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240,900 | rflamary/POT | ot/plot.py | plot1D_mat | def plot1D_mat(a, b, M, title=''):
""" Plot matrix M with the source and target 1D distribution
Creates a subplot with the source distribution a on the left and
target distribution b on the tot. The matrix M is shown in between.
Parameters
----------
a : np.array, shape (na,)
Source distribution
b : np.array, shape (nb,)
Target distribution
M : np.array, shape (na,nb)
Matrix to plot
"""
na, nb = M.shape
gs = gridspec.GridSpec(3, 3)
xa = np.arange(na)
xb = np.arange(nb)
ax1 = pl.subplot(gs[0, 1:])
pl.plot(xb, b, 'r', label='Target distribution')
pl.yticks(())
pl.title(title)
ax2 = pl.subplot(gs[1:, 0])
pl.plot(a, xa, 'b', label='Source distribution')
pl.gca().invert_xaxis()
pl.gca().invert_yaxis()
pl.xticks(())
pl.subplot(gs[1:, 1:], sharex=ax1, sharey=ax2)
pl.imshow(M, interpolation='nearest')
pl.axis('off')
pl.xlim((0, nb))
pl.tight_layout()
pl.subplots_adjust(wspace=0., hspace=0.2) | python | def plot1D_mat(a, b, M, title=''):
na, nb = M.shape
gs = gridspec.GridSpec(3, 3)
xa = np.arange(na)
xb = np.arange(nb)
ax1 = pl.subplot(gs[0, 1:])
pl.plot(xb, b, 'r', label='Target distribution')
pl.yticks(())
pl.title(title)
ax2 = pl.subplot(gs[1:, 0])
pl.plot(a, xa, 'b', label='Source distribution')
pl.gca().invert_xaxis()
pl.gca().invert_yaxis()
pl.xticks(())
pl.subplot(gs[1:, 1:], sharex=ax1, sharey=ax2)
pl.imshow(M, interpolation='nearest')
pl.axis('off')
pl.xlim((0, nb))
pl.tight_layout()
pl.subplots_adjust(wspace=0., hspace=0.2) | [
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... | Plot matrix M with the source and target 1D distribution
Creates a subplot with the source distribution a on the left and
target distribution b on the tot. The matrix M is shown in between.
Parameters
----------
a : np.array, shape (na,)
Source distribution
b : np.array, shape (nb,)
Target distribution
M : np.array, shape (na,nb)
Matrix to plot | [
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240,901 | rflamary/POT | ot/plot.py | plot2D_samples_mat | def plot2D_samples_mat(xs, xt, G, thr=1e-8, **kwargs):
""" Plot matrix M in 2D with lines using alpha values
Plot lines between source and target 2D samples with a color
proportional to the value of the matrix G between samples.
Parameters
----------
xs : ndarray, shape (ns,2)
Source samples positions
b : ndarray, shape (nt,2)
Target samples positions
G : ndarray, shape (na,nb)
OT matrix
thr : float, optional
threshold above which the line is drawn
**kwargs : dict
paameters given to the plot functions (default color is black if
nothing given)
"""
if ('color' not in kwargs) and ('c' not in kwargs):
kwargs['color'] = 'k'
mx = G.max()
for i in range(xs.shape[0]):
for j in range(xt.shape[0]):
if G[i, j] / mx > thr:
pl.plot([xs[i, 0], xt[j, 0]], [xs[i, 1], xt[j, 1]],
alpha=G[i, j] / mx, **kwargs) | python | def plot2D_samples_mat(xs, xt, G, thr=1e-8, **kwargs):
if ('color' not in kwargs) and ('c' not in kwargs):
kwargs['color'] = 'k'
mx = G.max()
for i in range(xs.shape[0]):
for j in range(xt.shape[0]):
if G[i, j] / mx > thr:
pl.plot([xs[i, 0], xt[j, 0]], [xs[i, 1], xt[j, 1]],
alpha=G[i, j] / mx, **kwargs) | [
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Plot lines between source and target 2D samples with a color
proportional to the value of the matrix G between samples.
Parameters
----------
xs : ndarray, shape (ns,2)
Source samples positions
b : ndarray, shape (nt,2)
Target samples positions
G : ndarray, shape (na,nb)
OT matrix
thr : float, optional
threshold above which the line is drawn
**kwargs : dict
paameters given to the plot functions (default color is black if
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240,902 | rflamary/POT | ot/gpu/da.py | sinkhorn_lpl1_mm | def sinkhorn_lpl1_mm(a, labels_a, b, M, reg, eta=0.1, numItermax=10,
numInnerItermax=200, stopInnerThr=1e-9, verbose=False,
log=False, to_numpy=True):
"""
Solve the entropic regularization optimal transport problem with nonconvex
group lasso regularization on GPU
If the input matrix are in numpy format, they will be uploaded to the
GPU first which can incur significant time overhead.
The function solves the following optimization problem:
.. math::
\gamma = arg\min_\gamma <\gamma,M>_F + reg\cdot\Omega_e(\gamma)
+ \eta \Omega_g(\gamma)
s.t. \gamma 1 = a
\gamma^T 1= b
\gamma\geq 0
where :
- M is the (ns,nt) metric cost matrix
- :math:`\Omega_e` is the entropic regularization term
:math:`\Omega_e(\gamma)=\sum_{i,j} \gamma_{i,j}\log(\gamma_{i,j})`
- :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.
- a and b are source and target weights (sum to 1)
The algorithm used for solving the problem is the generalised conditional
gradient as proposed in [5]_ [7]_
Parameters
----------
a : np.ndarray (ns,)
samples weights in the source domain
labels_a : np.ndarray (ns,)
labels of samples in the source domain
b : np.ndarray (nt,)
samples weights in the target domain
M : np.ndarray (ns,nt)
loss matrix
reg : float
Regularization term for entropic regularization >0
eta : float, optional
Regularization term for group lasso regularization >0
numItermax : int, optional
Max number of iterations
numInnerItermax : int, optional
Max number of iterations (inner sinkhorn solver)
stopInnerThr : float, optional
Stop threshold on error (inner sinkhorn solver) (>0)
verbose : bool, optional
Print information along iterations
log : bool, optional
record log if True
to_numpy : boolean, optional (default True)
If true convert back the GPU array result to numpy format.
