MOAB: Mesh Oriented datABase
(version 5.4.1)
|
A metric for comparing a matrix A with a target matrix W. More...
#include <AWMetric.hpp>
Public Member Functions | |
virtual MESQUITE_EXPORT | ~AWMetric () |
virtual MESQUITE_EXPORT std::string | get_name () const =0 |
virtual MESQUITE_EXPORT bool | evaluate (const MsqMatrix< 2, 2 > &A, const MsqMatrix< 2, 2 > &W, double &result, MsqError &err) |
Evaluate \(\mu(A,W)\). | |
virtual MESQUITE_EXPORT bool | evaluate (const MsqMatrix< 3, 3 > &A, const MsqMatrix< 3, 3 > &W, double &result, MsqError &err) |
Evaluate \(\mu(A,W)\). | |
virtual MESQUITE_EXPORT bool | evaluate_with_grad (const MsqMatrix< 2, 2 > &A, const MsqMatrix< 2, 2 > &W, double &result, MsqMatrix< 2, 2 > &deriv_wrt_A, MsqError &err) |
Gradient of \(\mu(A,W)\) with respect to components of A. | |
virtual MESQUITE_EXPORT bool | evaluate_with_grad (const MsqMatrix< 3, 3 > &A, const MsqMatrix< 3, 3 > &W, double &result, MsqMatrix< 3, 3 > &deriv_wrt_A, MsqError &err) |
Gradient of \(\mu(A,W)\) with respect to components of A. | |
virtual MESQUITE_EXPORT bool | evaluate_with_hess (const MsqMatrix< 2, 2 > &A, const MsqMatrix< 2, 2 > &W, double &result, MsqMatrix< 2, 2 > &deriv_wrt_A, MsqMatrix< 2, 2 > second_wrt_A[3], MsqError &err) |
Hessian of \(\mu(A,W)\) with respect to components of A. | |
virtual MESQUITE_EXPORT bool | evaluate_with_hess (const MsqMatrix< 3, 3 > &A, const MsqMatrix< 3, 3 > &W, double &result, MsqMatrix< 3, 3 > &deriv_wrt_A, MsqMatrix< 3, 3 > second_wrt_A[6], MsqError &err) |
Hessian of \(\mu(A,W)\) with respect to components of A. | |
Static Public Member Functions | |
static bool | invalid_determinant (double d) |
A metric for comparing a matrix A with a target matrix W.
Implement a scalar function \(\mu(A,W)\) where A and W are 2x2 or 3x3 matrices.
Definition at line 49 of file AWMetric.hpp.
MBMesquite::AWMetric::~AWMetric | ( | ) | [virtual] |
Definition at line 206 of file AWMetric.cpp.
{}
bool MBMesquite::AWMetric::evaluate | ( | const MsqMatrix< 2, 2 > & | A, |
const MsqMatrix< 2, 2 > & | W, | ||
double & | result, | ||
MsqError & | err | ||
) | [virtual] |
Evaluate \(\mu(A,W)\).
A | 2x2 active matrix |
W | 2x2 target matrix |
result | Output: value of function |
Reimplemented in MBMesquite::AWMetric3D, HessTestMetricAbs_2, HessTestMetricAbs, MBMesquite::AWMetricBarrier3D, MBMesquite::AWMetricNonBarrier3D, GradTestMetricAbs, MBMesquite::AWUntangleBeta, MBMesquite::AWShapeSizeB1, MBMesquite::AWSizeB1, MBMesquite::AWShape2DB1, MBMesquite::AWShape2DNB1, MBMesquite::AWShape2DNB2, MBMesquite::AWShapeOrientNB1, MBMesquite::AWShapeSizeOrientNB1, MBMesquite::AWSizeNB1, and FauxAbsShapeMetric.
Definition at line 208 of file AWMetric.cpp.
Referenced by MBMesquite::do_finite_difference(), MBMesquite::do_numerical_gradient(), TMetricTest< Metric, DIM >::eval(), and MBMesquite::AWQualityMetric::evaluate_internal().
{ return false; }
bool MBMesquite::AWMetric::evaluate | ( | const MsqMatrix< 3, 3 > & | A, |
const MsqMatrix< 3, 3 > & | W, | ||
double & | result, | ||
MsqError & | err | ||
) | [virtual] |
Evaluate \(\mu(A,W)\).
