MOAB: Mesh Oriented datABase
(version 5.3.1)
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00001 /* ***************************************************************** 00002 MESQUITE -- The Mesh Quality Improvement Toolkit 00003 00004 Copyright 2008 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 (2008) kraftche@cae.wisc.edu 00024 00025 ***************************************************************** */ 00026 00027 /** \file AWMetric.hpp 00028 * \brief 00029 * \author Jason Kraftcheck 00030 */ 00031 00032 #include "AWMetric.hpp" 00033 #include "TMetricBarrier.hpp" 00034 #include "MsqMatrix.hpp" 00035 #include "MsqError.hpp" 00036 #include <limits> 00037 00038 namespace MBMesquite 00039 { 00040 00041 template < unsigned Dim > 00042 static inline double do_finite_difference( int r, int c, AWMetric* metric, MsqMatrix< Dim, Dim > A, 00043 const MsqMatrix< Dim, Dim >& W, double value, MsqError& err ) 00044 { 00045 const double INITAL_STEP = std::max( 1e-6, fabs( 1e-14 * value ) ); 00046 const double init = A( r, c ); 00047 bool valid; 00048 double diff_value; 00049 for( double step = INITAL_STEP; step > std::numeric_limits< double >::epsilon(); step *= 0.1 ) 00050 { 00051 A( r, c ) = init + step; 00052 valid = metric->evaluate( A, W, diff_value, err ); 00053 MSQ_ERRZERO( err ); 00054 if( valid ) return ( diff_value - value ) / step; 00055 } 00056 00057 // If we couldn't find a valid step, try stepping in the other 00058 // direciton 00059 for( double step = INITAL_STEP; step > std::numeric_limits< double >::epsilon(); step *= 0.1 ) 00060 { 00061 A( r, c ) = init - step; 00062 valid = metric->evaluate( A, W, diff_value, err ); 00063 MSQ_ERRZERO( err ); 00064 if( valid ) return ( value - diff_value ) / step; 00065 } 00066 00067 // If that didn't work either, then give up. 00068 MSQ_SETERR( err ) 00069 ( "No valid step size for finite difference of 2D target metric.", MsqError::INTERNAL_ERROR ); 00070 return 0.0; 00071 } 00072 00073 template < unsigned Dim > 00074 static inline bool do_numerical_gradient( AWMetric* mu, MsqMatrix< Dim, Dim > A, const MsqMatrix< Dim, Dim >& W, 00075 double& result, MsqMatrix< Dim, Dim >& wrt_A, MsqError& err ) 00076 { 00077 bool valid; 00078 valid = mu->evaluate( A, W, result, err ); 00079 MSQ_ERRZERO( err ); 00080 if( MSQ_CHKERR( err ) || !valid ) return valid; 00081 00082 switch( Dim ) 00083 { 00084 case 3: 00085 wrt_A( 0, 2 ) = do_finite_difference( 0, 2, mu, A, W, result, err ); 00086 MSQ_ERRZERO( err ); 00087 wrt_A( 1, 2 ) = do_finite_difference( 1, 2, mu, A, W, result, err ); 00088 MSQ_ERRZERO( err ); 00089 wrt_A( 2, 0 ) = do_finite_difference( 2, 0, mu, A, W, result, err ); 00090 MSQ_ERRZERO( err ); 00091 wrt_A( 2, 1 ) = do_finite_difference( 2, 1, mu, A, W, result, err ); 00092 MSQ_ERRZERO( err ); 00093 wrt_A( 2, 2 ) = do_finite_difference( 2, 2, mu, A, W, result, err ); 00094 MSQ_ERRZERO( err ); 00095 case 2: 00096 wrt_A( 0, 1 ) = do_finite_difference( 0, 1, mu, A, W, result, err ); 00097 MSQ_ERRZERO( err ); 00098 wrt_A( 1, 0 ) = do_finite_difference( 1, 0, mu, A, W, result, err ); 00099 MSQ_ERRZERO( err ); 00100 wrt_A( 1, 1 ) = do_finite_difference( 1, 1, mu, A, W, result, err ); 00101 MSQ_ERRZERO( err ); 00102 case 1: 00103 wrt_A( 0, 0 ) = do_finite_difference( 0, 0, mu, A, W, result, err ); 00104 MSQ_ERRZERO( err ); 00105 break; 00106 default: 00107 assert( false ); 00108 } 00109 return true; 00110 } 00111 00112 template < unsigned Dim > 00113 static inline bool do_numerical_hessian( AWMetric* metric, MsqMatrix< Dim, Dim > A, const MsqMatrix< Dim, Dim >& W, 00114 double& value, MsqMatrix< Dim, Dim >& grad, MsqMatrix< Dim, Dim >* Hess, 00115 MsqError& err ) 00116 { 00117 // zero hessian data 00118 const int num_block = Dim * ( Dim + 1 ) / 2; 00119 for( int i = 0; i < num_block; ++i ) 00120 Hess[i].zero(); 00121 00122 // evaluate gradient for input values 00123 bool valid; 00124 valid = metric->evaluate_with_grad( A, W, value, grad, err ); 00125 if( MSQ_CHKERR( err ) || !valid ) return false; 00126 00127 // do finite difference for each term of A 00128 const double INITAL_STEP = std::max( 1e-6, fabs( 1e-14 * value ) ); 