MOAB: Mesh Oriented datABase
(version 5.4.1)
|
Untangle metric. More...
#include <TUntangleBeta.hpp>
Public Member Functions | |
TUntangleBeta (double gamma=0.0) | |
virtual MESQUITE_EXPORT | ~TUntangleBeta () |
virtual MESQUITE_EXPORT std::string | get_name () const |
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. | |
Private Member Functions | |
template<unsigned D> | |
bool | eval (const MsqMatrix< D, D > &T, double &result) |
template<unsigned D> | |
bool | grad (const MsqMatrix< D, D > &T, double &result, MsqMatrix< D, D > &first) |
template<unsigned D> | |
bool | hess (const MsqMatrix< D, D > &T, double &result, MsqMatrix< D, D > &first, MsqMatrix< D, D > *second) |
Private Attributes | |
double | mGamma |
Untangle metric.
\( \mu_n(T) = \frac{1}{8} {|\tau - \gamma| - (\tau - \gamma)}^3 \)
Section 3.2.7 of derivs.tex
Definition at line 47 of file TUntangleBeta.hpp.
MBMesquite::TUntangleBeta::TUntangleBeta | ( | double | gamma = 0.0 | ) | [inline] |
Definition at line 53 of file TUntangleBeta.hpp.
: mGamma( gamma ) {}
MBMesquite::TUntangleBeta::~TUntangleBeta | ( | ) | [virtual] |
Definition at line 40 of file TUntangleBeta.cpp.
{}
bool MBMesquite::TUntangleBeta::eval | ( | const MsqMatrix< DIM, DIM > & | T, |
double & | result | ||
) | [inline, private] |
Definition at line 48 of file TUntangleBeta.cpp.
References MBMesquite::det(), and mGamma.
virtual MESQUITE_EXPORT bool MBMesquite::TUntangleBeta::evaluate | ( | const MsqMatrix< 2, 2 > & | T, |
double & | result, | ||
MsqError & | err | ||
) | [virtual] |
Evaluate \(\mu(T)\).
T | 2x2 relative measure matrix (typically A W^-1) |
result | Output: value of function |
Reimplemented from MBMesquite::TMetric.
virtual MESQUITE_EXPORT bool MBMesquite::TUntangleBeta::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.
virtual MESQUITE_EXPORT bool MBMesquite::TUntangleBeta::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.
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. \[\left[\begin{array}{cc} \frac{\partial\mu}{\partial T_{0,0}} & \frac{\partial\mu}{\partial T_{0,1}} \\ \frac{\partial\mu}{\partial T_{1,0}} & \frac{\partial\mu}{\partial T_{1,1}} \\ \end{array}\right]\] |
Reimplemented from MBMesquite::TMetric.
virtual MESQUITE_EXPORT bool MBMesquite::TUntangleBeta::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.
virtual MESQUITE_EXPORT bool MBMesquite::TUntangleBeta::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.
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. \[\left[\begin{array}{cc|cc} \frac{\partial^{2}\mu}{\partial T_{0,0}^2} & \frac{\partial^{2}\mu}{\partial T_{0,0}\partial A_{0,1}} & \frac{\partial^{2}\mu}{\partial T_{0,0}\partial A_{1,0}} & \frac{\partial^{2}\mu}{\partial T_{0,0}\partial A_{1,1}} \\ \frac{\partial^{2}\mu}{\partial T_{0,0}\partial A_{0,1}} & \frac{\partial^{2}\mu}{\partial T_{0,1}^2} & \frac{\partial^{2}\mu}{\partial T_{0,1}\partial A_{1,0}} & \frac{\partial^{2}\mu}{\partial T_{0,1}\partial A_{1,1}} \\ \hline & & \frac{\partial^{2}\mu}{\partial T_{1,0}^2} & \frac{\partial^{2}\mu}{\partial T_{1,0}\partial A_{1,1}} \\ & & \frac{\partial^{2}\mu}{\partial T_{1,0}\partial A_{1,1}} & \frac{\partial^{2}\mu}{\partial T_{1,1}^2} \\ \end{array}\right]\] |
Reimplemented from MBMesquite::TMetric.
virtual MESQUITE_EXPORT bool MBMesquite::TUntangleBeta::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.
std::string MBMesquite::TUntangleBeta::get_name | ( | ) | const [virtual] |
Implements MBMesquite::TMetric.
Definition at line 42 of file TUntangleBeta.cpp.
{ return "untangle beta"; }
bool MBMesquite::TUntangleBeta::grad | ( | const MsqMatrix< DIM, DIM > & | T, |
double & | result, | ||
MsqMatrix< DIM, DIM > & | first | ||
) | [inline, private] |
Definition at line 58 of file TUntangleBeta.cpp.
References MBMesquite::det(), mGamma, and MBMesquite::transpose_adj().
bool MBMesquite::TUntangleBeta::hess | ( | const MsqMatrix< DIM, DIM > & | T, |
double & | result, | ||
MsqMatrix< DIM, DIM > & | first, | ||
MsqMatrix< DIM, DIM > * | second | ||
) | [inline, private] |
Definition at line 76 of file TUntangleBeta.cpp.
References MBMesquite::det(), mGamma, MBMesquite::pluseq_scaled_2nd_deriv_of_det(), MBMesquite::set_scaled_I(), MBMesquite::set_scaled_outer_product(), and MBMesquite::transpose_adj().
{ double tau = det( T ); if( tau < mGamma ) { const MsqMatrix< DIM, DIM > adjt = transpose_adj( T ); double d = mGamma - tau; result = d * d * d; deriv_wrt_T = -3 * d * d * adjt; set_scaled_outer_product( second_wrt_T, 6 * d, adjt ); pluseq_scaled_2nd_deriv_of_det( second_wrt_T, -3 * d * d, T ); } else { result = 0.0; deriv_wrt_T = MsqMatrix< DIM, DIM >( 0.0 ); set_scaled_I( second_wrt_T, 0.0 ); // zero everything } return true; }
double MBMesquite::TUntangleBeta::mGamma [private] |
Definition at line 50 of file TUntangleBeta.hpp.