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‎docs/source/all.rst‎

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@@ -6,8 +6,6 @@ Python modules
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ot
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--
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This module provide easy access to solvers for the most common OT problems
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.. automodule:: ot
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:members:
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.. automodule:: ot.optim
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:members:
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ot.da
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--------
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.. automodule:: ot.da
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:members:
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ot.utils
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--------
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‎ot/__init__.py‎

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# Python Optimal Transport toolbox
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"""Python Optimal Transport toolbox"""
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# All submodules and packages
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from . import lp
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from . import lp
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from . import bregman
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from . import optim
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from . import optim
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from . import utils
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from . import datasets
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from . import plot
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from . import da
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# OT functions
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from .lp import emd
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from .bregman import sinkhorn,barycenter
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from .bregman import sinkhorn, barycenter
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from .da import sinkhorn_lpl1_mm
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# utils functions
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from .utils import dist,unif
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from .utils import dist, unif
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__all__ = ["emd","sinkhorn","utils",'datasets','bregman','lp','plot','dist','unif','barycenter','sinkhorn_lpl1_mm','da','optim']
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__all__ = ["emd", "sinkhorn", "utils", 'datasets', 'bregman', 'lp', 'plot',
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'dist', 'unif', 'barycenter', 'sinkhorn_lpl1_mm', 'da', 'optim']

‎ot/bregman.py‎

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import numpy as np
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def sinkhorn(a,b, M, reg,numItermax = 1000,stopThr=1e-9,verbose=False,log=False):
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def sinkhorn(a,b, M, reg, numItermax = 1000, stopThr=1e-9, verbose=False, log=False):
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"""
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Solve the entropic regularization optimal transport problem and return the OT matrix
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Solve the entropic regularization optimal transport problem
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The function solves the following optimization problem:
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.. math::
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\gamma = arg\min_\gamma <\gamma,M>_F + reg\cdot\Omega(\gamma)
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‎ot/da.py‎

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# -*- coding: utf-8 -*-
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"""
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domain adaptation with optimal transport
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Domain adaptation with optimal transport
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"""
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import numpy as np
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from .bregman import sinkhorn
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def indices(a, func):
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return [i for (i, val) in enumerate(a) if func(val)]
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def sinkhorn_lpl1_mm(a,labels_a, b, M, reg, eta=0.1):
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def sinkhorn_lpl1_mm(a,labels_a, b, M, reg, eta=0.1,numItermax = 10,numInnerItermax = 200,stopInnerThr=1e-9,verbose=False,log=False):
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"""
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Solve the entropic regularization optimal transport problem with nonconvex group lasso regularization
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The function solves the following optimization problem:
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.. math::
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\gamma = arg\min_\gamma <\gamma,M>_F + reg\cdot\Omega_e(\gamma)+ \eta \Omega_g(\gamma)
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s.t. \gamma 1 = a
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\gamma^T 1= b
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\gamma\geq 0
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where :
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- M is the (ns,nt) metric cost matrix
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- :math:`\Omega_e` is the entropic regularization term :math:`\Omega_e(\gamma)=\sum_{i,j} \gamma_{i,j}\log(\gamma_{i,j})`
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- :math:`\Omega_g` is the group lasso regulaization term :math:`\Omega_g(\gamma)=\sum_{i,c} \|\gamma_{i,\mathcal{I}_c}\|^{1/2}_1` where :math:`\mathcal{I}_c` are the index of samples from class c in the source domain.
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- a and b are source and target weights (sum to 1)
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The algorithm used for solving the problem is the generalised conditional gradient as proposed in [5]_ [7]_
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Parameters
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----------
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a : np.ndarray (ns,)
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samples weights in the source domain
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labels_a : np.ndarray (ns,)
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labels of samples in the source domain
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b : np.ndarray (nt,)
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samples in the target domain
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M : np.ndarray (ns,nt)
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loss matrix
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reg: float
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Regularization term for entropic regularization >0
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eta: float, optional
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Regularization term for group lasso regularization >0
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numItermax: int, optional
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Max number of iterations
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numInnerItermax: int, optional
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Max number of iterations (inner sinkhorn solver)
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stopInnerThr: float, optional
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Stop threshold on error (inner sinkhorn solver) (>0)
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verbose : bool, optional
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Print information along iterations
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log : bool, optional
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record log if True
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Returns
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-------
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gamma: (ns x nt) ndarray
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Optimal transportation matrix for the given parameters
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log: dict
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log dictionary return only if log==True in parameters
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Examples
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--------
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>>> a=[.5,.5]
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>>> b=[.5,.5]
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>>> M=[[0.,1.],[1.,0.]]
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>>> ot.sinkhorn(a,b,M,1)
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array([[ 0.36552929, 0.13447071],
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[ 0.13447071, 0.36552929]])
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References
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----------
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.. [5] N. Courty; R. Flamary; D. Tuia; A. Rakotomamonjy, "Optimal Transport for Domain Adaptation," in IEEE Transactions on Pattern Analysis and Machine Intelligence , vol.PP, no.99, pp.1-1
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.. [7] Rakotomamonjy, A., Flamary, R., & Courty, N. (2015). Generalized conditional gradient: analysis of convergence and applications. arXiv preprint arXiv:1510.06567.
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See Also
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--------
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ot.lp.emd : Unregularized OT
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ot.bregman.sinkhorn : Entropic regularized OT
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ot.optim.cg : General regularized OT
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"""
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p=0.5
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epsilon = 1e-3
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W=np.zeros(M.shape)
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for cpt in range(10):
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for cpt in range(numItermax):
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Mreg = M + eta*W
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transp=sinkhorn(a,b,Mreg,reg,numItermax = 200)
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transp=sinkhorn(a,b,Mreg,reg,numItermax=numInnerItermax, stopThr=stopInnerThr)
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# the transport has been computed. Check if classes are really separated
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W = np.ones((Nini,Nfin))
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for t in range(Nfin):

