MOAB: Mesh Oriented datABase  (version 5.3.1)
MBMesquite::TShapeSize2DB2 Class Reference

#include <TShapeSize2DB2.hpp>

Inheritance diagram for MBMesquite::TShapeSize2DB2:
Collaboration diagram for MBMesquite::TShapeSize2DB2:

## Public Member Functions

virtual MESQUITE_EXPORT ~TShapeSize2DB2 ()
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.

## Detailed Description

$$\frac{ (|T|^2 - 2 sqrt(|T|^2 + 2 \tau) + 2) }{ (2 \tau) }$$

Definition at line 42 of file TShapeSize2DB2.hpp.

## Constructor & Destructor Documentation

 MBMesquite::TShapeSize2DB2::~TShapeSize2DB2 ( )  [virtual]

Definition at line 48 of file TShapeSize2DB2.cpp.

{}


## Member Function Documentation

 bool MBMesquite::TShapeSize2DB2::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 50 of file TShapeSize2DB2.cpp.

{
const double two_det = 2.0 * det( T );
if( invalid_determinant( two_det ) )
{  // barrier
MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
return false;
}

const double frob_sqr = sqr_Frobenius( T );
result                = ( frob_sqr - 2.0 * sqrt( frob_sqr + two_det ) + 2.0 ) / two_det;
return true;
}

 bool MBMesquite::TShapeSize2DB2::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 64 of file TShapeSize2DB2.cpp.

{
const double d = det( T );
if( invalid_determinant( d ) )
{  // barrier
MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
return false;
}
const double frob_sqr = sqr_Frobenius( T );
const double psi      = sqrt( frob_sqr + 2.0 * det( T ) );
const double v        = frob_sqr - 2.0 * psi + 2.0;
result                = v / ( 2 * d );

// deriv of V wrt T
MsqMatrix< 2, 2 > v_wrt_T( T );
if( psi > 1e-50 )
{
v_wrt_T *= ( 1.0 - 1.0 / psi );
v_wrt_T -= 1.0 / psi * adjt;
v_wrt_T *= 2;
}
else
{
std::cout << "Warning: Division by zero avoided in TShapeSize2DB2::evaluate_with_grad()" << std::endl;
}

// deriv of mu wrt T
deriv_wrt_T = v_wrt_T;
deriv_wrt_T *= 0.5 / d;
deriv_wrt_T -= v / ( 2 * d * d ) * adjt;

return true;
}

 bool MBMesquite::TShapeSize2DB2::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 100 of file TShapeSize2DB2.cpp.

{
const double d = det( T );
if( invalid_determinant( d ) )
{  // barrier
MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
return false;
}
const double frob_sqr = sqr_Frobenius( T );
const double psi      = sqrt( frob_sqr + 2.0 * det( T ) );
const double v        = frob_sqr - 2.0 * psi + 2.0;
result                = v / ( 2 * d );

// deriv of V wrt T
MsqMatrix< 2, 2 > v_wrt_T( T );
if( psi > 1e-50 )
{
v_wrt_T *= ( 1.0 - 1.0 / psi );
v_wrt_T -= 1.0 / psi * adjt;
v_wrt_T *= 2;
}
else
{
std::cout << "Warning: Division by zero avoided in TShapeSize2DB2::evaluate_with_hess()" << std::endl;
}

// deriv of mu wrt T
deriv_wrt_T = v_wrt_T;
deriv_wrt_T *= 0.5 / d;
deriv_wrt_T -= v / ( 2 * d * d ) * adjt;

// second of V wrt T
const double s    = T( 0, 1 ) - T( 1, 0 );
const double tr   = trace( T );
const double f    = -2.0 / ( psi * psi * psi );
second[0]( 0, 0 ) = second[1]( 0, 1 ) = second[2]( 1, 1 ) = f * s * s;
second[0]( 0, 1 ) = second[0]( 1, 0 ) = second[1]( 1, 1 ) = -f * s * tr;
second[1]( 0, 0 ) = second[2]( 0, 1 ) = second[2]( 1, 0 ) = f * s * tr;
second[0]( 1, 1 ) = second[2]( 0, 0 ) = -( second[1]( 1, 0 ) = -f * tr * tr );
pluseq_scaled_I( second, 2 );

// second of mu wrt T
const double x = 1.0 / ( 2 * d );
second[0] *= x;
second[1] *= x;
second[2] *= x;
pluseq_scaled_2nd_deriv_of_det( second, v / ( -2 * d * d ) );
pluseq_scaled_outer_product( second, v / ( d * d * d ), adjt );
pluseq_scaled_sum_outer_product( second, -1 / ( 2 * d * d ), v_wrt_T, adjt );

return true;
}

 std::string MBMesquite::TShapeSize2DB2::get_name ( ) const [virtual]

Reimplemented from MBMesquite::TMetricBarrier.

Definition at line 43 of file TShapeSize2DB2.cpp.

{
return "TShapeSize2DB2";
}


List of all members.

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