MOAB: Mesh Oriented datABase  (version 5.2.1)
MBMesquite::TShapeOrientNB1 Class Reference

#include <TShapeOrientNB1.hpp>

Inheritance diagram for MBMesquite::TShapeOrientNB1:
Collaboration diagram for MBMesquite::TShapeOrientNB1:

## Public Member Functions

virtual MESQUITE_EXPORT ~TShapeOrientNB1 ()
virtual MESQUITE_EXPORT std::string get_name () const
virtual MESQUITE_EXPORT bool evaluate (const MsqMatrix< 2, 2 > &T, double &result, MsqError &err)
Evaluate $$\mu(T)$$.
virtual MESQUITE_EXPORT bool evaluate_with_grad (const MsqMatrix< 2, 2 > &T, double &result, MsqMatrix< 2, 2 > &deriv_wrt_T, MsqError &err)
Gradient of $$\mu(T)$$ with respect to components of T.
virtual MESQUITE_EXPORT 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)
Hessian of $$\mu(T)$$ with respect to components of T.
virtual MESQUITE_EXPORT bool evaluate (const MsqMatrix< 3, 3 > &T, double &result, MsqError &err)
Evaluate $$\mu(T)$$.
virtual MESQUITE_EXPORT bool evaluate_with_grad (const MsqMatrix< 3, 3 > &T, double &result, MsqMatrix< 3, 3 > &deriv_wrt_T, MsqError &err)
Gradient of $$\mu(T)$$ with respect to components of T.
virtual MESQUITE_EXPORT 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)
Hessian of $$\mu(T)$$ with respect to components of T.

## Detailed Description

|T| - tr(T)/sqrt(n)

Definition at line 42 of file TShapeOrientNB1.hpp.

## Constructor & Destructor Documentation

 MBMesquite::TShapeOrientNB1::~TShapeOrientNB1 ( )  [virtual]

Definition at line 46 of file TShapeOrientNB1.cpp.

{}


## Member Function Documentation

 virtual MESQUITE_EXPORT bool MBMesquite::TShapeOrientNB1::evaluate ( const MsqMatrix< 2, 2 > & T, double & result, MsqError & err )  [virtual]

Evaluate $$\mu(T)$$.

Parameters:
 T 2x2 relative measure matrix (typically A W^-1) result Output: value of function
Returns:
false if function cannot be evaluated for given T (e.g. division by zero, etc.), true otherwise.

Reimplemented from MBMesquite::TMetric.

 virtual MESQUITE_EXPORT bool MBMesquite::TShapeOrientNB1::evaluate ( const MsqMatrix< 3, 3 > & T, double & result, MsqError & err )  [virtual]

Evaluate $$\mu(T)$$.

Parameters:
 T 3x3 relative measure matrix (typically A W^-1) result Output: value of function
Returns:
false if function cannot be evaluated for given T (e.g. division by zero, etc.), true otherwise.

Reimplemented from MBMesquite::TMetric.

 virtual MESQUITE_EXPORT bool MBMesquite::TShapeOrientNB1::evaluate_with_grad ( const MsqMatrix< 2, 2 > & T, double & result, MsqMatrix< 2, 2 > & deriv_wrt_T, MsqError & err )  [virtual]

Gradient of $$\mu(T)$$ with respect to components of T.

Parameters:
 T 2x2 relative measure matrix (typically A W^-1) result Output: value of function deriv_wrt_T Output: partial deriviatve of $$\mu$$ wrt each term of T, evaluated at passed T. $\left[\begin{array}{cc} \frac{\partial\mu}{\partial T_{0,0}} & \frac{\partial\mu}{\partial T_{0,1}} \\ \frac{\partial\mu}{\partial T_{1,0}} & \frac{\partial\mu}{\partial T_{1,1}} \\ \end{array}\right]$
Returns:
false if function cannot be evaluated for given T (e.g. division by zero, etc.), true otherwise.

