/usr/include/trilinos/TargetMetric3D.hpp is in libtrilinos-dev 10.4.0.dfsg-1ubuntu2.
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MESQUITE -- The Mesh Quality Improvement Toolkit
Copyright 2006 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
(2006) kraftche@cae.wisc.edu
***************************************************************** */
/** \file TargetMetric3D.hpp
* \brief
* \author Jason Kraftcheck
*/
#ifndef MSQ_TARGET_METRIC_3D_HPP
#define MSQ_TARGET_METRIC_3D_HPP
#include "Mesquite.hpp"
#include <string>
namespace MESQUITE_NS {
class MsqError;
template <unsigned R, unsigned C> class MsqMatrix;
/**\brief A metric for comparing a 3x3 matrix A with a 3x3 target matrix W
*
* Implement a scalar function \f$\mu(A,W)\f$ where A and W are 3x3 matrices.
*/
class TargetMetric3D {
public:
// used by code templatized to work with either this class or TargetMetric2D
enum { MATRIX_DIM = 3 };
MESQUITE_EXPORT virtual
~TargetMetric3D();
MESQUITE_EXPORT virtual
std::string get_name() const = 0;
/**\brief Evaluate \f$\mu(A,W)\f$
*
*\param A 3x3 active matrix
*\param W 3x3 target matrix
*\param result Output: value of function
*\return false if function cannot be evaluated for given A and W
* (e.g. division by zero, etc.), true otherwise.
*/
MESQUITE_EXPORT virtual
bool evaluate( const MsqMatrix<3,3>& A,
const MsqMatrix<3,3>& W,
double& result,
MsqError& err ) = 0;
/**\brief Gradient of \f$\mu(A,W)\f$ with respect to components of A
*
*\param A 3x3 active matrix
*\param W 3x3 target matrix
*\param result Output: value of function
*\param deriv_wrt_A Output: partial deriviatve of \f$\mu\f$ wrt each term of A,
* evaluated at passed A.
* \f[\left[\begin{array}{ccc}
* \frac{\partial\mu}{\partial A_{0,0}} &
* \frac{\partial\mu}{\partial A_{0,1}} &
* \frac{\partial\mu}{\partial A_{0,2}} \\
* \frac{\partial\mu}{\partial A_{1,0}} &
* \frac{\partial\mu}{\partial A_{1,1}} &
* \frac{\partial\mu}{\partial A_{1,2}} \\
* \frac{\partial\mu}{\partial A_{2,0}} &
* \frac{\partial\mu}{\partial A_{2,1}} &
* \frac{\partial\mu}{\partial A_{2,2}}
* \end{array}\right]\f]
*\return false if function cannot be evaluated for given A and W
* (e.g. division by zero, etc.), true otherwise.
*/
MESQUITE_EXPORT virtual
bool evaluate_with_grad( const MsqMatrix<3,3>& A,
const MsqMatrix<3,3>& W,
double& result,
MsqMatrix<3,3>& deriv_wrt_A,
MsqError& err );
/**\brief Hessian of \f$\mu(A,W)\f$ with respect to components of A
*
*\param A 3x3 active matrix
*\param W 3x3 target matrix
*\param result Output: value of function
*\param deriv_wrt_A Output: partial deriviatve of \f$\mu\f$ wrt each term of A,
* evaluated at passed A.
