src/math/SquareMatrix.hpp

/*
 * Copyright (c) 2005 The University of Notre Dame. All Rights Reserved.
 *
 * The University of Notre Dame grants you ("Licensee") a
 * non-exclusive, royalty free, license to use, modify and
 * redistribute this software in source and binary code form, provided
 * that the following conditions are met:
 *
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 *
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the
 *    distribution.
 *
 * This software is provided "AS IS," without a warranty of any
 * kind. All express or implied conditions, representations and
 * warranties, including any implied warranty of merchantability,
 * fitness for a particular purpose or non-infringement, are hereby
 * excluded.  The University of Notre Dame and its licensors shall not
 * be liable for any damages suffered by licensee as a result of
 * using, modifying or distributing the software or its
 * derivatives. In no event will the University of Notre Dame or its
 * licensors be liable for any lost revenue, profit or data, or for
 * direct, indirect, special, consequential, incidental or punitive
 * damages, however caused and regardless of the theory of liability,
 * arising out of the use of or inability to use software, even if the
 * University of Notre Dame has been advised of the possibility of
 * such damages.
 *
 * SUPPORT OPEN SCIENCE!  If you use OpenMD or its source code in your
 * research, please cite the appropriate papers when you publish your
 * work.  Good starting points are:
 *                                                                      
 * [1]  Meineke, et al., J. Comp. Chem. 26, 252-271 (2005).             
 * [2]  Fennell & Gezelter, J. Chem. Phys. 124, 234104 (2006).          
 * [3]  Sun, Lin & Gezelter, J. Chem. Phys. 128, 234107 (2008).          
 * [4]  Kuang & Gezelter,  J. Chem. Phys. 133, 164101 (2010).
 * [5]  Vardeman, Stocker & Gezelter, J. Chem. Theory Comput. 7, 834 (2011).
 */
 
/**
 * @file SquareMatrix.hpp
 * @author Teng Lin
 * @date 10/11/2004
 * @version 1.0
 */
#ifndef MATH_SQUAREMATRIX_HPP 
#define MATH_SQUAREMATRIX_HPP 

#include "math/RectMatrix.hpp"
#include "utils/NumericConstant.hpp"

namespace OpenMD {

  /**
   * @class SquareMatrix SquareMatrix.hpp "math/SquareMatrix.hpp"
   * @brief A square matrix class
   * \tparam Real the element type
   * \tparam Dim the dimension of the square matrix
   */
  template<typename Real, int Dim>
  class SquareMatrix : public RectMatrix<Real, Dim, Dim> {
  public:
    typedef Real ElemType;
    typedef Real* ElemPoinerType;

    /** default constructor */
    SquareMatrix() {
      for (unsigned int i = 0; i < Dim; i++)
        for (unsigned int j = 0; j < Dim; j++)
          this->data_[i][j] = 0.0;
    }

    /** Constructs and initializes every element of this matrix to a scalar */ 
    SquareMatrix(Real s) : RectMatrix<Real, Dim, Dim>(s){
    }

    /** Constructs and initializes from an array */ 
    SquareMatrix(Real* array) : RectMatrix<Real, Dim, Dim>(array){
    }


    /** copy constructor */
    SquareMatrix(const RectMatrix<Real, Dim, Dim>& m) : RectMatrix<Real, Dim, Dim>(m) {
    }
            
    /** copy assignment operator */
    SquareMatrix<Real, Dim>& operator =(const RectMatrix<Real, Dim, Dim>& m) {
      RectMatrix<Real, Dim, Dim>::operator=(m);
      return *this;
    }
                                   
