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trunk/src/math/SquareMatrix.hpp (file contents), Revision 70 by tim, Wed Oct 13 06:51:09 2004 UTC vs.
branches/development/src/math/SquareMatrix.hpp (file contents), Revision 1794 by gezelter, Thu Sep 6 19:44:06 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 32 | Line 49
49		#ifndef MATH_SQUAREMATRIX_HPP
50		#define MATH_SQUAREMATRIX_HPP
51
52	<	#include "Vector3d.hpp"
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{
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	<	/** Constructs and initializes every element of this matrix to a scalar */
77	<	SquareMatrix(double s) {
78	<	for (unsigned int i = 0; i < Dim; i++)
59	<	for (unsigned int j = 0; j < Dim; j++)
60	<	data_[i][j] = s;
61	<	}
76	>	/** Constructs and initializes every element of this matrix to a scalar */
77	>	SquareMatrix(Real s) : RectMatrix<Real, Dim, Dim>(s){
78	>	}
79
80	<	/** copy constructor */
81	<	SquareMatrix(const SquareMatrix<Real, Dim>& m) {
82	<	*this = m;
66	<	}
67	<
68	<	/** destructor*/
69	<	~SquareMatrix() {}
80	>	/** Constructs and initializes from an array */
81	>	SquareMatrix(Real* array) : RectMatrix<Real, Dim, Dim>(array){
82	>	}
83
71	–	/** copy assignment operator */
72	–	SquareMatrix<Real, Dim>& operator =(const SquareMatrix<Real, Dim>& m) {
73	–	for (unsigned int i = 0; i < Dim; i++)
74	–	for (unsigned int j = 0; j < Dim; j++)
75	–	data_[i][j] = m.data_[i][j];
76	–	}
77	–
78	–	/**
79	–	* Return the reference of a single element of this matrix.
80	–	* @return the reference of a single element of this matrix
81	–	* @param i row index
82	–	* @param j colum index
83	–	*/
84	–	double& operator()(unsigned int i, unsigned int j) {
85	–	return data_[i][j];
86	–	}
84
85	<	/**
86	<	* Return the value of a single element of this matrix.
87	<	* @return the value of a single element of this matrix
88	<	* @param i row index
89	<	* @param j colum index
90	<	*/
91	<	double operator()(unsigned int i, unsigned int j) const  {
92	<	return data_[i][j];
93	<	}
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	<	/**
98	<	* Returns a row of  this matrix as a vector.
99	<	* @return a row of  this matrix as a vector
100	<	* @param row the row index
101	<	*/
102	<	Vector<Real, Dim> getRow(unsigned int row) {
103	<	Vector<Real, Dim> v;
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	<	for (unsigned int i = 0; i < Dim; i++)
108	<	v[i] = data_[row][i];
107	>	return m;
108	>	}
109
110	<	return v;
111	<	}
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	<	/**
118	<	* Sets a row of  this matrix
114	<	* @param row the row index
115	<	* @param v the vector to be set
116	<	*/
117	<	void setRow(unsigned int row, const Vector<Real, Dim>& v) {
118	<	Vector<Real, Dim> v;
117	>	return result;
118	>	}
119
120	<	for (unsigned int i = 0; i < Dim; i++)
121	<	data_[row][i] = v[i];
122	<	}
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	<	/**
130	<	* Returns a column of  this matrix as a vector.
131	<	* @return a column of  this matrix as a vector
132	<	* @param col the column index
133	<	*/
134	<	Vector<Real, Dim> getColum(unsigned int col) {
130	<	Vector<Real, Dim> v;
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	<	for (unsigned int i = 0; i < Dim; i++)
137	<	v[i] = data_[i][col];
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
135	–	return v;
136	–	}
157
158	<	/**
159	<	* Sets a column of  this matrix
160	<	* @param col the column index
161	<	* @param v the vector to be set
162	<	*/
163	<	void setColum(unsigned int col, const Vector<Real, Dim>& v){
164	<	Vector<Real, Dim> v;
158	>	/** Tests if this matrix is symmetrix. */
159	>	bool isSymmetric() const {
160	>	for (unsigned int i = 0; i < Dim - 1; i++)
161	>	for (unsigned int j = i; j < Dim; j++)
162	>	if (fabs(this->data_[i][j] - this->data_[j][i]) > epsilon)
163	>	return false;
164	>
165	>	return true;
166	>	}
167
168	<	for (unsigned int i = 0; i < Dim; i++)
169	<	data_[i][col] = v[i];
170	<	}
168	>	/** Tests if this matrix is orthogonal. */
169	>	bool isOrthogonal() {
170	>	SquareMatrix<Real, Dim> tmp;
171
172	<	/** Negates the value of this matrix in place. */
151	<	inline void negate() {
152	<	for (unsigned int i = 0; i < Dim; i++)
153	<	for (unsigned int j = 0; j < Dim; j++)
154	<	data_[i][j] = -data_[i][j];
155	<	}
156	<
157	<	/**
158	<	* Sets the value of this matrix to the negation of matrix m.
