MOAB: Mesh Oriented datABase
(version 5.4.1)
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#include <TShapeSize3DB2.hpp>
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. |
3.3.12: (|T|^2 + |adj(T)|^2)/6 - 1
Definition at line 42 of file TShapeSize3DB2.hpp.
MBMesquite::TShapeSize3DB2::~TShapeSize3DB2 | ( | ) | [virtual] |
Definition at line 45 of file TShapeSize3DB2.cpp.
{}
bool MBMesquite::TShapeSize3DB2::evaluate | ( | const MsqMatrix< 3, 3 > & | T, |
double & | result, | ||
MsqError & | err | ||
) | [virtual] |
Evaluate \(\mu(T)\).
T | 3x3 relative measure matrix (typically A W^-1) |
result | Output: value of function |
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.
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. \[\left[\begin{array}{ccc} \frac{\partial\mu}{\partial T_{0,0}} & \frac{\partial\mu}{\partial T_{0,1}} & \frac{\partial\mu}{\partial T_{0,2}} \\ \frac{\partial\mu}{\partial T_{1,0}} & \frac{\partial\mu}{\partial T_{1,1}} & \frac{\partial\mu}{\partial T_{1,2}} \\ \frac{\partial\mu}{\partial T_{2,0}} & \frac{\partial\mu}{\partial T_{2,1}} & \frac{\partial\mu}{\partial T_{2,2}} \end{array}\right]\] |
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.
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]\] |
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"; }