Returns
-------
gamma : (ns x nt) ndarray
Optimal transportation matrix for the given parameters
log : dict
log dictionary return only if log==True in parameters
References
----------
.. [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
.. [7] Rakotomamonjy, A., Flamary, R., & Courty, N. (2015).
Generalized conditional gradient: analysis of convergence
and applications. arXiv preprint arXiv:1510.06567.
See Also
--------
ot.lp.emd : Unregularized OT
ot.bregman.sinkhorn : Entropic regularized OT
ot.optim.cg : General regularized OT
"""
a, labels_a, b, M = utils.to_gpu(a, labels_a, b, M)
p = 0.5
epsilon = 1e-3
indices_labels = []
labels_a2 = cp.asnumpy(labels_a)
classes = npp.unique(labels_a2)
for c in classes:
idxc, = utils.to_gpu(npp.where(labels_a2 == c))
indices_labels.append(idxc)
W = np.zeros(M.shape)
for cpt in range(numItermax):
Mreg = M + eta * W
transp = sinkhorn(a, b, Mreg, reg, numItermax=numInnerItermax,
stopThr=stopInnerThr, to_numpy=False)
# the transport has been computed. Check if classes are really
# separated
W = np.ones(M.shape)
for (i, c) in enumerate(classes):
majs = np.sum(transp[indices_labels[i]], axis=0)
majs = p * ((majs + epsilon)**(p - 1))
W[indices_labels[i]] = majs
if to_numpy:
return utils.to_np(transp)
else:
return transp | python | def sinkhorn_lpl1_mm(a, labels_a, b, M, reg, eta=0.1, numItermax=10,
numInnerItermax=200, stopInnerThr=1e-9, verbose=False,
log=False, to_numpy=True):
a, labels_a, b, M = utils.to_gpu(a, labels_a, b, M)
p = 0.5
epsilon = 1e-3
indices_labels = []
labels_a2 = cp.asnumpy(labels_a)
classes = npp.unique(labels_a2)
for c in classes:
idxc, = utils.to_gpu(npp.where(labels_a2 == c))
indices_labels.append(idxc)
W = np.zeros(M.shape)
for cpt in range(numItermax):
Mreg = M + eta * W
transp = sinkhorn(a, b, Mreg, reg, numItermax=numInnerItermax,
stopThr=stopInnerThr, to_numpy=False)
# the transport has been computed. Check if classes are really
# separated
W = np.ones(M.shape)
for (i, c) in enumerate(classes):
majs = np.sum(transp[indices_labels[i]], axis=0)
majs = p * ((majs + epsilon)**(p - 1))
W[indices_labels[i]] = majs
if to_numpy:
return utils.to_np(transp)
else:
return transp | [
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If the input matrix are in numpy format, they will be uploaded to the
GPU first which can incur significant time overhead.
The function solves the following optimization problem:
.. math::
\gamma = arg\min_\gamma <\gamma,M>_F + reg\cdot\Omega_e(\gamma)
+ \eta \Omega_g(\gamma)
s.t. \gamma 1 = a
\gamma^T 1= b
\gamma\geq 0
where :
- M is the (ns,nt) metric cost matrix
- :math:`\Omega_e` is the entropic regularization term
:math:`\Omega_e(\gamma)=\sum_{i,j} \gamma_{i,j}\log(\gamma_{i,j})`
- :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.
- a and b are source and target weights (sum to 1)
The algorithm used for solving the problem is the generalised conditional
gradient as proposed in [5]_ [7]_
Parameters
----------
a : np.ndarray (ns,)
samples weights in the source domain
labels_a : np.ndarray (ns,)
labels of samples in the source domain
b : np.ndarray (nt,)
samples weights in the target domain
M : np.ndarray (ns,nt)
loss matrix
reg : float
Regularization term for entropic regularization >0
eta : float, optional
Regularization term for group lasso regularization >0
numItermax : int, optional
Max number of iterations
numInnerItermax : int, optional
Max number of iterations (inner sinkhorn solver)
stopInnerThr : float, optional
Stop threshold on error (inner sinkhorn solver) (>0)
verbose : bool, optional
Print information along iterations
log : bool, optional
record log if True
to_numpy : boolean, optional (default True)
If true convert back the GPU array result to numpy format.
Returns
-------
gamma : (ns x nt) ndarray
Optimal transportation matrix for the given parameters
log : dict
log dictionary return only if log==True in parameters
References
----------
.. [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
.. [7] Rakotomamonjy, A., Flamary, R., & Courty, N. (2015).
Generalized conditional gradient: analysis of convergence
and applications. arXiv preprint arXiv:1510.06567.
See Also
--------
ot.lp.emd : Unregularized OT
ot.bregman.sinkhorn : Entropic regularized OT
ot.optim.cg : General regularized OT | [
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240,903 | rflamary/POT | ot/datasets.py | get_2D_samples_gauss | def get_2D_samples_gauss(n, m, sigma, random_state=None):
""" Deprecated see make_2D_samples_gauss """
return make_2D_samples_gauss(n, m, sigma, random_state=None) | python | def get_2D_samples_gauss(n, m, sigma, random_state=None):
return make_2D_samples_gauss(n, m, sigma, random_state=None) | [
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240,904 | rflamary/POT | ot/datasets.py | get_data_classif | def get_data_classif(dataset, n, nz=.5, theta=0, random_state=None, **kwargs):
""" Deprecated see make_data_classif """
return make_data_classif(dataset, n, nz=.5, theta=0, random_state=None, **kwargs) | python | def get_data_classif(dataset, n, nz=.5, theta=0, random_state=None, **kwargs):
return make_data_classif(dataset, n, nz=.5, theta=0, random_state=None, **kwargs) | [
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240,905 | rflamary/POT | ot/bregman.py | sinkhorn | def sinkhorn(a, b, M, reg, method='sinkhorn', numItermax=1000,
stopThr=1e-9, verbose=False, log=False, **kwargs):
u"""
Solve the entropic regularization optimal transport problem and return the OT matrix
The function solves the following optimization problem:
.. math::
\gamma = arg\min_\gamma <\gamma,M>_F + reg\cdot\Omega(\gamma)
s.t. \gamma 1 = a
\gamma^T 1= b
\gamma\geq 0
where :
- M is the (ns,nt) metric cost matrix
- :math:`\Omega` is the entropic regularization term :math:`\Omega(\gamma)=\sum_{i,j} \gamma_{i,j}\log(\gamma_{i,j})`
- a and b are source and target weights (sum to 1)
The algorithm used for solving the problem is the Sinkhorn-Knopp matrix scaling algorithm as proposed in [2]_
Parameters
----------
a : np.ndarray (ns,)
samples weights in the source domain
b : np.ndarray (nt,) or np.ndarray (nt,nbb)
samples in the target domain, compute sinkhorn with multiple targets
and fixed M if b is a matrix (return OT loss + dual variables in log)
M : np.ndarray (ns,nt)
loss matrix
reg : float
Regularization term >0
method : str
method used for the solver either 'sinkhorn', 'greenkhorn', 'sinkhorn_stabilized' or
'sinkhorn_epsilon_scaling', see those function for specific parameters
numItermax : int, optional
Max number of iterations
stopThr : float, optional
Stop threshol on error (>0)
verbose : bool, optional
Print information along iterations
log : bool, optional
record log if True
Returns
-------
gamma : (ns x nt) ndarray
Optimal transportation matrix for the given parameters
log : dict
log dictionary return only if log==True in parameters
Examples
--------
>>> import ot
>>> a=[.5,.5]
>>> b=[.5,.5]
>>> M=[[0.,1.],[1.,0.]]
