NOX::LineSearch::Utils::Slope Class Reference

Common line search utilites for computing the slope of a function. More...

#include <NOX_LineSearch_Utils_Slope.H>

Public Member Functions
	Slope ()
	Constructor (requires call to reset() to initialize object).
	Slope (const Teuchos::RCP< NOX::GlobalData > &gd)
	Constructor.
virtual	~Slope ()
	Destructor.
void	reset (const Teuchos::RCP< NOX::GlobalData > &gd)
	Reset method.
double	computeSlope (const NOX::Abstract::Vector &dir, const NOX::Abstract::Group &grp)
	Compute the inner product of the given direction and the gradient associated with the given group.
double	computeSlopeWithOutJac (const NOX::Abstract::Vector &dir, const NOX::Abstract::Group &grp)
	This is a variant of the computeSlope() method above optimized to work with out having to compute an explicit Jacobian.

Detailed Description

Common line search utilites for computing the slope of a function.

This class provides routines for computing the slope of a give function. There are two methods, one that uses a Jacobian and the other that estimates the action of the Jacobian by directional derivatives.

Member Function Documentation

computeSlope()

double NOX::LineSearch::Utils::Slope::computeSlope	(	const NOX::Abstract::Vector &	dir,
		const NOX::Abstract::Group &	grp
	)

Compute the inner product of the given direction and the gradient associated with the given group.

Calculates and returns

Here represents the input parameter dir and is the gradient associated with the given group.

References NOX::Abstract::Group::applyJacobian(), NOX::Abstract::Vector::clone(), NOX::Abstract::Group::getF(), NOX::Abstract::Group::getGradient(), NOX::Abstract::Vector::innerProduct(), NOX::Abstract::Group::isF(), NOX::Abstract::Group::isGradient(), NOX::Abstract::Group::Ok, and NOX::ShapeCopy.

computeSlopeWithOutJac()

double NOX::LineSearch::Utils::Slope::computeSlopeWithOutJac	(	const NOX::Abstract::Vector &	dir,
		const NOX::Abstract::Group &	grp
	)

This is a variant of the computeSlope() method above optimized to work with out having to compute an explicit Jacobian.

Calculates and returns
\f[
\zeta = d^T \nabla f(x) = d^TJ^TF
\f]

Here \f$d\f$ represents the input parameter \c dir \f$\nabla
f(x)\f$ is the gradient associated with the given group (for nonlinear solves this equates to \f$ J^TF \f$ where \f$ J \f$ is the Jacobian and \f$ F \f$ is the original nonlinear function).

We can rewrite this equation as:

\f[ d^TJ^TF = F^TJd \f]

which allows us to use directional derivatives to estimate \f$ J^TF \f$:

\f[ F^TJd = F^T \frac{F(x + \eta d) - F(x)}{\eta} \f]

This may allow for faster computations of the slope if the Jacobian is expensive to evaluate.

where is a scalar perturbation calculated by:

is a constant fixed at 1.0e-6.

References NOX::Abstract::Group::clone(), NOX::Abstract::Vector::clone(), NOX::Abstract::Group::getF(), NOX::Abstract::Group::getX(), NOX::Abstract::Group::isF(), NOX::Abstract::Vector::norm(), and NOX::ShapeCopy.

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

• NOX_LineSearch_Utils_Slope.H
• NOX_LineSearch_Utils_Slope.C