MOAB: Mesh Oriented datABase  (version 5.4.1)
Public Member Functions
MBMesquite::TShapeSize3DB2 Class Reference

#include <TShapeSize3DB2.hpp>

+ Inheritance diagram for MBMesquite::TShapeSize3DB2:
+ Collaboration diagram for MBMesquite::TShapeSize3DB2:

Public Member Functions

virtual MESQUITE_EXPORT std::string get_name () const
virtual MESQUITE_EXPORT ~TShapeSize3DB2 ()
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

3.3.12: (|T|^2 + |adj(T)|^2)/6 - 1

Definition at line 42 of file TShapeSize3DB2.hpp.

Constructor & Destructor Documentation

MBMesquite::TShapeSize3DB2::~TShapeSize3DB2 ( ) [virtual]

Definition at line 45 of file TShapeSize3DB2.cpp.

{}

Member Function Documentation

bool MBMesquite::TShapeSize3DB2::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 47 of file TShapeSize3DB2.cpp.

References MBMesquite::adj(), MBMesquite::MsqError::BARRIER_VIOLATED, MBMesquite::barrier_violated_msg, MBMesquite::det(), MBMesquite::TMetricBarrier::invalid_determinant(), MSQ_SETERR, and MBMesquite::sqr_Frobenius().

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

    const double f = sqr_Frobenius( T );
    const double g = sqr_Frobenius( adj( T ) );
    result         = ( f + g ) / ( 6 * tau ) - 1;
    return true;
}
bool MBMesquite::TShapeSize3DB2::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 62 of file TShapeSize3DB2.cpp.

References MBMesquite::adj(), MBMesquite::MsqError::BARRIER_VIOLATED, MBMesquite::barrier_violated_msg, MBMesquite::det(), MBMesquite::TMetricBarrier::invalid_determinant(), MSQ_SETERR, MBMesquite::sqr_Frobenius(), T, MBMesquite::transpose(), 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 f = sqr_Frobenius( T );
    const double g = sqr_Frobenius( adj( T ) );
    result         = ( f + g ) / ( 6 * tau );

    deriv_wrt_T = -transpose( T ) * T;
    deriv_wrt_T( 0, 0 ) += 1 + f;
    deriv_wrt_T( 1, 1 ) += 1 + f;
    deriv_wrt_T( 2, 2 ) += 1 + f;
    deriv_wrt_T = T * deriv_wrt_T;
    deriv_wrt_T -= 3 * result * transpose_adj( T );
    deriv_wrt_T *= 1.0 / ( 3 * tau );

    result -= 1.0;
    return true;
}
bool MBMesquite::TShapeSize3DB2::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 90 of file TShapeSize3DB2.cpp.

References MBMesquite::adj(), MBMesquite::MsqError::BARRIER_VIOLATED, MBMesquite::barrier_violated_msg, MBMesquite::det(), MBMesquite::hess_scale(), MBMesquite::TMetricBarrier::invalid_determinant(), MSQ_SETERR, 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_2nd_deriv_norm_sqr_adj(), MBMesquite::sqr_Frobenius(), T, MBMesquite::transpose(), 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 f = sqr_Frobenius( T );
    const double g = sqr_Frobenius( adj( T ) );
    result         = ( f + g ) / ( 6 * tau );

    MsqMatrix< 3, 3 > dtau = transpose_adj( T );
    MsqMatrix< 3, 3 > dg   = -transpose( T ) * T;
    dg( 0, 0 ) += f;
    dg( 1, 1 ) += f;
    dg( 2, 2 ) += f;
    dg = T * dg;
    dg *= 2;

    wrt_T = T;
    wrt_T += 0.5 * dg;
    wrt_T *= 1.0 / 3.0;
    wrt_T -= result * dtau;
    wrt_T *= 1.0 / tau;

    set_scaled_2nd_deriv_norm_sqr_adj( second, 1.0 / 6.0, T );
    pluseq_scaled_I( second, 1.0 / 3.0 );
    pluseq_scaled_sum_outer_product( second, -1. / 3. / tau, T, dtau );
    pluseq_scaled_sum_outer_product( second, -1. / 6. / tau, dg, dtau );
    pluseq_scaled_outer_product( second, 2 * result / tau, dtau );
    pluseq_scaled_2nd_deriv_of_det( second, -result, T );
    hess_scale( second, 1.0 / tau );

    result -= 1.0;
    return true;
}
std::string MBMesquite::TShapeSize3DB2::get_name ( ) const [virtual]

Reimplemented from MBMesquite::TMetricBarrier.

Definition at line 40 of file TShapeSize3DB2.cpp.

{
    return "TShapeSize3DB2";
}

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