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Comparing:
trunk/src/math/SquareMatrix.hpp (file contents), Revision 74 by tim, Wed Oct 13 23:53:40 2004 UTC vs.
branches/development/src/math/SquareMatrix.hpp (file contents), Revision 1787 by gezelter, Wed Aug 29 18:13:11 2012 UTC

#	Line 1 | Line 1
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. Redistributions of source code must retain the above copyright
10	+	*    notice, this list of conditions and the following disclaimer.
11	+	*
12	+	* 2. Redistributions in binary form must reproduce the above copyright
13	+	*    notice, this list of conditions and the following disclaimer in the
14	+	*    documentation and/or other materials provided with the
15	+	*    distribution.
16	+	*
17	+	* This software is provided "AS IS," without a warranty of any
18	+	* kind. All express or implied conditions, representations and
19	+	* warranties, including any implied warranty of merchantability,
20	+	* fitness for a particular purpose or non-infringement, are hereby
21	+	* excluded.  The University of Notre Dame and its licensors shall not
22	+	* be liable for any damages suffered by licensee as a result of
23	+	* using, modifying or distributing the software or its
24	+	* derivatives. In no event will the University of Notre Dame or its
25	+	* licensors be liable for any lost revenue, profit or data, or for
26	+	* direct, indirect, special, consequential, incidental or punitive
27	+	* damages, however caused and regardless of the theory of liability,
28	+	* arising out of the use of or inability to use software, even if the
29	+	* University of Notre Dame has been advised of the possibility of
30	+	* such damages.
31	+	*
32	+	* SUPPORT OPEN SCIENCE!  If you use OpenMD or its source code in your
33	+	* research, please cite the appropriate papers when you publish your
34	+	* work.  Good starting points are:
35	+	*
36	+	* [1]  Meineke, et al., J. Comp. Chem. 26, 252-271 (2005).
37	+	* [2]  Fennell & Gezelter, J. Chem. Phys. 124, 234104 (2006).
38	+	* [3]  Sun, Lin & Gezelter, J. Chem. Phys. 128, 24107 (2008).
39	+	* [4]  Kuang & Gezelter,  J. Chem. Phys. 133, 164101 (2010).
40	+	* [5]  Vardeman, Stocker & Gezelter, J. Chem. Theory Comput. 7, 834 (2011).
41		*/
42	<
42	>
43		/**
44		* @file SquareMatrix.hpp
45		* @author Teng Lin
#	Line 33 | Line 50
50		#define MATH_SQUAREMATRIX_HPP
51
52		#include "math/RectMatrix.hpp"
53	+	#include "utils/NumericConstant.hpp"
54
55	<	namespace oopse {
55	>	namespace OpenMD {
56
57	<	/**
58	<	* @class SquareMatrix SquareMatrix.hpp "math/SquareMatrix.hpp"
59	<	* @brief A square matrix class
60	<	* @template Real the element type
61	<	* @template Dim the dimension of the square matrix
62	<	*/
63	<	template<typename Real, int Dim>
64	<	class SquareMatrix : public RectMatrix<Real, Dim, Dim> {
65	<	public:
57	>	/**
