MOAB: Mesh Oriented datABase  (version 5.4.1)
Public Member Functions
MBMesquite::TShapeOrientB2 Class Reference

#include <TShapeOrientB2.hpp>

+ Inheritance diagram for MBMesquite::TShapeOrientB2:
+ Collaboration diagram for MBMesquite::TShapeOrientB2:

Public Member Functions

virtual MESQUITE_EXPORT std::string get_name () const
virtual MESQUITE_EXPORT ~TShapeOrientB2 ()
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|^2 - 1/n trace(T) abs(trace(T)))/(2tau)

Section 3.3.3 of derivs.tex (7/2009)

Definition at line 45 of file TShapeOrientB2.hpp.

Constructor & Destructor Documentation

MBMesquite::TShapeOrientB2::~TShapeOrientB2 ( ) [virtual]

Definition at line 47 of file TShapeOrientB2.cpp.

{}

Member Function Documentation

bool MBMesquite::TShapeOrientB2::evaluate ( const MsqMatrix< 2, 2 > &  T,
double &  result,
MsqError &  err 
) [virtual]

Evaluate \(\mu(T)\).

Parameters:
T2x2 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 TShapeOrientB2.cpp.

References MBMesquite::MsqError::BARRIER_VIOLATED, MBMesquite::barrier_violated_msg, MBMesquite::det(), MBMesquite::TMetric::invalid_determinant(), MSQ_SETERR, MBMesquite::sqr_Frobenius(), and MBMesquite::trace().

{
    double tau = det( T );
    if( TMetric::invalid_determinant( tau ) )
    {
        MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
        return false;
    }
    const double tr = trace( T );
    result          = ( 0.5 / tau ) * ( sqr_Frobenius( T ) - 0.5 * tr * fabs( tr ) );
    return true;
}
bool MBMesquite::TShapeOrientB2::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 133 of file TShapeOrientB2.cpp.

References MBMesquite::MsqError::BARRIER_VIOLATED, MBMesquite::barrier_violated_msg, MBMesquite::det(), MBMesquite::TMetric::invalid_determinant(), MBMesquite::MSQ_ONE_THIRD, MSQ_SETERR, MBMesquite::sqr_Frobenius(), and MBMesquite::trace().

{
    double tau = det( T );
    if( TMetric::invalid_determinant( tau ) )
    {
        MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
        return false;
    }
    const double tr = trace( T );
    result          = ( 0.5 / tau ) * ( sqr_Frobenius( T ) - MSQ_ONE_THIRD * tr * fabs( tr ) );
    return true;
}
bool MBMesquite::TShapeOrientB2::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:
T2x2 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.

\[\left[\begin{array}{cc} \frac{\partial\mu}{\partial T_{0,0}} & \frac{\partial\mu}{\partial T_{0,1}} \\ \frac{\partial\mu}{\partial T_{1,0}} & \frac{\partial\mu}{\partial T_{1,1}} \\ \end{array}\right]\]

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 62 of file TShapeOrientB2.cpp.

References b, MBMesquite::MsqError::BARRIER_VIOLATED, MBMesquite::barrier_violated_msg, MBMesquite::det(), MBMesquite::TMetric::invalid_determinant(), MSQ_SETERR, MBMesquite::pluseq_scaled_I(), MBMesquite::sqr_Frobenius(), T, MBMesquite::trace(), and MBMesquite::transpose_adj().

{
    double tau = det( T );
    if( TMetric::invalid_determinant( tau ) )
    {
        MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
        return false;
    }
    const double b = 0.5 / tau;

    const double tr = trace( T );
    const double f  = 0.5 * fabs( tr );
    result          = sqr_Frobenius( T ) - f * tr;

    deriv_wrt_T = T;
    pluseq_scaled_I( deriv_wrt_T, -f );
    deriv_wrt_T *= 2 * tau;
    deriv_wrt_T -= result * transpose_adj( T );

    result *= b;
    deriv_wrt_T *= b / tau;

    return true;
}
bool MBMesquite::TShapeOrientB2::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 146 of file TShapeOrientB2.cpp.

References b, MBMesquite::MsqError::BARRIER_VIOLATED, MBMesquite::barrier_violated_msg, MBMesquite::det(), MBMesquite::TMetric::invalid_determinant(), MBMesquite::MSQ_ONE_THIRD, MSQ_SETERR, MBMesquite::pluseq_scaled_I(), MBMesquite::sqr_Frobenius(), T, MBMesquite::trace(), and MBMesquite::transpose_adj().

{
    double tau = det( T );
    if( TMetric::invalid_determinant( tau ) )
    {
        MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
        return false;
    }
    const double b = 0.5 / tau;

    const double tr = trace( T );
    const double f  = MSQ_ONE_THIRD * fabs( tr );
    result          = sqr_Frobenius( T ) - f * tr;

    deriv_wrt_T = T;
    pluseq_scaled_I( deriv_wrt_T, -f );
    deriv_wrt_T *= 2 * tau;
    deriv_wrt_T -= result * transpose_adj( T );

    result *= b;
    deriv_wrt_T *= b / tau;

    return true;
}
bool MBMesquite::TShapeOrientB2::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:
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.