    /** Retunrs  an identity matrix*/

    static SquareMatrix<Real, Dim> identity() {
      SquareMatrix<Real, Dim> m;
                
      for (unsigned int i = 0; i < Dim; i++) 
        for (unsigned int j = 0; j < Dim; j++) 
          if (i == j)
            m(i, j) = 1.0;
          else
            m(i, j) = 0.0;

      return m;
    }

    /** 
     * Retunrs  the inversion of this matrix. 
     * @todo need implementation
     */
    SquareMatrix<Real, Dim>  inverse() {
      SquareMatrix<Real, Dim> result;

      return result;
    }        

    /**
     * Returns the determinant of this matrix.
     * @todo need implementation
     */
    Real determinant() const {
      Real det;
      return det;
    }
    
    /** Returns the trace of this matrix. */
    Real trace() const {
      Real tmp = 0;
               
      for (unsigned int i = 0; i < Dim ; i++)
        tmp += this->data_[i][i];

      return tmp;
    }

    /** Tests if this matrix is symmetrix. */            
    bool isSymmetric() const {
      for (unsigned int i = 0; i < Dim - 1; i++)
        for (unsigned int j = i; j < Dim; j++)
          if (fabs(this->data_[i][j] - this->data_[j][i]) > epsilon) 
            return false;
                        
      return true;
    }

    /** Tests if this matrix is orthogonal. */            
    bool isOrthogonal() {
      SquareMatrix<Real, Dim> tmp;

      tmp = *this * transpose();

      return tmp.isDiagonal();
    }

    /** Tests if this matrix is diagonal. */
    bool isDiagonal() const {
      for (unsigned int i = 0; i < Dim ; i++)
        for (unsigned int j = 0; j < Dim; j++)
          if (i !=j && fabs(this->data_[i][j]) > epsilon) 
            return false;
                        
      return true;
    }

    /** 
     * Returns a column vector that contains the elements from the
     * diagonal of m in the order R(0) = m(0,0), R(1) = m(1,1), and so
     * on.
     */
    Vector<Real, Dim> diagonals() const {
      Vector<Real, Dim> result;
      for (unsigned int i = 0; i < Dim; i++) {
        result(i) = this->data_[i][i];
      }
      return result;
    }

    /** Tests if this matrix is the unit matrix. */
    bool isUnitMatrix() const {
      if (!isDiagonal())
        return false;
                
      for (unsigned int i = 0; i < Dim ; i++)
        if (fabs(this->data_[i][i] - 1) > epsilon)
          return false;
                    
      return true;
    }         

    /** Return the transpose of this matrix */
    SquareMatrix<Real,  Dim> transpose() const{
      SquareMatrix<Real,  Dim> result;
                
      for (unsigned int i = 0; i < Dim; i++)
        for (unsigned int j = 0; j < Dim; j++)              
          result(j, i) = this->data_[i][j];

      return result;
    }
            
    /** @todo need implementation */
    void diagonalize() {
      //jacobi(m, eigenValues, ortMat);
    }

    /**
     * Jacobi iteration routines for computing eigenvalues/eigenvectors of 
     * real symmetric matrix
     *
     * @return true if success, otherwise return false
     * @param a symmetric matrix whose eigenvectors are to be computed. On return, the matrix is
     *     overwritten
     * @param d will contain the eigenvalues of the matrix On return of this function
     * @param v the columns of this matrix will contain the eigenvectors. The eigenvectors are 
     *    normalized and mutually orthogonal. 
     */
           
    static int jacobi(SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& d, 
                      SquareMatrix<Real, Dim>& v);
  };//end SquareMatrix


  /*=========================================================================

  Program:   Visualization Toolkit
  Module:    $RCSfile: SquareMatrix.hpp,v $

  Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
  All rights reserved.
  See Copyright.txt or http://www.kitware.com/Copyright.htm for details.

  This software is distributed WITHOUT ANY WARRANTY; without even
  the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
  PURPOSE.  See the above copyright notice for more information.