>>> ot.sinkhorn(a,b,M,1)
array([[ 0.36552929, 0.13447071],
[ 0.13447071, 0.36552929]])
References
----------
.. [2] M. Cuturi, Sinkhorn Distances : Lightspeed Computation of Optimal Transport, Advances in Neural Information Processing Systems (NIPS) 26, 2013
.. [9] Schmitzer, B. (2016). Stabilized Sparse Scaling Algorithms for Entropy Regularized Transport Problems. arXiv preprint arXiv:1610.06519.
.. [10] Chizat, L., Peyré, G., Schmitzer, B., & Vialard, F. X. (2016). Scaling algorithms for unbalanced transport problems. arXiv preprint arXiv:1607.05816.
See Also
--------
ot.lp.emd : Unregularized OT
ot.optim.cg : General regularized OT
ot.bregman.sinkhorn_knopp : Classic Sinkhorn [2]
ot.bregman.sinkhorn_stabilized: Stabilized sinkhorn [9][10]
ot.bregman.sinkhorn_epsilon_scaling: Sinkhorn with epslilon scaling [9][10]
"""
if method.lower() == 'sinkhorn':
def sink():
return sinkhorn_knopp(a, b, M, reg, numItermax=numItermax,
stopThr=stopThr, verbose=verbose, log=log, **kwargs)
elif method.lower() == 'greenkhorn':
def sink():
return greenkhorn(a, b, M, reg, numItermax=numItermax,
stopThr=stopThr, verbose=verbose, log=log)
elif method.lower() == 'sinkhorn_stabilized':
def sink():
return sinkhorn_stabilized(a, b, M, reg, numItermax=numItermax,
stopThr=stopThr, verbose=verbose, log=log, **kwargs)
elif method.lower() == 'sinkhorn_epsilon_scaling':
def sink():
return sinkhorn_epsilon_scaling(
a, b, M, reg, numItermax=numItermax,
stopThr=stopThr, verbose=verbose, log=log, **kwargs)
else:
print('Warning : unknown method using classic Sinkhorn Knopp')
def sink():
return sinkhorn_knopp(a, b, M, reg, numItermax=numItermax,
stopThr=stopThr, verbose=verbose, log=log, **kwargs)
return sink() | python | def sinkhorn(a, b, M, reg, method='sinkhorn', numItermax=1000,
stopThr=1e-9, verbose=False, log=False, **kwargs):
u"""
Solve the entropic regularization optimal transport problem and return the OT matrix
The function solves the following optimization problem:
.. math::
\gamma = arg\min_\gamma <\gamma,M>_F + reg\cdot\Omega(\gamma)
s.t. \gamma 1 = a
\gamma^T 1= b
\gamma\geq 0
where :
- M is the (ns,nt) metric cost matrix
- :math:`\Omega` is the entropic regularization term :math:`\Omega(\gamma)=\sum_{i,j} \gamma_{i,j}\log(\gamma_{i,j})`
- a and b are source and target weights (sum to 1)
The algorithm used for solving the problem is the Sinkhorn-Knopp matrix scaling algorithm as proposed in [2]_
Parameters
----------
a : np.ndarray (ns,)
samples weights in the source domain
b : np.ndarray (nt,) or np.ndarray (nt,nbb)
samples in the target domain, compute sinkhorn with multiple targets
and fixed M if b is a matrix (return OT loss + dual variables in log)
M : np.ndarray (ns,nt)
loss matrix
reg : float
Regularization term >0
method : str
method used for the solver either 'sinkhorn', 'greenkhorn', 'sinkhorn_stabilized' or
'sinkhorn_epsilon_scaling', see those function for specific parameters
numItermax : int, optional
Max number of iterations
stopThr : float, optional
Stop threshol on error (>0)
verbose : bool, optional
Print information along iterations
log : bool, optional
record log if True
Returns
-------
gamma : (ns x nt) ndarray
Optimal transportation matrix for the given parameters
log : dict
log dictionary return only if log==True in parameters
Examples
--------
>>> import ot
>>> a=[.5,.5]
>>> b=[.5,.5]
>>> M=[[0.,1.],[1.,0.]]
>>> ot.sinkhorn(a,b,M,1)
array([[ 0.36552929, 0.13447071],
[ 0.13447071, 0.36552929]])
References
----------
.. [2] M. Cuturi, Sinkhorn Distances : Lightspeed Computation of Optimal Transport, Advances in Neural Information Processing Systems (NIPS) 26, 2013
.. [9] Schmitzer, B. (2016). Stabilized Sparse Scaling Algorithms for Entropy Regularized Transport Problems. arXiv preprint arXiv:1610.06519.
.. [10] Chizat, L., Peyré, G., Schmitzer, B., & Vialard, F. X. (2016). Scaling algorithms for unbalanced transport problems. arXiv preprint arXiv:1607.05816.