159	<	* @param m the source matrix
160	<	*/
161	<	inline void negate(const SquareMatrix<Real, Dim>& m) {
162	<	for (unsigned int i = 0; i < Dim; i++)
163	<	for (unsigned int j = 0; j < Dim; j++)
164	<	data_[i][j] = -m.data_[i][j];
165	<	}
166	<
167	<	/**
168	<	* Sets the value of this matrix to the sum of itself and m (*this += m).
169	<	* @param m the other matrix
170	<	*/
171	<	inline void add( const SquareMatrix<Real, Dim>& m ) {
172	<	for (unsigned int i = 0; i < Dim; i++)
173	<	for (unsigned int j = 0; j < Dim; j++)
174	<	data_[i][j] += m.data_[i][j];
175	<	}
176	<
177	<	/**
178	<	* Sets the value of this matrix to the sum of m1 and m2 (*this = m1 + m2).
179	<	* @param m1 the first matrix
180	<	* @param m2 the second matrix
181	<	*/
182	<	inline void add( const SquareMatrix<Real, Dim>& m1, const SquareMatrix<Real, Dim>& m2 ) {
183	<	for (unsigned int i = 0; i < Dim; i++)
184	<	for (unsigned int j = 0; j < Dim; j++)
185	<	data_[i][j] = m1.data_[i][j] + m2.data_[i][j];
186	<	}
187	<
188	<	/**
189	<	* Sets the value of this matrix to the difference  of itself and m (*this -= m).
190	<	* @param m the other matrix
191	<	*/
192	<	inline void sub( const SquareMatrix<Real, Dim>& m ) {
193	<	for (unsigned int i = 0; i < Dim; i++)
194	<	for (unsigned int j = 0; j < Dim; j++)
195	<	data_[i][j] -= m.data_[i][j];
196	<	}
197	<
198	<	/**
199	<	* Sets the value of this matrix to the difference of matrix m1 and m2 (*this = m1 - m2).
200	<	* @param m1 the first matrix
201	<	* @param m2 the second matrix
202	<	*/
203	<	inline void sub( const SquareMatrix<Real, Dim>& m1, const Vector  &m2){
204	<	for (unsigned int i = 0; i < Dim; i++)
205	<	for (unsigned int j = 0; j < Dim; j++)
206	<	data_[i][j] = m1.data_[i][j] - m2.data_[i][j];
207	<	}
208	<
209	<	/**
210	<	* Sets the value of this matrix to the scalar multiplication of itself (*this *= s).
211	<	* @param s the scalar value
212	<	*/
213	<	inline void mul( double s ) {
214	<	for (unsigned int i = 0; i < Dim; i++)
215	<	for (unsigned int j = 0; j < Dim; j++)
216	<	data_[i][j] *= s;
217	<	}
172	>	tmp = *this * transpose();
173
174	<	/**
175	<	* Sets the value of this matrix to the scalar multiplication of matrix m  (*this = s * m).
221	<	* @param s the scalar value
222	<	* @param m the matrix
223	<	*/
224	<	inline void mul( double s, const SquareMatrix<Real, Dim>& m ) {
225	<	for (unsigned int i = 0; i < Dim; i++)
226	<	for (unsigned int j = 0; j < Dim; j++)
227	<	data_[i][j] = s * m.data_[i][j];
228	<	}
174	>	return tmp.isDiagonal();
175	>	}
176
177	<	/**
178	<	* Sets the value of this matrix to the  multiplication of this matrix and matrix m
179	<	* (*this = *this * m).