  =========================================================================*/

#define VTK_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)

#define VTK_MAX_ROTATIONS 20

  // Jacobi iteration for the solution of eigenvectors/eigenvalues of a nxn
  // real symmetric matrix. Square nxn matrix a; size of matrix in n;
  // output eigenvalues in w; and output eigenvectors in v. Resulting
  // eigenvalues/vectors are sorted in decreasing order; eigenvectors are
  // normalized.
  template<typename Real, int Dim>
  int SquareMatrix<Real, Dim>::jacobi(SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& w, 
                                      SquareMatrix<Real, Dim>& v) {
    const int n = Dim;  
    int i, j, k, iq, ip, numPos;
    Real tresh, theta, tau, t, sm, s, h, g, c, tmp;
    Real bspace[4], zspace[4];
    Real *b = bspace;
    Real *z = zspace;

    // only allocate memory if the matrix is large
    if (n > 4) {
      b = new Real[n];
      z = new Real[n]; 
    }

    // initialize
    for (ip=0; ip<n; ip++) {
      for (iq=0; iq<n; iq++) {
        v(ip, iq) = 0.0;
      }
      v(ip, ip) = 1.0;
    }
    for (ip=0; ip<n; ip++) {
      b[ip] = w[ip] = a(ip, ip);
      z[ip] = 0.0;
    }

    // begin rotation sequence
    for (i=0; i<VTK_MAX_ROTATIONS; i++) {
      sm = 0.0;
      for (ip=0; ip<n-1; ip++) {
        for (iq=ip+1; iq<n; iq++) {
          sm += fabs(a(ip, iq));
        }
      }
      if (sm == 0.0) {
        break;
      }

      if (i < 3) {                                // first 3 sweeps
        tresh = 0.2*sm/(n*n);
      } else {
        tresh = 0.0;
      }

      for (ip=0; ip<n-1; ip++) {
        for (iq=ip+1; iq<n; iq++) {
          g = 100.0*fabs(a(ip, iq));

          // after 4 sweeps
          if (i > 3 && (fabs(w[ip])+g) == fabs(w[ip])
              && (fabs(w[iq])+g) == fabs(w[iq])) {
            a(ip, iq) = 0.0;
          } else if (fabs(a(ip, iq)) > tresh) {
            h = w[iq] - w[ip];
            if ( (fabs(h)+g) == fabs(h)) {
              t = (a(ip, iq)) / h;
            } else {
              theta = 0.5*h / (a(ip, iq));
              t = 1.0 / (fabs(theta)+sqrt(1.0+theta*theta));
              if (theta < 0.0) {
                t = -t;
              }
            }
            c = 1.0 / sqrt(1+t*t);
            s = t*c;
            tau = s/(1.0+c);
            h = t*a(ip, iq);
            z[ip] -= h;
            z[iq] += h;
            w[ip] -= h;
            w[iq] += h;
            a(ip, iq)=0.0;

            // ip already shifted left by 1 unit
            for (j = 0;j <= ip-1;j++) {
              VTK_ROTATE(a,j,ip,j,iq);
            }
            // ip and iq already shifted left by 1 unit
            for (j = ip+1;j <= iq-1;j++) {
              VTK_ROTATE(a,ip,j,j,iq);
            }
            // iq already shifted left by 1 unit
            for (j=iq+1; j<n; j++) {
              VTK_ROTATE(a,ip,j,iq,j);
            }
            for (j=0; j<n; j++) {
              VTK_ROTATE(v,j,ip,j,iq);
            }
          }
        }
      }

      for (ip=0; ip<n; ip++) {
        b[ip] += z[ip];
        w[ip] = b[ip];
        z[ip] = 0.0;
      }
    }

    //// this is NEVER called
    if ( i >= VTK_MAX_ROTATIONS ) {
      std::cout << "vtkMath::Jacobi: Error extracting eigenfunctions" << std::endl;
      if (n > 4) {
        delete[] b;
        delete[] z;
      }      
      return 0;
    }

