MOAB: Mesh Oriented datABase  (version 5.3.1)
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, 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, 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:
 T 2x2 relative measure matrix (typically A W^-1) result Output: 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:
 T 3x3 relative measure matrix (typically A W^-1) result Output: 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 185 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:
 T 2x2 relative measure matrix (typically A W^-1) result Output: value of function deriv_wrt_T Output: 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().

    {
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:
 T 3x3 relative measure matrix (typically A W^-1) result Output: value of function deriv_wrt_T Output: 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 191 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, MsqError & err )  [inline, virtual]

Hessian of $$\mu(T)$$ with respect to components of T.

Parameters:
 T 3x3 relative measure matrix (typically A W^-1) result Output: value of function deriv_wrt_T Output: partial deriviatve of $$\mu$$ wrt each term of T, evaluated at passed T. second_wrt_T Output: 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.

    {
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, MsqError & err )  [inline, virtual]

Hessian of $$\mu(T)$$ with respect to components of T.

Parameters:
 T 3x3 relative measure matrix (typically A W^-1) result Output: value of function deriv_wrt_T Output: partial deriviatve of $$\mu$$ wrt each term of T, evaluated at passed T. second_wrt_T Output: 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 198 of file TMetricTest.cpp.

    {
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";
}


List of all members.

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