See Also
--------
ot.lp.emd : Unregularized OT
ot.optim.cg : General regularized OT
ot.bregman.sinkhorn_knopp : Classic Sinkhorn [2]
ot.bregman.sinkhorn_stabilized: Stabilized sinkhorn [9][10]
ot.bregman.sinkhorn_epsilon_scaling: Sinkhorn with epslilon scaling [9][10]
"""
if method.lower() == 'sinkhorn':
def sink():
return sinkhorn_knopp(a, b, M, reg, numItermax=numItermax,
stopThr=stopThr, verbose=verbose, log=log, **kwargs)
elif method.lower() == 'greenkhorn':
def sink():
return greenkhorn(a, b, M, reg, numItermax=numItermax,
stopThr=stopThr, verbose=verbose, log=log)
elif method.lower() == 'sinkhorn_stabilized':
def sink():
return sinkhorn_stabilized(a, b, M, reg, numItermax=numItermax,
stopThr=stopThr, verbose=verbose, log=log, **kwargs)
elif method.lower() == 'sinkhorn_epsilon_scaling':
def sink():
return sinkhorn_epsilon_scaling(
a, b, M, reg, numItermax=numItermax,
stopThr=stopThr, verbose=verbose, log=log, **kwargs)
else:
print('Warning : unknown method using classic Sinkhorn Knopp')
def sink():
return sinkhorn_knopp(a, b, M, reg, numItermax=numItermax,
stopThr=stopThr, verbose=verbose, log=log, **kwargs)
return sink() | [
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Solve the entropic regularization optimal transport problem and return the OT matrix
The function solves the following optimization problem:
.. math::
\gamma = arg\min_\gamma <\gamma,M>_F + reg\cdot\Omega(\gamma)
s.t. \gamma 1 = a
\gamma^T 1= b
\gamma\geq 0
where :
- M is the (ns,nt) metric cost matrix
- :math:`\Omega` is the entropic regularization term :math:`\Omega(\gamma)=\sum_{i,j} \gamma_{i,j}\log(\gamma_{i,j})`
- a and b are source and target weights (sum to 1)
The algorithm used for solving the problem is the Sinkhorn-Knopp matrix scaling algorithm as proposed in [2]_
Parameters
----------
a : np.ndarray (ns,)
samples weights in the source domain
b : np.ndarray (nt,) or np.ndarray (nt,nbb)
samples in the target domain, compute sinkhorn with multiple targets
and fixed M if b is a matrix (return OT loss + dual variables in log)
M : np.ndarray (ns,nt)
loss matrix
reg : float
Regularization term >0
method : str
method used for the solver either 'sinkhorn', 'greenkhorn', 'sinkhorn_stabilized' or
'sinkhorn_epsilon_scaling', see those function for specific parameters
numItermax : int, optional
Max number of iterations
stopThr : float, optional
Stop threshol on error (>0)
verbose : bool, optional
Print information along iterations
log : bool, optional
record log if True
Returns
-------
gamma : (ns x nt) ndarray
Optimal transportation matrix for the given parameters
log : dict
log dictionary return only if log==True in parameters
Examples
--------
>>> import ot
>>> a=[.5,.5]
>>> b=[.5,.5]
>>> M=[[0.,1.],[1.,0.]]
>>> ot.sinkhorn(a,b,M,1)
array([[ 0.36552929, 0.13447071],
[ 0.13447071, 0.36552929]])
References
----------
.. [2] M. Cuturi, Sinkhorn Distances : Lightspeed Computation of Optimal Transport, Advances in Neural Information Processing Systems (NIPS) 26, 2013
.. [9] Schmitzer, B. (2016). Stabilized Sparse Scaling Algorithms for Entropy Regularized Transport Problems. arXiv preprint arXiv:1610.06519.
.. [10] Chizat, L., Peyré, G., Schmitzer, B., & Vialard, F. X. (2016). Scaling algorithms for unbalanced transport problems. arXiv preprint arXiv:1607.05816.
See Also
--------
ot.lp.emd : Unregularized OT
ot.optim.cg : General regularized OT
ot.bregman.sinkhorn_knopp : Classic Sinkhorn [2]
ot.bregman.sinkhorn_stabilized: Stabilized sinkhorn [9][10]
ot.bregman.sinkhorn_epsilon_scaling: Sinkhorn with epslilon scaling [9][10] | [
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240,906 | rflamary/POT | ot/bregman.py | sinkhorn2 | def sinkhorn2(a, b, M, reg, method='sinkhorn', numItermax=1000,
stopThr=1e-9, verbose=False, log=False, **kwargs):
u"""
Solve the entropic regularization optimal transport problem and return the loss
The function solves the following optimization problem:
.. math::
W = \min_\gamma <\gamma,M>_F + reg\cdot\Omega(\gamma)
s.t. \gamma 1 = a
\gamma^T 1= b
\gamma\geq 0
where :
- M is the (ns,nt) metric cost matrix
- :math:`\Omega` is the entropic regularization term :math:`\Omega(\gamma)=\sum_{i,j} \gamma_{i,j}\log(\gamma_{i,j})`
- a and b are source and target weights (sum to 1)
The algorithm used for solving the problem is the Sinkhorn-Knopp matrix scaling algorithm as proposed in [2]_
Parameters
----------
a : np.ndarray (ns,)
samples weights in the source domain
b : np.ndarray (nt,) or np.ndarray (nt,nbb)
samples in the target domain, compute sinkhorn with multiple targets
and fixed M if b is a matrix (return OT loss + dual variables in log)
M : np.ndarray (ns,nt)
loss matrix
reg : float
Regularization term >0
method : str
method used for the solver either 'sinkhorn', 'sinkhorn_stabilized' or
'sinkhorn_epsilon_scaling', see those function for specific parameters
numItermax : int, optional
Max number of iterations
stopThr : float, optional
Stop threshol on error (>0)
verbose : bool, optional
Print information along iterations
log : bool, optional
record log if True
Returns
-------
W : (nt) ndarray or float
Optimal transportation matrix for the given parameters
log : dict
log dictionary return only if log==True in parameters
Examples
--------
>>> import ot
>>> a=[.5,.5]
>>> b=[.5,.5]
>>> M=[[0.,1.],[1.,0.]]
