Wrapper class for all steepest descent variants. More...

#include <steepestDescent.h>

Collaboration diagram for xerus::SteepestDescentVariant:

[legend]

Public Member Functions
	SteepestDescentVariant (size_t _numSteps, value_t _convergenceEpsilon, bool _symPosOp, TTRetractionII _retraction)
	fully defining constructor. alternatively SteepestDescentVariant can be created by copying a predefined variant and modifying it More...

	SteepestDescentVariant (TTRetractionII _retraction)
	definition using only the retraction. In the following an operator() including either convergenceEpsilon or numSteps must be called or the algorithm will never terminate More...

double	operator() (const TTOperator &_A, TTTensor &_x, const TTTensor &_b, value_t _convergenceEpsilon, PerformanceData &_perfData=NoPerfData) const

double	operator() (const TTOperator &_A, TTTensor &_x, const TTTensor &_b, size_t _numSteps, PerformanceData &_perfData=NoPerfData) const

double	operator() (const TTOperator &_A, TTTensor &_x, const TTTensor &_b, PerformanceData &_perfData=NoPerfData) const

double	operator() (TTTensor &_x, const TTTensor &_b, value_t _convergenceEpsilon, PerformanceData &_perfData=NoPerfData) const

double	operator() (TTTensor &_x, const TTTensor &_b, size_t _numSteps, PerformanceData &_perfData=NoPerfData) const

double	operator() (TTTensor &_x, const TTTensor &_b, PerformanceData &_perfData=NoPerfData) const

Public Attributes
bool	assumeSymmetricPositiveDefiniteOperator
	calculates the gradient as b-Ax instead of A^T(b-Ax) More...

value_t	convergenceEpsilon
	default value for the change in the residual at which the algorithm assumes it is converged More...

size_t	numSteps
	maximum number of steps to perform. set to 0 for infinite More...

TTOperator *	preconditioner

TTRetractionII	retraction
	the retraction to project from point + tangent vector to a new point on the manifold More...

Protected Member Functions
double	solve (const TTOperator *_Ap, TTTensor &_x, const TTTensor &_b, size_t _numSteps, value_t _convergenceEpsilon, PerformanceData &_perfData=NoPerfData) const

Detailed Description

Wrapper class for all steepest descent variants.

Note: only implemented for TTTensors at the moment.

By creating a new object of this class and modifying the member variables, the behaviour of the solver can be modified.

Definition at line 45 of file steepestDescent.h.

Constructor & Destructor Documentation

◆ SteepestDescentVariant() [1/2]

xerus::SteepestDescentVariant::SteepestDescentVariant	(	size_t	_numSteps,
		value_t	_convergenceEpsilon,
		bool	_symPosOp,
		TTRetractionII	_retraction
	)

inline

fully defining constructor. alternatively SteepestDescentVariant can be created by copying a predefined variant and modifying it

Definition at line 60 of file steepestDescent.h.

◆ SteepestDescentVariant() [2/2]

xerus::SteepestDescentVariant::SteepestDescentVariant ( TTRetractionII _retraction )

inline

definition using only the retraction. In the following an operator() including either convergenceEpsilon or numSteps must be called or the algorithm will never terminate

Definition at line 66 of file steepestDescent.h.

Member Function Documentation

◆ operator()() [1/6]

double xerus::SteepestDescentVariant::operator()	(	const TTOperator &	_A,
		TTTensor &	_x,
		const TTTensor &	_b,
		value_t	_convergenceEpsilon,
		PerformanceData &	_perfData = `NoPerfData`
	)		const

inline

call to solve \( A\cdot x = b\) for \( x \) (in a least-squares sense)

Parameters

	_A	operator to solve for
[in,out]	_x	in: initial guess, out: solution as found by the algorithm
	_b	right-hand side of the equation to be solved
	_convergenceEpsilon	minimum change in residual / energy under which the algorithm terminates
	_perfData	vector of performance data (residuals after every microiteration)

Returns: the residual \(|Ax-b|\) of the final _x

Definition at line 79 of file steepestDescent.h.

◆ operator()() [2/6]

double xerus::SteepestDescentVariant::operator()	(	const TTOperator &	_A,
		TTTensor &	_x,
		const TTTensor &	_b,
		size_t	_numSteps,
		PerformanceData &	_perfData = `NoPerfData`
	)		const

inline

call to solve \( A\cdot x = b\) for \( x \) (in a least-squares sense)

Parameters

	_A	operator to solve for
[in,out]	_x	in: initial guess, out: solution as found by the algorithm
	_b	right-hand side of the equation to be solved
	_numHalfSweeps	maximum number of half-sweeps to perform
	_perfData	vector of performance data (residuals after every microiteration)

Returns: the residual \(|Ax-b|\) of the final _x

Definition at line 92 of file steepestDescent.h.