*\param second_wrt_A Output: 9x9 matrix of second partial deriviatve of \f$\mu\f$ wrt
* each term of A, 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 A_{0,0}^2} &
* \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{0,1}} &
* \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{0,2}} &
* \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{1,0}} &
* \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{1,1}} &
* \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{1,2}} &
* \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{2,0}} &
* \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{2,1}} &
* \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{2,2}} \\
* \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{0,1}} &
* \frac{\partial^{2}\mu}{\partial A_{0,1}^2} &
* \frac{\partial^{2}\mu}{\partial A_{0,1}\partial A_{0,2}} &
* \frac{\partial^{2}\mu}{\partial A_{0,1}\partial A_{1,0}} &
* \frac{\partial^{2}\mu}{\partial A_{0,1}\partial A_{1,1}} &
* \frac{\partial^{2}\mu}{\partial A_{0,1}\partial A_{1,2}} &
* \frac{\partial^{2}\mu}{\partial A_{0,1}\partial A_{2,0}} &
* \frac{\partial^{2}\mu}{\partial A_{0,1}\partial A_{2,1}} &
* \frac{\partial^{2}\mu}{\partial A_{0,1}\partial A_{2,2}} \\
* \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{0,2}} &
* \frac{\partial^{2}\mu}{\partial A_{0,1}\partial A_{0,2}} &
* \frac{\partial^{2}\mu}{\partial A_{0,2}^2} &
* \frac{\partial^{2}\mu}{\partial A_{0,2}\partial A_{1,0}} &
* \frac{\partial^{2}\mu}{\partial A_{0,2}\partial A_{1,1}} &
* \frac{\partial^{2}\mu}{\partial A_{0,2}\partial A_{1,2}} &
* \frac{\partial^{2}\mu}{\partial A_{0,2}\partial A_{2,0}} &
* \frac{\partial^{2}\mu}{\partial A_{0,2}\partial A_{2,1}} &
* \frac{\partial^{2}\mu}{\partial A_{0,2}\partial A_{2,2}} \\
* \hline & & &
* \frac{\partial^{2}\mu}{\partial A_{1,0}^2} &
* \frac{\partial^{2}\mu}{\partial A_{1,0}\partial A_{1,1}} &
* \frac{\partial^{2}\mu}{\partial A_{1,0}\partial A_{1,2}} &
* \frac{\partial^{2}\mu}{\partial A_{1,0}\partial A_{2,0}} &
* \frac{\partial^{2}\mu}{\partial A_{1,0}\partial A_{2,1}} &
* \frac{\partial^{2}\mu}{\partial A_{1,0}\partial A_{2,2}} \\
* & & &
* \frac{\partial^{2}\mu}{\partial A_{1,0}\partial A_{1,1}} &
* \frac{\partial^{2}\mu}{\partial A_{1,1}^2} &
* \frac{\partial^{2}\mu}{\partial A_{1,1}\partial A_{1,2}} &
* \frac{\partial^{2}\mu}{\partial A_{1,1}\partial A_{2,0}} &
* \frac{\partial^{2}\mu}{\partial A_{1,1}\partial A_{2,1}} &
* \frac{\partial^{2}\mu}{\partial A_{1,1}\partial A_{2,2}} \\
* & & &
* \frac{\partial^{2}\mu}{\partial A_{1,0}\partial A_{1,2}} &
* \frac{\partial^{2}\mu}{\partial A_{1,1}\partial A_{1,2}} &
* \frac{\partial^{2}\mu}{\partial A_{1,2}^2} &
* \frac{\partial^{2}\mu}{\partial A_{1,2}\partial A_{2,0}} &
* \frac{\partial^{2}\mu}{\partial A_{1,2}\partial A_{2,1}} &
* \frac{\partial^{2}\mu}{\partial A_{1,2}\partial A_{2,2}} \\
* \hline & & & & & &
* \frac{\partial^{2}\mu}{\partial A_{2,0}^2} &
* \frac{\partial^{2}\mu}{\partial A_{2,0}\partial A_{2,1}} &
* \frac{\partial^{2}\mu}{\partial A_{2,0}\partial A_{2,2}} \\
* & & & & & &
* \frac{\partial^{2}\mu}{\partial A_{2,0}\partial A_{2,1}} &
* \frac{\partial^{2}\mu}{\partial A_{2,1}^2} &
* \frac{\partial^{2}\mu}{\partial A_{2,1}\partial A_{2,2}} \\
* & & & & & &
* \frac{\partial^{2}\mu}{\partial A_{2,0}\partial A_{2,2}} &
* \frac{\partial^{2}\mu}{\partial A_{2,1}\partial A_{2,2}} &
* \frac{\partial^{2}\mu}{\partial A_{2,2}^2} \\
* \end{array}\right]\f]
*
*\return false if function cannot be evaluated for given A and W
* (e.g. division by zero, etc.), true otherwise.
*/
MESQUITE_EXPORT virtual
bool evaluate_with_hess( const MsqMatrix<3,3>& A,
const MsqMatrix<3,3>& W,
double& result,
MsqMatrix<3,3>& deriv_wrt_A,
MsqMatrix<3,3> second_wrt_A[6],
MsqError& err );
protected:
static inline bool invalid_determinant( double d )
{ return d < 1e-12; }
};
} // namespace Mesquite
#endif
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