180	<	* @param m the matrix
181	<	*/
182	<	inline void mul(const SquareMatrix<Real, Dim>& m ) {
183	<	SquareMatrix<Real, Dim> tmp(*this);
184	<
185	<	for (unsigned int i = 0; i < Dim; i++)
239	<	for (unsigned int j = 0; j < Dim; j++) {
240	<
241	<	data_[i][j] = 0.0;
242	<	for (unsigned int k = 0; k < Dim; k++)
243	<	data_[i][j]  = tmp.data_[i][k] * m.data_[k][j]
244	<	}
245	<	}
246	<
247	<	/**
248	<	* Sets the value of this matrix to the  left multiplication of matrix m into itself
249	<	* (*this = m *  *this).
250	<	* @param m the matrix
251	<	*/
252	<	inline void leftmul(const SquareMatrix<Real, Dim>& m ) {
253	<	SquareMatrix<Real, Dim> tmp(*this);
254	<
255	<	for (unsigned int i = 0; i < Dim; i++)
256	<	for (unsigned int j = 0; j < Dim; j++) {
257	<
258	<	data_[i][j] = 0.0;
259	<	for (unsigned int k = 0; k < Dim; k++)
260	<	data_[i][j]  = m.data_[i][k] * tmp.data_[k][j]
261	<	}
262	<	}
177	>	/** Tests if this matrix is diagonal. */
178	>	bool isDiagonal() const {
179	>	for (unsigned int i = 0; i < Dim ; i++)
180	>	for (unsigned int j = 0; j < Dim; j++)
181	>	if (i !=j && fabs(this->data_[i][j]) > epsilon)
182	>	return false;
183	>
184	>	return true;
185	>	}
186
187	<	/**
188	<	* Sets the value of this matrix to the  multiplication of matrix m1 and matrix m2
189	<	* (*this = m1 * m2).
190	<	* @param m1 the first  matrix
191	<	* @param m2 the second matrix
192	<	*/
193	<	inline void mul(const SquareMatrix<Real, Dim>& m1,
194	<	const SquareMatrix<Real, Dim>& m2 ) {
195	<	for (unsigned int i = 0; i < Dim; i++)
196	<	for (unsigned int j = 0; j < Dim; j++) {
187	>	/**
188	>	* Returns a column vector that contains the elements from the
189	>	* diagonal of m in the order R(0) = m(0,0), R(1) = m(1,1), and so
190	>	* on.
191	>	*/
192	>	Vector<Real, Dim> diagonals() const {
193	>	Vector<Real, Dim> result;
194	>	for (unsigned int i = 0; i < Dim; i++) {
195	>	result(i) = this->data_[i][i];
196	>	}
197	>	return result;
198	>	}
199	>
200	>	/** Tests if this matrix is the unit matrix. */
201	>	bool isUnitMatrix() const {
202	>	if (!isDiagonal())
203	>	return false;
204	>
205	>	for (unsigned int i = 0; i < Dim ; i++)
206	>	if (fabs(this->data_[i][i] - 1) > epsilon)
207	>	return false;
208
209	<	data_[i][j] = 0.0;
210	<	for (unsigned int k = 0; k < Dim; k++)
277	<	data_[i][j]  = m1.data_[i][k] * m2.data_[k][j]
278	<	}
209	>	return true;
210	>	}
211
212	<	}
213	<
214	<	/**
215	<	* Sets the value of this matrix to the scalar division of itself  (*this /= s ).
216	<	* @param s the scalar value
217	<	*/
218	<	inline void div( double s) {
219	<	for (unsigned int i = 0; i < Dim; i++)
220	<	for (unsigned int j = 0; j < Dim; j++)
221	<	data_[i][j] /= s;
290	<	}
291	<
292	<	inline SquareMatrix<Real, Dim>& operator=(const SquareMatrix<Real, Dim>& v) {
293	<	if (this == &v)
294	<	return *this;
295	<
296	<	for (unsigned int i = 0; i < Dim; i++)
297	<	data_[i] = v[i];
212	>	/** Return the transpose of this matrix */
213	>	SquareMatrix<Real,  Dim> transpose() const{
214	>	SquareMatrix<Real,  Dim> result;
215	>
216	>	for (unsigned int i = 0; i < Dim; i++)
217	>	for (unsigned int j = 0; j < Dim; j++)
218	>	result(j, i) = this->data_[i][j];
219	>
220	>	return result;
221	>	}
222
223	<	return *this;
224	<	}
225	<
226	<	/**
303	<	* Sets the value of this matrix to the scalar division of matrix v1  (*this = v1 / s ).