\[\left[\begin{array}{cc|cc} \frac{\partial^{2}\mu}{\partial T_{0,0}^2} & \frac{\partial^{2}\mu}{\partial T_{0,0}\partial A_{0,1}} & \frac{\partial^{2}\mu}{\partial T_{0,0}\partial A_{1,0}} & \frac{\partial^{2}\mu}{\partial T_{0,0}\partial A_{1,1}} \\ \frac{\partial^{2}\mu}{\partial T_{0,0}\partial A_{0,1}} & \frac{\partial^{2}\mu}{\partial T_{0,1}^2} & \frac{\partial^{2}\mu}{\partial T_{0,1}\partial A_{1,0}} & \frac{\partial^{2}\mu}{\partial T_{0,1}\partial A_{1,1}} \\ \hline & & \frac{\partial^{2}\mu}{\partial T_{1,0}^2} & \frac{\partial^{2}\mu}{\partial T_{1,0}\partial A_{1,1}} \\ & & \frac{\partial^{2}\mu}{\partial T_{1,0}\partial A_{1,1}} & \frac{\partial^{2}\mu}{\partial T_{1,1}^2} \\ \end{array}\right]\]

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 90 of file TShapeOrientB2.cpp.

References b, MBMesquite::MsqError::BARRIER_VIOLATED, MBMesquite::barrier_violated_msg, MBMesquite::det(), MBMesquite::TMetric::invalid_determinant(), MSQ_SETERR, MBMesquite::pluseq_scaled_2nd_deriv_of_det(), MBMesquite::pluseq_scaled_I(), MBMesquite::pluseq_scaled_outer_product(), MBMesquite::pluseq_scaled_outer_product_I_I(), MBMesquite::set_scaled_sum_outer_product(), MBMesquite::sqr_Frobenius(), T, MBMesquite::trace(), and MBMesquite::transpose_adj().

{
    double tau = det( T );
    if( TMetric::invalid_determinant( tau ) )
    {
        MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
        return false;
    }
    const double b = 0.5 / tau;

    // calculate non-barrier value (ShapeOrientAlt1)
    const double tr = trace( T );
    const double f  = 0.5 * fabs( tr );
    result          = sqr_Frobenius( T ) - f * tr;

    // calculate non-barrier first derivatives
    deriv_wrt_T = T;
    pluseq_scaled_I( deriv_wrt_T, -f );
    deriv_wrt_T *= 2;

    // calculate barrier second derivs
    const MsqMatrix< 2, 2 > adjt = transpose_adj( T );
    set_scaled_sum_outer_product( second_wrt_T, -b / tau, deriv_wrt_T, adjt );
    pluseq_scaled_outer_product( second_wrt_T, result / ( tau * tau * tau ), adjt );
    pluseq_scaled_2nd_deriv_of_det( second_wrt_T, -result * b / tau, T );
    // calculate non-barrier barrier portion of second derivs
    pluseq_scaled_I( second_wrt_T, 1 / tau );
    pluseq_scaled_outer_product_I_I( second_wrt_T, 0.5 / tau * ( tr < 0 ? 1 : -1 ) );

    // calculate barrier derivs from non-barrier
    deriv_wrt_T *= tau;
    deriv_wrt_T -= result * adjt;
    deriv_wrt_T *= b / tau;

    // barrier value from non-barrier
    result *= b;
    return true;
}
bool MBMesquite::TShapeOrientB2::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 174 of file TShapeOrientB2.cpp.

References b, MBMesquite::MsqError::BARRIER_VIOLATED, MBMesquite::barrier_violated_msg, MBMesquite::det(), MBMesquite::TMetric::invalid_determinant(), MBMesquite::MSQ_ONE_THIRD, MSQ_SETERR, MBMesquite::pluseq_scaled_2nd_deriv_of_det(), MBMesquite::pluseq_scaled_I(), MBMesquite::pluseq_scaled_outer_product(), MBMesquite::pluseq_scaled_outer_product_I_I(), MBMesquite::set_scaled_sum_outer_product(), MBMesquite::sqr_Frobenius(), T, MBMesquite::trace(), and MBMesquite::transpose_adj().

{
    double tau = det( T );
    if( TMetric::invalid_determinant( tau ) )
    {
        MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
        result = 0.0;
        return false;
    }
    const double b = 0.5 / tau;

    // calculate non-barrier value (ShapeOrientAlt1)
    const double tr = trace( T );
    const double f  = MSQ_ONE_THIRD * fabs( tr );
    result          = sqr_Frobenius( T ) - f * tr;

    // calculate non-barrier first derivatives
    deriv_wrt_T = T;
    pluseq_scaled_I( deriv_wrt_T, -f );
    deriv_wrt_T *= 2;

    // calculate barrier second derivs
    const MsqMatrix< 3, 3 > adjt = transpose_adj( T );
    set_scaled_sum_outer_product( second_wrt_T, -b / tau, deriv_wrt_T, adjt );
    pluseq_scaled_outer_product( second_wrt_T, result / ( tau * tau * tau ), adjt );
    pluseq_scaled_2nd_deriv_of_det( second_wrt_T, -result * b / tau, T );
    // calculate non-barrier barrier portion of second derivs
    pluseq_scaled_I( second_wrt_T, 1 / tau );
    pluseq_scaled_outer_product_I_I( second_wrt_T, MSQ_ONE_THIRD / tau * ( tr < 0 ? 1 : -1 ) );

    // calculate barrier derivs from non-barrier
    deriv_wrt_T *= tau;
    deriv_wrt_T -= result * adjt;
    deriv_wrt_T *= b / tau;

    // barrier value from non-barrier
    result *= b;
    return true;
}
std::string MBMesquite::TShapeOrientB2::get_name ( ) const [virtual]

Reimplemented from MBMesquite::TMetricBarrier.

Definition at line 42 of file TShapeOrientB2.cpp.

{
    return "TShapeOrientB2";
}

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