A | 3x3 active matrix |
W | 3x3 target matrix |
result | Output: value of function |
Reimplemented in MBMesquite::AWMetric2D, HessTestMetricAbs_2, HessTestMetricAbs, GradTestMetricAbs, MBMesquite::AWMetricBarrier2D, MBMesquite::AWMetricNonBarrier2D, MBMesquite::AWShapeOrientNB1, MBMesquite::AWShapeSizeOrientNB1, MBMesquite::AWSizeNB1, MBMesquite::AWSizeB1, MBMesquite::AWUntangleBeta, MBMesquite::AWShapeSizeB1, and FauxAbsShapeMetric.
Definition at line 216 of file AWMetric.cpp.
{ return false; }
bool MBMesquite::AWMetric::evaluate_with_grad | ( | const MsqMatrix< 2, 2 > & | A, |
const MsqMatrix< 2, 2 > & | W, | ||
double & | result, | ||
MsqMatrix< 2, 2 > & | deriv_wrt_A, | ||
MsqError & | err | ||
) | [virtual] |
Gradient of \(\mu(A,W)\) with respect to components of A.
A | 2x2 active matrix |
W | 2x2 target matrix |
result | Output: value of function |
deriv_wrt_A | Output: partial deriviatve of \(\mu\) wrt each term of A, evaluated at passed A. \[\left[\begin{array}{cc} \frac{\partial\mu}{\partial A_{0,0}} & \frac{\partial\mu}{\partial A_{0,1}} \\ \frac{\partial\mu}{\partial A_{1,0}} & \frac{\partial\mu}{\partial A_{1,1}} \\ \end{array}\right]\] |
Reimplemented in HessTestMetricAbs_2, HessTestMetricAbs, MBMesquite::AWUntangleBeta, MBMesquite::AWSizeB1, MBMesquite::AWShape2DNB1, MBMesquite::AWShape2DNB2, MBMesquite::AWShapeOrientNB1, MBMesquite::AWShapeSizeOrientNB1, and MBMesquite::AWSizeNB1.
Definition at line 224 of file AWMetric.cpp.
References MBMesquite::do_numerical_gradient().
Referenced by MBMesquite::do_numerical_hessian(), MBMesquite::AWQualityMetric::evaluate_with_gradient(), TMetricTest< Metric, DIM >::grad(), TMetricTest< Metric, DIM >::num_grad(), AWMetricTest::test_numerical_gradient_2D(), and AWMetricTest::test_numerical_gradient_3D().
{ return do_numerical_gradient( this, A, W, result, wrt_A, err ); }
bool MBMesquite::AWMetric::evaluate_with_grad | ( | const MsqMatrix< 3, 3 > & | A, |
const MsqMatrix< 3, 3 > & | W, | ||
double & | result, | ||
MsqMatrix< 3, 3 > & | deriv_wrt_A, | ||
MsqError & | err | ||
) | [virtual] |
Gradient of \(\mu(A,W)\) with respect to components of A.
A | 3x3 active matrix |
W | 3x3 target matrix |
result | Output: value of function |
deriv_wrt_A | Output: partial deriviatve of \(\mu\) wrt each term of A, evaluated at passed A. \[\left[\begin{array}{ccc} \frac{\partial\mu}{\partial A_{0,0}} & \frac{\partial\mu}{\partial A_{0,1}} & \frac{\partial\mu}{\partial A_{0,2}} \\ \frac{\partial\mu}{\partial A_{1,0}} & \frac{\partial\mu}{\partial A_{1,1}} & \frac{\partial\mu}{\partial A_{1,2}} \\ \frac{\partial\mu}{\partial A_{2,0}} & \frac{\partial\mu}{\partial A_{2,1}} & \frac{\partial\mu}{\partial A_{2,2}} \end{array}\right]\] |
Reimplemented in HessTestMetricAbs_2, HessTestMetricAbs, MBMesquite::AWShapeOrientNB1, MBMesquite::AWShapeSizeOrientNB1, MBMesquite::AWSizeNB1, MBMesquite::AWUntangleBeta, and MBMesquite::AWSizeB1.
Definition at line 233 of file AWMetric.cpp.
References MBMesquite::do_numerical_gradient().
{ return do_numerical_gradient( this, A, W, result, wrt_A, err ); }
bool MBMesquite::AWMetric::evaluate_with_hess | ( | const MsqMatrix< 2, 2 > & | A, |
const MsqMatrix< 2, 2 > & | W, | ||
double & | result, | ||
MsqMatrix< 2, 2 > & | deriv_wrt_A, | ||
MsqMatrix< 2, 2 > | second_wrt_A[3], | ||
MsqError & | err | ||
) | [virtual] |
Hessian of \(\mu(A,W)\) with respect to components of A.