304	<	* @paran v1 the source matrix
305	<	* @param s the scalar value
306	<	*/
307	<	inline void div( const SquareMatrix<Real, Dim>& v1, double s ) {
308	<	for (unsigned int i = 0; i < Dim; i++)
309	<	data_[i] = v1.data_[i] / s;
310	<	}
223	>	/** @todo need implementation */
224	>	void diagonalize() {
225	>	//jacobi(m, eigenValues, ortMat);
226	>	}
227
228	<	/**
229	<	*  Multiples a scalar into every element of this matrix.
230	<	* @param s the scalar value
231	<	*/
232	<	SquareMatrix<Real, Dim>& operator *=(const double s) {
233	<	this->mul(s);
234	<	return *this;
235	<	}
228	>	/**
229	>	* Jacobi iteration routines for computing eigenvalues/eigenvectors of
230	>	* real symmetric matrix
231	>	*
232	>	* @return true if success, otherwise return false
233	>	* @param a symmetric matrix whose eigenvectors are to be computed. On return, the matrix is
234	>	*     overwritten
235	>	* @param w will contain the eigenvalues of the matrix On return of this function
236	>	* @param v the columns of this matrix will contain the eigenvectors. The eigenvectors are
237	>	*    normalized and mutually orthogonal.
238	>	*/
239	>
240	>	static int jacobi(SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& d,
241	>	SquareMatrix<Real, Dim>& v);
242	>	};//end SquareMatrix
243
321	–	/**
322	–	*  Divides every element of this matrix by a scalar.
323	–	* @param s the scalar value
324	–	*/
325	–	SquareMatrix<Real, Dim>& operator /=(const double s) {
326	–	this->div(s);
327	–	return *this;
328	–	}
244
245	<	/**
331	<	* Sets the value of this matrix to the sum of the other matrix and itself (*this += m).
332	<	* @param m the other matrix
333	<	*/
334	<	SquareMatrix<Real, Dim>& operator += (const SquareMatrix<Real, Dim>& m) {
335	<	add(m);
336	<	return *this;
337	<	}
245	>	/*=========================================================================
246
247	<	/**
248	<	* Sets the value of this matrix to the differerence of itself and the other matrix (*this -= m)
341	<	* @param m the other matrix
342	<	*/
343	<	SquareMatrix<Real, Dim>& operator -= (const SquareMatrix<Real, Dim>& m){
344	<	sub(m);
345	<	return *this;
346	<	}
247	>	Program:   Visualization Toolkit
248	>	Module:    $RCSfile: SquareMatrix.hpp,v $
249
250	<	/** set this matrix to an identity matrix*/
250	>	Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
251	>	All rights reserved.
252	>	See Copyright.txt or http://www.kitware.com/Copyright.htm for details.
253
254	<	void identity() {
255	<	for (unsigned int i = 0; i < Dim; i++)
256	<	for (unsigned int i = 0; i < Dim; i++)
353	<	if (i == j)
354	<	data_[i][j] = 1.0;
355	<	else
356	<	data_[i][j] = 0.0;
357	<	}
254	>	This software is distributed WITHOUT ANY WARRANTY; without even
255	>	the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
256	>	PURPOSE.  See the above copyright notice for more information.
257
258	<	/** Sets the value of this matrix to  the inversion of itself. */
360	<	void  inverse() {
361	<	inverse(*this);
362	<	}
258	>	=========================================================================*/
259
260	<	/**
261	<	* Sets the value of this matrix to  the inversion of other matrix.