‎ot/lp/__init__.py‎

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# -*- coding: utf-8 -*-
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"""
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Solvers for the original linear program OT problem
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"""
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import numpy as np
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# import compiled emd
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from .emd import emd_c
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import numpy as np
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def emd(a,b,M):
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"""
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Solves the Earth Movers distance problem and returns the optimal transport matrix
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def emd(a, b, M):
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"""Solves the Earth Movers distance problem and returns the OT matrix
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.. math::
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\gamma = arg\min_\gamma <\gamma,M>_F
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\gamma = arg\min_\gamma <\gamma,M>_F
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s.t. \gamma 1 = a
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\gamma^T 1= b
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\gamma^T 1= b
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\gamma\geq 0
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where :
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- M is the metric cost matrix
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- a and b are the sample weights
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Uses the algorithm proposed in [1]_
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Parameters
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----------
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a : (ns,) ndarray, float64
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Source histogram (uniform weigth if empty list)
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b : (nt,) ndarray, float64
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Target histogram (uniform weigth if empty list)
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M : (ns,nt) ndarray, float64
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loss matrix
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loss matrix
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Returns
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-------
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gamma: (ns x nt) ndarray
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Optimal transportation matrix for the given parameters
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Examples
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--------
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Simple example with obvious solution. The function emd accepts lists and
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perform automatic conversion to numpy arrays
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perform automatic conversion to numpy arrays
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>>> a=[.5,.5]
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>>> b=[.5,.5]
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>>> M=[[0.,1.],[1.,0.]]
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>>> ot.emd(a,b,M)
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array([[ 0.5, 0. ],
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[ 0. , 0.5]])
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References
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----------
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.. [1] Bonneel, N., Van De Panne, M., Paris, S., & Heidrich, W. (2011, December). Displacement interpolation using Lagrangian mass transport. In ACM Transactions on Graphics (TOG) (Vol. 30, No. 6, p. 158). ACM.
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.. [1] Bonneel, N., Van De Panne, M., Paris, S., & Heidrich, W.
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(2011, December). Displacement interpolation using Lagrangian mass
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transport. In ACM Transactions on Graphics (TOG) (Vol. 30, No. 6, p.
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158). ACM.
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See Also
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--------
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ot.bregman.sinkhorn : Entropic regularized OT
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ot.optim.cg : General regularized OT
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"""
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a=np.asarray(a,dtype=np.float64)
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b=np.asarray(b,dtype=np.float64)
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M=np.asarray(M,dtype=np.float64)
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if len(a)==0:
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a=np.ones((M.shape[0],),dtype=np.float64)/M.shape[0]
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if len(b)==0:
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b=np.ones((M.shape[1],),dtype=np.float64)/M.shape[1]
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return emd_c(a,b,M)
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ot.optim.cg : General regularized OT"""
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a = np.asarray(a, dtype=np.float64)
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b = np.asarray(b, dtype=np.float64)
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M = np.asarray(M, dtype=np.float64)
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if len(a) == 0:
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a = np.ones((M.shape[0], ), dtype=np.float64)/M.shape[0]
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if len(b) == 0:
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b = np.ones((M.shape[1], ), dtype=np.float64)/M.shape[1]
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return emd_c(a, b, M)

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