MOAB: Mesh Oriented datABase  (version 5.4.0)
AWMetric.hpp
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00001 /* *****************************************************************
00002     MESQUITE -- The Mesh Quality Improvement Toolkit
00003 
00004     Copyright 2006 Sandia National Laboratories.  Developed at the
00005     University of Wisconsin--Madison under SNL contract number
00006     624796.  The U.S. Government and the University of Wisconsin
00007     retain certain rights to this software.
00008 
00009     This library is free software; you can redistribute it and/or
00010     modify it under the terms of the GNU Lesser General Public
00011     License as published by the Free Software Foundation; either
00012     version 2.1 of the License, or (at your option) any later version.
00013 
00014     This library is distributed in the hope that it will be useful,
00015     but WITHOUT ANY WARRANTY; without even the implied warranty of
00016     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
00017     Lesser General Public License for more details.
00018 
00019     You should have received a copy of the GNU Lesser General Public License
00020     (lgpl.txt) along with this library; if not, write to the Free Software
00021     Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
00022 
00023     (2006) kraftche@cae.wisc.edu
00024 
00025   ***************************************************************** */
00026 
00027 /** \file AWMetric.hpp
00028  *  \brief
00029  *  \author Jason Kraftcheck
00030  */
00031 
00032 #ifndef MSQ_AW_METRIC_HPP
00033 #define MSQ_AW_METRIC_HPP
00034 
00035 #include "Mesquite.hpp"
00036 #include <string>
00037 
00038 namespace MBMesquite
00039 {
00040 
00041 class MsqError;
00042 template < unsigned R, unsigned C >
00043 class MsqMatrix;
00044 
00045 /**\brief A metric for comparing a matrix A with a target matrix W
00046  *
00047  * Implement a scalar function \f$\mu(A,W)\f$ where A and W are 2x2 or 3x3 matrices.
00048  */
00049 class AWMetric
00050 {
00051   public:
00052     MESQUITE_EXPORT virtual ~AWMetric();
00053 
00054     MESQUITE_EXPORT virtual std::string get_name() const = 0;
00055 
00056     /**\brief Evaluate \f$\mu(A,W)\f$
00057      *
00058      *\param A 2x2 active matrix
00059      *\param W 2x2 target matrix
00060      *\param result Output: value of function
00061      *\return false if function cannot be evaluated for given A and W
00062      *          (e.g. division by zero, etc.), true otherwise.
00063      */
00064     MESQUITE_EXPORT virtual bool evaluate( const MsqMatrix< 2, 2 >& A,
00065                                            const MsqMatrix< 2, 2 >& W,
00066                                            double& result,
00067                                            MsqError& err );
00068 
00069     /**\brief Evaluate \f$\mu(A,W)\f$
00070      *
00071      *\param A 3x3 active matrix
00072      *\param W 3x3 target matrix
00073      *\param result Output: value of function
00074      *\return false if function cannot be evaluated for given A and W
00075      *          (e.g. division by zero, etc.), true otherwise.
00076      */
00077     MESQUITE_EXPORT virtual bool evaluate( const MsqMatrix< 3, 3 >& A,
00078                                            const MsqMatrix< 3, 3 >& W,
00079                                            double& result,
00080                                            MsqError& err );
00081 
00082     /**\brief Gradient of \f$\mu(A,W)\f$ with respect to components of A
00083      *
00084      *\param A 2x2 active matrix
00085      *\param W 2x2 target matrix
00086      *\param result Output: value of function
00087      *\param deriv_wrt_A Output: partial deriviatve of \f$\mu\f$ wrt each term of A,
00088      *                           evaluated at passed A.
00089      *                           \f[\left[\begin{array}{cc}
00090      *                            \frac{\partial\mu}{\partial A_{0,0}} &
00091      *                            \frac{\partial\mu}{\partial A_{0,1}} \\
00092      *                            \frac{\partial\mu}{\partial A_{1,0}} &
00093      *                            \frac{\partial\mu}{\partial A_{1,1}} \\
00094      *                            \end{array}\right]\f]
00095      *\return false if function cannot be evaluated for given A and W
00096      *          (e.g. division by zero, etc.), true otherwise.