    // sort eigenfunctions                 these changes do not affect accuracy 
    for (j=0; j<n-1; j++) {                  // boundary incorrect
      k = j;
      tmp = w[k];
      for (i=j+1; i<n; i++) {                // boundary incorrect, shifted already
        if (w[i] >= tmp) {                   // why exchage if same?
          k = i;
          tmp = w[k];
        }
      }
      if (k != j) {
        w[k] = w[j];
        w[j] = tmp;
        for (i=0; i<n; i++) {
          tmp = v(i, j);
          v(i, j) = v(i, k);
          v(i, k) = tmp;
        }
      }
    }
    // insure eigenvector consistency (i.e., Jacobi can compute vectors that
    // are negative of one another (.707,.707,0) and (-.707,-.707,0). This can
    // reek havoc in hyperstreamline/other stuff. We will select the most
    // positive eigenvector.
    int ceil_half_n = (n >> 1) + (n & 1);
    for (j=0; j<n; j++) {
      for (numPos=0, i=0; i<n; i++) {
        if ( v(i, j) >= 0.0 ) {
          numPos++;
        }
      }
      //    if ( numPos < ceil(RealType(n)/RealType(2.0)) )
      if ( numPos < ceil_half_n) {
        for (i=0; i<n; i++) {
          v(i, j) *= -1.0;
        }
      }
    }

