MOAB: Mesh Oriented datABase  (version 5.3.1)
MBMesquite::TShapeOrientB1 Class Reference

#include <TShapeOrientB1.hpp>

+ Inheritance diagram for MBMesquite::TShapeOrientB1:
+ Collaboration diagram for MBMesquite::TShapeOrientB1:

Public Member Functions

virtual MESQUITE_EXPORT std::string get_name () const
virtual MESQUITE_EXPORT ~TShapeOrientB1 ()
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| - tr(T)/sqrt(n))/(2 tau)

Definition at line 42 of file TShapeOrientB1.hpp.


Constructor & Destructor Documentation

Definition at line 48 of file TShapeOrientB1.cpp.

{}

Member Function Documentation

bool MBMesquite::TShapeOrientB1::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 50 of file TShapeOrientB1.cpp.

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

{
    const double tau = det( T );
    if( TMetric::invalid_determinant( tau ) )
    {  // barrier
        MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
        return false;
    }
    result = 0.5 / tau * ( Frobenius( T ) - trace( T ) / MSQ_SQRT_TWO );
    return true;
}
bool MBMesquite::TShapeOrientB1::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 120 of file TShapeOrientB1.cpp.

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

{
    const double tau = det( T );
    if( TMetric::invalid_determinant( tau ) )
    {  // barrier
        MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
        return false;
    }
    result = 0.5 / tau * ( Frobenius( T ) - trace( T ) / MSQ_SQRT_THREE );
    return true;
}
bool MBMesquite::TShapeOrientB1::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 TShapeOrientB1.cpp.

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

{
    const double norm    = Frobenius( T );
    const double invroot = 1.0 / MSQ_SQRT_TWO;
    const double tau     = det( T );
    if( TMetric::invalid_determinant( tau ) )
    {  // barrier
        MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
        return false;
    }
    const double inv_tau = 1.0 / tau;
    const double invnorm = 1.0 / norm;

    result = 0.5 * inv_tau * ( norm - invroot * trace( T ) );

    deriv_wrt_T = invnorm * T;
    pluseq_scaled_I( deriv_wrt_T, -invroot );
    deriv_wrt_T *= 0.5;
    deriv_wrt_T -= result * transpose_adj( T );
    deriv_wrt_T *= inv_tau;
    return true;
}
bool MBMesquite::TShapeOrientB1::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 132 of file TShapeOrientB1.cpp.

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

{
    const double norm    = Frobenius( T );
    const double invroot = 1.0 / MSQ_SQRT_THREE;
    const double tau     = det( T );
    if( TMetric::invalid_determinant( tau ) )
    {  // barrier
        MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
        return false;
    }
    const double inv_tau = 1.0 / tau;
    const double invnorm = 1.0 / norm;

    result = 0.5 * inv_tau * ( norm - invroot * trace( T ) );

    deriv_wrt_T = invnorm * T;
    pluseq_scaled_I( deriv_wrt_T, -invroot );
    deriv_wrt_T *= 0.5;
    deriv_wrt_T -= result * transpose_adj( T );
    deriv_wrt_T *= inv_tau;
    return true;
}
bool MBMesquite::TShapeOrientB1::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 86 of file TShapeOrientB1.cpp.

References MBMesquite::MsqError::BARRIER_VIOLATED, MBMesquite::barrier_violated_msg, MBMesquite::det(), MBMesquite::Frobenius(), MBMesquite::TMetric::invalid_determinant(), MSQ_SETERR, MBMesquite::MSQ_SQRT_TWO, MBMesquite::pluseq_scaled_2nd_deriv_of_det(), MBMesquite::pluseq_scaled_I(), MBMesquite::pluseq_scaled_outer_product(), MBMesquite::pluseq_scaled_sum_outer_product(), MBMesquite::pluseq_scaled_sum_outer_product_I(), MBMesquite::set_scaled_outer_product(), T, MBMesquite::trace(), and MBMesquite::transpose_adj().