Reimplemented from MBMesquite::TMetric.

 virtual MESQUITE_EXPORT bool MBMesquite::TShapeOrientNB1::evaluate_with_grad ( const MsqMatrix< 3, 3 > & T, double & result, MsqMatrix< 3, 3 > & deriv_wrt_T, MsqError & err )  [virtual]

Gradient of $$\mu(T)$$ with respect to components of T.

Parameters:
 T 3x3 relative measure matrix (typically A W^-1) result Output: value of function deriv_wrt_T Output: partial deriviatve of $$\mu$$ wrt each term of T, evaluated at passed T. $\left[\begin{array}{ccc} \frac{\partial\mu}{\partial T_{0,0}} & \frac{\partial\mu}{\partial T_{0,1}} & \frac{\partial\mu}{\partial T_{0,2}} \\ \frac{\partial\mu}{\partial T_{1,0}} & \frac{\partial\mu}{\partial T_{1,1}} & \frac{\partial\mu}{\partial T_{1,2}} \\ \frac{\partial\mu}{\partial T_{2,0}} & \frac{\partial\mu}{\partial T_{2,1}} & \frac{\partial\mu}{\partial T_{2,2}} \end{array}\right]$
Returns:
false if function cannot be evaluated for given T (e.g. division by zero, etc.), true otherwise.

Reimplemented from MBMesquite::TMetric.

 virtual MESQUITE_EXPORT bool MBMesquite::TShapeOrientNB1::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 )  [virtual]

Hessian of $$\mu(T)$$ with respect to components of T.

Parameters:
 T 3x3 relative measure matrix (typically A W^-1) result Output: value of function deriv_wrt_T Output: partial deriviatve of $$\mu$$ wrt each term of T, evaluated at passed T. second_wrt_T Output: 9x9 matrix of second partial deriviatve of $$\mu$$ 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. $\left[\begin{array}{cc|cc} \frac{\partial^{2}\mu}{\partial T_{0,0}^2} & \frac{\partial^{2}\mu}{\partial T_{0,0}\partial A_{0,1}} & \frac{\partial^{2}\mu}{\partial T_{0,0}\partial A_{1,0}} & \frac{\partial^{2}\mu}{\partial T_{0,0}\partial A_{1,1}} \\ \frac{\partial^{2}\mu}{\partial T_{0,0}\partial A_{0,1}} & \frac{\partial^{2}\mu}{\partial T_{0,1}^2} & \frac{\partial^{2}\mu}{\partial T_{0,1}\partial A_{1,0}} & \frac{\partial^{2}\mu}{\partial T_{0,1}\partial A_{1,1}} \\ \hline & & \frac{\partial^{2}\mu}{\partial T_{1,0}^2} & \frac{\partial^{2}\mu}{\partial T_{1,0}\partial A_{1,1}} \\ & & \frac{\partial^{2}\mu}{\partial T_{1,0}\partial A_{1,1}} & \frac{\partial^{2}\mu}{\partial T_{1,1}^2} \\ \end{array}\right]$
Returns:
false if function cannot be evaluated for given T (e.g. division by zero, etc.), true otherwise.

Reimplemented from MBMesquite::TMetric.

 virtual MESQUITE_EXPORT bool MBMesquite::TShapeOrientNB1::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 )  [virtual]

Hessian of $$\mu(T)$$ with respect to components of T.

Parameters:
 T 3x3 relative measure matrix (typically A W^-1) result Output: value of function deriv_wrt_T Output: partial deriviatve of $$\mu$$ wrt each term of T, evaluated at passed T. second_wrt_T Output: 9x9 matrix of second partial deriviatve of $$\mu$$ 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. $\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]$
Returns:
false if function cannot be evaluated for given T (e.g. division by zero, etc.), true otherwise.

Reimplemented from MBMesquite::TMetric.

 std::string MBMesquite::TShapeOrientNB1::get_name ( ) const [virtual]

Reimplemented from MBMesquite::TMetricNonBarrier.

Definition at line 41 of file TShapeOrientNB1.cpp.

{
return "TShapeOrientNB1";
}


List of all members.

The documentation for this class was generated from the following files: