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. Acknowledgement of the program authors must be made in any
 *    publication of scientific results based in part on use of the
 *    program.  An acceptable form of acknowledgement is citation of
 *    the article in which the program was described (Matthew
 *    A. Meineke, Charles F. Vardeman II, Teng Lin, Christopher
 *    J. Fennell and J. Daniel Gezelter, "OOPSE: An Object-Oriented
 *    Parallel Simulation Engine for Molecular Dynamics,"
 *    J. Comput. Chem. 26, pp. 252-271 (2005))
 *
 * 2. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 *
 * 3. 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.
 */
 
/**
 * @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 oopse {

  /**
   * @class SquareMatrix SquareMatrix.hpp "math/SquareMatrix.hpp"
   * @brief A square matrix class
   * @template Real the element type
   * @template 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;
    }

    /** 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 w 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;
      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(double(n)/double(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<double, 6> Mat6x6d;
}
#endif //MATH_SQUAREMATRIX_HPP 

Revision:	2752
Committed:	Tue May 16 02:06:37 2006 UTC (18 years, 2 months ago) by gezelter
File size:	11295 byte(s)
Log Message:	* empty log message *
#	User	Rev	Content
1	gezelter	2204	/*
2	gezelter	1930	* Copyright (c) 2005 The University of Notre Dame. All Rights Reserved.
3	tim	1563	*
4	gezelter	1930	* 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	tim	1563	*/
41	gezelter	1930
42	tim	1563	/**
43			* @file SquareMatrix.hpp
44			* @author Teng Lin
45			* @date 10/11/2004
46			* @version 1.0
47			*/
48	gezelter	2204	#ifndef MATH_SQUAREMATRIX_HPP
49	tim	1563	#define MATH_SQUAREMATRIX_HPP
50
51	tim	1567	#include "math/RectMatrix.hpp"
52	gezelter	2752	#include "utils/NumericConstant.hpp"
53	tim	1563
54			namespace oopse {
55
56	gezelter	2204	/**
57			* @class SquareMatrix SquareMatrix.hpp "math/SquareMatrix.hpp"
58			* @brief A square matrix class
59			* @template Real the element type
60			* @template Dim the dimension of the square matrix
61			*/
62			template<typename Real, int Dim>
63			class SquareMatrix : public RectMatrix<Real, Dim, Dim> {
64			public:
65			typedef Real ElemType;
66			typedef Real* ElemPoinerType;
67	tim	1563
68	gezelter	2204	/** default constructor */
69			SquareMatrix() {
70			for (unsigned int i = 0; i < Dim; i++)
71			for (unsigned int j = 0; j < Dim; j++)
72			this->data_[i][j] = 0.0;
73			}
74	tim	1563
75	gezelter	2204	/** Constructs and initializes every element of this matrix to a scalar */
76			SquareMatrix(Real s) : RectMatrix<Real, Dim, Dim>(s){
77			}
78	tim	1644
79	gezelter	2204	/** Constructs and initializes from an array */
80			SquareMatrix(Real* array) : RectMatrix<Real, Dim, Dim>(array){
81			}
82	tim	1644
83
84	gezelter	2204	/** copy constructor */
85			SquareMatrix(const RectMatrix<Real, Dim, Dim>& m) : RectMatrix<Real, Dim, Dim>(m) {
86			}
87	tim	1563
88	gezelter	2204	/** copy assignment operator */
89			SquareMatrix<Real, Dim>& operator =(const RectMatrix<Real, Dim, Dim>& m) {
90			RectMatrix<Real, Dim, Dim>::operator=(m);
91			return *this;
92			}
93	tim	1630
94	gezelter	2204	/** Retunrs an identity matrix*/
95	tim	1567
96	gezelter	2204	static SquareMatrix<Real, Dim> identity() {
97			SquareMatrix<Real, Dim> m;
98	tim	1630
99	gezelter	2204	for (unsigned int i = 0; i < Dim; i++)
100			for (unsigned int j = 0; j < Dim; j++)
101			if (i == j)
102			m(i, j) = 1.0;
103			else
104			m(i, j) = 0.0;
105	tim	1563
106	gezelter	2204	return m;
107			}
108	tim	1567
109	gezelter	2204	/**
110			* Retunrs the inversion of this matrix.
111			* @todo need implementation
112			*/
113			SquareMatrix<Real, Dim> inverse() {
114			SquareMatrix<Real, Dim> result;
115	tim	1563
116	gezelter	2204	return result;
117			}
118	tim	1563
119	gezelter	2204	/**
120			* Returns the determinant of this matrix.
