MOAB: Mesh Oriented datABase  (version 5.2.1)
TUntangleBeta.cpp
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00001 /* *****************************************************************
00002     MESQUITE -- The Mesh Quality Improvement Toolkit
00003 
00004     Copyright 2009 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     (2009) kraftche@cae.wisc.edu
00024 
00025   ***************************************************************** */
00026 
00027 /** \file TUntangleBeta.cpp
00028  *  \brief
00029  *  \author Jason Kraftcheck
00030  */
00031 
00032 #include "Mesquite.hpp"
00033 #include "TUntangleBeta.hpp"
00034 #include "TMPDerivs.hpp"
00035 #include "TMPCommon.hpp"
00036 
00037 namespace MBMesquite
00038 {
00039 
00040 TUntangleBeta::~TUntangleBeta() {}
00041 
00042 std::string TUntangleBeta::get_name() const
00043 {
00044     return "untangle beta";
00045 }
00046 
00047 template < unsigned DIM >
00048 inline bool TUntangleBeta::eval( const MsqMatrix< DIM, DIM >& T, double& result )
00049 {
00050     double tau = det( T );
00051     double d   = tau - mGamma;
00052     double f   = fabs( d ) - d;
00053     result     = 0.125 * f * f * f;
00054     return true;
00055 }
00056 
00057 template < unsigned DIM >
00058 inline bool TUntangleBeta::grad( const MsqMatrix< DIM, DIM >& T, double& result, MsqMatrix< DIM, DIM >& deriv_wrt_T )
00059 {
00060     double tau = det( T );
00061     if( tau < mGamma )
00062     {
00063         double d    = mGamma - tau;
00064         result      = d * d * d;
00065         deriv_wrt_T = -3 * d * d * transpose_adj( T );
00066     }
00067     else
00068     {
00069         result      = 0.0;
00070         deriv_wrt_T = MsqMatrix< DIM, DIM >( 0.0 );
00071     }
00072     return true;
00073 }
00074 
00075 template < unsigned DIM >
00076 inline bool TUntangleBeta::hess( const MsqMatrix< DIM, DIM >& T, double& result, MsqMatrix< DIM, DIM >& deriv_wrt_T,
00077                                  MsqMatrix< DIM, DIM >* second_wrt_T )
00078 {
00079     double tau = det( T );
00080     if( tau < mGamma )
00081     {
00082         const MsqMatrix< DIM, DIM > adjt = transpose_adj( T );
00083         double d                         = mGamma - tau;
00084         result                           = d * d * d;
00085         deriv_wrt_T                      = -3 * d * d * adjt;
00086         set_scaled_outer_product( second_wrt_T, 6 * d, adjt );
00087         pluseq_scaled_2nd_deriv_of_det( second_wrt_T, -3 * d * d, T );
00088     }
00089     else
00090     {
00091         result      = 0.0;
00092         deriv_wrt_T = MsqMatrix< DIM, DIM >( 0.0 );
00093         set_scaled_I( second_wrt_T, 0.0 );  // zero everything
00094     }
00095     return true;
00096 }
00097 
00098 TMP_T_TEMPL_IMPL_COMMON( TUntangleBeta )
00099 
00100 }  // namespace MBMesquite
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