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MOAB: Mesh Oriented datABase
(version 5.2.1)
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MOAB: Mesh Oriented datABase
(version 5.2.1)
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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, const MsqMatrix< 2, 2 >& W, double& result, 00065 MsqError& err ); 00066 00067 /**\brief Evaluate \f$\mu(A,W)\f$ 00068 * 00069 *\param A 3x3 active matrix 00070 *\param W 3x3 target matrix 00071 *\param result Output: value of function 00072 *\return false if function cannot be evaluated for given A and W 00073 * (e.g. division by zero, etc.), true otherwise. 00074 */ 00075 MESQUITE_EXPORT virtual bool evaluate( const MsqMatrix< 3, 3 >& A, const MsqMatrix< 3, 3 >& W, double& result, 00076 MsqError& err ); 00077 00078 /**\brief Gradient of \f$\mu(A,W)\f$ with respect to components of A 00079 * 00080 *\param A 2x2 active matrix 00081 *\param W 2x2 target matrix 00082 *\param result Output: value of function 00083 *\param deriv_wrt_A Output: partial deriviatve of \f$\mu\f$ wrt each term of A, 00084 * evaluated at passed A. 00085 * \f[\left[\begin{array}{cc} 00086 * \frac{\partial\mu}{\partial A_{0,0}} & 00087 * \frac{\partial\mu}{\partial A_{0,1}} \\ 00088 * \frac{\partial\mu}{\partial A_{1,0}} & 00089 * \frac{\partial\mu}{\partial A_{1,1}} \\ 00090 * \end{array}\right]\f] 00091 *\return false if function cannot be evaluated for given A and W 00092 * (e.g. division by zero, etc.), true otherwise. 00093 */ 00094 MESQUITE_EXPORT virtual bool evaluate_with_grad( const MsqMatrix< 2, 2 >& A, const MsqMatrix< 2, 2 >& W, 00095 double& result, MsqMatrix< 2, 2 >& deriv_wrt_A, MsqError& err ); 00096 00097 /**\brief Gradient of \f$\mu(A,W)\f$ with respect to components of A 00098 * 00099 *\param A 3x3 active matrix 00100 *\param W 3x3 target matrix 00101 *\param result Output: value of function 00102 *\param deriv_wrt_A Output: partial deriviatve of \f$\mu\f$ wrt each term of A, 00103 * evaluated at passed A. 00104 * \f[\left[\begin{array}{ccc} 00105 * \frac{\partial\mu}{\partial A_{0,0}} & 00106 * \frac{\partial\mu}{\partial A_{0,1}} & 00107 * \frac{\partial\mu}{\partial A_{0,2}} \\ 00108 * \frac{\partial\mu}{\partial A_{1,0}} & 00109 * \frac{\partial\mu}{\partial A_{1,1}} & 00110 * \frac{\partial\mu}{\partial A_{1,2}} \\ 00111 * \frac{\partial\mu}{\partial A_{2,0}} & 00112 * \frac{\partial\mu}{\partial A_{2,1}} & 00113 * \frac{\partial\mu}{\partial A_{2,2}} 00114 * \end{array}\right]\f] 00115 *\return false if function cannot be evaluated for given A and W 00116 * (e.g. division by zero, etc.), true otherwise. 00117 */ 00118 MESQUITE_EXPORT virtual bool evaluate_with_grad( const MsqMatrix< 3, 3 >& A, const MsqMatrix< 3, 3 >& W, 00119 double& result, MsqMatrix< 3, 3 >& deriv_wrt_A, MsqError& err ); 00120 00121 /**\brief Hessian of \f$\mu(A,W)\f$ with respect to components of A 00122 * 00123 *\param A 2x2 active matrix 00124 *\param W 2x2 target matrix 00125 *\param result Output: value of function 00126 *\param deriv_wrt_A Output: partial deriviatve of \f$\mu\f$ wrt each term of A, 00127 * evaluated at passed A. 00128 *\param second_wrt_A Output: 4x4 matrix of second partial deriviatve of \f$\mu\f$ wrt 00129 * each term of A, in row-major order. The symmetric 00130 * matrix is decomposed into 2x2 blocks and only the upper diagonal 00131 * blocks, in row-major order, are returned. 