MOAB: Mesh Oriented datABase
(version 5.4.1)
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#include <TShapeSize2DNB2.hpp>
Public Member Functions | |
virtual MESQUITE_EXPORT | ~TShapeSize2DNB2 () |
virtual MESQUITE_EXPORT std::string | get_name () const |
virtual MESQUITE_EXPORT bool | evaluate (const MsqMatrix< 2, 2 > &T, double &result, MsqError &err) |
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. |
3.2.4: \( \frac{|T|^2+2}{2\psi(T)} - 1 \)
Definition at line 42 of file TShapeSize2DNB2.hpp.
MBMesquite::TShapeSize2DNB2::~TShapeSize2DNB2 | ( | ) | [virtual] |
Definition at line 45 of file TShapeSize2DNB2.cpp.
{}
bool MBMesquite::TShapeSize2DNB2::evaluate | ( | const MsqMatrix< 2, 2 > & | T, |
double & | result, | ||
MsqError & | err | ||
) | [virtual] |
\( \mu(T) = \frac{|T|^2+2}{2\psi(T)} - 1 \) \( \psi(T) = \sqrt{|T|^2 + 2 \tau}\) \( \tau = det(T) \)
Reimplemented from MBMesquite::TMetric.
Definition at line 51 of file TShapeSize2DNB2.cpp.
References MBMesquite::det(), MBMesquite::divide(), and MBMesquite::sqr_Frobenius().
{ double frob_sqr = sqr_Frobenius( T ); double psi = sqrt( frob_sqr + 2.0 * det( T ) ); double a = 1e-12; while( !MBMesquite::divide( frob_sqr + 2, 2 * psi, result ) ) { MsqMatrix< 2, 2 > Tdelta( T ); Tdelta( 0, 0 ) += a; Tdelta( 1, 1 ) += a; a *= 2.0; frob_sqr = sqr_Frobenius( Tdelta ); psi = sqrt( frob_sqr + 2.0 * det( Tdelta ) ); if( psi > 1e-50 ) result = ( frob_sqr + 2 ) / 2 * psi; } result -= 1.0; return true; }
bool MBMesquite::TShapeSize2DNB2::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 72 of file TShapeSize2DNB2.cpp.
References MBMesquite::det(), MBMesquite::divide(), MBMesquite::sqr_Frobenius(), and MBMesquite::transpose_adj().
{ double frob_sqr = sqr_Frobenius( T ); double psi = sqrt( frob_sqr + 2.0 * det( T ) ); double a = 1e-12; while( !MBMesquite::divide( frob_sqr + 2, 2 * psi, result ) ) { MsqMatrix< 2, 2 > Tdelta( T ); Tdelta( 0, 0 ) += a; Tdelta( 1, 1 ) += a; a *= 2.0; frob_sqr = sqr_Frobenius( Tdelta ); psi = sqrt( frob_sqr + 2.0 * det( Tdelta ) ); if( psi > 1e-50 ) result = ( frob_sqr + 2 ) / 2 * psi; } // MsqMatrix<2,2> d_psi = 1.0/psi * (T + transpose_adj(T)); // deriv_wrt_T = (1.0/psi) * (T - result * d_psi); if( psi > 1e-50 ) { const double f = result / ( psi * psi ); deriv_wrt_T = transpose_adj( T ); deriv_wrt_T *= -f; deriv_wrt_T += ( 1.0 / psi - f ) * T; } result -= 1.0; return true; }
bool MBMesquite::TShapeSize2DNB2::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 107 of file TShapeSize2DNB2.cpp.
References MBMesquite::det(), MBMesquite::divide(), MBMesquite::pluseq_scaled_I(), MBMesquite::pluseq_scaled_outer_product(), MBMesquite::pluseq_scaled_sum_outer_product(), MBMesquite::set_scaled_2nd_deriv_wrt_psi(), MBMesquite::sqr_Frobenius(), T, and MBMesquite::transpose_adj().
{ double frob_sqr = sqr_Frobenius( T ); double psi = sqrt( frob_sqr + 2.0 * det( T ) ); double a = 1e-12; while( !MBMesquite::divide( frob_sqr + 2, 2 * psi, result ) ) { MsqMatrix< 2, 2 > Tdelta( T ); Tdelta( 0, 0 ) += a; Tdelta( 1, 1 ) += a; a *= 2.0; frob_sqr = sqr_Frobenius( Tdelta ); psi = sqrt( frob_sqr + 2.0 * det( Tdelta ) ); if( psi > 1e-50 ) result = ( frob_sqr + 2 ) / 2 * psi; } const double inv_psi = 1.0 / psi; MsqMatrix< 2, 2 > d_psi = T + transpose_adj( T ); d_psi *= inv_psi; deriv_wrt_T = d_psi; deriv_wrt_T *= -result; deriv_wrt_T += T; deriv_wrt_T *= inv_psi; set_scaled_2nd_deriv_wrt_psi( second, -result * inv_psi, psi, T ); pluseq_scaled_outer_product( second, 2 * result * inv_psi * inv_psi, d_psi ); pluseq_scaled_sum_outer_product( second, -inv_psi * inv_psi, d_psi, T ); pluseq_scaled_I( second, inv_psi ); result -= 1.0; return true; }
std::string MBMesquite::TShapeSize2DNB2::get_name | ( | ) | const [virtual] |
Implements MBMesquite::TMetric.
Definition at line 40 of file TShapeSize2DNB2.cpp.
{ return "TShapeSize2DNB2"; }