58	>	* @class SquareMatrix SquareMatrix.hpp "math/SquareMatrix.hpp"
59	>	* @brief A square matrix class
60	>	* @template Real the element type
61	>	* @template Dim the dimension of the square matrix
62	>	*/
63	>	template<typename Real, int Dim>
64	>	class SquareMatrix : public RectMatrix<Real, Dim, Dim> {
65	>	public:
66	>	typedef Real ElemType;
67	>	typedef Real* ElemPoinerType;
68
69	<	/** default constructor */
70	<	SquareMatrix() {
71	<	for (unsigned int i = 0; i < Dim; i++)
72	<	for (unsigned int j = 0; j < Dim; j++)
73	<	data_[i][j] = 0.0;
74	<	}
69	>	/** default constructor */
70	>	SquareMatrix() {
71	>	for (unsigned int i = 0; i < Dim; i++)
72	>	for (unsigned int j = 0; j < Dim; j++)
73	>	this->data_[i][j] = 0.0;
74	>	}
75
76	<	/** copy constructor */
77	<	SquareMatrix(const RectMatrix<Real, Dim, Dim>& m)  : RectMatrix<Real, Dim, Dim>(m) {
78	<	}
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*/
76	>	/** Constructs and initializes every element of this matrix to a scalar */
77	>	SquareMatrix(Real s) : RectMatrix<Real, Dim, Dim>(s){
78	>	}
79
80	<	static SquareMatrix<Real, Dim> identity() {
81	<	SquareMatrix<Real, Dim> m;
82	<
71	<	for (unsigned int i = 0; i < Dim; i++)
72	<	for (unsigned int j = 0; j < Dim; j++)
73	<	if (i == j)
74	<	m(i, j) = 1.0;
75	<	else
76	<	m(i, j) = 0.0;
80	>	/** Constructs and initializes from an array */
81	>	SquareMatrix(Real* array) : RectMatrix<Real, Dim, Dim>(array){
82	>	}
83
78	–	return m;
79	–	}
84
85	<	/** Retunrs  the inversion of this matrix. */
86	<	SquareMatrix<Real, Dim>  inverse() {
87	<	SquareMatrix<Real, Dim> result;
85	>	/** copy constructor */
86	>	SquareMatrix(const RectMatrix<Real, Dim, Dim>& m) : RectMatrix<Real, Dim, Dim>(m) {
87	>	}
88	>
89	>	/** copy assignment operator */
90	>	SquareMatrix<Real, Dim>& operator =(const RectMatrix<Real, Dim, Dim>& m) {
91	>	RectMatrix<Real, Dim, Dim>::operator=(m);
92	>	return *this;
93	>	}
94	>
95	>	/** Retunrs  an identity matrix*/
96
97	<	return result;
98	<	}
97	>	static SquareMatrix<Real, Dim> identity() {
98	>	SquareMatrix<Real, Dim> m;
99	>
100	>	for (unsigned int i = 0; i < Dim; i++)
101	>	for (unsigned int j = 0; j < Dim; j++)
102	>	if (i == j)
103	>	m(i, j) = 1.0;
104	>	else
105	>	m(i, j) = 0.0;
106
107	<
107	>	return m;
108	>	}
109
110	<	/** Returns the determinant of this matrix. */
111	<	double determinant() const {
112	<	double det;
113	<	return det;
114	<	}
110	>	/**
111	>	* Retunrs  the inversion of this matrix.
112	>	* @todo need implementation
113	>	*/
114	>	SquareMatrix<Real, Dim>  inverse() {
115	>	SquareMatrix<Real, Dim> result;
116
117	<	/** Returns the trace of this matrix. */
118	<	double trace() const {
98	<	double tmp = 0;
99	<
100	<	for (unsigned int i = 0; i < Dim ; i++)
101	<	tmp += data_[i][i];
117	>	return result;
118	>	}
119
120	<	return tmp;
121	<	}
120	>	/**
121	>	* Returns the determinant of this matrix.