{
    const double norm    = Frobenius( T );
    const double invroot = 1.0 / MSQ_SQRT_TWO;
    const double tau     = det( T );
    if( TMetric::invalid_determinant( tau ) )
    {  // barrier
        MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
        return false;
    }
    const double inv_tau = 1.0 / tau;
    const double invnorm = 1.0 / norm;

    const double f = norm - invroot * trace( T );
    result         = 0.5 * inv_tau * f;

    const MsqMatrix< 2, 2 > adjt = transpose_adj( T );
    deriv_wrt_T                  = invnorm * T;
    pluseq_scaled_I( deriv_wrt_T, -invroot );
    deriv_wrt_T *= 0.5;
    deriv_wrt_T -= result * adjt;
    deriv_wrt_T *= inv_tau;

    const double a = 0.5 * inv_tau * invnorm;
    set_scaled_outer_product( second_wrt_T, -a * invnorm * invnorm, T );
    pluseq_scaled_I( second_wrt_T, a );
    pluseq_scaled_outer_product( second_wrt_T, f * inv_tau * inv_tau * inv_tau, adjt );
    pluseq_scaled_2nd_deriv_of_det( second_wrt_T, -0.5 * f * inv_tau * inv_tau, T );
    pluseq_scaled_sum_outer_product( second_wrt_T, -0.5 * inv_tau * inv_tau * invnorm, T, adjt );
    pluseq_scaled_sum_outer_product_I( second_wrt_T, 0.5 * inv_tau * inv_tau * invroot, adjt );
    return true;
}
bool MBMesquite::TShapeOrientB1::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 156 of file TShapeOrientB1.cpp.

References MBMesquite::MsqError::BARRIER_VIOLATED, MBMesquite::barrier_violated_msg, MBMesquite::det(), MBMesquite::Frobenius(), MBMesquite::TMetric::invalid_determinant(), 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::pluseq_scaled_sum_outer_product_I(), MBMesquite::set_scaled_outer_product(), T, MBMesquite::trace(), and MBMesquite::transpose_adj().

{
    const double norm    = Frobenius( T );
    const double invroot = 1.0 / MSQ_SQRT_THREE;
    const double tau     = det( T );
    if( TMetric::invalid_determinant( tau ) )
    {  // barrier
        MSQ_SETERR( err )( barrier_violated_msg, MsqError::BARRIER_VIOLATED );
        return false;
    }
    const double inv_tau = 1.0 / tau;
    const double invnorm = 1.0 / norm;

    const double f = norm - invroot * trace( T );
    result         = 0.5 * inv_tau * f;

    const MsqMatrix< 3, 3 > adjt = transpose_adj( T );
    deriv_wrt_T                  = invnorm * T;
    pluseq_scaled_I( deriv_wrt_T, -invroot );
    deriv_wrt_T *= 0.5;
    deriv_wrt_T -= result * adjt;
    deriv_wrt_T *= inv_tau;

    const double a = 0.5 * inv_tau * invnorm;
    set_scaled_outer_product( second_wrt_T, -a * invnorm * invnorm, T );
    pluseq_scaled_I( second_wrt_T, a );
    pluseq_scaled_outer_product( second_wrt_T, f * inv_tau * inv_tau * inv_tau, adjt );
    pluseq_scaled_2nd_deriv_of_det( second_wrt_T, -0.5 * f * inv_tau * inv_tau, T );
    pluseq_scaled_sum_outer_product( second_wrt_T, -0.5 * inv_tau * inv_tau * invnorm, T, adjt );
    pluseq_scaled_sum_outer_product_I( second_wrt_T, 0.5 * inv_tau * inv_tau * invroot, adjt );
    return true;
}
std::string MBMesquite::TShapeOrientB1::get_name ( ) const [virtual]

Reimplemented from MBMesquite::TMetricBarrier.

Definition at line 43 of file TShapeOrientB1.cpp.

{
    return "TShapeOrientB1";
}

List of all members.


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