MBMesquite::AWUntangleBeta Class Reference

#include <AWUntangleBeta.hpp>

Inheritance diagram for MBMesquite::AWUntangleBeta:

Collaboration diagram for MBMesquite::AWUntangleBeta:

Public Member Functions
MESQUITE_EXPORT	AWUntangleBeta (double gamma=0.5)
virtual MESQUITE_EXPORT	~AWUntangleBeta ()
virtual MESQUITE_EXPORT std::string	get_name () const
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.
Private Member Functions
template<unsigned D>
bool	eval (const MsqMatrix< D, D > &A, const MsqMatrix< D, D > &W, double &result)
template<unsigned D>
bool	grad (const MsqMatrix< D, D > &A, const MsqMatrix< D, D > &W, double &result, MsqMatrix< D, D > &first)
Private Attributes
double	mGamma

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Detailed Description

\( \left\{ |\alpha - \gamma \, \omega| - ( \alpha - \gamma \, \omega ) \right\}^p \)

Definition at line 42 of file AWUntangleBeta.hpp.

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Constructor & Destructor Documentation

MESQUITE_EXPORT MBMesquite::AWUntangleBeta::AWUntangleBeta

(

double

gamma = 0.5

)

[inline]

Definition at line 49 of file AWUntangleBeta.hpp.

: mGamma( gamma ) {}

MBMesquite::AWUntangleBeta::~AWUntangleBeta

(

)

[virtual]

Definition at line 46 of file AWUntangleBeta.cpp.

{}

---

Member Function Documentation

template<unsigned DIM>

bool MBMesquite::AWUntangleBeta::eval	(	const MsqMatrix< DIM, DIM > &	A,
		const MsqMatrix< DIM, DIM > &	W,
		double &	result
	)		[inline, private]

Definition at line 51 of file AWUntangleBeta.cpp.

References MBMesquite::det(), mGamma, and MBMesquite::P.

{
    const double alpha = det( A );
    const double omega = det( W );
    double tmp         = alpha - mGamma * omega;
    tmp                = fabs( tmp ) - tmp;
    result             = tmp;
    for( int i = 1; i < P; ++i )
        result *= tmp;

    return true;
}

virtual MESQUITE_EXPORT bool MBMesquite::AWUntangleBeta::evaluate	(	const MsqMatrix< 2, 2 > &	A,
		const MsqMatrix< 2, 2 > &	W,
		double &	result,
		MsqError &	err
	)		[virtual]

Evaluate \(\mu(A,W)\).

Parameters:

A	2x2 active matrix
W	2x2 target matrix
result	Output: value of function

Returns:

false if function cannot be evaluated for given A and W (e.g. division by zero, etc.), true otherwise.

Reimplemented from MBMesquite::AWMetric.

virtual MESQUITE_EXPORT bool MBMesquite::AWUntangleBeta::evaluate	(	const MsqMatrix< 3, 3 > &	A,
		const MsqMatrix< 3, 3 > &	W,
		double &	result,
		MsqError &	err
	)		[virtual]

Evaluate \(\mu(A,W)\).

Parameters:

A	3x3 active matrix
W	3x3 target matrix
result	Output: value of function

Returns:

false if function cannot be evaluated for given A and W (e.g. division by zero, etc.), true otherwise.

Reimplemented from MBMesquite::AWMetric.

virtual MESQUITE_EXPORT bool MBMesquite::AWUntangleBeta::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.

Parameters:

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. \[\left[\begin{array}{cc} \frac{\partial\mu}{\partial A_{0,0}} & \frac{\partial\mu}{\partial A_{0,1}} \\ \frac{\partial\mu}{\partial A_{1,0}} & \frac{\partial\mu}{\partial A_{1,1}} \\ \end{array}\right]\]

Returns:

false if function cannot be evaluated for given A and W (e.g. division by zero, etc.), true otherwise.

Reimplemented from MBMesquite::AWMetric.

virtual MESQUITE_EXPORT bool MBMesquite::AWUntangleBeta::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.

Parameters:

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. \[\left[\begin{array}{ccc} \frac{\partial\mu}{\partial A_{0,0}} & \frac{\partial\mu}{\partial A_{0,1}} & \frac{\partial\mu}{\partial A_{0,2}} \\ \frac{\partial\mu}{\partial A_{1,0}} & \frac{\partial\mu}{\partial A_{1,1}} & \frac{\partial\mu}{\partial A_{1,2}} \\ \frac{\partial\mu}{\partial A_{2,0}} & \frac{\partial\mu}{\partial A_{2,1}} & \frac{\partial\mu}{\partial A_{2,2}} \end{array}\right]\]

Returns:

false if function cannot be evaluated for given A and W (e.g. division by zero, etc.), true otherwise.

Reimplemented from MBMesquite::AWMetric.

std::string MBMesquite::AWUntangleBeta::get_name

(

)

const [virtual]

Implements MBMesquite::AWMetric.

Definition at line 41 of file AWUntangleBeta.cpp.

{
    return "AWUntangleBeta";
}

template<unsigned DIM>

bool MBMesquite::AWUntangleBeta::grad	(	const MsqMatrix< DIM, DIM > &	A,
		const MsqMatrix< DIM, DIM > &	W,
		double &	result,
		MsqMatrix< DIM, DIM > &	first
	)		[inline, private]

Definition at line 65 of file AWUntangleBeta.cpp.

References MBMesquite::det(), mGamma, MBMesquite::P, and MBMesquite::transpose_adj().

{
    const double alpha = det( A );
    const double omega = det( W );
    double tmp         = 2 * ( mGamma * omega - alpha );
    if( tmp < 0.0 )
    {
        result = 0.0;
        deriv  = MsqMatrix< DIM, DIM >( 0.0 );
        return true;
    }

    double prod = 1.0;
    for( int i = 1; i < P; ++i )
        prod *= tmp;
    result = prod * tmp;

    deriv = -2 * P * prod * transpose_adj( A );
    return true;
}

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Member Data Documentation

double MBMesquite::AWUntangleBeta::mGamma [private]

Definition at line 45 of file AWUntangleBeta.hpp.

Referenced by eval(), and grad().

List of all members.

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The documentation for this class was generated from the following files:

• AWUntangleBeta.hpp
• AWUntangleBeta.cpp