>>> ot.sinkhorn2(a,b,M,1)
array([ 0.26894142])
References
----------
.. [2] M. Cuturi, Sinkhorn Distances : Lightspeed Computation of Optimal Transport, Advances in Neural Information Processing Systems (NIPS) 26, 2013
.. [9] Schmitzer, B. (2016). Stabilized Sparse Scaling Algorithms for Entropy Regularized Transport Problems. arXiv preprint arXiv:1610.06519.
.. [10] Chizat, L., Peyré, G., Schmitzer, B., & Vialard, F. X. (2016). Scaling algorithms for unbalanced transport problems. arXiv preprint arXiv:1607.05816.
[21] Altschuler J., Weed J., Rigollet P. : Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration, Advances in Neural Information Processing Systems (NIPS) 31, 2017
See Also
--------
ot.lp.emd : Unregularized OT
ot.optim.cg : General regularized OT
ot.bregman.sinkhorn_knopp : Classic Sinkhorn [2]
ot.bregman.greenkhorn : Greenkhorn [21]
ot.bregman.sinkhorn_stabilized: Stabilized sinkhorn [9][10]
ot.bregman.sinkhorn_epsilon_scaling: Sinkhorn with epslilon scaling [9][10]
"""
if method.lower() == 'sinkhorn':
def sink():
return sinkhorn_knopp(a, b, M, reg, numItermax=numItermax,
stopThr=stopThr, verbose=verbose, log=log, **kwargs)
elif method.lower() == 'sinkhorn_stabilized':
def sink():
return sinkhorn_stabilized(a, b, M, reg, numItermax=numItermax,
stopThr=stopThr, verbose=verbose, log=log, **kwargs)
elif method.lower() == 'sinkhorn_epsilon_scaling':
def sink():
return sinkhorn_epsilon_scaling(
a, b, M, reg, numItermax=numItermax,
stopThr=stopThr, verbose=verbose, log=log, **kwargs)
else:
print('Warning : unknown method using classic Sinkhorn Knopp')
def sink():
return sinkhorn_knopp(a, b, M, reg, **kwargs)
b = np.asarray(b, dtype=np.float64)
if len(b.shape) < 2:
b = b.reshape((-1, 1))
return sink() | python | def sinkhorn2(a, b, M, reg, method='sinkhorn', numItermax=1000,
stopThr=1e-9, verbose=False, log=False, **kwargs):
u"""
Solve the entropic regularization optimal transport problem and return the loss
The function solves the following optimization problem:
.. math::
W = \min_\gamma <\gamma,M>_F + reg\cdot\Omega(\gamma)
s.t. \gamma 1 = a
\gamma^T 1= b
\gamma\geq 0
where :
- M is the (ns,nt) metric cost matrix
- :math:`\Omega` is the entropic regularization term :math:`\Omega(\gamma)=\sum_{i,j} \gamma_{i,j}\log(\gamma_{i,j})`
- a and b are source and target weights (sum to 1)
The algorithm used for solving the problem is the Sinkhorn-Knopp matrix scaling algorithm as proposed in [2]_
Parameters
----------
a : np.ndarray (ns,)
samples weights in the source domain
b : np.ndarray (nt,) or np.ndarray (nt,nbb)
samples in the target domain, compute sinkhorn with multiple targets
and fixed M if b is a matrix (return OT loss + dual variables in log)
M : np.ndarray (ns,nt)
loss matrix
reg : float
Regularization term >0
method : str
method used for the solver either 'sinkhorn', 'sinkhorn_stabilized' or
'sinkhorn_epsilon_scaling', see those function for specific parameters
numItermax : int, optional
Max number of iterations
stopThr : float, optional
Stop threshol on error (>0)
verbose : bool, optional
Print information along iterations
log : bool, optional
record log if True
Returns
-------
W : (nt) ndarray or float
Optimal transportation matrix for the given parameters
log : dict
log dictionary return only if log==True in parameters
Examples
--------
>>> import ot
>>> a=[.5,.5]
>>> b=[.5,.5]
>>> M=[[0.,1.],[1.,0.]]
>>> ot.sinkhorn2(a,b,M,1)
array([ 0.26894142])
References
----------
.. [2] M. Cuturi, Sinkhorn Distances : Lightspeed Computation of Optimal Transport, Advances in Neural Information Processing Systems (NIPS) 26, 2013
.. [9] Schmitzer, B. (2016). Stabilized Sparse Scaling Algorithms for Entropy Regularized Transport Problems. arXiv preprint arXiv:1610.06519.
.. [10] Chizat, L., Peyré, G., Schmitzer, B., & Vialard, F. X. (2016). Scaling algorithms for unbalanced transport problems. arXiv preprint arXiv:1607.05816.
