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263 | /* *****************************************************************
MESQUITE -- The Mesh Quality Improvement Toolkit
Copyright 2010 Sandia National Laboratories. Developed at the
University of Wisconsin--Madison under SNL contract number
624796. The U.S. Government and the University of Wisconsin
retain certain rights to this software.
This library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
This library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License
(lgpl.txt) along with this library; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
(2010) [email protected]
***************************************************************** */
/** \file TMetric.hpp
* \brief
* \author Jason Kraftcheck
*/
#ifndef MSQ_T_METRIC_HPP
#define MSQ_T_METRIC_HPP
#include "Mesquite.hpp"
#include <string>
namespace MBMesquite
{
class MsqError;
template < unsigned R, unsigned C >
class MsqMatrix;
class TMetric
{
public:
MESQUITE_EXPORT virtual ~TMetric();
MESQUITE_EXPORT virtual std::string get_name() const = 0;
/**\brief Evaluate \f$\mu(T)\f$
*
*\param T 2x2 relative measure matrix (typically A W^-1)
*\param result Output: value of function
*\return false if function cannot be evaluated for given T
* (e.g. division by zero, etc.), true otherwise.
*/
MESQUITE_EXPORT virtual bool evaluate( const MsqMatrix< 2, 2 >& T, double& result, MsqError& err );<--- Virtual function in base class<--- Virtual function in base class<--- Virtual function in base class<--- Virtual function in base class
/**\brief Evaluate \f$\mu(T)\f$
*
*\param T 3x3 relative measure matrix (typically A W^-1)
*\param result Output: value of function
*\return false if function cannot be evaluated for given T
* (e.g. division by zero, etc.), true otherwise.
*/
MESQUITE_EXPORT virtual bool evaluate( const MsqMatrix< 3, 3 >& T, double& result, MsqError& err );<--- Virtual function in base class<--- Virtual function in base class<--- Virtual function in base class<--- Virtual function in base class
/**\brief Gradient of \f$\mu(T)\f$ with respect to components of T
*
*\param T 2x2 relative measure matrix (typically A W^-1)
*\param result Output: value of function
*\param deriv_wrt_T Output: partial deriviatve of \f$\mu\f$ wrt each term of T,
* evaluated at passed T.
* \f[\left[\begin{array}{cc}
* \frac{\partial\mu}{\partial T_{0,0}} &
* \frac{\partial\mu}{\partial T_{0,1}} \\
* \frac{\partial\mu}{\partial T_{1,0}} &
* \frac{\partial\mu}{\partial T_{1,1}} \\
* \end{array}\right]\f]
*\return false if function cannot be evaluated for given T
* (e.g. division by zero, etc.), true otherwise.
*/
MESQUITE_EXPORT virtual bool evaluate_with_grad( const MsqMatrix< 2, 2 >& T,
double& result,
MsqMatrix< 2, 2 >& deriv_wrt_T,
MsqError& err );
/**\brief Gradient of \f$\mu(T)\f$ with respect to components of T
*
*\param T 3x3 relative measure matrix (typically A W^-1)
*\param result Output: value of function
*\param deriv_wrt_T Output: partial deriviatve of \f$\mu\f$ wrt each term of T,
* evaluated at passed T.
* \f[\left[\begin{array}{ccc}
* \frac{\partial\mu}{\partial T_{0,0}} &
* \frac{\partial\mu}{\partial T_{0,1}} &
* \frac{\partial\mu}{\partial T_{0,2}} \\
* \frac{\partial\mu}{\partial T_{1,0}} &
* \frac{\partial\mu}{\partial T_{1,1}} &
* \frac{\partial\mu}{\partial T_{1,2}} \\
* \frac{\partial\mu}{\partial T_{2,0}} &
* \frac{\partial\mu}{\partial T_{2,1}} &
* \frac{\partial\mu}{\partial T_{2,2}}
* \end{array}\right]\f]
*\return false if function cannot be evaluated for given T
* (e.g. division by zero, etc.), true otherwise.
*/
MESQUITE_EXPORT virtual bool evaluate_with_grad( const MsqMatrix< 3, 3 >& T,
double& result,
MsqMatrix< 3, 3 >& deriv_wrt_T,
MsqError& err );
/**\brief Hessian of \f$\mu(T)\f$ with respect to components of T
*
*\param T 3x3 relative measure matrix (typically A W^-1)
*\param result Output: value of function
*\param deriv_wrt_T Output: partial deriviatve of \f$\mu\f$ wrt each term of T,
* evaluated at passed T.
