MOAB: Mesh Oriented datABase  (version 5.4.1)
Public Member Functions
HessTestMetricRel_2 Class Reference
+ Inheritance diagram for HessTestMetricRel_2:
+ Collaboration diagram for HessTestMetricRel_2:

Public Member Functions

std::string get_name () const
bool evaluate (const MsqMatrix< 2, 2 > &T, double &result, MsqError &err)
 Evaluate \(\mu(T)\).
bool evaluate_with_grad (const MsqMatrix< 2, 2 > &T, double &result, MsqMatrix< 2, 2 > &d, MsqError &err)
 Gradient of \(\mu(T)\) with respect to components of T.
bool evaluate_with_hess (const MsqMatrix< 2, 2 > &T, double &result, MsqMatrix< 2, 2 > &d, MsqMatrix< 2, 2 > d2[3], MsqError &err)
 Hessian of \(\mu(T)\) with respect to components of T.
bool evaluate (const MsqMatrix< 3, 3 > &T, double &result, MsqError &err)
 Evaluate \(\mu(T)\).
bool evaluate_with_grad (const MsqMatrix< 3, 3 > &T, double &result, MsqMatrix< 3, 3 > &d, MsqError &err)
 Gradient of \(\mu(T)\) with respect to components of T.
bool evaluate_with_hess (const MsqMatrix< 3, 3 > &T, double &result, MsqMatrix< 3, 3 > &d, MsqMatrix< 3, 3 > d2[6], MsqError &err)
 Hessian of \(\mu(T)\) with respect to components of T.

Detailed Description

Simple target metric for testing second partial derivatives. \(\mu(T) = |T|\) \(\frac{\partial\mu}{\partial T} = \frac{1}{|T|} T \) \(\frac{\partial^{2}\mu}{\partial t_{i,i}^2} = \frac{1}{|T|} - \frac{t_{i,i}^2}{|T|^3}\) \(\frac{\partial^{2}\mu}{\partial t_{i,j} \partial t_{k,l} (i \ne k or j \ne l)} = -\frac{t_{i,j} a_{k,l}}{|T|^3}\)

Definition at line 148 of file TMetricTest.cpp.

Member Function Documentation

bool HessTestMetricRel_2::evaluate ( const MsqMatrix< 2, 2 > &  T,
double &  result,
MsqError &  err 
) [inline, 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 156 of file TMetricTest.cpp.

References MBMesquite::Frobenius().

    {
        result = Frobenius( T );
        return true;
    }
bool HessTestMetricRel_2::evaluate ( const MsqMatrix< 3, 3 > &  T,
double &  result,
MsqError &  err 
) [inline, 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 188 of file TMetricTest.cpp.

References MBMesquite::Frobenius().

    {
        result = Frobenius( T );
        return true;
    }
bool HessTestMetricRel_2::evaluate_with_grad ( const MsqMatrix< 2, 2 > &  T,
double &  result,
MsqMatrix< 2, 2 > &  deriv_wrt_T,
MsqError &  err 
) [inline, 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 162 of file TMetricTest.cpp.

References MBMesquite::Frobenius().

Referenced by TMetricTest< Metric, DIM >::test_numerical_gradient_2D(), and TMetricTest< Metric, DIM >::test_numerical_gradient_3D().

    {
        result = Frobenius( T );
        d      = T / result;
        return true;
    }
bool HessTestMetricRel_2::evaluate_with_grad ( const MsqMatrix< 3, 3 > &  T,
double &  result,
MsqMatrix< 3, 3 > &  deriv_wrt_T,
MsqError &  err 
) [inline, 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 194 of file TMetricTest.cpp.

References MBMesquite::Frobenius().

    {
        result = Frobenius( T );
        d      = T / result;
        return true;
    }
bool HessTestMetricRel_2::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 
) [inline, 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 169 of file TMetricTest.cpp.

References MBMesquite::Frobenius(), MBMesquite::MsqMatrix< R, C >::row(), and MBMesquite::transpose().

Referenced by TMetricTest< Metric, DIM >::test_numerical_hessian_2D(), and TMetricTest< Metric, DIM >::test_numerical_hessian_3D().

    {
        result = Frobenius( T );
        d      = T / result;
        int h  = 0;
        for( int r = 0; r < 2; ++r )
        {
            int i = h;
            for( int c = r; c < 2; ++c )
                d2[h++] = transpose( T.row( r ) ) * T.row( c ) / -( result * result * result );
            d2[i] += MsqMatrix< 2, 2 >( 1.0 / result );
        }
        return true;
    }
bool HessTestMetricRel_2::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 
) [inline, 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 201 of file TMetricTest.cpp.

References MBMesquite::Frobenius(), MBMesquite::MsqMatrix< R, C >::row(), and MBMesquite::transpose().

    {
        result = Frobenius( T );
        d      = T / result;
        int h  = 0;
        for( int r = 0; r < 3; ++r )
        {
            int i = h;
            for( int c = r; c < 3; ++c )
                d2[h++] = transpose( T.row( r ) ) * T.row( c ) / -( result * result * result );
            d2[i] += MsqMatrix< 3, 3 >( 1.0 / result );
        }
        return true;
    }
std::string HessTestMetricRel_2::get_name ( ) const [inline, virtual]

Implements MBMesquite::TMetric.

Definition at line 151 of file TMetricTest.cpp.

    {
        return "HessTest2";
    }

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