[21] Altschuler J., Weed J., Rigollet P. : Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration, Advances in Neural Information Processing Systems (NIPS) 31, 2017
See Also
--------
ot.lp.emd : Unregularized OT
ot.optim.cg : General regularized OT
ot.bregman.sinkhorn_knopp : Classic Sinkhorn [2]
ot.bregman.greenkhorn : Greenkhorn [21]
ot.bregman.sinkhorn_stabilized: Stabilized sinkhorn [9][10]
ot.bregman.sinkhorn_epsilon_scaling: Sinkhorn with epslilon scaling [9][10]
"""
if method.lower() == 'sinkhorn':
def sink():
return sinkhorn_knopp(a, b, M, reg, numItermax=numItermax,
stopThr=stopThr, verbose=verbose, log=log, **kwargs)
elif method.lower() == 'sinkhorn_stabilized':
def sink():
return sinkhorn_stabilized(a, b, M, reg, numItermax=numItermax,
stopThr=stopThr, verbose=verbose, log=log, **kwargs)
elif method.lower() == 'sinkhorn_epsilon_scaling':
def sink():
return sinkhorn_epsilon_scaling(
a, b, M, reg, numItermax=numItermax,
stopThr=stopThr, verbose=verbose, log=log, **kwargs)
else:
print('Warning : unknown method using classic Sinkhorn Knopp')
def sink():
return sinkhorn_knopp(a, b, M, reg, **kwargs)
b = np.asarray(b, dtype=np.float64)
if len(b.shape) < 2:
b = b.reshape((-1, 1))
return sink() | [
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Solve the entropic regularization optimal transport problem and return the loss
The function solves the following optimization problem:
.. math::
W = \min_\gamma <\gamma,M>_F + reg\cdot\Omega(\gamma)
s.t. \gamma 1 = a
\gamma^T 1= b
\gamma\geq 0
where :
- M is the (ns,nt) metric cost matrix
- :math:`\Omega` is the entropic regularization term :math:`\Omega(\gamma)=\sum_{i,j} \gamma_{i,j}\log(\gamma_{i,j})`
- a and b are source and target weights (sum to 1)
The algorithm used for solving the problem is the Sinkhorn-Knopp matrix scaling algorithm as proposed in [2]_
Parameters
----------
a : np.ndarray (ns,)
samples weights in the source domain
b : np.ndarray (nt,) or np.ndarray (nt,nbb)
samples in the target domain, compute sinkhorn with multiple targets
and fixed M if b is a matrix (return OT loss + dual variables in log)
M : np.ndarray (ns,nt)
loss matrix
reg : float
Regularization term >0
method : str
method used for the solver either 'sinkhorn', 'sinkhorn_stabilized' or
'sinkhorn_epsilon_scaling', see those function for specific parameters
numItermax : int, optional
Max number of iterations
stopThr : float, optional
Stop threshol on error (>0)
verbose : bool, optional
Print information along iterations
log : bool, optional
record log if True
Returns
-------
W : (nt) ndarray or float
Optimal transportation matrix for the given parameters
log : dict
log dictionary return only if log==True in parameters
Examples
--------
>>> import ot
>>> a=[.5,.5]
>>> b=[.5,.5]
>>> M=[[0.,1.],[1.,0.]]
>>> ot.sinkhorn2(a,b,M,1)
array([ 0.26894142])
References
----------
.. [2] M. Cuturi, Sinkhorn Distances : Lightspeed Computation of Optimal Transport, Advances in Neural Information Processing Systems (NIPS) 26, 2013
.. [9] Schmitzer, B. (2016). Stabilized Sparse Scaling Algorithms for Entropy Regularized Transport Problems. arXiv preprint arXiv:1610.06519.
.. [10] Chizat, L., Peyré, G., Schmitzer, B., & Vialard, F. X. (2016). Scaling algorithms for unbalanced transport problems. arXiv preprint arXiv:1607.05816.
[21] Altschuler J., Weed J., Rigollet P. : Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration, Advances in Neural Information Processing Systems (NIPS) 31, 2017
See Also
--------
ot.lp.emd : Unregularized OT
ot.optim.cg : General regularized OT
ot.bregman.sinkhorn_knopp : Classic Sinkhorn [2]
ot.bregman.greenkhorn : Greenkhorn [21]
ot.bregman.sinkhorn_stabilized: Stabilized sinkhorn [9][10]
ot.bregman.sinkhorn_epsilon_scaling: Sinkhorn with epslilon scaling [9][10] | [
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240,907 | rflamary/POT | ot/bregman.py | geometricBar | def geometricBar(weights, alldistribT):
"""return the weighted geometric mean of distributions"""
assert(len(weights) == alldistribT.shape[1])
return np.exp(np.dot(np.log(alldistribT), weights.T)) | python | def geometricBar(weights, alldistribT):
assert(len(weights) == alldistribT.shape[1])
return np.exp(np.dot(np.log(alldistribT), weights.T)) | [
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240,908 | rflamary/POT | ot/bregman.py | geometricMean | def geometricMean(alldistribT):
"""return the geometric mean of distributions"""
return np.exp(np.mean(np.log(alldistribT), axis=1)) | python | def geometricMean(alldistribT):
return np.exp(np.mean(np.log(alldistribT), axis=1)) | [
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240,909 | rflamary/POT | ot/bregman.py | projR | def projR(gamma, p):
"""return the KL projection on the row constrints """
return np.multiply(gamma.T, p / np.maximum(np.sum(gamma, axis=1), 1e-10)).T | python | def projR(gamma, p):
return np.multiply(gamma.T, p / np.maximum(np.sum(gamma, axis=1), 1e-10)).T | [
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240,910 | rflamary/POT | ot/bregman.py | projC | def projC(gamma, q):
"""return the KL projection on the column constrints """
return np.multiply(gamma, q / np.maximum(np.sum(gamma, axis=0), 1e-10)) | python | def projC(gamma, q):
return np.multiply(gamma, q / np.maximum(np.sum(gamma, axis=0), 1e-10)) | [
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240,911 | rflamary/POT | ot/bregman.py | barycenter | def barycenter(A, M, reg, weights=None, numItermax=1000,
stopThr=1e-4, verbose=False, log=False):
"""Compute the entropic regularized wasserstein barycenter of distributions A
The function solves the following optimization problem:
.. math::
\mathbf{a} = arg\min_\mathbf{a} \sum_i W_{reg}(\mathbf{a},\mathbf{a}_i)
where :
- :math:`W_{reg}(\cdot,\cdot)` is the entropic regularized Wasserstein distance (see ot.bregman.sinkhorn)
- :math:`\mathbf{a}_i` are training distributions in the columns of matrix :math:`\mathbf{A}`
- reg and :math:`\mathbf{M}` are respectively the regularization term and the cost matrix for OT
The algorithm used for solving the problem is the Sinkhorn-Knopp matrix scaling algorithm as proposed in [3]_
Parameters
----------
A : np.ndarray (d,n)
n training distributions a_i of size d
M : np.ndarray (d,d)
loss matrix for OT
reg : float
Regularization term >0
weights : np.ndarray (n,)
Weights of each histogram a_i on the simplex (barycentric coodinates)
numItermax : int, optional
Max number of iterations
stopThr : float, optional
Stop threshol on error (>0)
verbose : bool, optional
Print information along iterations
log : bool, optional
record log if True
Returns
-------
a : (d,) ndarray
Wasserstein barycenter
log : dict
log dictionary return only if log==True in parameters
References
----------
.. [3] Benamou, J. D., Carlier, G., Cuturi, M., Nenna, L., & Peyré, G. (2015). Iterative Bregman projections for regularized transportation problems. SIAM Journal on Scientific Computing, 37(2), A1111-A1138.