*\param second_wrt_T Output: 9x9 matrix of second partial deriviatve of \f$\mu\f$ wrt
* each term of T, in row-major order. The symmetric
* matrix is decomposed into 3x3 blocks and only the upper diagonal
* blocks, in row-major order, are returned.
* \f[\left[\begin{array}{cc|cc}
* \frac{\partial^{2}\mu}{\partial T_{0,0}^2} &
* \frac{\partial^{2}\mu}{\partial T_{0,0}\partial A_{0,1}} &
* \frac{\partial^{2}\mu}{\partial T_{0,0}\partial A_{1,0}} &
* \frac{\partial^{2}\mu}{\partial T_{0,0}\partial A_{1,1}} \\
* \frac{\partial^{2}\mu}{\partial T_{0,0}\partial A_{0,1}} &
* \frac{\partial^{2}\mu}{\partial T_{0,1}^2} &
* \frac{\partial^{2}\mu}{\partial T_{0,1}\partial A_{1,0}} &
* \frac{\partial^{2}\mu}{\partial T_{0,1}\partial A_{1,1}} \\
* \hline & &
* \frac{\partial^{2}\mu}{\partial T_{1,0}^2} &
* \frac{\partial^{2}\mu}{\partial T_{1,0}\partial A_{1,1}} \\
* & &
* \frac{\partial^{2}\mu}{\partial T_{1,0}\partial A_{1,1}} &
* \frac{\partial^{2}\mu}{\partial T_{1,1}^2} \\
* \end{array}\right]\f]
*
*\return false if function cannot be evaluated for given T
* (e.g. division by zero, etc.), true otherwise.
*/
MESQUITE_EXPORT virtual bool evaluate_with_hess( const MsqMatrix< 2, 2 >& T,
double& result,
MsqMatrix< 2, 2 >& deriv_wrt_T,
MsqMatrix< 2, 2 > second_wrt_T[3],
MsqError& err );
/**\brief Hessian of \f$\mu(T)\f$ with respect to components of T
*
*\param T 3x3 relative measure matrix (typically A W^-1)
*\param result Output: value of function
*\param deriv_wrt_T Output: partial deriviatve of \f$\mu\f$ wrt each term of T,
* evaluated at passed T.
*\param second_wrt_T Output: 9x9 matrix of second partial deriviatve of \f$\mu\f$ wrt
* each term of T, in row-major order. The symmetric
* matrix is decomposed into 3x3 blocks and only the upper diagonal
* blocks, in row-major order, are returned.
* \f[\left[\begin{array}{ccc|ccc|ccc}
* \frac{\partial^{2}\mu}{\partial T_{0,0}^2} &
* \frac{\partial^{2}\mu}{\partial T_{0,0}\partial T_{0,1}} &
* \frac{\partial^{2}\mu}{\partial T_{0,0}\partial T_{0,2}} &
* \frac{\partial^{2}\mu}{\partial T_{0,0}\partial T_{1,0}} &
* \frac{\partial^{2}\mu}{\partial T_{0,0}\partial T_{1,1}} &
* \frac{\partial^{2}\mu}{\partial T_{0,0}\partial T_{1,2}} &
* \frac{\partial^{2}\mu}{\partial T_{0,0}\partial T_{2,0}} &
* \frac{\partial^{2}\mu}{\partial T_{0,0}\partial T_{2,1}} &
* \frac{\partial^{2}\mu}{\partial T_{0,0}\partial T_{2,2}} \\
* \frac{\partial^{2}\mu}{\partial T_{0,0}\partial T_{0,1}} &
* \frac{\partial^{2}\mu}{\partial T_{0,1}^2} &
* \frac{\partial^{2}\mu}{\partial T_{0,1}\partial T_{0,2}} &
* \frac{\partial^{2}\mu}{\partial T_{0,1}\partial T_{1,0}} &
* \frac{\partial^{2}\mu}{\partial T_{0,1}\partial T_{1,1}} &
* \frac{\partial^{2}\mu}{\partial T_{0,1}\partial T_{1,2}} &
* \frac{\partial^{2}\mu}{\partial T_{0,1}\partial T_{2,0}} &
* \frac{\partial^{2}\mu}{\partial T_{0,1}\partial T_{2,1}} &
* \frac{\partial^{2}\mu}{\partial T_{0,1}\partial T_{2,2}} \\
* \frac{\partial^{2}\mu}{\partial T_{0,0}\partial T_{0,2}} &
* \frac{\partial^{2}\mu}{\partial T_{0,1}\partial T_{0,2}} &
* \frac{\partial^{2}\mu}{\partial T_{0,2}^2} &
* \frac{\partial^{2}\mu}{\partial T_{0,2}\partial T_{1,0}} &
