Barycenters

Implementations for optimal transport barycenters are still particularly experimental. They work in principle but they do not yet provide mathematically sound sub-optimality control for truncation. Also the setup of such problems is considerably more complex.

class MultiScaleOT.TMultiScaleSetupBarycenterContainer
__init__(*args, **kwargs)

Overloaded function.

  1. __init__(self: MultiScaleOT.TMultiScaleSetupBarycenterContainer) -> None

  2. __init__(self: MultiScaleOT.TMultiScaleSetupBarycenterContainer, nMarginals: int) -> None

getAlpha(self: MultiScaleOT.TMultiScaleSetupBarycenterContainer, nMarginal: int, nLayer: int) → numpy.ndarray[numpy.float64]
getBeta(self: MultiScaleOT.TMultiScaleSetupBarycenterContainer, nMarginal: int, nLayer: int) → numpy.ndarray[numpy.float64]
setAlpha(self: MultiScaleOT.TMultiScaleSetupBarycenterContainer, alpha: numpy.ndarray[numpy.float64], nMarginal: int, nLayer: int) → None

Set dual variable alpha of marginal nMarginal at layer nLayer to alpha and then propagates values to all coarser layers by maximization over child nodes.

Parameters:

  • alpha – 1d double array with new values for dual variable. Size needs to equal number of cells in that layer.

  • nMarginal – id of marginal on which dual variable is to be set.

  • nLayer – id of layer on which dual variable is to be set.

setBeta(self: MultiScaleOT.TMultiScaleSetupBarycenterContainer, beta: numpy.ndarray[numpy.float64], nMarginal: int, nLayer: int) → None

Set dual variable beta of marginal nMarginal at layer nLayer to beta and then propagates values to all coarser layers by maximization over child nodes.

Parameters:

  • beta – 1d double array with new values for dual variable. Size needs to equal number of cells in that layer.

  • nMarginal – id of marginal on which dual variable is to be set.

  • nLayer – id of layer on which dual variable is to be set.

setCenterMarginal(self: MultiScaleOT.TMultiScaleSetupBarycenterContainer, arg0: MultiScaleOT.TMultiScaleSetup) → None
setCostFunctionProvider(self: MultiScaleOT.TMultiScaleSetupBarycenterContainer, nMarginal: int, costFunctionProvider: THierarchicalCostFunctionProvider) → None

Set nMarginal-th cost function in barycenter problem to costFunctionProvider.

setMarginal(self: MultiScaleOT.TMultiScaleSetupBarycenterContainer, nMarginal: int, MultiScaleSetup: MultiScaleOT.TMultiScaleSetup, weight: float) → None

Set nMarginal-th marginal in barycenter problem to MultiScaleSetup with weight-coefficient weight.

setupDuals(self: MultiScaleOT.TMultiScaleSetupBarycenterContainer) → None
class MultiScaleOT.TSinkhornSolverBarycenter

Solver for optimal transport barycenter.

__init__(self: MultiScaleOT.TSinkhornSolverBarycenter, epsScalingHandler: MultiScaleOT.TEpsScalingHandler, layerCoarsest: int, layerFinest: int, errorGoal: float, MultiScaleSetupBarycenterContainer: MultiScaleOT.TMultiScaleSetupBarycenterContainer, cfg: MultiScaleOT.TSinkhornSolverParameters = <MultiScaleOT.TSinkhornSolverParameters object at 0x7aa40bf8aff0>) → None
findKernelLine(self: MultiScaleOT.TSinkhornSolverBarycenter, nMarginal: int, layerFinest: int, a: int, mode: int, slack: float) → tuple
Parameters:

  • nMarginal – index of reference marginal

  • layerFinest – index of desired layer

  • a – index of kernel line to be determined

  • mode – 0: rows, 1: columns

  • slack – threshold below maximal value up to which entries are included

getCostFunctionProvider(self: MultiScaleOT.TSinkhornSolverBarycenter, arg0: int) → MultiScaleOT.THierarchicalCostFunctionProvider
getKernel(self: MultiScaleOT.TSinkhornSolverBarycenter, arg0: int) → MultiScaleOT.TKernelMatrix
getKernelCSRData(self: MultiScaleOT.TSinkhornSolverBarycenter, arg0: int) → MultiScaleOT.TSparseCSRContainer
getKernelCSRDataTuple(self: MultiScaleOT.TSinkhornSolverBarycenter, arg0: int) → tuple
getKernelPosData(self: MultiScaleOT.TSinkhornSolverBarycenter, arg0: int) → MultiScaleOT.TSparsePosContainer
getKernelPosDataTuple(self: MultiScaleOT.TSinkhornSolverBarycenter, arg0: int) → tuple
getMarginalX(self: MultiScaleOT.TSinkhornSolverBarycenter, arg0: int) → numpy.ndarray[numpy.float64]

Return 1st marginal of current coupling between nMarginal-th reference measure and current barycenter candidate.

getMarginalY(self: MultiScaleOT.TSinkhornSolverBarycenter, arg0: int) → numpy.ndarray[numpy.float64]

Return 2nd marginal of current coupling between nMarginal-th reference measure and current barycenter candidate.

getU(self: MultiScaleOT.TSinkhornSolverBarycenter, arg0: int) → numpy.ndarray[numpy.float64]
getV(self: MultiScaleOT.TSinkhornSolverBarycenter, arg0: int) → numpy.ndarray[numpy.float64]
class MultiScaleOT.TSinkhornSolverBarycenterKLMarginals

Solver for optimal transport barycenter with KL soft marginals.

__init__(self: MultiScaleOT.TSinkhornSolverBarycenterKLMarginals, epsScalingHandler: MultiScaleOT.TEpsScalingHandler, layerCoarsest: int, layerFinest: int, errorGoal: float, MultiScaleSetupBarycenterContainer: MultiScaleOT.TMultiScaleSetupBarycenterContainer, kappa: float, cfg: MultiScaleOT.TSinkhornSolverParameters = <MultiScaleOT.TSinkhornSolverParameters object at 0x7aa42075f970>) → None
getScorePrimal(self: MultiScaleOT.TSinkhornSolverBarycenterKLMarginals) → float