00097      */
00098     MESQUITE_EXPORT virtual bool evaluate_with_grad( const MsqMatrix< 2, 2 >& A,
00099                                                      const MsqMatrix< 2, 2 >& W,
00100                                                      double& result,
00101                                                      MsqMatrix< 2, 2 >& deriv_wrt_A,
00102                                                      MsqError& err );
00103 
00104     /**\brief Gradient of \f$\mu(A,W)\f$ with respect to components of A
00105      *
00106      *\param A 3x3 active matrix
00107      *\param W 3x3 target matrix
00108      *\param result Output: value of function
00109      *\param deriv_wrt_A Output: partial deriviatve of \f$\mu\f$ wrt each term of A,
00110      *                           evaluated at passed A.
00111      *                           \f[\left[\begin{array}{ccc}
00112      *                            \frac{\partial\mu}{\partial A_{0,0}} &
00113      *                            \frac{\partial\mu}{\partial A_{0,1}} &
00114      *                            \frac{\partial\mu}{\partial A_{0,2}} \\
00115      *                            \frac{\partial\mu}{\partial A_{1,0}} &
00116      *                            \frac{\partial\mu}{\partial A_{1,1}} &
00117      *                            \frac{\partial\mu}{\partial A_{1,2}} \\
00118      *                            \frac{\partial\mu}{\partial A_{2,0}} &
00119      *                            \frac{\partial\mu}{\partial A_{2,1}} &
00120      *                            \frac{\partial\mu}{\partial A_{2,2}}
00121      *                            \end{array}\right]\f]
00122      *\return false if function cannot be evaluated for given A and W
00123      *          (e.g. division by zero, etc.), true otherwise.
00124      */
00125     MESQUITE_EXPORT virtual bool evaluate_with_grad( const MsqMatrix< 3, 3 >& A,
00126                                                      const MsqMatrix< 3, 3 >& W,
00127                                                      double& result,
00128                                                      MsqMatrix< 3, 3 >& deriv_wrt_A,
00129                                                      MsqError& err );
00130 
00131     /**\brief Hessian of \f$\mu(A,W)\f$ with respect to components of A
00132      *
00133      *\param A 2x2 active matrix
00134      *\param W 2x2 target matrix
00135      *\param result Output: value of function
00136      *\param deriv_wrt_A Output: partial deriviatve of \f$\mu\f$ wrt each term of A,
00137      *                           evaluated at passed A.
00138      *\param second_wrt_A Output: 4x4 matrix of second partial deriviatve of \f$\mu\f$ wrt
00139      *                           each term of A, in row-major order.  The symmetric
00140      *                           matrix is decomposed into 2x2 blocks and only the upper diagonal
00141      *                           blocks, in row-major order, are returned.
00142      *                           \f[\left[\begin{array}{cc|cc}
00143      *                           \frac{\partial^{2}\mu}{\partial A_{0,0}^2} &
00144      *                           \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{0,1}} &
00145      *                           \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{1,0}} &
00146      *                           \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{1,1}} \\
00147      *                           \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{0,1}} &
00148      *                           \frac{\partial^{2}\mu}{\partial A_{0,1}^2} &
00149      *                           \frac{\partial^{2}\mu}{\partial A_{0,1}\partial A_{1,0}} &
00150      *                           \frac{\partial^{2}\mu}{\partial A_{0,1}\partial A_{1,1}} \\
00151      *                           \hline & &
00152      *                           \frac{\partial^{2}\mu}{\partial A_{1,0}^2} &
00153      *                           \frac{\partial^{2}\mu}{\partial A_{1,0}\partial A_{1,1}} \\
00154      *                           & &
00155      *                           \frac{\partial^{2}\mu}{\partial A_{1,0}\partial A_{1,1}} &
00156      *                           \frac{\partial^{2}\mu}{\partial A_{1,1}^2} \\
00157      *                            \end{array}\right]\f]
00158      *
00159      *\return false if function cannot be evaluated for given A and W
00160      *          (e.g. division by zero, etc.), true otherwise.