00132 * \f[\left[\begin{array}{cc|cc} 00133 * \frac{\partial^{2}\mu}{\partial A_{0,0}^2} & 00134 * \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{0,1}} & 00135 * \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{1,0}} & 00136 * \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{1,1}} \\ 00137 * \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{0,1}} & 00138 * \frac{\partial^{2}\mu}{\partial A_{0,1}^2} & 00139 * \frac{\partial^{2}\mu}{\partial A_{0,1}\partial A_{1,0}} & 00140 * \frac{\partial^{2}\mu}{\partial A_{0,1}\partial A_{1,1}} \\ 00141 * \hline & & 00142 * \frac{\partial^{2}\mu}{\partial A_{1,0}^2} & 00143 * \frac{\partial^{2}\mu}{\partial A_{1,0}\partial A_{1,1}} \\ 00144 * & & 00145 * \frac{\partial^{2}\mu}{\partial A_{1,0}\partial A_{1,1}} & 00146 * \frac{\partial^{2}\mu}{\partial A_{1,1}^2} \\ 00147 * \end{array}\right]\f] 00148 * 00149 *\return false if function cannot be evaluated for given A and W 00150 * (e.g. division by zero, etc.), true otherwise. 00151 */ 00152 MESQUITE_EXPORT virtual bool evaluate_with_hess( const MsqMatrix< 2, 2 >& A, const MsqMatrix< 2, 2 >& W, 00153 double& result, MsqMatrix< 2, 2 >& deriv_wrt_A, 00154 MsqMatrix< 2, 2 > second_wrt_A[3], MsqError& err ); 00155 00156 /**\brief Hessian of \f$\mu(A,W)\f$ with respect to components of A 00157 * 00158 *\param A 3x3 active matrix 00159 *\param W 3x3 target matrix 00160 *\param result Output: value of function 00161 *\param deriv_wrt_A Output: partial deriviatve of \f$\mu\f$ wrt each term of A, 00162 * evaluated at passed A. 00163 *\param second_wrt_A Output: 9x9 matrix of second partial deriviatve of \f$\mu\f$ wrt 00164 * each term of A, in row-major order. The symmetric 00165 * matrix is decomposed into 3x3 blocks and only the upper diagonal 00166 * blocks, in row-major order, are returned. 00167 * \f[\left[\begin{array}{ccc|ccc|ccc} 00168 * \frac{\partial^{2}\mu}{\partial A_{0,0}^2} & 00169 * \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{0,1}} & 00170 * \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{0,2}} & 00171 * \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{1,0}} & 00172 * \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{1,1}} & 00173 * \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{1,2}} & 00174 * \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{2,0}} & 00175 * \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{2,1}} & 00176 * \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{2,2}} \\ 00177 * \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{0,1}} & 00178 * \frac{\partial^{2}\mu}{\partial A_{0,1}^2} & 00179 * \frac{\partial^{2}\mu}{\partial A_{0,1}\partial A_{0,2}} & 00180 * \frac{\partial^{2}\mu}{\partial A_{0,1}\partial A_{1,0}} & 00181 * \frac{\partial^{2}\mu}{\partial A_{0,1}\partial A_{1,1}} & 00182 * \frac{\partial^{2}\mu}{\partial A_{0,1}\partial A_{1,2}} & 00183 * \frac{\partial^{2}\mu}{\partial A_{0,1}\partial A_{2,0}} & 00184 * \frac{\partial^{2}\mu}{\partial A_{0,1}\partial A_{2,1}} & 00185 * \frac{\partial^{2}\mu}{\partial A_{0,1}\partial A_{2,2}} \\ 00186 * \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{0,2}} & 00187 * \frac{\partial^{2}\mu}{\partial A_{0,1}\partial A_{0,2}} & 00188 * \frac{\partial^{2}\mu}{\partial A_{0,2}^2} & 00189 * \frac{\partial^{2}\mu}{\partial A_{0,2}\partial A_{1,0}} & 00190 * \frac{\partial^{2}\mu}{\partial A_{0,2}\partial A_{1,1}} & 00191 * \frac{\partial^{2}\mu}{\partial