121			* @todo need implementation
122			*/
123			Real determinant() const {
124			Real det;
125			return det;
126			}
127	tim	1563
128	gezelter	2204	/** Returns the trace of this matrix. */
129			Real trace() const {
130			Real tmp = 0;
131	tim	1630
132	gezelter	2204	for (unsigned int i = 0; i < Dim ; i++)
133			tmp += this->data_[i][i];
134	tim	1563
135	gezelter	2204	return tmp;
136			}
137	tim	1563
138	gezelter	2204	/** Tests if this matrix is symmetrix. */
139			bool isSymmetric() const {
140			for (unsigned int i = 0; i < Dim - 1; i++)
141			for (unsigned int j = i; j < Dim; j++)
142	gezelter	2752	if (fabs(this->data_[i][j] - this->data_[j][i]) > epsilon)
143	gezelter	2204	return false;
144	tim	1630
145	gezelter	2204	return true;
146			}
147	tim	1563
148	gezelter	2204	/** Tests if this matrix is orthogonal. */
149			bool isOrthogonal() {
150			SquareMatrix<Real, Dim> tmp;
151	tim	1563
152	gezelter	2204	tmp = this transpose();
153	tim	1563
154	gezelter	2204	return tmp.isDiagonal();
155			}
156	tim	1563
157	gezelter	2204	/** Tests if this matrix is diagonal. */
158			bool isDiagonal() const {
159			for (unsigned int i = 0; i < Dim ; i++)
160			for (unsigned int j = 0; j < Dim; j++)
161	gezelter	2752	if (i !=j && fabs(this->data_[i][j]) > epsilon)
162	gezelter	2204	return false;
163	tim	1630
164	gezelter	2204	return true;
165			}
166	tim	1630
167	gezelter	2204	/** Tests if this matrix is the unit matrix. */
168			bool isUnitMatrix() const {
169			if (!isDiagonal())
170			return false;
171	tim	1563
172	gezelter	2204	for (unsigned int i = 0; i < Dim ; i++)
173	gezelter	2752	if (fabs(this->data_[i][i] - 1) > epsilon)
174	gezelter	2204	return false;
175	tim	1630
176	gezelter	2204	return true;
177			}
178	tim	1563
179	gezelter	2204	/** Return the transpose of this matrix */
180			SquareMatrix<Real, Dim> transpose() const{
181			SquareMatrix<Real, Dim> result;
182	tim	1957
183	gezelter	2204	for (unsigned int i = 0; i < Dim; i++)
184			for (unsigned int j = 0; j < Dim; j++)
185			result(j, i) = this->data_[i][j];
186	tim	1957
187	gezelter	2204	return result;
188			}
189	tim	1957
190	gezelter	2204	/** @todo need implementation */
191			void diagonalize() {
192			//jacobi(m, eigenValues, ortMat);
193			}
194	tim	1569
195	gezelter	2204	/**
196			* Jacobi iteration routines for computing eigenvalues/eigenvectors of
197			* real symmetric matrix
198			*
199			* @return true if success, otherwise return false
200			* @param a symmetric matrix whose eigenvectors are to be computed. On return, the matrix is
201			* overwritten
202			* @param w will contain the eigenvalues of the matrix On return of this function
203			* @param v the columns of this matrix will contain the eigenvectors. The eigenvectors are
204			* normalized and mutually orthogonal.
205			*/
206	tim	1630
207	gezelter	2204	static int jacobi(SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& d,
208			SquareMatrix<Real, Dim>& v);
209			};//end SquareMatrix
210	tim	1563
211	tim	1569
212	gezelter	2204	/*=========================================================================
213	tim	1569
214	tim	1616	Program: Visualization Toolkit
215			Module: $RCSfile: SquareMatrix.hpp,v $
216	tim	1569
217	tim	1616	Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
218			All rights reserved.
219			See Copyright.txt or http://www.kitware.com/Copyright.htm for details.
220
221	gezelter	2204	This software is distributed WITHOUT ANY WARRANTY; without even
222			the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
223			PURPOSE. See the above copyright notice for more information.
224	tim	1616
225	gezelter	2204	=========================================================================*/
226	tim	1616
227	gezelter	2204	#define VTK_ROTATE(a,i,j,k,l) g=a(i, j);h=a(k, l);a(i, j)=g-s(h+gtau); \
228			a(k, l)=h+s(g-htau)
229	tim	1616
230			#define VTK_MAX_ROTATIONS 20
231
232	gezelter	2204	// Jacobi iteration for the solution of eigenvectors/eigenvalues of a nxn
233			// real symmetric matrix. Square nxn matrix a; size of matrix in n;
234			// output eigenvalues in w; and output eigenvectors in v. Resulting
235			// eigenvalues/vectors are sorted in decreasing order; eigenvectors are
236			// normalized.