00129 double value2; 00130 MsqMatrix< Dim, Dim > grad2; 00131 for( unsigned r = 0; r < Dim; ++r ) 00132 { // for each row of A 00133 for( unsigned c = 0; c < Dim; ++c ) 00134 { // for each column of A 00135 const double in_val = A( r, c ); 00136 double step; 00137 for( step = INITAL_STEP; step > std::numeric_limits< double >::epsilon(); step *= 0.1 ) 00138 { 00139 A( r, c ) = in_val + step; 00140 valid = metric->evaluate_with_grad( A, W, value2, grad2, err ); 00141 MSQ_ERRZERO( err ); 00142 if( valid ) break; 00143 } 00144 00145 // if no valid step size, try step in other direction 00146 if( !valid ) 00147 { 00148 for( step = -INITAL_STEP; step < -std::numeric_limits< double >::epsilon(); step *= 0.1 ) 00149 { 00150 A( r, c ) = in_val + step; 00151 valid = metric->evaluate_with_grad( A, W, value2, grad2, err ); 00152 MSQ_ERRZERO( err ); 00153 if( valid ) break; 00154 } 00155 00156 // if still no valid step size, give up. 00157 if( !valid ) 00158 { 00159 MSQ_SETERR( err ) 00160 ( "No valid step size for finite difference of 2D target metric.", MsqError::INTERNAL_ERROR ); 00161 return false; 00162 } 00163 } 00164 00165 // restore A. 00166 A( r, c ) = in_val; 00167 00168 // add values into result matrix 00169 // values of grad2, in row-major order, are a single 9-value row of the Hessian 00170 grad2 -= grad; 00171 grad2 /= step; 00172 for( unsigned b = 0; b < r; ++b ) 00173 { 00174 const int idx = Dim * b - b * ( b + 1 ) / 2 + r; 00175 Hess[idx].add_column( c, transpose( grad2.row( b ) ) ); 00176 } 00177 for( unsigned b = r; b < Dim; ++b ) 00178 { 00179 const int idx = Dim * r - r * ( r + 1 ) / 2 + b; 00180 Hess[idx].add_row( c, grad2.row( b ) ); 00181 } 00182 } // for (c) 00183 } // for (r) 00184 00185 // Values in non-diagonal blocks were added twice. 00186 for( unsigned r = 0, h = 1; r < Dim - 1; ++r, ++h ) 00187 for( unsigned c = r + 1; c < Dim; ++c, ++h ) 00188 Hess[h] *= 0.5; 00189 00190 return true; 00191 } 00192 00193 AWMetric::~AWMetric() {} 00194 00195 bool AWMetric::evaluate( const MsqMatrix< 2, 2 >& /*A*/, const MsqMatrix< 2, 2 >& /*W*/, double& /*result*/, 00196 MsqError& /*err*/ ) 00197 { 00198 return false; 00199 } 00200 00201 bool AWMetric::evaluate( const MsqMatrix< 3, 3 >& /*A*/, const MsqMatrix< 3, 3 >& /*W*/, double& /*result*/, 00202 MsqError& /*err*/ ) 00203 { 00204 return false; 00205 } 00206 00207 bool AWMetric::evaluate_with_grad( const MsqMatrix< 2, 2 >& A, const MsqMatrix< 2, 2 >& W, double& result, 00208 MsqMatrix< 2, 2 >& wrt_A, MsqError& err ) 00209 { 00210 return do_numerical_gradient( this, A, W, result, wrt_A, err ); 00211 } 00212 00213 bool AWMetric::evaluate_with_grad( const MsqMatrix< 3, 3 >& A, const MsqMatrix< 3, 3 >& W, double& result, 00214 MsqMatrix< 3, 3 >& wrt_A, MsqError& err ) 00215 { 00216 return do_numerical_gradient( this, A, W, result, wrt_A, err ); 00217 } 00218 00219 bool AWMetric::evaluate_with_hess( const MsqMatrix< 2, 2 >& A, const MsqMatrix< 2, 2 >& W, double& result, 00220 MsqMatrix< 2, 2 >& deriv_wrt_A, MsqMatrix< 2, 2 > hess_wrt_A[3], MsqError& err ) 00221 { 00222 return do_numerical_hessian( this, A, W, result, deriv_wrt_A, hess_wrt_A, err ); 00223 } 00224 00225 bool AWMetric::evaluate_with_hess( const MsqMatrix< 3, 3 >& A, const MsqMatrix< 3, 3 >& W, double& result, 00226 MsqMatrix< 3, 3 >& deriv_wrt_A, MsqMatrix< 3, 3 > hess_wrt_A[6], MsqError& err ) 00227 { 00228 return do_numerical_hessian( this, A, W, result, deriv_wrt_A, hess_wrt_A, err ); 00229 } 00230 00231 AWMetric2D::~AWMetric2D() {} 00232 AWMetric3D::~AWMetric3D() {} 00233 00234 bool AWMetric2D::evaluate( const MsqMatrix< 3, 3 >&, const MsqMatrix< 3, 3 >&, double&, MsqError& err ) 00235 { 00236 MSQ_SETERR( err ) 00237 ( "2D target metric cannot be evaluated for volume elements", MsqError::UNSUPPORTED_ELEMENT ); 00238 return false; 00239 } 00240 00241 bool AWMetric3D::evaluate( const MsqMatrix< 2, 2 >&, const MsqMatrix< 2, 2 >&, double&, MsqError& err ) 00242 { 00243 MSQ_SETERR( err ) 00244 ( "2D target metric cannot be evaluated for volume elements", MsqError::UNSUPPORTED_ELEMENT ); 00245 return false; 00246 } 00247 00248 } // namespace MBMesquite