122	>	* @todo need implementation
123	>	*/
124	>	Real determinant() const {
125	>	Real det;
126	>	return det;
127	>	}
128
129	<	/** Tests if this matrix is symmetrix. */
130	<	bool isSymmetric() const {
131	<	for (unsigned int i = 0; i < Dim - 1; i++)
132	<	for (unsigned int j = i; j < Dim; j++)
133	<	if (fabs(data_[i][j] - data_[j][i]) > oopse::epsilon)
134	<	return false;
112	<
113	<	return true;
114	<	}
129	>	/** Returns the trace of this matrix. */
130	>	Real trace() const {
131	>	Real tmp = 0;
132	>
133	>	for (unsigned int i = 0; i < Dim ; i++)
134	>	tmp += this->data_[i][i];
135
136	<	/** Tests if this matrix is orthogona. */
137	<	bool isOrthogonal() {
138	<	SquareMatrix<Real, Dim> tmp;
136	>	return tmp;
137	>	}
138	>
139	>	/**
140	>	* Returns the tensor contraction (double dot product) of two rank 2
141	>	* tensors (or Matrices)
142	>	* @param t1 first tensor
143	>	* @param t2 second tensor
144	>	* @return the tensor contraction (double dot product) of t1 and t2
145	>	*/
146	>	Real doubleDot( const SquareMatrix<Real, Dim>& t1, const SquareMatrix<Real, Dim>& t2 ) {
147	>	Real tmp;
148	>	tmp = 0;
149	>
150	>	for (unsigned int i = 0; i < Dim; i++)
151	>	for (unsigned int j =0; j < Dim; j++)
152	>	tmp += t1[i][j] * t2[i][j];
153	>
154	>	return tmp;
155	>	}
156
157	<	tmp = *this * transpose();
157	>	/** Tests if this matrix is symmetrix. */
158	>	bool isSymmetric() const {
159	>	for (unsigned int i = 0; i < Dim - 1; i++)
160	>	for (unsigned int j = i; j < Dim; j++)
161	>	if (fabs(this->data_[i][j] - this->data_[j][i]) > epsilon)
162	>	return false;
163	>
164	>	return true;
165	>	}
166
167	<	return tmp.isUnitMatrix();
168	<	}
167	>	/** Tests if this matrix is orthogonal. */
168	>	bool isOrthogonal() {
169	>	SquareMatrix<Real, Dim> tmp;
170
171	<	/** Tests if this matrix is diagonal. */
126	<	bool isDiagonal() const {
127	<	for (unsigned int i = 0; i < Dim ; i++)
128	<	for (unsigned int j = 0; j < Dim; j++)
129	<	if (i !=j && fabs(data_[i][j]) > oopse::epsilon)
130	<	return false;
131	<
132	<	return true;
133	<	}
171	>	tmp = *this * transpose();
172
173	<	/** Tests if this matrix is the unit matrix. */
174	<	bool isUnitMatrix() const {
137	<	if (!isDiagonal())
138	<	return false;
139	<
140	<	for (unsigned int i = 0; i < Dim ; i++)
141	<	if (fabs(data_[i][i] - 1) > oopse::epsilon)
142	<	return false;
143	<
144	<	return true;
145	<	}
173	>	return tmp.isDiagonal();
174	>	}
175
176	<	};//end SquareMatrix
176	>	/** Tests if this matrix is diagonal. */
177	>	bool isDiagonal() const {
178	>	for (unsigned int i = 0; i < Dim ; i++)
179	>	for (unsigned int j = 0; j < Dim; j++)
180	>	if (i !=j && fabs(this->data_[i][j]) > epsilon)
181	>	return false;
182	>
183	>	return true;
184	>	}
185
186	+	/**
187	+	* Returns a column vector that contains the elements from the
188	+	* diagonal of m in the order R(0) = m(0,0), R(1) = m(1,1), and so
189	+	* on.
190	+	*/
191	+	Vector<Real, Dim> diagonals() const {
192	+	Vector<Real, Dim> result;
193	+	for (unsigned int i = 0; i < Dim; i++) {
194	+	result(i) = this->data_[i][i];
195	+	}
196	+	return result;
197	+	}
198	+
199	+	/** Tests if this matrix is the unit matrix. */
200	+	bool isUnitMatrix() const {
201	+	if (!isDiagonal())
202	+	return false;
203	+
204	+	for (unsigned int i = 0; i < Dim ; i++)
205	+	if (fabs(this->data_[i][i] - 1) > epsilon)
206	+	return false;
207	+
208	+	return true;
209	+	}
210	+
211	+	/** Return the transpose of this matrix */
212	+	SquareMatrix<Real,  Dim> transpose() const{
213	+	SquareMatrix<Real,  Dim> result;
214	+
215	+	for (unsigned int i = 0; i < Dim; i++)
216	+	for (unsigned int j = 0; j < Dim; j++)
217	+	result(j, i) = this->data_[i][j];
218	+
219	+	return result;
220	+	}
221	+
222	+	/** @todo need implementation */
223	+	void diagonalize() {
224	+	//jacobi(m, eigenValues, ortMat);
225	+	}
226	+
227	+	/**
228	+	* Jacobi iteration routines for computing eigenvalues/eigenvectors of
229	+	* real symmetric matrix
230	+	*
231	+	* @return true if success, otherwise return false
232	+	* @param a symmetric matrix whose eigenvectors are to be computed. On return, the matrix is
233	+	*     overwritten
234	+	* @param w will contain the eigenvalues of the matrix On return of this function
235	+	* @param v the columns of this matrix will contain the eigenvectors. The eigenvectors are
236	+	*    normalized and mutually orthogonal.