A | 2x2 active matrix |
W | 2x2 target matrix |
result | Output: value of function |
deriv_wrt_A | Output: partial deriviatve of \(\mu\) wrt each term of A, evaluated at passed A. |
second_wrt_A | Output: 4x4 matrix of second partial deriviatve of \(\mu\) wrt each term of A, in row-major order. The symmetric matrix is decomposed into 2x2 blocks and only the upper diagonal blocks, in row-major order, are returned. \[\left[\begin{array}{cc|cc} \frac{\partial^{2}\mu}{\partial A_{0,0}^2} & \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{0,1}} & \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{1,0}} & \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{1,1}} \\ \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{0,1}} & \frac{\partial^{2}\mu}{\partial A_{0,1}^2} & \frac{\partial^{2}\mu}{\partial A_{0,1}\partial A_{1,0}} & \frac{\partial^{2}\mu}{\partial A_{0,1}\partial A_{1,1}} \\ \hline & & \frac{\partial^{2}\mu}{\partial A_{1,0}^2} & \frac{\partial^{2}\mu}{\partial A_{1,0}\partial A_{1,1}} \\ & & \frac{\partial^{2}\mu}{\partial A_{1,0}\partial A_{1,1}} & \frac{\partial^{2}\mu}{\partial A_{1,1}^2} \\ \end{array}\right]\] |
Reimplemented in HessTestMetricAbs_2, MBMesquite::AWShapeSizeOrientNB1, and MBMesquite::AWSizeNB1.
Definition at line 242 of file AWMetric.cpp.
References MBMesquite::do_numerical_hessian().
Referenced by MBMesquite::AWQualityMetric::evaluate_with_Hessian(), MBMesquite::AWQualityMetric::evaluate_with_Hessian_diagonal(), TMetricTest< Metric, DIM >::hess(), TMetricTest< Metric, DIM >::num_hess(), AWMetricTest::test_numerical_hessian_2D(), and AWMetricTest::test_numerical_hessian_3D().
{ return do_numerical_hessian( this, A, W, result, deriv_wrt_A, hess_wrt_A, err ); }
bool MBMesquite::AWMetric::evaluate_with_hess | ( | const MsqMatrix< 3, 3 > & | A, |
const MsqMatrix< 3, 3 > & | W, | ||
double & | result, | ||
MsqMatrix< 3, 3 > & | deriv_wrt_A, | ||
MsqMatrix< 3, 3 > | second_wrt_A[6], | ||
MsqError & | err | ||
) | [virtual] |
Hessian of \(\mu(A,W)\) with respect to components of A.
A | 3x3 active matrix |
W | 3x3 target matrix |
result | Output: value of function |
deriv_wrt_A | Output: partial deriviatve of \(\mu\) wrt each term of A, evaluated at passed A. |
second_wrt_A | Output: 9x9 matrix of second partial deriviatve of \(\mu\) wrt each term of A, 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 A_{0,0}^2} & \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{0,1}} & \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{0,2}} & \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{1,0}} & \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{1,1}} & \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{1,2}} & \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{2,0}} & \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{2,1}} & \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{2,2}} \\ \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{0,1}} & \frac{\partial^{2}\mu}{\partial A_{0,1}^2} & \frac{\partial^{2}\mu}{\partial A_{0,1}\partial A_{0,2}} & \frac{\partial^{2}\mu}{\partial A_{0,1}\partial A_{1,0}} & \frac{\partial^{2}\mu}{\partial A_{0,1}\partial A_{1,1}} & \frac{\partial^{2}\mu}{\partial A_{0,1}\partial A_{1,2}} & \frac{\partial^{2}\mu}{\partial A_{0,1}\partial A_{2,0}} & \frac{\partial^{2}\mu}{\partial A_{0,1}\partial A_{2,1}} & \frac{\partial^{2}\mu}{\partial