suppy.feasibility#

Linear algorithms#

Hyperslab algorithms \((lb \leq Ax \leq ub)\)#

SequentialAMSHyperslab(A, lb, ub[, ...])

SequentialAMSHyperslab class for sequentially applying the AMS algorithm on hyperslabs.

SimultaneousAMSHyperslab(A, lb, ub[, ...])

SimultaneousAMSHyperslab class for simultaneous application of the AMS algorithm on hyperslabs.

StringAveragedAMSHyperslab(A, lb, ub, strings)

StringAveragedAMSHyperslab is a string averaged implementation of the AMS algorithm.

BlockIterativeAMSHyperslab(A, lb, ub, weights)

Block Iterative AMS Algorithm for hyperslabs.

SequentialWeightedAMSHyperslab(A, lb, ub[, ...])

SARTHyperslab(A, lb, ub[, ...])

SART Hyperslab class for simultaneous application of the SART algorithm on hyperslabs.

ExtrapolatedLandweberHyperslab(A, lb, ub[, ...])

Extrapolated Landweber algorithm for solving linear inequalities of the form lb <= Ax <= ub.

BlockIterativeExtrapolatedLandweberHyperslab(A, ...)

Block-iterative variant of the Extrapolated Landweber algorithm for hyperslabs, solving lb <= Ax <= ub block by block.

AdaptiveStepLandweberHyperslab(A, lb, ub[, ...])

Adaptive step-size Landweber algorithm for solving linear inequalities of the form lb <= Ax <= ub.

Hyperplane algorithms \(( Ax \leq b)\)#

KaczmarzMethod(A, b[, ...])

Kaczmarz method for sequentially solving linear equality constraints.

SimultaneousKaczmarzMethod(A, b[, ...])

SimultaneousKaczmarzMethod is an implementation of the Kaczmarz algorithm that performs simultaneous projections and proximity calculations.

StringAveragedKaczmarz(A, b, strings[, ...])

StringAveragedKaczmarz is an implementation of the HyperplaneAlgorithm that performs string averaged projections.

BlockIterativeKaczmarz(A, b, weights[, ...])

Block iterative Kaczmarz algorithm for solving linear equality constraints in a block-wise manner.

ExtrapolatedLandweberHyperplane(A, b[, ...])

Extrapolated Landweber algorithm for solving linear equalities of the form Ax = b.

AdaptiveStepLandweberHyperplane(A, b[, ...])

Landweber algorithm with adaptive step size for solving linear equalities of the form Ax = b.

DROPHyperplane(A, b[, ...])

Diagonally Relaxed Orthogonal Projections (DROP) algorithm for solving linear equalities of the form Ax = b.

Halfspace algorithms \(( Ax = b)\)#

SequentialAMSHalfspace(A, b[, ...])

SequentialAMS class for sequentially applying the AMS algorithm.

SimultaneousAMSHalfspace(A, b[, ...])

SimultaneousAMS is an implementation of the AMS (Alternating Minimization Scheme) algorithm that performs simultaneous projections and proximity calculations.

StringAveragedAMSHalfspace(A, b, strings[, ...])

StringAveragedAMS is an implementation of the HalfspaceAlgorithm that performs string averaged projections.

BlockIterativeAMSHalfspace(A, b, weights[, ...])

Block Iterative AMS Algorithm.

SequentialWeightedAMSHalfspace(A, b[, ...])

ExtrapolatedLandweberHalfspace(A, b[, ...])

Extrapolated Landweber method for solving linear inequalities of the form Ax <= b.

AdaptiveStepLandweberHalfspace(A, b[, ...])

Adaptive step-size Landweber algorithm for solving linear inequalities of the form Ax <= b.

ARM algorithms#

SequentialARM(A, lb, ub[, ...])

SequentialARM is a class that implements a sequential algorithm for Adaptive Relaxation Method (ARM).

SimultaneousARM(A, lb, ub[, ...])

SimultaneousARM is a class that implements an ARM (Adaptive Relaxation Method) algorithm for solving feasibility problems.

StringAveragedARM(A, lb, ub, strings[, ...])

String Averaged ARM Algorithm.

Split feasibility#

Split feasibility problems have the goal of finding \(x \in C\) such that \(Ax \in Q\). \(C\) is a convex subset of the input space \(\mathscr{H}_1\) and \(Q\) a convex subset in the target space \(\mathscr{H}_2\) with the two spaces connected by the linear operator \(A:\mathscr{H}_1 \rightarrow \mathscr{H}_2\). The base class for split feasibility problems is SplitFeasibility.

Split algorithms#

CQAlgorithm(A, C_projection, Q_projection[, ...])

Implementation for the CQ algorithm to solve split feasibility problems.

Underlying base class#

SplitFeasibility(A[, ...])

Abstract base class used to represent split feasibility problems.