Wrapper class for all geometric (ie. Riemannian) CG variants. More...

#include <cg.h>

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

	GeometricCGVariant (TTRetractionI _retraction, TTVectorTransport _vectorTransport)
	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...

TTRetractionI	retraction
	the retraction type I to project from point + tangent vector to a new point on the manifold More...

TTVectorTransport	vectorTransport
	the vector transport from old tangent space to new one 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 geometric (ie. Riemannian) CG 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.

cf. Boumal, Absil. doi: 10.1016/j.laa.2015.02.027 cf. Hager, Zhang. https://www.math.lsu.edu/~hozhang/papers/cgsurvey.pdf for the beta rules

Definition at line 41 of file cg.h.

Constructor & Destructor Documentation

◆ GeometricCGVariant() [1/2]

xerus::GeometricCGVariant::GeometricCGVariant	(	size_t	_numSteps,
		value_t	_convergenceEpsilon,
		bool	_symPosOp,
		TTRetractionI	_retraction,
		TTVectorTransport	_vectorTransport
	)

inline

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

Definition at line 56 of file cg.h.

◆ GeometricCGVariant() [2/2]

xerus::GeometricCGVariant::GeometricCGVariant	(	TTRetractionI	_retraction,
		TTVectorTransport	_vectorTransport
	)

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 65 of file cg.h.

Member Function Documentation

◆ operator()() [1/6]

double xerus::GeometricCGVariant::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 cg.h.

◆ operator()() [2/6]

double xerus::GeometricCGVariant::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 cg.h.

◆ operator()() [3/6]

double xerus::GeometricCGVariant::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 cg.h.

◆ operator()() [4/6]

double xerus::GeometricCGVariant::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 cg.h.

◆ operator()() [5/6]

double xerus::GeometricCGVariant::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 cg.h.

◆ operator()() [6/6]

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

inline

Definition at line 132 of file cg.h.

◆ solve()

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

protected

Definition at line 38 of file cg.cpp.

Member Data Documentation

◆ assumeSymmetricPositiveDefiniteOperator

bool xerus::GeometricCGVariant::assumeSymmetricPositiveDefiniteOperator

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

Definition at line 48 of file cg.h.

◆ convergenceEpsilon

value_t xerus::GeometricCGVariant::convergenceEpsilon

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

Definition at line 47 of file cg.h.

◆ numSteps

size_t xerus::GeometricCGVariant::numSteps

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

Definition at line 46 of file cg.h.

◆ retraction

TTRetractionI xerus::GeometricCGVariant::retraction

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

Definition at line 50 of file cg.h.

◆ vectorTransport

TTVectorTransport xerus::GeometricCGVariant::vectorTransport

the vector transport from old tangent space to new one

Definition at line 51 of file cg.h.

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

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

Public Member Functions

Public Attributes

Protected Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ GeometricCGVariant() [1/2]

◆ GeometricCGVariant() [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

◆ retraction

◆ vectorTransport