MOAB: Mesh Oriented datABase  (version 5.4.0)
TShapeSize2DNB1.cpp
Go to the documentation of this file.
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 TShapeSize2DNB1.cpp
00028  *  \brief
00029  *  \author Jason Kraftcheck
00030  */
00031 
00032 #include "Mesquite.hpp"
00033 #include "TShapeSize2DNB1.hpp"
00034 #include "MsqMatrix.hpp"
00035 #include "TMPDerivs.hpp"
00036 
00037 #include <iostream>
00038 
00039 namespace MBMesquite
00040 {
00041 
00042 std::string TShapeSize2DNB1::get_name() const
00043 {
00044     return "TShapeSize2DNB1";
00045 }
00046 
00047 TShapeSize2DNB1::~TShapeSize2DNB1() {}
00048 
00049 /** \f$ \mu(T) = |T|^2 - 2 \psi(T) + 2 \f$
00050  *  \f$ \psi(T) = \sqrt{|T|^2 + 2 \tau} \f$
00051  *  \f$ \tau = det(T) \f$
00052  */
00053 bool TShapeSize2DNB1::evaluate( const MsqMatrix< 2, 2 >& T, double& result, MsqError& /*err*/ )
00054 {
00055     double frob_sqr = sqr_Frobenius( T );
00056     double psi      = sqrt( frob_sqr + 2.0 * det( T ) );
00057 
00058     MsqMatrix< 2, 2 > Tdelta( T );
00059     while( fabs( psi ) < DBL_EPSILON )
00060     {
00061         Tdelta( 0, 0 ) += 1e-12;
00062         Tdelta( 1, 1 ) += 1e-12;
00063         frob_sqr = sqr_Frobenius( Tdelta );
00064         psi      = sqrt( frob_sqr + 2.0 * det( Tdelta ) );
00065     }
00066 
00067     result = frob_sqr - 2.0 * psi + 2.0;
00068     return true;
00069 }
00070 
00071 bool TShapeSize2DNB1::evaluate_with_grad( const MsqMatrix< 2, 2 >& T,
00072                                           double& result,
00073                                           MsqMatrix< 2, 2 >& deriv_wrt_T,
00074                                           MsqError& /*err*/ )
00075 {
00076     double frob_sqr = sqr_Frobenius( T );
00077     double psi      = sqrt( frob_sqr + 2.0 * det( T ) );
00078 
00079     MsqMatrix< 2, 2 > Tdelta( T );
00080     while( fabs( psi ) < DBL_EPSILON )
00081     {
00082         Tdelta( 0, 0 ) += 1e-12;
00083         Tdelta( 1, 1 ) += 1e-12;
00084         frob_sqr = sqr_Frobenius( Tdelta );
00085         psi      = sqrt( frob_sqr + 2.0 * det( Tdelta ) );
00086     }
00087 
00088     result = frob_sqr - 2.0 * psi + 2.0;
00089 
00090     deriv_wrt_T = T;
00091     if( psi > 1e-50 )
00092     {
00093         deriv_wrt_T *= ( 1.0 - 1.0 / psi );
00094         deriv_wrt_T -= 1.0 / psi * transpose_adj( T );
00095         deriv_wrt_T *= 2;
00096     }
00097     else
00098     {
00099         std::cout << "Warning: Division by zero avoided in TShapeSize2DNB2::evaluate_with_grad()" << std::endl;
00100     }
00101 
00102     return true;
00103 }
00104 
00105 bool TShapeSize2DNB1::evaluate_with_hess( const MsqMatrix< 2, 2 >& T,
00106                                           double& result,
00107                                           MsqMatrix< 2, 2 >& deriv_wrt_T,
00108                                           MsqMatrix< 2, 2 > second[3],
00109                                           MsqError& /*err*/ )
00110 {
00111     double frob_sqr = sqr_Frobenius( T );
00112     double psi      = sqrt( frob_sqr + 2.0 * det( T ) );
00113 
00114     MsqMatrix< 2, 2 > Tdelta( T );
00115     while( fabs( psi ) < DBL_EPSILON )
00116     {
00117         Tdelta( 0, 0 ) += 1e-12;
00118         Tdelta( 1, 1 ) += 1e-12;
00119         frob_sqr = sqr_Frobenius( Tdelta );
00120         psi      = sqrt( frob_sqr + 2.0 * det( Tdelta ) );
00121     }
00122 
00123     result = frob_sqr - 2.0 * psi + 2.0;
00124 
00125     deriv_wrt_T = T;
00126     if( psi > 1e-50 )
00127     {
00128         deriv_wrt_T *= ( 1.0 - 1.0 / psi );
00129         deriv_wrt_T -= 1.0 / psi * transpose_adj( T );
00130         deriv_wrt_T *= 2;
00131     }
00132     else
00133     {
00134         std::cout << "Warning: Division by zero avoided in TShapeSize2DNB2::evaluate_with_hess()" << std::endl;
00135     }
00136 
00137     set_scaled_2nd_deriv_wrt_psi( second, -2.0, psi, T );
00138     pluseq_scaled_I( second, 2 );
00139 
00140     return true;
00141 }
00142 
00143 }  // namespace MBMesquite
 All Classes Namespaces Files Functions Variables Typedefs Enumerations Enumerator Friends Defines