00161      */
00162     MESQUITE_EXPORT virtual bool evaluate_with_hess( const MsqMatrix< 2, 2 >& A,
00163                                                      const MsqMatrix< 2, 2 >& W,
00164                                                      double& result,
00165                                                      MsqMatrix< 2, 2 >& deriv_wrt_A,
00166                                                      MsqMatrix< 2, 2 > second_wrt_A[3],
00167                                                      MsqError& err );
00168 
00169     /**\brief Hessian of \f$\mu(A,W)\f$ with respect to components of A
00170      *
00171      *\param A 3x3 active matrix
00172      *\param W 3x3 target matrix
00173      *\param result Output: value of function
00174      *\param deriv_wrt_A Output: partial deriviatve of \f$\mu\f$ wrt each term of A,
00175      *                           evaluated at passed A.
00176      *\param second_wrt_A Output: 9x9 matrix of second partial deriviatve of \f$\mu\f$ wrt
00177      *                           each term of A, in row-major order.  The symmetric
00178      *                           matrix is decomposed into 3x3 blocks and only the upper diagonal
00179      *                           blocks, in row-major order, are returned.
00180      *                           \f[\left[\begin{array}{ccc|ccc|ccc}
00181      *                           \frac{\partial^{2}\mu}{\partial A_{0,0}^2} &
00182      *                           \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{0,1}} &
00183      *                           \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{0,2}} &
00184      *                           \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{1,0}} &
00185      *                           \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{1,1}} &
00186      *                           \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{1,2}} &
00187      *                           \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{2,0}} &
00188      *                           \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{2,1}} &
00189      *                           \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{2,2}} \\
00190      *                           \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{0,1}} &
00191      *                           \frac{\partial^{2}\mu}{\partial A_{0,1}^2} &
00192      *                           \frac{\partial^{2}\mu}{\partial A_{0,1}\partial A_{0,2}} &
00193      *                           \frac{\partial^{2}\mu}{\partial A_{0,1}\partial A_{1,0}} &
00194      *                           \frac{\partial^{2}\mu}{\partial A_{0,1}\partial A_{1,1}} &
00195      *                           \frac{\partial^{2}\mu}{\partial A_{0,1}\partial A_{1,2}} &
00196      *                           \frac{\partial^{2}\mu}{\partial A_{0,1}\partial A_{2,0}} &
00197      *                           \frac{\partial^{2}\mu}{\partial A_{0,1}\partial A_{2,1}} &
00198      *                           \frac{\partial^{2}\mu}{\partial A_{0,1}\partial A_{2,2}} \\
00199      *                           \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{0,2}} &
00200      *                           \frac{\partial^{2}\mu}{\partial A_{0,1}\partial A_{0,2}} &
00201      *                           \frac{\partial^{2}\mu}{\partial A_{0,2}^2} &
00202      *                           \frac{\partial^{2}\mu}{\partial A_{0,2}\partial A_{1,0}} &
00203      *                           \frac{\partial^{2}\mu}{\partial A_{0,2}\partial A_{1,1}} &
00204      *                           \frac{\partial^{2}\mu}{\partial A_{0,2}\partial A_{1,2}} &
00205      *                           \frac{\partial^{2}\mu}{\partial A_{0,2}\partial A_{2,0}} &
00206      *                           \frac{\partial^{2}\mu}{\partial A_{0,2}\partial A_{2,1}} &
00207      *                           \frac{\partial^{2}\mu}{\partial A_{0,2}\partial A_{2,2}} \\
00208      *                           \hline & & &
00209      *                           \frac{\partial^{2}\mu}{\partial A_{1,0}^2} &
00210      *                           \frac{\partial^{2}\mu}{\partial A_{1,0}\partial A_{1,1}} &
00211      *                           \frac{\partial^{2}\mu}{\partial A_{1,0}\partial A_{1,2}} &
00212      *                           \frac{\partial^{2}\mu}{\partial A_{1,0}\partial A_{2,0}} &
00213      *                           \frac{\partial^{2}\mu}{\partial A_{1,0}\partial A_{2,1}} &