237			template<typename Real, int Dim>
238			int SquareMatrix<Real, Dim>::jacobi(SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& w,
239			SquareMatrix<Real, Dim>& v) {
240			const int n = Dim;
241			int i, j, k, iq, ip, numPos;
242			Real tresh, theta, tau, t, sm, s, h, g, c, tmp;
243			Real bspace[4], zspace[4];
244			Real *b = bspace;
245			Real *z = zspace;
246	tim	1616
247	gezelter	2204	// only allocate memory if the matrix is large
248			if (n > 4) {
249			b = new Real[n];
250			z = new Real[n];
251			}
252	tim	1616
253	gezelter	2204	// initialize
254			for (ip=0; ip<n; ip++) {
255			for (iq=0; iq<n; iq++) {
256			v(ip, iq) = 0.0;
257			}
258			v(ip, ip) = 1.0;
259			}
260			for (ip=0; ip<n; ip++) {
261			b[ip] = w[ip] = a(ip, ip);
262			z[ip] = 0.0;
263			}
264	tim	1569
265	gezelter	2204	// begin rotation sequence
266			for (i=0; i<VTK_MAX_ROTATIONS; i++) {
267			sm = 0.0;
268			for (ip=0; ip<n-1; ip++) {
269			for (iq=ip+1; iq<n; iq++) {
270			sm += fabs(a(ip, iq));
271			}
272			}
273			if (sm == 0.0) {
274			break;
275			}
276	tim	1569
277	gezelter	2204	if (i < 3) { // first 3 sweeps
278			tresh = 0.2sm/(nn);
279			} else {
280			tresh = 0.0;
281			}
282	tim	1569
283	gezelter	2204	for (ip=0; ip<n-1; ip++) {
284			for (iq=ip+1; iq<n; iq++) {
285			g = 100.0*fabs(a(ip, iq));
286	tim	1569
287	gezelter	2204	// after 4 sweeps
288			if (i > 3 && (fabs(w[ip])+g) == fabs(w[ip])
289			&& (fabs(w[iq])+g) == fabs(w[iq])) {
290			a(ip, iq) = 0.0;
291			} else if (fabs(a(ip, iq)) > tresh) {
292			h = w[iq] - w[ip];
293			if ( (fabs(h)+g) == fabs(h)) {
294			t = (a(ip, iq)) / h;
295			} else {
296			theta = 0.5*h / (a(ip, iq));
297			t = 1.0 / (fabs(theta)+sqrt(1.0+theta*theta));
298			if (theta < 0.0) {
299			t = -t;
300			}
301			}
302			c = 1.0 / sqrt(1+t*t);
303			s = t*c;
304			tau = s/(1.0+c);
305			h = t*a(ip, iq);
306			z[ip] -= h;
307			z[iq] += h;
308			w[ip] -= h;
309			w[iq] += h;
310			a(ip, iq)=0.0;
311	tim	1569
312	gezelter	2204	// ip already shifted left by 1 unit
313			for (j = 0;j <= ip-1;j++) {
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			VTK_ROTATE(a,ip,j,j,iq);
319			}
320			// iq already shifted left by 1 unit
321			for (j=iq+1; j<n; j++) {
322			VTK_ROTATE(a,ip,j,iq,j);
323			}
324			for (j=0; j<n; j++) {
325			VTK_ROTATE(v,j,ip,j,iq);
326			}
327			}
328			}
329			}
330	tim	1586
331	gezelter	2204	for (ip=0; ip<n; ip++) {
332			b[ip] += z[ip];
333			w[ip] = b[ip];
334			z[ip] = 0.0;
335			}
336			}
337	tim	1586
338	gezelter	2204	//// this is NEVER called
339			if ( i >= VTK_MAX_ROTATIONS ) {
340			std::cout << "vtkMath::Jacobi: Error extracting eigenfunctions" << std::endl;
341			return 0;
342			}
343	tim	1569
344	gezelter	2204	// sort eigenfunctions these changes do not affect accuracy
345			for (j=0; j<n-1; j++) { // boundary incorrect
346			k = j;
347			tmp = w[k];
348			for (i=j+1; i<n; i++) { // boundary incorrect, shifted already
349			if (w[i] >= tmp) { // why exchage if same?
350			k = i;
351			tmp = w[k];
352			}
353			}
354			if (k != j) {
355			w[k] = w[j];
356			w[j] = tmp;
357			for (i=0; i<n; i++) {
358			tmp = v(i, j);
359			v(i, j) = v(i, k);
360			v(i, k) = tmp;
361			}
362			}
363			}
364			// insure eigenvector consistency (i.e., Jacobi can compute vectors that
365			// are negative of one another (.707,.707,0) and (-.707,-.707,0). This can
366			// reek havoc in hyperstreamline/other stuff. We will select the most
367			// positive eigenvector.
368			int ceil_half_n = (n >> 1) + (n & 1);
369			for (j=0; j<n; j++) {
370			for (numPos=0, i=0; i<n; i++) {
371			if ( v(i, j) >= 0.0 ) {
372			numPos++;
373			}
374			}
375			// if ( numPos < ceil(double(n)/double(2.0)) )
376			if ( numPos < ceil_half_n) {
377			for (i=0; i<n; i++) {
378			v(i, j) *= -1.0;
379			}
380			}
381			}
382	tim	1569
383	gezelter	2204	if (n > 4) {
384			delete [] b;
385			delete [] z;
386	tim	1569	}
387	gezelter	2204	return 1;
388			}
389	tim	1569
390
391	tim	2634	typedef SquareMatrix<double, 6> Mat6x6d;
392	tim	1569	}
393	tim	1616	#endif //MATH_SQUAREMATRIX_HPP
394	tim	1569