237	+	*/
238	+
239	+	static int jacobi(SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& d,
240	+	SquareMatrix<Real, Dim>& v);
241	+	};//end SquareMatrix
242	+
243	+
244	+	/*=========================================================================
245	+
246	+	Program:   Visualization Toolkit
247	+	Module:    $RCSfile: SquareMatrix.hpp,v $
248	+
249	+	Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
250	+	All rights reserved.
251	+	See Copyright.txt or http://www.kitware.com/Copyright.htm for details.
252	+
253	+	This software is distributed WITHOUT ANY WARRANTY; without even
254	+	the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
255	+	PURPOSE.  See the above copyright notice for more information.
256	+
257	+	=========================================================================*/
258	+
259	+	#define VTK_ROTATE(a,i,j,k,l) g=a(i, j);h=a(k, l);a(i, j)=g-s*(h+g*tau); \
260	+	a(k, l)=h+s*(g-h*tau)
261	+
262	+	#define VTK_MAX_ROTATIONS 20
263	+
264	+	// Jacobi iteration for the solution of eigenvectors/eigenvalues of a nxn
265	+	// real symmetric matrix. Square nxn matrix a; size of matrix in n;
266	+	// output eigenvalues in w; and output eigenvectors in v. Resulting
267	+	// eigenvalues/vectors are sorted in decreasing order; eigenvectors are
268	+	// normalized.
269	+	template<typename Real, int Dim>
270	+	int SquareMatrix<Real, Dim>::jacobi(SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& w,
271	+	SquareMatrix<Real, Dim>& v) {
272	+	const int n = Dim;
273	+	int i, j, k, iq, ip, numPos;
274	+	Real tresh, theta, tau, t, sm, s, h, g, c, tmp;
275	+	Real bspace[4], zspace[4];
276	+	Real *b = bspace;
277	+	Real *z = zspace;
278	+
279	+	// only allocate memory if the matrix is large
280	+	if (n > 4) {
281	+	b = new Real[n];
282	+	z = new Real[n];
283	+	}
284	+
285	+	// initialize
286	+	for (ip=0; ip<n; ip++) {
287	+	for (iq=0; iq<n; iq++) {
288	+	v(ip, iq) = 0.0;
289	+	}
290	+	v(ip, ip) = 1.0;
291	+	}
292	+	for (ip=0; ip<n; ip++) {
293	+	b[ip] = w[ip] = a(ip, ip);
294	+	z[ip] = 0.0;
295	+	}
296	+
297	+	// begin rotation sequence
298	+	for (i=0; i<VTK_MAX_ROTATIONS; i++) {
299	+	sm = 0.0;
300	+	for (ip=0; ip<n-1; ip++) {
301	+	for (iq=ip+1; iq<n; iq++) {
302	+	sm += fabs(a(ip, iq));
303	+	}
304	+	}
305	+	if (sm == 0.0) {
306	+	break;
307	+	}
308	+
309	+	if (i < 3) {                                // first 3 sweeps
310	+	tresh = 0.2*sm/(n*n);
311	+	} else {
312	+	tresh = 0.0;
313	+	}
314	+
315	+	for (ip=0; ip<n-1; ip++) {
316	+	for (iq=ip+1; iq<n; iq++) {
317	+	g = 100.0*fabs(a(ip, iq));
318	+
319	+	// after 4 sweeps
320	+	if (i > 3 && (fabs(w[ip])+g) == fabs(w[ip])
321	+	&& (fabs(w[iq])+g) == fabs(w[iq])) {
322	+	a(ip, iq) = 0.0;
323	+	} else if (fabs(a(ip, iq)) > tresh) {
324	+	h = w[iq] - w[ip];
325	+	if ( (fabs(h)+g) == fabs(h)) {
