MBMesquite::AWShape2DNB1 Class Reference

#include <AWShape2DNB1.hpp>

Inheritance diagram for MBMesquite::AWShape2DNB1:

Collaboration diagram for MBMesquite::AWShape2DNB1:

Public Member Functions
virtual MESQUITE_EXPORT	~AWShape2DNB1 ()
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

\( |\omega A^t A - \alpha W^t W|^2 \)

Definition at line 42 of file AWShape2DNB1.hpp.

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Constructor & Destructor Documentation

MBMesquite::AWShape2DNB1::~AWShape2DNB1

(

)

[virtual]

Definition at line 45 of file AWShape2DNB1.cpp.

{}

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Member Function Documentation

bool MBMesquite::AWShape2DNB1::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 AWShape2DNB1.cpp.

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

{
    MsqMatrix< 2, 2 > tmp = det( W ) * transpose( A ) * A;
    tmp -= det( A ) * W * transpose( W );
    result = sqr_Frobenius( tmp );
    return true;
}

bool MBMesquite::AWShape2DNB1::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 AWShape2DNB1.cpp.

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

{
    const double alpha          = det( A );
    const double omega          = det( W );
    const MsqMatrix< 2, 2 > AtA = transpose( A ) * A;
    const MsqMatrix< 2, 2 > WtW = transpose( W ) * W;
    const MsqMatrix< 2, 2 > AWt = A * transpose( W );
    const double alphaWtW       = alpha * sqr_Frobenius( WtW );
    const double omegaAtA       = omega * sqr_Frobenius( AtA );
    const double omegaAWt       = omega * sqr_Frobenius( AWt );
    result                      = omega * omegaAtA;
    result += alpha * alphaWtW;
    result -= 2 * alpha * omegaAWt;

    deriv_wrt_A = 4 * omega * omega * A * transpose( A ) * A;
    deriv_wrt_A -= 4 * alpha * omega * AWt * W;
    deriv_wrt_A += 2 * ( alphaWtW - omegaAWt ) * transpose_adj( A );
    return true;
}

std::string MBMesquite::AWShape2DNB1::get_name

(

)

const [virtual]

Reimplemented from MBMesquite::AWMetricNonBarrier.

Definition at line 40 of file AWShape2DNB1.cpp.

{
    return "AWShape2DNB1";
}

List of all members.

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

• AWShape2DNB1.hpp
• AWShape2DNB1.cpp