MOAB: Mesh Oriented datABase  (version 5.2.1)
MBMesquite::TShapeSize3DB4 Class Reference

#include <TShapeSize3DB4.hpp>

+ Inheritance diagram for MBMesquite::TShapeSize3DB4:
+ Collaboration diagram for MBMesquite::TShapeSize3DB4:

Public Member Functions

MESQUITE_EXPORT TShapeSize3DB4 (double gamma=2.0)
virtual MESQUITE_EXPORT ~TShapeSize3DB4 ()
virtual MESQUITE_EXPORT std::string get_name () const
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.

Private Attributes

double mGamma

Detailed Description

|T|^3 / (3 * sqrt(3) * tau) - 1 + gamma * (tau + 1/tau - 2)

Definition at line 42 of file TShapeSize3DB4.hpp.


Constructor & Destructor Documentation

Definition at line 49 of file TShapeSize3DB4.hpp.

: mGamma( gamma ) {}

Definition at line 47 of file TShapeSize3DB4.cpp.

{}

Member Function Documentation

bool MBMesquite::TShapeSize3DB4::evaluate ( const MsqMatrix< 3, 3 > &  T,
double &  result,
MsqError err 
) [virtual]

Evaluate \(\mu(T)\).

Parameters:
T3x3 relative measure matrix (typically A W^-1)
resultOutput: 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 TShapeSize3DB4.cpp.

References MBMesquite::MsqError::BARRIER_VIOLATED, MBMesquite::barrier_violated_msg, MBMesquite::det(), MBMesquite::Frobenius(), MBMesquite::TMetricBarrier::invalid_determinant(), mGamma, MSQ_SETERR, and MBMesquite::MSQ_SQRT_THREE.

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

    const double norm = Frobenius( T );
    result            = norm * norm * norm / ( 3 * MSQ_SQRT_THREE * tau ) - 1 + mGamma * ( tau + 1 / tau - 2 );
    return true;
}
bool MBMesquite::TShapeSize3DB4::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:
T3x3 relative measure matrix (typically A W^-1)
resultOutput: value of function
deriv_wrt_TOutput: 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 63 of file TShapeSize3DB4.cpp.

References MBMesquite::MsqError::BARRIER_VIOLATED, MBMesquite::barrier_violated_msg, MBMesquite::det(), MBMesquite::Frobenius(), MBMesquite::TMetricBarrier::invalid_determinant(), mGamma, MSQ_SETERR, MBMesquite::MSQ_SQRT_THREE, T, and MBMesquite::transpose_adj().

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

    const double norm    = Frobenius( T );
    const double f       = norm * norm / 3.0;
    const double g       = norm / ( MSQ_SQRT_THREE * tau );
    const double inv_tau = 1.0 / tau;
    result               = f * g - 1 + mGamma * ( tau + inv_tau - 2 );

    deriv = g * T;
    deriv += ( mGamma * ( 1 - inv_tau * inv_tau ) - f * g * inv_tau ) * transpose_adj( T );

    return true;
}
bool MBMesquite::TShapeSize3DB4::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:
T3x3 relative measure matrix (typically A W^-1)
resultOutput: value of function
deriv_wrt_TOutput: partial deriviatve of \(\mu\) wrt each term of T, evaluated at passed T.
second_wrt_TOutput: 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 85 of file TShapeSize3DB4.cpp.

References MBMesquite::MsqError::BARRIER_VIOLATED, MBMesquite::barrier_violated_msg, MBMesquite::det(), MBMesquite::Frobenius(), MBMesquite::TMetricBarrier::invalid_determinant(), mGamma, MSQ_SETERR, MBMesquite::MSQ_SQRT_THREE, MBMesquite::pluseq_scaled_2nd_deriv_of_det(), MBMesquite::pluseq_scaled_I(), MBMesquite::pluseq_scaled_outer_product(), MBMesquite::pluseq_scaled_sum_outer_product(), MBMesquite::set_scaled_outer_product(), T, and MBMesquite::transpose_adj().

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

    const double norm    = Frobenius( T );
    const double f       = norm * norm / 3.0;
    const double h       = 1 / ( MSQ_SQRT_THREE * tau );
    const double g       = norm * h;
    const double inv_tau = 1.0 / tau;
    result               = f * g - 1 + mGamma * ( tau + inv_tau - 2 );

    const double g1              = mGamma * ( 1 - inv_tau * inv_tau );
    const MsqMatrix< 3, 3 > adjt = transpose_adj( T );
    deriv                        = g * T;
    deriv += ( g1 - f * g * inv_tau ) * adjt;

    if( norm > 1e-50 )
    {
        const double inv_norm = 1 / norm;
        set_scaled_outer_product( second, h * inv_norm, T );
        pluseq_scaled_I( second, norm * h );
        pluseq_scaled_2nd_deriv_of_det( second, g1 - f * g * inv_tau, T );
        pluseq_scaled_outer_product( second, ( f * g + mGamma * inv_tau ) * 2 * inv_tau * inv_tau, adjt );
        pluseq_scaled_sum_outer_product( second, -g * inv_tau, T, adjt );
    }
    else
    {
        std::cout << "Warning: Division by zero avoided in TShapeSize3DB4::evaluate_with_hess()" << std::endl;
    }

    return true;
}
std::string MBMesquite::TShapeSize3DB4::get_name ( ) const [virtual]

Reimplemented from MBMesquite::TMetricBarrier.

Definition at line 42 of file TShapeSize3DB4.cpp.

{
    return "TShapeSize3DB4";
}

Member Data Documentation

Definition at line 45 of file TShapeSize3DB4.hpp.

Referenced by evaluate(), evaluate_with_grad(), and evaluate_with_hess().

List of all members.


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