MOAB: Mesh Oriented datABase
(version 5.4.1)
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#include <TShapeSizeNB3.hpp>
Public Member Functions | |
TShapeSizeNB3 (double gamma=2.0) | |
virtual MESQUITE_EXPORT | ~TShapeSizeNB3 () |
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 Attributes | |
double | mGamma |
2D: \( |T - adj T^t|^2 + \gamma (\tau - 1)^2 = 2 |T|^2 - 4 \tau + \gamma (\tau - 1)^2 \) 3D: \( 2 |T|^3 - 3 \sqrt{3} \tau + \gamma (\tau - 1)^2 \)
Definition at line 44 of file TShapeSizeNB3.hpp.
MBMesquite::TShapeSizeNB3::TShapeSizeNB3 | ( | double | gamma = 2.0 | ) | [inline] |
Definition at line 47 of file TShapeSizeNB3.hpp.
: mGamma( gamma ) {}
MBMesquite::TShapeSizeNB3::~TShapeSizeNB3 | ( | ) | [virtual] |
Definition at line 45 of file TShapeSizeNB3.cpp.
{}
bool MBMesquite::TShapeSizeNB3::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.
Definition at line 47 of file TShapeSizeNB3.cpp.
References MBMesquite::det(), mGamma, and MBMesquite::sqr_Frobenius().
{ const double nT = sqr_Frobenius( T ); const double tau = det( T ); const double tau1 = tau - 1; result = 2 * nT - 4 * tau + mGamma * tau1 * tau1; return true; }
bool MBMesquite::TShapeSizeNB3::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 97 of file TShapeSizeNB3.cpp.
References MBMesquite::det(), MBMesquite::Frobenius(), mGamma, and MBMesquite::MSQ_SQRT_THREE.
bool MBMesquite::TShapeSizeNB3::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.
Definition at line 56 of file TShapeSizeNB3.cpp.
References MBMesquite::det(), mGamma, MBMesquite::sqr_Frobenius(), T, and MBMesquite::transpose_adj().
{ const double nT = sqr_Frobenius( T ); const double tau = det( T ); const double tau1 = tau - 1; result = 2 * nT - 4 * tau + mGamma * tau1 * tau1; deriv_wrt_T = T; deriv_wrt_T *= 4; deriv_wrt_T += ( 2 * mGamma * tau1 - 4 ) * transpose_adj( T ); return true; }
bool MBMesquite::TShapeSizeNB3::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 106 of file TShapeSizeNB3.cpp.
References MBMesquite::det(), MBMesquite::Frobenius(), mGamma, MBMesquite::MSQ_SQRT_THREE, T, and MBMesquite::transpose_adj().
{ const double nT = Frobenius( T ); const double tau = det( T ); const double tau1 = tau - 1; result = nT * nT * nT - 3 * MSQ_SQRT_THREE * tau + mGamma * tau1 * tau1; wrt_T = T; wrt_T *= 3 * nT; wrt_T -= ( 3 * MSQ_SQRT_THREE - 2 * mGamma * tau1 ) * transpose_adj( T ); return true; }
bool MBMesquite::TShapeSizeNB3::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.
Definition at line 73 of file TShapeSizeNB3.cpp.
References MBMesquite::det(), mGamma, MBMesquite::pluseq_scaled_2nd_deriv_of_det(), MBMesquite::pluseq_scaled_I(), MBMesquite::set_scaled_outer_product(), MBMesquite::sqr_Frobenius(), T, and MBMesquite::transpose_adj().
{ const double nT = sqr_Frobenius( T ); const double tau = det( T ); const double tau1 = tau - 1; result = 2 * nT - 4 * tau + mGamma * tau1 * tau1; const double f = 2 * mGamma * tau1 - 4; const MsqMatrix< 2, 2 > adjt = transpose_adj( T ); deriv_wrt_T = T; deriv_wrt_T *= 4; deriv_wrt_T += f * adjt; set_scaled_outer_product( second, 2 * mGamma, adjt ); pluseq_scaled_I( second, 4 ); pluseq_scaled_2nd_deriv_of_det( second, f ); return true; }
bool MBMesquite::TShapeSizeNB3::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 123 of file TShapeSizeNB3.cpp.
References MBMesquite::det(), MBMesquite::Frobenius(), mGamma, MBMesquite::MSQ_SQRT_THREE, MBMesquite::pluseq_scaled_2nd_deriv_of_det(), MBMesquite::pluseq_scaled_I(), MBMesquite::pluseq_scaled_outer_product(), MBMesquite::set_scaled_outer_product(), T, and MBMesquite::transpose_adj().
{ const double nT = Frobenius( T ); const double tau = det( T ); const double tau1 = tau - 1; result = nT * nT * nT - 3 * MSQ_SQRT_THREE * tau + mGamma * tau1 * tau1; const double f = ( 3 * MSQ_SQRT_THREE - 2 * mGamma * tau1 ); const MsqMatrix< 3, 3 > adjt = transpose_adj( T ); wrt_T = T; wrt_T *= 3 * nT; wrt_T -= f * adjt; set_scaled_outer_product( second, 2 * mGamma, adjt ); pluseq_scaled_2nd_deriv_of_det( second, -f, T ); pluseq_scaled_I( second, 3 * nT ); // Could perturb T a bit if the norm is zero, but that would just // result in the coefficent of the outer product being practically // zero, so just skip the outer product in that case. // Anyway nT approaches zero as T does, so the limit of this term // as nT approaches zero is zero. if( nT > 1e-100 ) // NOTE: nT is always positive pluseq_scaled_outer_product( second, 3 / nT, T ); return true; }
std::string MBMesquite::TShapeSizeNB3::get_name | ( | ) | const [virtual] |
Reimplemented from MBMesquite::TMetricNonBarrier.
Definition at line 40 of file TShapeSizeNB3.cpp.
{ return "TShapeSizeNB3"; }
double MBMesquite::TShapeSizeNB3::mGamma [private] |
Definition at line 80 of file TShapeSizeNB3.hpp.
Referenced by evaluate(), evaluate_with_grad(), and evaluate_with_hess().