"""
if weights is None:
weights = np.ones(A.shape[1]) / A.shape[1]
else:
assert(len(weights) == A.shape[1])
if log:
log = {'err': []}
# M = M/np.median(M) # suggested by G. Peyre
K = np.exp(-M / reg)
cpt = 0
err = 1
UKv = np.dot(K, np.divide(A.T, np.sum(K, axis=0)).T)
u = (geometricMean(UKv) / UKv.T).T
while (err > stopThr and cpt < numItermax):
cpt = cpt + 1
UKv = u * np.dot(K, np.divide(A, np.dot(K, u)))
u = (u.T * geometricBar(weights, UKv)).T / UKv
if cpt % 10 == 1:
err = np.sum(np.std(UKv, axis=1))
# log and verbose print
if log:
log['err'].append(err)
if verbose:
if cpt % 200 == 0:
print(
'{:5s}|{:12s}'.format('It.', 'Err') + '\n' + '-' * 19)
print('{:5d}|{:8e}|'.format(cpt, err))
if log:
log['niter'] = cpt
return geometricBar(weights, UKv), log
else:
return geometricBar(weights, UKv) | python | def barycenter(A, M, reg, weights=None, numItermax=1000,
stopThr=1e-4, verbose=False, log=False):
if weights is None:
weights = np.ones(A.shape[1]) / A.shape[1]
else:
assert(len(weights) == A.shape[1])
if log:
log = {'err': []}
# M = M/np.median(M) # suggested by G. Peyre
K = np.exp(-M / reg)
cpt = 0
err = 1
UKv = np.dot(K, np.divide(A.T, np.sum(K, axis=0)).T)
u = (geometricMean(UKv) / UKv.T).T
while (err > stopThr and cpt < numItermax):
cpt = cpt + 1
UKv = u * np.dot(K, np.divide(A, np.dot(K, u)))
u = (u.T * geometricBar(weights, UKv)).T / UKv
if cpt % 10 == 1:
err = np.sum(np.std(UKv, axis=1))
# log and verbose print
if log:
log['err'].append(err)
if verbose:
if cpt % 200 == 0:
print(
'{:5s}|{:12s}'.format('It.', 'Err') + '\n' + '-' * 19)
print('{:5d}|{:8e}|'.format(cpt, err))
if log:
log['niter'] = cpt
return geometricBar(weights, UKv), log
else:
return geometricBar(weights, UKv) | [
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The function solves the following optimization problem:
.. math::
\mathbf{a} = arg\min_\mathbf{a} \sum_i W_{reg}(\mathbf{a},\mathbf{a}_i)
where :
- :math:`W_{reg}(\cdot,\cdot)` is the entropic regularized Wasserstein distance (see ot.bregman.sinkhorn)
- :math:`\mathbf{a}_i` are training distributions in the columns of matrix :math:`\mathbf{A}`
- reg and :math:`\mathbf{M}` are respectively the regularization term and the cost matrix for OT
The algorithm used for solving the problem is the Sinkhorn-Knopp matrix scaling algorithm as proposed in [3]_
Parameters
----------
A : np.ndarray (d,n)
n training distributions a_i of size d
M : np.ndarray (d,d)
loss matrix for OT
reg : float
Regularization term >0
weights : np.ndarray (n,)
Weights of each histogram a_i on the simplex (barycentric coodinates)
numItermax : int, optional
Max number of iterations
stopThr : float, optional
Stop threshol on error (>0)
verbose : bool, optional
Print information along iterations
log : bool, optional
record log if True
Returns
-------
a : (d,) ndarray
Wasserstein barycenter
log : dict
log dictionary return only if log==True in parameters
References
----------
.. [3] Benamou, J. D., Carlier, G., Cuturi, M., Nenna, L., & Peyré, G. (2015). Iterative Bregman projections for regularized transportation problems. SIAM Journal on Scientific Computing, 37(2), A1111-A1138. | [
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] | c5108efc7b6702e1af3928bef1032e6b37734d1c | https://github.com/rflamary/POT/blob/c5108efc7b6702e1af3928bef1032e6b37734d1c/ot/bregman.py#L989-L1082 |
240,912 | rflamary/POT | ot/bregman.py | convolutional_barycenter2d | def convolutional_barycenter2d(A, reg, weights=None, numItermax=10000, stopThr=1e-9, stabThr=1e-30, verbose=False, log=False):
"""Compute the entropic regularized wasserstein barycenter of distributions A
where A is a collection of 2D images.
The function solves the following optimization problem:
.. math::
\mathbf{a} = arg\min_\mathbf{a} \sum_i W_{reg}(\mathbf{a},\mathbf{a}_i)
where :
- :math:`W_{reg}(\cdot,\cdot)` is the entropic regularized Wasserstein distance (see ot.bregman.sinkhorn)
- :math:`\mathbf{a}_i` are training distributions (2D images) in the mast two dimensions of matrix :math:`\mathbf{A}`
- reg is the regularization strength scalar value
The algorithm used for solving the problem is the Sinkhorn-Knopp matrix scaling algorithm as proposed in [21]_
Parameters
----------
A : np.ndarray (n,w,h)
n distributions (2D images) of size w x h
reg : float
Regularization term >0
weights : np.ndarray (n,)
Weights of each image on the simplex (barycentric coodinates)
numItermax : int, optional
Max number of iterations
stopThr : float, optional
Stop threshol on error (>0)
stabThr : float, optional
Stabilization threshold to avoid numerical precision issue
verbose : bool, optional
Print information along iterations
log : bool, optional
record log if True
Returns
-------
a : (w,h) ndarray
2D Wasserstein barycenter
log : dict
log dictionary return only if log==True in parameters
References
----------
.. [21] Solomon, J., De Goes, F., Peyré, G., Cuturi, M., Butscher, A., Nguyen, A. & Guibas, L. (2015).