    if (n > 4) {
      delete [] b;
      delete [] z;
    }
    return 1;
  }


  typedef SquareMatrix<RealType, 6> Mat6x6d;
}
#endif //MATH_SQUAREMATRIX_HPP 

Revision:	1924
Committed:	Mon Aug 5 21:46:11 2013 UTC (11 years, 8 months ago) by gezelter
File size:	11845 byte(s)
Log Message:	Ewald fixes
#	User	Rev	Content
1	gezelter	507	/*
2	gezelter	246	* Copyright (c) 2005 The University of Notre Dame. All Rights Reserved.
3	tim	70	*
4	gezelter	246	* 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	gezelter	1390	* 1. Redistributions of source code must retain the above copyright
10	gezelter	246	* notice, this list of conditions and the following disclaimer.
11			*
12	gezelter	1390	* 2. Redistributions in binary form must reproduce the above copyright
13	gezelter	246	* 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	gezelter	1390	*
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	gezelter	1879	* [3] Sun, Lin & Gezelter, J. Chem. Phys. 128, 234107 (2008).
39	gezelter	1782	* [4] Kuang & Gezelter, J. Chem. Phys. 133, 164101 (2010).
40			* [5] Vardeman, Stocker & Gezelter, J. Chem. Theory Comput. 7, 834 (2011).
41	tim	70	*/
42	gezelter	246
43	tim	70	/**
44			* @file SquareMatrix.hpp
45			* @author Teng Lin
46			* @date 10/11/2004
47			* @version 1.0
48			*/
49	gezelter	507	#ifndef MATH_SQUAREMATRIX_HPP
50	tim	70	#define MATH_SQUAREMATRIX_HPP
51
52	tim	74	#include "math/RectMatrix.hpp"
53	gezelter	956	#include "utils/NumericConstant.hpp"
54	tim	70
55	gezelter	1390	namespace OpenMD {
56	tim	70
57	gezelter	507	/**
58			* @class SquareMatrix SquareMatrix.hpp "math/SquareMatrix.hpp"
59			* @brief A square matrix class
60	gezelter	1879	* \tparam Real the element type
61			* \tparam Dim the dimension of the square matrix
62	gezelter	507	*/
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	tim	70
69	gezelter	507	/** 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	tim	70
76	gezelter	507	/** Constructs and initializes every element of this matrix to a scalar */
77			SquareMatrix(Real s) : RectMatrix<Real, Dim, Dim>(s){
78			}
79	tim	151
80	gezelter	507	/** Constructs and initializes from an array */
81			SquareMatrix(Real* array) : RectMatrix<Real, Dim, Dim>(array){
82			}
83	tim	151
84
85	gezelter	507	/** copy constructor */
86			SquareMatrix(const RectMatrix<Real, Dim, Dim>& m) : RectMatrix<Real, Dim, Dim>(m) {
87			}
88	tim	70
89	gezelter	507	/** 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	tim	137
95	gezelter	507	/** Retunrs an identity matrix*/
96	tim	74
97	gezelter	507	static SquareMatrix<Real, Dim> identity() {
98			SquareMatrix<Real, Dim> m;
99	tim	137
100	gezelter	507	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	tim	70
107	gezelter	507	return m;
108			}
109	tim	74
110	gezelter	507	/**
111			* Retunrs the inversion of this matrix.
112			* @todo need implementation
113			*/
114			SquareMatrix<Real, Dim> inverse() {
115			SquareMatrix<Real, Dim> result;
116	tim	70
117	gezelter	507	return result;
118			}
119	tim	70
120	gezelter	507	/**
121			* Returns the determinant of this matrix.
122			* @todo need implementation
123			*/
124			Real determinant() const {
125			Real det;
126			return det;
127			}
128	gezelter	1879
129	gezelter	507	/** Returns the trace of this matrix. */
130			Real trace() const {
131			Real tmp = 0;
132	tim	137
133	gezelter	507	for (unsigned int i = 0; i < Dim ; i++)
134			tmp += this->data_[i][i];
135	tim	70
136	gezelter	507	return tmp;
137			}
138	tim	70
139	gezelter	507	/** Tests if this matrix is symmetrix. */
140			bool isSymmetric() const {
141			for (unsigned int i = 0; i < Dim - 1; i++)
142			for (unsigned int j = i; j < Dim; j++)
143	gezelter	956	if (fabs(this->data_[i][j] - this->data_[j][i]) > epsilon)
144	gezelter	507	return false;
145	tim	137
146	gezelter	507	return true;
147			}
148	tim	70
149	gezelter	507	/** Tests if this matrix is orthogonal. */
150			bool isOrthogonal() {
151			SquareMatrix<Real, Dim> tmp;