A_{0,2}\partial A_{1,2}} & 00192 * \frac{\partial^{2}\mu}{\partial A_{0,2}\partial A_{2,0}} & 00193 * \frac{\partial^{2}\mu}{\partial A_{0,2}\partial A_{2,1}} & 00194 * \frac{\partial^{2}\mu}{\partial A_{0,2}\partial A_{2,2}} \\ 00195 * \hline & & & 00196 * \frac{\partial^{2}\mu}{\partial A_{1,0}^2} & 00197 * \frac{\partial^{2}\mu}{\partial A_{1,0}\partial A_{1,1}} & 00198 * \frac{\partial^{2}\mu}{\partial A_{1,0}\partial A_{1,2}} & 00199 * \frac{\partial^{2}\mu}{\partial A_{1,0}\partial A_{2,0}} & 00200 * \frac{\partial^{2}\mu}{\partial A_{1,0}\partial A_{2,1}} & 00201 * \frac{\partial^{2}\mu}{\partial A_{1,0}\partial A_{2,2}} \\ 00202 * & & & 00203 * \frac{\partial^{2}\mu}{\partial A_{1,0}\partial A_{1,1}} & 00204 * \frac{\partial^{2}\mu}{\partial A_{1,1}^2} & 00205 * \frac{\partial^{2}\mu}{\partial A_{1,1}\partial A_{1,2}} & 00206 * \frac{\partial^{2}\mu}{\partial A_{1,1}\partial A_{2,0}} & 00207 * \frac{\partial^{2}\mu}{\partial A_{1,1}\partial A_{2,1}} & 00208 * \frac{\partial^{2}\mu}{\partial A_{1,1}\partial A_{2,2}} \\ 00209 * & & & 00210 * \frac{\partial^{2}\mu}{\partial A_{1,0}\partial A_{1,2}} & 00211 * \frac{\partial^{2}\mu}{\partial A_{1,1}\partial A_{1,2}} & 00212 * \frac{\partial^{2}\mu}{\partial A_{1,2}^2} & 00213 * \frac{\partial^{2}\mu}{\partial A_{1,2}\partial A_{2,0}} & 00214 * \frac{\partial^{2}\mu}{\partial A_{1,2}\partial A_{2,1}} & 00215 * \frac{\partial^{2}\mu}{\partial A_{1,2}\partial A_{2,2}} \\ 00216 * \hline & & & & & & 00217 * \frac{\partial^{2}\mu}{\partial A_{2,0}^2} & 00218 * \frac{\partial^{2}\mu}{\partial A_{2,0}\partial A_{2,1}} & 00219 * \frac{\partial^{2}\mu}{\partial A_{2,0}\partial A_{2,2}} \\ 00220 * & & & & & & 00221 * \frac{\partial^{2}\mu}{\partial A_{2,0}\partial A_{2,1}} & 00222 * \frac{\partial^{2}\mu}{\partial A_{2,1}^2} & 00223 * \frac{\partial^{2}\mu}{\partial A_{2,1}\partial A_{2,2}} \\ 00224 * & & & & & & 00225 * \frac{\partial^{2}\mu}{\partial A_{2,0}\partial A_{2,2}} & 00226 * \frac{\partial^{2}\mu}{\partial A_{2,1}\partial A_{2,2}} & 00227 * \frac{\partial^{2}\mu}{\partial A_{2,2}^2} \\ 00228 * \end{array}\right]\f] 00229 * 00230 *\return false if function cannot be evaluated for given A and W 00231 * (e.g. division by zero, etc.), true otherwise. 00232 */ 00233 MESQUITE_EXPORT virtual bool evaluate_with_hess( const MsqMatrix< 3, 3 >& A, const MsqMatrix< 3, 3 >& W, 00234 double& result, MsqMatrix< 3, 3 >& deriv_wrt_A, 00235 MsqMatrix< 3, 3 > second_wrt_A[6], MsqError& err ); 00236 00237 static inline bool invalid_determinant( double d ) 00238 { 00239 return d < 1e-12; 00240 } 00241 }; 00242 00243 class AWMetric2D : public AWMetric 00244 { 00245 public: 00246 MESQUITE_EXPORT virtual ~AWMetric2D(); 00247 00248 /**\brief Evaluate \f$\mu(A,W)\f$ 00249 * 00250 * This method always returns an error for 2D-only metrics 00251 */ 00252 MESQUITE_EXPORT virtual bool evaluate( const MsqMatrix< 3, 3 >& A, const MsqMatrix< 3, 3 >& W, double& result, 00253 MsqError& err ); 00254 }; 00255 00256 class AWMetric3D : public AWMetric 00257 { 00258 public: 00259 MESQUITE_EXPORT virtual ~AWMetric3D(); 00260 00261 /**\brief Evaluate \f$\mu(A,W)\f$ 00262 * 00263 * This method always returns an error for 3D-only metrics 00264 */ 00265 MESQUITE_EXPORT virtual bool evaluate( const MsqMatrix< 2, 2 >& A, const MsqMatrix< 2, 2 >& W, double& result, 00266 MsqError& err ); 00267 }; 00268 00269 } // namespace MBMesquite 00270 00271 #endif
1.7.6.1 