* \frac{\partial^{2}\mu}{\partial T_{0,2}\partial T_{1,1}} &
* \frac{\partial^{2}\mu}{\partial T_{0,2}\partial T_{1,2}} &
* \frac{\partial^{2}\mu}{\partial T_{0,2}\partial T_{2,0}} &
* \frac{\partial^{2}\mu}{\partial T_{0,2}\partial T_{2,1}} &
* \frac{\partial^{2}\mu}{\partial T_{0,2}\partial T_{2,2}} \\
* \hline & & &
* \frac{\partial^{2}\mu}{\partial T_{1,0}^2} &
* \frac{\partial^{2}\mu}{\partial T_{1,0}\partial T_{1,1}} &
* \frac{\partial^{2}\mu}{\partial T_{1,0}\partial T_{1,2}} &
* \frac{\partial^{2}\mu}{\partial T_{1,0}\partial T_{2,0}} &
* \frac{\partial^{2}\mu}{\partial T_{1,0}\partial T_{2,1}} &
* \frac{\partial^{2}\mu}{\partial T_{1,0}\partial T_{2,2}} \\
* & & &
* \frac{\partial^{2}\mu}{\partial T_{1,0}\partial T_{1,1}} &
* \frac{\partial^{2}\mu}{\partial T_{1,1}^2} &
* \frac{\partial^{2}\mu}{\partial T_{1,1}\partial T_{1,2}} &
* \frac{\partial^{2}\mu}{\partial T_{1,1}\partial T_{2,0}} &
* \frac{\partial^{2}\mu}{\partial T_{1,1}\partial T_{2,1}} &
* \frac{\partial^{2}\mu}{\partial T_{1,1}\partial T_{2,2}} \\
* & & &
* \frac{\partial^{2}\mu}{\partial T_{1,0}\partial T_{1,2}} &
* \frac{\partial^{2}\mu}{\partial T_{1,1}\partial T_{1,2}} &
* \frac{\partial^{2}\mu}{\partial T_{1,2}^2} &
* \frac{\partial^{2}\mu}{\partial T_{1,2}\partial T_{2,0}} &
* \frac{\partial^{2}\mu}{\partial T_{1,2}\partial T_{2,1}} &
* \frac{\partial^{2}\mu}{\partial T_{1,2}\partial T_{2,2}} \\
* \hline & & & & & &
* \frac{\partial^{2}\mu}{\partial T_{2,0}^2} &
* \frac{\partial^{2}\mu}{\partial T_{2,0}\partial T_{2,1}} &
* \frac{\partial^{2}\mu}{\partial T_{2,0}\partial T_{2,2}} \\
* & & & & & &
* \frac{\partial^{2}\mu}{\partial T_{2,0}\partial T_{2,1}} &
* \frac{\partial^{2}\mu}{\partial T_{2,1}^2} &
* \frac{\partial^{2}\mu}{\partial T_{2,1}\partial T_{2,2}} \\
* & & & & & &
* \frac{\partial^{2}\mu}{\partial T_{2,0}\partial T_{2,2}} &
* \frac{\partial^{2}\mu}{\partial T_{2,1}\partial T_{2,2}} &
* \frac{\partial^{2}\mu}{\partial T_{2,2}^2} \\
* \end{array}\right]\f]
*\return false if function cannot be evaluated for given T
* (e.g. division by zero, etc.), true otherwise.
*/
MESQUITE_EXPORT virtual bool evaluate_with_hess( const MsqMatrix< 3, 3 >& T,
double& result,
MsqMatrix< 3, 3 >& deriv_wrt_T,
MsqMatrix< 3, 3 > second_wrt_T[6],
MsqError& err );
static inline bool invalid_determinant( double d )
{
return d < 1e-12;
}
};
class TMetric2D : public TMetric
{
public:
MESQUITE_EXPORT virtual ~TMetric2D();
/**\brief Evaluate \f$\mu(T)\f$
*
* This method always returns an error for 2D-only metrics
*/
MESQUITE_EXPORT virtual bool evaluate( const MsqMatrix< 3, 3 >& T, double& result, MsqError& err );<--- Function in derived class<--- Function in derived class<--- Function in derived class<--- Function in derived class
};
class TMetric3D : public TMetric
{
public:
MESQUITE_EXPORT virtual ~TMetric3D();
/**\brief Evaluate \f$\mu(T)\f$
*
* This method always returns an error for 3D-only metrics
*/
MESQUITE_EXPORT virtual bool evaluate( const MsqMatrix< 2, 2 >& T, double& result, MsqError& err );<--- Function in derived class<--- Function in derived class<--- Function in derived class<--- Function in derived class
};
} // namespace MBMesquite
#endif
|