152	tim	70
153	gezelter	507	tmp = this transpose();
154	tim	70
155	gezelter	507	return tmp.isDiagonal();
156			}
157	tim	70
158	gezelter	507	/** Tests if this matrix is diagonal. */
159			bool isDiagonal() const {
160			for (unsigned int i = 0; i < Dim ; i++)
161			for (unsigned int j = 0; j < Dim; j++)
162	gezelter	956	if (i !=j && fabs(this->data_[i][j]) > epsilon)
163	gezelter	507	return false;
164	tim	137
165	gezelter	507	return true;
166			}
167	tim	137
168	gezelter	1782	/**
169			* Returns a column vector that contains the elements from the
170			* diagonal of m in the order R(0) = m(0,0), R(1) = m(1,1), and so
171			* on.
172			*/
173			Vector<Real, Dim> diagonals() const {
174			Vector<Real, Dim> result;
175			for (unsigned int i = 0; i < Dim; i++) {
176			result(i) = this->data_[i][i];
177			}
178			return result;
179			}
180
181	gezelter	507	/** Tests if this matrix is the unit matrix. */
182			bool isUnitMatrix() const {
183			if (!isDiagonal())
184			return false;
185	tim	70
186	gezelter	507	for (unsigned int i = 0; i < Dim ; i++)
187	gezelter	956	if (fabs(this->data_[i][i] - 1) > epsilon)
188	gezelter	507	return false;
189	tim	137
190	gezelter	507	return true;
191			}
192	tim	70
193	gezelter	507	/** Return the transpose of this matrix */
194			SquareMatrix<Real, Dim> transpose() const{
195			SquareMatrix<Real, Dim> result;
196	tim	273
197	gezelter	507	for (unsigned int i = 0; i < Dim; i++)
198			for (unsigned int j = 0; j < Dim; j++)
199			result(j, i) = this->data_[i][j];
200	tim	273
201	gezelter	507	return result;
202			}
203	tim	273
204	gezelter	507	/** @todo need implementation */
205			void diagonalize() {
206			//jacobi(m, eigenValues, ortMat);
207			}
208	tim	76
209	gezelter	507	/**
210			* Jacobi iteration routines for computing eigenvalues/eigenvectors of
211			* real symmetric matrix
212			*
213			* @return true if success, otherwise return false
214			* @param a symmetric matrix whose eigenvectors are to be computed. On return, the matrix is
215			* overwritten
216	gezelter	1879	* @param d will contain the eigenvalues of the matrix On return of this function
217	gezelter	507	* @param v the columns of this matrix will contain the eigenvectors. The eigenvectors are
218			* normalized and mutually orthogonal.
219			*/
220	tim	137
221	gezelter	507	static int jacobi(SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& d,
222			SquareMatrix<Real, Dim>& v);
223			};//end SquareMatrix
224	tim	70
225	tim	76
226	gezelter	507	/*=========================================================================
227	tim	76
228	tim	123	Program: Visualization Toolkit
229			Module: $RCSfile: SquareMatrix.hpp,v $
230	tim	76
231	tim	123	Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
232			All rights reserved.
233			See Copyright.txt or http://www.kitware.com/Copyright.htm for details.
234
235	gezelter	507	This software is distributed WITHOUT ANY WARRANTY; without even
236			the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
237			PURPOSE. See the above copyright notice for more information.
238	tim	123
239	gezelter	507	=========================================================================*/
240	tim	123
241	gezelter	507	#define VTK_ROTATE(a,i,j,k,l) g=a(i, j);h=a(k, l);a(i, j)=g-s(h+gtau); \
242			a(k, l)=h+s(g-htau)
243	tim	123
244			#define VTK_MAX_ROTATIONS 20
245
246	gezelter	507	// Jacobi iteration for the solution of eigenvectors/eigenvalues of a nxn
247			// real symmetric matrix. Square nxn matrix a; size of matrix in n;
248			// output eigenvalues in w; and output eigenvectors in v. Resulting
249			// eigenvalues/vectors are sorted in decreasing order; eigenvectors are
250			// normalized.
251			template<typename Real, int Dim>
252			int SquareMatrix<Real, Dim>::jacobi(SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& w,
253			SquareMatrix<Real, Dim>& v) {
254			const int n = Dim;
255			int i, j, k, iq, ip, numPos;
256			Real tresh, theta, tau, t, sm, s, h, g, c, tmp;