366	<	* @ param m the source matrix
367	<	*/
368	<	void inverse(const SquareMatrix<Real, Dim>& m);
369	<
370	<	/** Sets the value of this matrix to  the transpose of itself. */
371	<	void transpose() {
372	<	for (unsigned int i = 0; i < Dim - 1; i++)
373	<	for (unsigned int j = i; j < Dim; j++)
374	<	std::swap(data_[i][j], data_[j][i]);
375	<	}
260	>	#define VTK_ROTATE(a,i,j,k,l) g=a(i, j);h=a(k, l);a(i, j)=g-s*(h+g*tau); \
261	>	a(k, l)=h+s*(g-h*tau)
262
263	<	/**
378	<	* Sets the value of this matrix to  the transpose of other matrix.
379	<	* @ param m the source matrix
380	<	*/
381	<	void transpose(const SquareMatrix<Real, Dim>& m) {
382	<
383	<	if (this == &m) {
384	<	transpose();
385	<	} else {
386	<	for (unsigned int i = 0; i < Dim; i++)
387	<	for (unsigned int j =0; j < Dim; j++)
388	<	data_[i][j] = m.data_[i][j];
389	<	}
390	<	}
263	>	#define VTK_MAX_ROTATIONS 20
264
265	<	/** Returns the determinant of this matrix. */
266	<	double determinant() const {
265	>	// Jacobi iteration for the solution of eigenvectors/eigenvalues of a nxn
266	>	// real symmetric matrix. Square nxn matrix a; size of matrix in n;
267	>	// output eigenvalues in w; and output eigenvectors in v. Resulting
268	>	// eigenvalues/vectors are sorted in decreasing order; eigenvectors are
269	>	// normalized.
270	>	template<typename Real, int Dim>
271	>	int SquareMatrix<Real, Dim>::jacobi(SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& w,
272	>	SquareMatrix<Real, Dim>& v) {
273	>	const int n = Dim;
274	>	int i, j, k, iq, ip, numPos;
275	>	Real tresh, theta, tau, t, sm, s, h, g, c, tmp;
276	>	Real bspace[4], zspace[4];
277	>	Real *b = bspace;
278	>	Real *z = zspace;
279
280	<	}
280	>	// only allocate memory if the matrix is large
281	>	if (n > 4) {
282	>	b = new Real[n];
283	>	z = new Real[n];
284	>	}
285
286	<	/** Returns the trace of this matrix. */
287	<	double trace() const {
288	<	double tmp = 0;
289	<
290	<	for (unsigned int i = 0; i < Dim ; i++)
291	<	tmp += data_[i][i];
286	>	// initialize
287	>	for (ip=0; ip<n; ip++) {
288	>	for (iq=0; iq<n; iq++) {
289	>	v(ip, iq) = 0.0;
290	>	}
291	>	v(ip, ip) = 1.0;
292	>	}
293	>	for (ip=0; ip<n; ip++) {
294	>	b[ip] = w[ip] = a(ip, ip);
295	>	z[ip] = 0.0;
296	>	}
297
298	<	return tmp;
299	<	}
298	>	// begin rotation sequence
299	>	for (i=0; i<VTK_MAX_ROTATIONS; i++) {
300	>	sm = 0.0;
301	>	for (ip=0; ip<n-1; ip++) {
302	>	for (iq=ip+1; iq<n; iq++) {
303	>	sm += fabs(a(ip, iq));
304	>	}
305	>	}
306	>	if (sm == 0.0) {
307	>	break;
308	>	}
309
310	<	/** Tests if this matrix is symmetrix. */
311	<	bool isSymmetric() const {
312	<	for (unsigned int i = 0; i < Dim - 1; i++)
313	<	for (unsigned int j = i; j < Dim; j++)
314	<	if (fabs(data_[i][j] - data_[j][i]) > epsilon)
412	<	return false;
413	<
414	<	return true;
415	<	}
310	>	if (i < 3) {                                // first 3 sweeps
311	>	tresh = 0.2*sm/(n*n);
312	>	} else {
313	>	tresh = 0.0;
314	>	}
315
316	<	/** Tests if this matrix is orthogona. */
317	<	bool isOrthogonal() const {
