |
> |
} |
328 |
> |
} |
329 |
|
|
330 |
< |
for (ip=0; ip<n; ip++) |
331 |
< |
{ |
332 |
< |
b[ip] += z[ip]; |
333 |
< |
w[ip] = b[ip]; |
334 |
< |
z[ip] = 0.0; |
335 |
< |
} |
322 |
< |
} |
330 |
> |
for (ip=0; ip<n; ip++) { |
331 |
> |
b[ip] += z[ip]; |
332 |
> |
w[ip] = b[ip]; |
333 |
> |
z[ip] = 0.0; |
334 |
> |
} |
335 |
> |
} |
336 |
|
|
337 |
< |
//// this is NEVER called |
338 |
< |
if ( i >= VTK_MAX_ROTATIONS ) |
339 |
< |
{ |
340 |
< |
std::cout << "vtkMath::Jacobi: Error extracting eigenfunctions" << std::endl; |
341 |
< |
return 0; |
329 |
< |
} |
337 |
> |
//// this is NEVER called |
338 |
> |
if ( i >= VTK_MAX_ROTATIONS ) { |
339 |
> |
std::cout << "vtkMath::Jacobi: Error extracting eigenfunctions" << std::endl; |
340 |
> |
return 0; |
341 |
> |
} |
342 |
|
|
343 |
< |
// sort eigenfunctions these changes do not affect accuracy |
344 |
< |
for (j=0; j<n-1; j++) // boundary incorrect |
345 |
< |
{ |
346 |
< |
k = j; |
347 |
< |
tmp = w[k]; |
348 |
< |
for (i=j+1; i<n; i++) // boundary incorrect, shifted already |
349 |
< |
{ |
350 |
< |
if (w[i] >= tmp) // why exchage if same? |
351 |
< |
{ |
352 |
< |
k = i; |
353 |
< |
tmp = w[k]; |
354 |
< |
} |
355 |
< |
} |
356 |
< |
if (k != j) |
357 |
< |
{ |
358 |
< |
w[k] = w[j]; |
359 |
< |
w[j] = tmp; |
360 |
< |
for (i=0; i<n; i++) |
361 |
< |
{ |
362 |
< |
tmp = v(i, j); |
363 |
< |
v(i, j) = v(i, k); |
364 |
< |
v(i, k) = tmp; |
365 |
< |
} |
366 |
< |
} |
367 |
< |
} |
368 |
< |
// insure eigenvector consistency (i.e., Jacobi can compute vectors that |
369 |
< |
// are negative of one another (.707,.707,0) and (-.707,-.707,0). This can |
370 |
< |
// reek havoc in hyperstreamline/other stuff. We will select the most |
371 |
< |
// positive eigenvector. |
372 |
< |
int ceil_half_n = (n >> 1) + (n & 1); |
373 |
< |
for (j=0; j<n; j++) |
374 |
< |
{ |
375 |
< |
for (numPos=0, i=0; i<n; i++) |
376 |
< |
{ |
377 |
< |
if ( v(i, j) >= 0.0 ) |
378 |
< |
{ |
379 |
< |
numPos++; |
380 |
< |
} |
369 |
< |
} |
370 |
< |
// if ( numPos < ceil(double(n)/double(2.0)) ) |
371 |
< |
if ( numPos < ceil_half_n) |
372 |
< |
{ |
373 |
< |
for(i=0; i<n; i++) |
374 |
< |
{ |
375 |
< |
v(i, j) *= -1.0; |
376 |
< |
} |
377 |
< |
} |
378 |
< |
} |
343 |
> |
// sort eigenfunctions these changes do not affect accuracy |
344 |
> |
for (j=0; j<n-1; j++) { // boundary incorrect |
345 |
> |
k = j; |
346 |
> |
tmp = w[k]; |
347 |
> |
for (i=j+1; i<n; i++) { // boundary incorrect, shifted already |
348 |
> |
if (w[i] >= tmp) { // why exchage if same? |
349 |
> |
k = i; |
350 |
> |
tmp = w[k]; |
351 |
> |
} |
352 |
> |
} |
353 |
> |
if (k != j) { |
354 |
> |
w[k] = w[j]; |
355 |
> |
w[j] = tmp; |
356 |
> |
for (i=0; i<n; i++) { |
357 |
> |
tmp = v(i, j); |
358 |
> |
v(i, j) = v(i, k); |
359 |
> |
v(i, k) = tmp; |
360 |
> |
} |
361 |
> |
} |
362 |
> |
} |
363 |
> |
// insure eigenvector consistency (i.e., Jacobi can compute vectors that |
364 |
> |
// are negative of one another (.707,.707,0) and (-.707,-.707,0). This can |
365 |
> |
// reek havoc in hyperstreamline/other stuff. We will select the most |
366 |
> |
// positive eigenvector. |
367 |
> |
int ceil_half_n = (n >> 1) + (n & 1); |
368 |
> |
for (j=0; j<n; j++) { |
369 |
> |
for (numPos=0, i=0; i<n; i++) { |
370 |
> |
if ( v(i, j) >= 0.0 ) { |
371 |
> |
numPos++; |
372 |
> |
} |
373 |
> |
} |
374 |
> |
// if ( numPos < ceil(double(n)/double(2.0)) ) |
375 |
> |
if ( numPos < ceil_half_n) { |
376 |
> |
for (i=0; i<n; i++) { |
377 |
> |
v(i, j) *= -1.0; |
378 |
> |
} |
379 |
> |
} |
380 |
> |
} |
381 |
|
|
382 |
< |
if (n > 4) |
383 |
< |
{ |
384 |
< |
delete [] b; |
383 |
< |
delete [] z; |
384 |
< |
} |
385 |
< |
return 1; |
382 |
> |
if (n > 4) { |
383 |
> |
delete [] b; |
384 |
> |
delete [] z; |
385 |
|
} |
386 |
+ |
return 1; |
387 |
+ |
} |
388 |
|
|
389 |
|
|
390 |
|
} |