257			Real bspace[4], zspace[4];
258			Real *b = bspace;
259			Real *z = zspace;
260	tim	123
261	gezelter	507	// only allocate memory if the matrix is large
262			if (n > 4) {
263			b = new Real[n];
264			z = new Real[n];
265			}
266	tim	123
267	gezelter	507	// initialize
268			for (ip=0; ip<n; ip++) {
269			for (iq=0; iq<n; iq++) {
270			v(ip, iq) = 0.0;
271			}
272			v(ip, ip) = 1.0;
273			}
274			for (ip=0; ip<n; ip++) {
275			b[ip] = w[ip] = a(ip, ip);
276			z[ip] = 0.0;
277			}
278	tim	76
279	gezelter	507	// begin rotation sequence
280			for (i=0; i<VTK_MAX_ROTATIONS; i++) {
281			sm = 0.0;
282			for (ip=0; ip<n-1; ip++) {
283			for (iq=ip+1; iq<n; iq++) {
284			sm += fabs(a(ip, iq));
285			}
286			}
287			if (sm == 0.0) {
288			break;
289			}
290	tim	76
291	gezelter	507	if (i < 3) { // first 3 sweeps
292			tresh = 0.2sm/(nn);
293			} else {
294			tresh = 0.0;
295			}
296	tim	76
297	gezelter	507	for (ip=0; ip<n-1; ip++) {
298			for (iq=ip+1; iq<n; iq++) {
299			g = 100.0*fabs(a(ip, iq));
300	tim	76
301	gezelter	507	// after 4 sweeps
302			if (i > 3 && (fabs(w[ip])+g) == fabs(w[ip])
303			&& (fabs(w[iq])+g) == fabs(w[iq])) {
304			a(ip, iq) = 0.0;
305			} else if (fabs(a(ip, iq)) > tresh) {
306			h = w[iq] - w[ip];
307			if ( (fabs(h)+g) == fabs(h)) {
308			t = (a(ip, iq)) / h;
309			} else {
310			theta = 0.5*h / (a(ip, iq));
311			t = 1.0 / (fabs(theta)+sqrt(1.0+theta*theta));
312			if (theta < 0.0) {
313			t = -t;
314			}
315			}
316			c = 1.0 / sqrt(1+t*t);
317			s = t*c;
318			tau = s/(1.0+c);
319			h = t*a(ip, iq);
320			z[ip] -= h;
321			z[iq] += h;
322			w[ip] -= h;
323			w[iq] += h;
324			a(ip, iq)=0.0;
325	tim	76
326	gezelter	507	// ip already shifted left by 1 unit
327			for (j = 0;j <= ip-1;j++) {
328			VTK_ROTATE(a,j,ip,j,iq);
329			}
330			// ip and iq already shifted left by 1 unit
331			for (j = ip+1;j <= iq-1;j++) {
332			VTK_ROTATE(a,ip,j,j,iq);
333			}
334			// iq already shifted left by 1 unit
335			for (j=iq+1; j<n; j++) {
336			VTK_ROTATE(a,ip,j,iq,j);
337			}
338			for (j=0; j<n; j++) {
339			VTK_ROTATE(v,j,ip,j,iq);
340			}
341			}
342			}
343			}
344	tim	93
345	gezelter	507	for (ip=0; ip<n; ip++) {
346			b[ip] += z[ip];
347			w[ip] = b[ip];
348			z[ip] = 0.0;
349			}
350			}
351	tim	93
352	gezelter	507	//// this is NEVER called
353			if ( i >= VTK_MAX_ROTATIONS ) {
354			std::cout << "vtkMath::Jacobi: Error extracting eigenfunctions" << std::endl;
355	gezelter	1879	if (n > 4) {
356			delete[] b;
357			delete[] z;
358			}
359	gezelter	507	return 0;
360			}
361	tim	76
362	gezelter	507	// sort eigenfunctions these changes do not affect accuracy
363			for (j=0; j<n-1; j++) { // boundary incorrect
364			k = j;
365			tmp = w[k];
366			for (i=j+1; i<n; i++) { // boundary incorrect, shifted already
367			if (w[i] >= tmp) { // why exchage if same?
368			k = i;
369			tmp = w[k];
370			}
371			}
372			if (k != j) {
373			w[k] = w[j];
374			w[j] = tmp;
375			for (i=0; i<n; i++) {
376			tmp = v(i, j);
377			v(i, j) = v(i, k);
378			v(i, k) = tmp;
379			}
380			}
381			}
382			// insure eigenvector consistency (i.e., Jacobi can compute vectors that
383			// are negative of one another (.707,.707,0) and (-.707,-.707,0). This can
384			// reek havoc in hyperstreamline/other stuff. We will select the most
385			// positive eigenvector.
386			int ceil_half_n = (n >> 1) + (n & 1);
387			for (j=0; j<n; j++) {
388			for (numPos=0, i=0; i<n; i++) {
389			if ( v(i, j) >= 0.0 ) {
390			numPos++;
391			}
392			}
393	tim	963	// if ( numPos < ceil(RealType(n)/RealType(2.0)) )
394	gezelter	507	if ( numPos < ceil_half_n) {
395			for (i=0; i<n; i++) {
396			v(i, j) *= -1.0;
397			}
398			}
399			}
400	tim	76
401	gezelter	507	if (n > 4) {
402			delete [] b;
403			delete [] z;
404	tim	76	}
405	gezelter	507	return 1;
406			}
407	tim	76
408
409	tim	963	typedef SquareMatrix<RealType, 6> Mat6x6d;
410	tim	76	}
411	tim	123	#endif //MATH_SQUAREMATRIX_HPP
412	tim	76