318	<	SquareMatrix<Real, Dim> t(*this);
316	>	for (ip=0; ip<n-1; ip++) {
317	>	for (iq=ip+1; iq<n; iq++) {
318	>	g = 100.0*fabs(a(ip, iq));
319
320	<	t.transpose();
320	>	// after 4 sweeps
321	>	if (i > 3 && (fabs(w[ip])+g) == fabs(w[ip])
322	>	&& (fabs(w[iq])+g) == fabs(w[iq])) {
323	>	a(ip, iq) = 0.0;
324	>	} else if (fabs(a(ip, iq)) > tresh) {
325	>	h = w[iq] - w[ip];
326	>	if ( (fabs(h)+g) == fabs(h)) {
327	>	t = (a(ip, iq)) / h;
328	>	} else {
329	>	theta = 0.5*h / (a(ip, iq));
330	>	t = 1.0 / (fabs(theta)+sqrt(1.0+theta*theta));
331	>	if (theta < 0.0) {
332	>	t = -t;
333	>	}
334	>	}
335	>	c = 1.0 / sqrt(1+t*t);
336	>	s = t*c;
337	>	tau = s/(1.0+c);
338	>	h = t*a(ip, iq);
339	>	z[ip] -= h;
340	>	z[iq] += h;
341	>	w[ip] -= h;
342	>	w[iq] += h;
343	>	a(ip, iq)=0.0;
344
345	<	return isUnitMatrix(*this * t);
346	<	}
345	>	// ip already shifted left by 1 unit
346	>	for (j = 0;j <= ip-1;j++) {
347	>	VTK_ROTATE(a,j,ip,j,iq);
348	>	}
349	>	// ip and iq already shifted left by 1 unit
350	>	for (j = ip+1;j <= iq-1;j++) {
351	>	VTK_ROTATE(a,ip,j,j,iq);
352	>	}
353	>	// iq already shifted left by 1 unit
354	>	for (j=iq+1; j<n; j++) {
355	>	VTK_ROTATE(a,ip,j,iq,j);
356	>	}
357	>	for (j=0; j<n; j++) {
358	>	VTK_ROTATE(v,j,ip,j,iq);
359	>	}
360	>	}
361	>	}
362	>	}
363
364	<	/** Tests if this matrix is diagonal. */
365	<	bool isDiagonal() const {
366	<	for (unsigned int i = 0; i < Dim ; i++)
367	<	for (unsigned int j = 0; j < Dim; j++)
368	<	if (i !=j && fabs(data_[i][j]) > epsilon)
431	<	return false;
432	<
433	<	return true;
434	<	}
435	<
436	<	/** Tests if this matrix is the unit matrix. */
437	<	bool isUnitMatrix() const {
438	<	if (!isDiagonal())
439	<	return false;
440	<
441	<	for (unsigned int i = 0; i < Dim ; i++)
442	<	if (fabs(data_[i][i] - 1) > epsilon)
443	<	return false;
444	<
445	<	return true;
446	<	}
447	<
448	<	protected:
449	<	double data_[Dim][Dim]; /**< matrix element */
450	<
451	<	};//end SquareMatrix
452	<
453	<
454	<	/** Negate the value of every element of this matrix. */
455	<	template<typename Real, int Dim>
456	<	inline SquareMatrix<Real, Dim> operator -(const SquareMatrix& m) {
457	<	SquareMatrix<Real, Dim> result(m);
458	<
459	<	result.negate();
460	<
461	<	return result;
364	>	for (ip=0; ip<n; ip++) {
365	>	b[ip] += z[ip];
366	>	w[ip] = b[ip];
367	>	z[ip] = 0.0;
368	>	}
369		}
463	–
464	–	/**
465	–	* Return the sum of two matrixes  (m1 + m2).
466	–	* @return the sum of two matrixes
467	–	* @param m1 the first matrix
468	–	* @param m2 the second matrix
469	–	*/
470	–	template<typename Real, int Dim>
471	–	inline SquareMatrix<Real, Dim> operator + (const SquareMatrix<Real, Dim>& m1,
472	–	const SquareMatrix<Real, Dim>& m2) {
473	–	SquareMatrix<Real, Dim>result;
370
371	<	result.add(m1, m2);
372	<
373	<	return result;
371	>	//// this is NEVER called
372	>	if ( i >= VTK_MAX_ROTATIONS ) {
373	>	std::cout << "vtkMath::Jacobi: Error extracting eigenfunctions" << std::endl;
374	>	return 0;
375		}
479	–
480	–	/**
481	–	* Return the difference of two matrixes  (m1 - m2).