◆ operator()() [3/6]

double xerus::SteepestDescentVariant::operator()	(	const TTOperator &	_A,
		TTTensor &	_x,
		const TTTensor &	_b,
		PerformanceData &	_perfData = `NoPerfData`
	)		const

inline

call to solve \( A\cdot x = b\) for \( x \) (in a least-squares sense)

Parameters

	_A	operator to solve for
[in,out]	_x	in: initial guess, out: solution as found by the algorithm
	_b	right-hand side of the equation to be solved
	_perfData	vector of performance data (residuals after every microiteration)

Returns: the residual \(|Ax-b|\) of the final _x

Definition at line 104 of file steepestDescent.h.

◆ operator()() [4/6]

double xerus::SteepestDescentVariant::operator()	(	TTTensor &	_x,
		const TTTensor &	_b,
		value_t	_convergenceEpsilon,
		PerformanceData &	_perfData = `NoPerfData`
	)		const

inline

call to minimze \( \|x - b\|^2 \) for \( x \)

Parameters

[in,out]	_x	in: initial guess, out: solution as found by the algorithm
	_b	right-hand side of the equation to be solved
	_convergenceEpsilon	minimum change in residual / energy under which the algorithm terminates
	_perfData	vector of performance data (residuals after every microiteration)

Returns: the residual \(|x-b|\) of the final _x

Definition at line 116 of file steepestDescent.h.

◆ operator()() [5/6]

double xerus::SteepestDescentVariant::operator()	(	TTTensor &	_x,
		const TTTensor &	_b,
		size_t	_numSteps,
		PerformanceData &	_perfData = `NoPerfData`
	)		const

inline

call to minimze \( \|x - b\|^2 \) for \( x \)

Parameters

[in,out]	_x	in: initial guess, out: solution as found by the algorithm
	_b	right-hand side of the equation to be solved
	_numHalfSweeps	maximum number of half-sweeps to perform
	_perfData	vector of performance data (residuals after every microiteration)

Returns: the residual \(|x-b|\) of the final _x

Definition at line 128 of file steepestDescent.h.

◆ operator()() [6/6]

double xerus::SteepestDescentVariant::operator()	(	TTTensor &	_x,
		const TTTensor &	_b,
		PerformanceData &	_perfData = `NoPerfData`
	)		const

inline

Definition at line 132 of file steepestDescent.h.

◆ solve()

value_t xerus::SteepestDescentVariant::solve	(	const TTOperator *	_Ap,
		TTTensor &	_x,
		const TTTensor &	_b,
		size_t	_numSteps,
		value_t	_convergenceEpsilon,
		PerformanceData &	_perfData = `NoPerfData`
	)		const

protected

Definition at line 83 of file steepestDescent.cpp.

Member Data Documentation

◆ assumeSymmetricPositiveDefiniteOperator

bool xerus::SteepestDescentVariant::assumeSymmetricPositiveDefiniteOperator

calculates the gradient as b-Ax instead of A^T(b-Ax)

Definition at line 52 of file steepestDescent.h.

◆ convergenceEpsilon

value_t xerus::SteepestDescentVariant::convergenceEpsilon

default value for the change in the residual at which the algorithm assumes it is converged

Definition at line 51 of file steepestDescent.h.

◆ numSteps

size_t xerus::SteepestDescentVariant::numSteps

maximum number of steps to perform. set to 0 for infinite

Definition at line 50 of file steepestDescent.h.

◆ preconditioner

TTOperator* xerus::SteepestDescentVariant::preconditioner

Definition at line 53 of file steepestDescent.h.

◆ retraction

TTRetractionII xerus::SteepestDescentVariant::retraction

the retraction to project from point + tangent vector to a new point on the manifold

Definition at line 55 of file steepestDescent.h.

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

/home/gitlab-runner/builds/9071116c/0/xerus/xerus/include/xerus/algorithms/steepestDescent.h
/home/gitlab-runner/builds/9071116c/0/xerus/xerus/src/xerus/algorithms/steepestDescent.cpp

Public Member Functions

Public Attributes

Protected Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ SteepestDescentVariant() [1/2]

◆ SteepestDescentVariant() [2/2]

Member Function Documentation

◆ operator()() [1/6]

◆ operator()() [2/6]

◆ operator()() [3/6]

◆ operator()() [4/6]

◆ operator()() [5/6]

◆ operator()() [6/6]

◆ solve()

Member Data Documentation

◆ assumeSymmetricPositiveDefiniteOperator

◆ convergenceEpsilon

◆ numSteps

◆ preconditioner

◆ retraction