A_{0,1}\partial A_{2,2}} \\ \frac{\partial^{2}\mu}{\partial A_{0,0}\partial A_{0,2}} & \frac{\partial^{2}\mu}{\partial A_{0,1}\partial A_{0,2}} & \frac{\partial^{2}\mu}{\partial A_{0,2}^2} & \frac{\partial^{2}\mu}{\partial A_{0,2}\partial A_{1,0}} & \frac{\partial^{2}\mu}{\partial A_{0,2}\partial A_{1,1}} & \frac{\partial^{2}\mu}{\partial A_{0,2}\partial A_{1,2}} & \frac{\partial^{2}\mu}{\partial A_{0,2}\partial A_{2,0}} & \frac{\partial^{2}\mu}{\partial A_{0,2}\partial A_{2,1}} & \frac{\partial^{2}\mu}{\partial A_{0,2}\partial A_{2,2}} \\ \hline & & & \frac{\partial^{2}\mu}{\partial A_{1,0}^2} & \frac{\partial^{2}\mu}{\partial A_{1,0}\partial A_{1,1}} & \frac{\partial^{2}\mu}{\partial A_{1,0}\partial A_{1,2}} & \frac{\partial^{2}\mu}{\partial A_{1,0}\partial A_{2,0}} & \frac{\partial^{2}\mu}{\partial A_{1,0}\partial A_{2,1}} & \frac{\partial^{2}\mu}{\partial A_{1,0}\partial A_{2,2}} \\ & & & \frac{\partial^{2}\mu}{\partial A_{1,0}\partial A_{1,1}} & \frac{\partial^{2}\mu}{\partial A_{1,1}^2} & \frac{\partial^{2}\mu}{\partial A_{1,1}\partial A_{1,2}} & \frac{\partial^{2}\mu}{\partial A_{1,1}\partial A_{2,0}} & \frac{\partial^{2}\mu}{\partial A_{1,1}\partial A_{2,1}} & \frac{\partial^{2}\mu}{\partial A_{1,1}\partial A_{2,2}} \\ & & & \frac{\partial^{2}\mu}{\partial A_{1,0}\partial A_{1,2}} & \frac{\partial^{2}\mu}{\partial A_{1,1}\partial A_{1,2}} & \frac{\partial^{2}\mu}{\partial A_{1,2}^2} & \frac{\partial^{2}\mu}{\partial A_{1,2}\partial A_{2,0}} & \frac{\partial^{2}\mu}{\partial A_{1,2}\partial A_{2,1}} & \frac{\partial^{2}\mu}{\partial A_{1,2}\partial A_{2,2}} \\ \hline & & & & & & \frac{\partial^{2}\mu}{\partial A_{2,0}^2} & \frac{\partial^{2}\mu}{\partial A_{2,0}\partial A_{2,1}} & \frac{\partial^{2}\mu}{\partial A_{2,0}\partial A_{2,2}} \\ & & & & & & \frac{\partial^{2}\mu}{\partial A_{2,0}\partial A_{2,1}} & \frac{\partial^{2}\mu}{\partial A_{2,1}^2} & \frac{\partial^{2}\mu}{\partial A_{2,1}\partial A_{2,2}} \\ & & & & & & \frac{\partial^{2}\mu}{\partial A_{2,0}\partial A_{2,2}} & \frac{\partial^{2}\mu}{\partial A_{2,1}\partial A_{2,2}} & \frac{\partial^{2}\mu}{\partial A_{2,2}^2} \\ \end{array}\right]\] |
Reimplemented in HessTestMetricAbs_2, MBMesquite::AWShapeSizeOrientNB1, and MBMesquite::AWSizeNB1.
Definition at line 252 of file AWMetric.cpp.
References MBMesquite::do_numerical_hessian().
{ return do_numerical_hessian( this, A, W, result, deriv_wrt_A, hess_wrt_A, err ); }
virtual MESQUITE_EXPORT std::string MBMesquite::AWMetric::get_name | ( | ) | const [pure virtual] |
Implemented in HessTestMetricAbs_2, HessTestMetricAbs, GradTestMetricAbs, MBMesquite::AWMetricBarrier, MBMesquite::AWMetricNonBarrier, MBMesquite::AWUntangleBeta, MBMesquite::AWShapeSizeB1, MBMesquite::AWSizeB1, MBMesquite::AWShape2DB1, MBMesquite::AWShape2DNB1, MBMesquite::AWShape2DNB2, MBMesquite::AWShapeOrientNB1, MBMesquite::AWShapeSizeOrientNB1, MBMesquite::AWSizeNB1, and FauxAbsShapeMetric.
Referenced by MBMesquite::AWQualityMetric::get_name().
static bool MBMesquite::AWMetric::invalid_determinant | ( | double | d | ) | [inline, static] |
Reimplemented in MBMesquite::AWMetricBarrier, and MBMesquite::AWMetricNonBarrier.
Definition at line 253 of file AWMetric.hpp.
Referenced by MBMesquite::AWShape2DB1::evaluate(), MBMesquite::AWShapeSizeB1::evaluate(), MBMesquite::AWSizeB1::evaluate(), and MBMesquite::AWSizeB1::evaluate_with_grad().
{
return d < 1e-12;
}