482	–	* @return the sum of two matrixes
483	–	* @param m1 the first matrix
484	–	* @param m2 the second matrix
485	–	*/
486	–	template<typename Real, int Dim>
487	–	inline SquareMatrix<Real, Dim> operator - (const SquareMatrix<Real, Dim>& m1,
488	–	const SquareMatrix<Real, Dim>& m2) {
489	–	SquareMatrix<Real, Dim>result;
376
377	<	result.sub(m1, m2);
378	<
379	<	return result;
377	>	// sort eigenfunctions                 these changes do not affect accuracy
378	>	for (j=0; j<n-1; j++) {                  // boundary incorrect
379	>	k = j;
380	>	tmp = w[k];
381	>	for (i=j+1; i<n; i++) {                // boundary incorrect, shifted already
382	>	if (w[i] >= tmp) {                   // why exchage if same?
383	>	k = i;
384	>	tmp = w[k];
385	>	}
386	>	}
387	>	if (k != j) {
388	>	w[k] = w[j];
389	>	w[j] = tmp;
390	>	for (i=0; i<n; i++) {
391	>	tmp = v(i, j);
392	>	v(i, j) = v(i, k);
393	>	v(i, k) = tmp;
394	>	}
395	>	}
396		}
397	<
398	<	/**
399	<	* Return the multiplication of two matrixes  (m1 * m2).
400	<	* @return the multiplication of two matrixes
401	<	* @param m1 the first matrix
402	<	* @param m2 the second matrix
403	<	*/
404	<	template<typename Real, int Dim>
405	<	inline SquareMatrix<Real, Dim> operator *(const SquareMatrix<Real, Dim>& m1,
406	<	const SquareMatrix<Real, Dim>& m2) {
407	<	SquareMatrix<Real, Dim> result;
408	<
409	<	result.mul(m1, m2);
410	<
411	<	return result;
397	>	// insure eigenvector consistency (i.e., Jacobi can compute vectors that
398	>	// are negative of one another (.707,.707,0) and (-.707,-.707,0). This can
399	>	// reek havoc in hyperstreamline/other stuff. We will select the most
400	>	// positive eigenvector.
401	>	int ceil_half_n = (n >> 1) + (n & 1);
402	>	for (j=0; j<n; j++) {
403	>	for (numPos=0, i=0; i<n; i++) {
404	>	if ( v(i, j) >= 0.0 ) {
405	>	numPos++;
406	>	}
407	>	}
408	>	//    if ( numPos < ceil(RealType(n)/RealType(2.0)) )
409	>	if ( numPos < ceil_half_n) {
410	>	for (i=0; i<n; i++) {
411	>	v(i, j) *= -1.0;
412	>	}
413	>	}
414		}
511	–
512	–	/**
513	–	* Return the multiplication of  matrixes m  and vector v (m * v).
514	–	* @return the multiplication of matrixes and vector
515	–	* @param m the matrix
516	–	* @param v the vector
517	–	*/
518	–	template<typename Real, int Dim>
519	–	inline Vector<Real, Dim> operator *(const SquareMatrix<Real, Dim>& m,
520	–	const SquareMatrix<Real, Dim>& v) {
521	–	Vector<Real, Dim> result;
415
416	<	for (unsigned int i = 0; i < Dim ; i++)
417	<	for (unsigned int j = 0; j < Dim ; j++)
418	<	result[i] += m(i, j) * v[j];
526	<
527	<	return result;
416	>	if (n > 4) {
417	>	delete [] b;
418	>	delete [] z;
419		}
420	+	return 1;
421	+	}
422	+
423	+
424	+	typedef SquareMatrix<RealType, 6> Mat6x6d;
425		}
426		#endif //MATH_SQUAREMATRIX_HPP
427	+

Comparing:
trunk/src/math/SquareMatrix.hpp (property svn:keywords), Revision 70 by tim, Wed Oct 13 06:51:09 2004 UTC vs.
branches/development/src/math/SquareMatrix.hpp (property svn:keywords), Revision 1794 by gezelter, Thu Sep 6 19:44:06 2012 UTC

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