00214      *                           \frac{\partial^{2}\mu}{\partial A_{1,0}\partial A_{2,2}} \\
00215      *                           & & &
00216      *                           \frac{\partial^{2}\mu}{\partial A_{1,0}\partial A_{1,1}} &
00217      *                           \frac{\partial^{2}\mu}{\partial A_{1,1}^2} &
00218      *                           \frac{\partial^{2}\mu}{\partial A_{1,1}\partial A_{1,2}} &
00219      *                           \frac{\partial^{2}\mu}{\partial A_{1,1}\partial A_{2,0}} &
00220      *                           \frac{\partial^{2}\mu}{\partial A_{1,1}\partial A_{2,1}} &
00221      *                           \frac{\partial^{2}\mu}{\partial A_{1,1}\partial A_{2,2}} \\
00222      *                           & & &
00223      *                           \frac{\partial^{2}\mu}{\partial A_{1,0}\partial A_{1,2}} &
00224      *                           \frac{\partial^{2}\mu}{\partial A_{1,1}\partial A_{1,2}} &
00225      *                           \frac{\partial^{2}\mu}{\partial A_{1,2}^2} &
00226      *                           \frac{\partial^{2}\mu}{\partial A_{1,2}\partial A_{2,0}} &
00227      *                           \frac{\partial^{2}\mu}{\partial A_{1,2}\partial A_{2,1}} &
00228      *                           \frac{\partial^{2}\mu}{\partial A_{1,2}\partial A_{2,2}} \\
00229      *                           \hline & & & & & &
00230      *                           \frac{\partial^{2}\mu}{\partial A_{2,0}^2} &
00231      *                           \frac{\partial^{2}\mu}{\partial A_{2,0}\partial A_{2,1}} &
00232      *                           \frac{\partial^{2}\mu}{\partial A_{2,0}\partial A_{2,2}} \\
00233      *                           & & & & & &
00234      *                           \frac{\partial^{2}\mu}{\partial A_{2,0}\partial A_{2,1}} &
00235      *                           \frac{\partial^{2}\mu}{\partial A_{2,1}^2} &
00236      *                           \frac{\partial^{2}\mu}{\partial A_{2,1}\partial A_{2,2}} \\
00237      *                           & & & & & &
00238      *                           \frac{\partial^{2}\mu}{\partial A_{2,0}\partial A_{2,2}} &
00239      *                           \frac{\partial^{2}\mu}{\partial A_{2,1}\partial A_{2,2}} &
00240      *                           \frac{\partial^{2}\mu}{\partial A_{2,2}^2} \\
00241      *                            \end{array}\right]\f]
00242      *
00243      *\return false if function cannot be evaluated for given A and W
00244      *          (e.g. division by zero, etc.), true otherwise.
00245      */
00246     MESQUITE_EXPORT virtual bool evaluate_with_hess( const MsqMatrix< 3, 3 >& A,
00247                                                      const MsqMatrix< 3, 3 >& W,
00248                                                      double& result,
00249                                                      MsqMatrix< 3, 3 >& deriv_wrt_A,
00250                                                      MsqMatrix< 3, 3 > second_wrt_A[6],
00251                                                      MsqError& err );
00252 
00253     static inline bool invalid_determinant( double d )
00254     {
00255         return d < 1e-12;
00256     }
00257 };
00258 
00259 class AWMetric2D : public AWMetric
00260 {
00261   public:
00262     MESQUITE_EXPORT virtual ~AWMetric2D();
00263 
00264     /**\brief Evaluate \f$\mu(A,W)\f$
00265      *
00266      * This method always returns an error for 2D-only metrics
00267      */
00268     MESQUITE_EXPORT virtual bool evaluate( const MsqMatrix< 3, 3 >& A,
00269                                            const MsqMatrix< 3, 3 >& W,
00270                                            double& result,
00271                                            MsqError& err );
00272 };
00273 
00274 class AWMetric3D : public AWMetric
00275 {
00276   public:
00277     MESQUITE_EXPORT virtual ~AWMetric3D();
00278 
00279     /**\brief Evaluate \f$\mu(A,W)\f$
00280      *
00281      * This method always returns an error for 3D-only metrics
00282      */
00283     MESQUITE_EXPORT virtual bool evaluate( const MsqMatrix< 2, 2 >& A,
00284                                            const MsqMatrix< 2, 2 >& W,
00285                                            double& result,
00286                                            MsqError& err );
00287 };
00288 
00289 }  // namespace MBMesquite
00290 
00291 #endif
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