326	+	t = (a(ip, iq)) / h;
327	+	} else {
328	+	theta = 0.5*h / (a(ip, iq));
329	+	t = 1.0 / (fabs(theta)+sqrt(1.0+theta*theta));
330	+	if (theta < 0.0) {
331	+	t = -t;
332	+	}
333	+	}
334	+	c = 1.0 / sqrt(1+t*t);
335	+	s = t*c;
336	+	tau = s/(1.0+c);
337	+	h = t*a(ip, iq);
338	+	z[ip] -= h;
339	+	z[iq] += h;
340	+	w[ip] -= h;
341	+	w[iq] += h;
342	+	a(ip, iq)=0.0;
343	+
344	+	// ip already shifted left by 1 unit
345	+	for (j = 0;j <= ip-1;j++) {
346	+	VTK_ROTATE(a,j,ip,j,iq);
347	+	}
348	+	// ip and iq already shifted left by 1 unit
349	+	for (j = ip+1;j <= iq-1;j++) {
350	+	VTK_ROTATE(a,ip,j,j,iq);
351	+	}
352	+	// iq already shifted left by 1 unit
353	+	for (j=iq+1; j<n; j++) {
354	+	VTK_ROTATE(a,ip,j,iq,j);
355	+	}
356	+	for (j=0; j<n; j++) {
357	+	VTK_ROTATE(v,j,ip,j,iq);
358	+	}
359	+	}
360	+	}
361	+	}
362	+
363	+	for (ip=0; ip<n; ip++) {
364	+	b[ip] += z[ip];
365	+	w[ip] = b[ip];
366	+	z[ip] = 0.0;
367	+	}
368	+	}
369	+
370	+	//// this is NEVER called
371	+	if ( i >= VTK_MAX_ROTATIONS ) {
372	+	std::cout << "vtkMath::Jacobi: Error extracting eigenfunctions" << std::endl;
373	+	return 0;
374	+	}
375	+
376	+	// sort eigenfunctions                 these changes do not affect accuracy
377	+	for (j=0; j<n-1; j++) {                  // boundary incorrect
378	+	k = j;
379	+	tmp = w[k];
380	+	for (i=j+1; i<n; i++) {                // boundary incorrect, shifted already
381	+	if (w[i] >= tmp) {                   // why exchage if same?
382	+	k = i;
383	+	tmp = w[k];
384	+	}
385	+	}
386	+	if (k != j) {
387	+	w[k] = w[j];
388	+	w[j] = tmp;
389	+	for (i=0; i<n; i++) {
390	+	tmp = v(i, j);
391	+	v(i, j) = v(i, k);
392	+	v(i, k) = tmp;
393	+	}
394	+	}
395	+	}
396	+	// insure eigenvector consistency (i.e., Jacobi can compute vectors that
397	+	// are negative of one another (.707,.707,0) and (-.707,-.707,0). This can
398	+	// reek havoc in hyperstreamline/other stuff. We will select the most
399	+	// positive eigenvector.
400	+	int ceil_half_n = (n >> 1) + (n & 1);
401	+	for (j=0; j<n; j++) {
402	+	for (numPos=0, i=0; i<n; i++) {
403	+	if ( v(i, j) >= 0.0 ) {
404	+	numPos++;
405	+	}
406	+	}
407	+	//    if ( numPos < ceil(RealType(n)/RealType(2.0)) )
408	+	if ( numPos < ceil_half_n) {
409	+	for (i=0; i<n; i++) {
410	+	v(i, j) *= -1.0;
411	+	}
412	+	}
413	+	}
414	+
415	+	if (n > 4) {
416	+	delete [] b;
417	+	delete [] z;
418	+	}
419	+	return 1;
420	+	}
421	+
422	+
423	+	typedef SquareMatrix<RealType, 6> Mat6x6d;
424		}
425		#endif //MATH_SQUAREMATRIX_HPP
426	+

Comparing:
trunk/src/math/SquareMatrix.hpp (property svn:keywords), Revision 74 by tim, Wed Oct 13 23:53:40 2004 UTC vs.
branches/development/src/math/SquareMatrix.hpp (property svn:keywords), Revision 1787 by gezelter, Wed Aug 29 18:13:11 2012 UTC

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