MOAB: Mesh Oriented datABase  (version 5.2.1)
MBMesquite::TSizeB1 Class Reference

#include <TSizeB1.hpp>

Inheritance diagram for MBMesquite::TSizeB1:
Collaboration diagram for MBMesquite::TSizeB1:

## Public Member Functions

virtual MESQUITE_EXPORT ~TSizeB1 ()
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

det(T) + 1/det(T) - 2

Definition at line 42 of file TSizeB1.hpp.

## Constructor & Destructor Documentation

 MBMesquite::TSizeB1::~TSizeB1 ( )  [virtual]

Definition at line 47 of file TSizeB1.cpp.

{}


## Member Function Documentation

 bool MBMesquite::TSizeB1::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.

Definition at line 49 of file TSizeB1.cpp.

{
double d = det( T );
if( TMetric::invalid_determinant( d ) )
{
MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
return false;
}
result = d + 1.0 / d - 2.0;
return true;
}

 bool MBMesquite::TSizeB1::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.

Definition at line 94 of file TSizeB1.cpp.

{
double d = det( T );
if( TMetric::invalid_determinant( d ) )
{
MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
return false;
}
result = d + 1.0 / d - 2.0;
return true;
}

 bool MBMesquite::TSizeB1::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.

Definition at line 61 of file TSizeB1.cpp.

{
double d = det( T );
if( TMetric::invalid_determinant( d ) )
{
MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
return false;
}
result      = d + 1.0 / d - 2.0;
deriv_wrt_T = ( 1 - 1 / ( d * d ) ) * transpose_adj( T );
return true;
}

 bool MBMesquite::TSizeB1::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.

Definition at line 106 of file TSizeB1.cpp.

{
double d = det( T );
if( TMetric::invalid_determinant( d ) )
{
MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
return false;
}
result      = d + 1.0 / d - 2.0;
deriv_wrt_T = ( 1 - 1 / ( d * d ) ) * transpose_adj( T );
return true;
}

 bool MBMesquite::TSizeB1::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.

Definition at line 75 of file TSizeB1.cpp.

{
double d = det( T );
if( TMetric::invalid_determinant( d ) )
{
MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
return false;
}
result                 = d + 1.0 / d - 2.0;
const double f         = 1 - 1 / ( d * d );

set_scaled_outer_product( second_wrt_T, 2 / ( d * d * d ), adjt );
pluseq_scaled_2nd_deriv_of_det( second_wrt_T, f, T );
return true;
}

 bool MBMesquite::TSizeB1::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.

Definition at line 120 of file TSizeB1.cpp.

{
double d = det( T );
if( TMetric::invalid_determinant( d ) )
{
MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
return false;
}
result                 = d + 1.0 / d - 2.0;
const double f         = 1 - 1 / ( d * d );

set_scaled_outer_product( second_wrt_T, 2 / ( d * d * d ), adjt );
pluseq_scaled_2nd_deriv_of_det( second_wrt_T, f, T );
return true;
}

 std::string MBMesquite::TSizeB1::get_name ( ) const [virtual]

Reimplemented from MBMesquite::TMetricBarrier.

Definition at line 42 of file TSizeB1.cpp.

{
return "TSizeB1";
}


List of all members.

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