MBMesquite::AWShape2DNB2 Class Reference

#include <AWShape2DNB2.hpp>

Inheritance diagram for MBMesquite::AWShape2DNB2:

Collaboration diagram for MBMesquite::AWShape2DNB2:

Public Member Functions
virtual MESQUITE_EXPORT	~AWShape2DNB2 ()
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_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.

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Detailed Description

\( |A(adj \, W) - [W ( adj\, A )]^t|^2 \)

Definition at line 42 of file AWShape2DNB2.hpp.

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Constructor & Destructor Documentation

MBMesquite::AWShape2DNB2::~AWShape2DNB2

(

)

[virtual]

Definition at line 45 of file AWShape2DNB2.cpp.

{}

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Member Function Documentation

bool MBMesquite::AWShape2DNB2::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.

Definition at line 47 of file AWShape2DNB2.cpp.

References MBMesquite::adj(), MBMesquite::det(), and MBMesquite::sqr_Frobenius().

{
    result = sqr_Frobenius( A * adj( W ) );
    result += sqr_Frobenius( W * adj( A ) );
    result -= 4 * det( A ) * det( W );
    return true;
}

bool MBMesquite::AWShape2DNB2::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.

Definition at line 55 of file AWShape2DNB2.cpp.

References MBMesquite::adj(), MBMesquite::det(), MBMesquite::sqr_Frobenius(), and MBMesquite::transpose().

{
    const double alpha           = det( A );
    const double omega           = det( W );
    const MsqMatrix< 2, 2 > adjA = adj( A );
    result                       = sqr_Frobenius( A * adj( W ) );
    result += sqr_Frobenius( W * adjA );
    result -= 4 * alpha * omega;

    deriv_wrt_A = A * adj( transpose( W ) * W );
    deriv_wrt_A -= omega * transpose( adjA );
    deriv_wrt_A *= 4;
    return true;
}

std::string MBMesquite::AWShape2DNB2::get_name

(

)

const [virtual]

Reimplemented from MBMesquite::AWMetricNonBarrier.

Definition at line 40 of file AWShape2DNB2.cpp.

{
    return "AWShape2DNB2";
}

List of all members.

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

• AWShape2DNB2.hpp
• AWShape2DNB2.cpp