Convolutional wasserstein distances: Efficient optimal transportation on geometric domains
ACM Transactions on Graphics (TOG), 34(4), 66
"""
if weights is None:
weights = np.ones(A.shape[0]) / A.shape[0]
else:
assert(len(weights) == A.shape[0])
if log:
log = {'err': []}
b = np.zeros_like(A[0, :, :])
U = np.ones_like(A)
KV = np.ones_like(A)
cpt = 0
err = 1
# build the convolution operator
t = np.linspace(0, 1, A.shape[1])
[Y, X] = np.meshgrid(t, t)
xi1 = np.exp(-(X - Y)**2 / reg)
def K(x):
return np.dot(np.dot(xi1, x), xi1)
while (err > stopThr and cpt < numItermax):
bold = b
cpt = cpt + 1
b = np.zeros_like(A[0, :, :])
for r in range(A.shape[0]):
KV[r, :, :] = K(A[r, :, :] / np.maximum(stabThr, K(U[r, :, :])))
b += weights[r] * np.log(np.maximum(stabThr, U[r, :, :] * KV[r, :, :]))
b = np.exp(b)
for r in range(A.shape[0]):
U[r, :, :] = b / np.maximum(stabThr, KV[r, :, :])
if cpt % 10 == 1:
err = np.sum(np.abs(bold - b))
# log and verbose print
if log:
log['err'].append(err)
if verbose:
if cpt % 200 == 0:
print('{:5s}|{:12s}'.format('It.', 'Err') + '\n' + '-' * 19)
print('{:5d}|{:8e}|'.format(cpt, err))
if log:
log['niter'] = cpt
log['U'] = U
return b, log
else:
return b | python | def convolutional_barycenter2d(A, reg, weights=None, numItermax=10000, stopThr=1e-9, stabThr=1e-30, verbose=False, log=False):
if weights is None:
weights = np.ones(A.shape[0]) / A.shape[0]
else:
assert(len(weights) == A.shape[0])
if log:
log = {'err': []}
b = np.zeros_like(A[0, :, :])
U = np.ones_like(A)
KV = np.ones_like(A)
cpt = 0
err = 1
# build the convolution operator
t = np.linspace(0, 1, A.shape[1])
[Y, X] = np.meshgrid(t, t)
xi1 = np.exp(-(X - Y)**2 / reg)
def K(x):
return np.dot(np.dot(xi1, x), xi1)
while (err > stopThr and cpt < numItermax):
bold = b
cpt = cpt + 1
b = np.zeros_like(A[0, :, :])
for r in range(A.shape[0]):
KV[r, :, :] = K(A[r, :, :] / np.maximum(stabThr, K(U[r, :, :])))
b += weights[r] * np.log(np.maximum(stabThr, U[r, :, :] * KV[r, :, :]))
b = np.exp(b)
for r in range(A.shape[0]):
U[r, :, :] = b / np.maximum(stabThr, KV[r, :, :])
if cpt % 10 == 1:
err = np.sum(np.abs(bold - b))
# log and verbose print
if log:
log['err'].append(err)
if verbose:
if cpt % 200 == 0:
print('{:5s}|{:12s}'.format('It.', 'Err') + '\n' + '-' * 19)
print('{:5d}|{:8e}|'.format(cpt, err))
if log:
log['niter'] = cpt
log['U'] = U
return b, log
else:
return b | [
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... | Compute the entropic regularized wasserstein barycenter of distributions A
where A is a collection of 2D images.
The function solves the following optimization problem:
.. math::
\mathbf{a} = arg\min_\mathbf{a} \sum_i W_{reg}(\mathbf{a},\mathbf{a}_i)
where :
- :math:`W_{reg}(\cdot,\cdot)` is the entropic regularized Wasserstein distance (see ot.bregman.sinkhorn)
- :math:`\mathbf{a}_i` are training distributions (2D images) in the mast two dimensions of matrix :math:`\mathbf{A}`
- reg is the regularization strength scalar value
The algorithm used for solving the problem is the Sinkhorn-Knopp matrix scaling algorithm as proposed in [21]_
Parameters
----------
A : np.ndarray (n,w,h)
n distributions (2D images) of size w x h
reg : float
Regularization term >0
weights : np.ndarray (n,)
Weights of each image on the simplex (barycentric coodinates)
numItermax : int, optional
Max number of iterations
stopThr : float, optional
Stop threshol on error (>0)
stabThr : float, optional
Stabilization threshold to avoid numerical precision issue
verbose : bool, optional
Print information along iterations
log : bool, optional
record log if True
Returns
-------
a : (w,h) ndarray
2D Wasserstein barycenter
log : dict
log dictionary return only if log==True in parameters
References
----------
.. [21] Solomon, J., De Goes, F., Peyré, G., Cuturi, M., Butscher, A., Nguyen, A. & Guibas, L. (2015).
Convolutional wasserstein distances: Efficient optimal transportation on geometric domains
ACM Transactions on Graphics (TOG), 34(4), 66 | [
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240,913 | rflamary/POT | ot/bregman.py | unmix | def unmix(a, D, M, M0, h0, reg, reg0, alpha, numItermax=1000,
stopThr=1e-3, verbose=False, log=False):
"""
Compute the unmixing of an observation with a given dictionary using Wasserstein distance
The function solve the following optimization problem:
.. math::
\mathbf{h} = arg\min_\mathbf{h} (1- \\alpha) W_{M,reg}(\mathbf{a},\mathbf{Dh})+\\alpha W_{M0,reg0}(\mathbf{h}_0,\mathbf{h})
where :
- :math:`W_{M,reg}(\cdot,\cdot)` is the entropic regularized Wasserstein distance with M loss matrix (see ot.bregman.sinkhorn)
- :math:`\mathbf{a}` is an observed distribution, :math:`\mathbf{h}_0` is aprior on unmixing
- reg and :math:`\mathbf{M}` are respectively the regularization term and the cost matrix for OT data fitting
- reg0 and :math:`\mathbf{M0}` are respectively the regularization term and the cost matrix for regularization
- :math:`\\alpha`weight data fitting and regularization
The optimization problem is solved suing the algorithm described in [4]
Parameters
----------
a : np.ndarray (d)
observed distribution
D : np.ndarray (d,n)
dictionary matrix
M : np.ndarray (d,d)
loss matrix
M0 : np.ndarray (n,n)
loss matrix
h0 : np.ndarray (n,)
prior on h
reg : float
Regularization term >0 (Wasserstein data fitting)
reg0 : float
Regularization term >0 (Wasserstein reg with h0)
alpha : float
How much should we trust the prior ([0,1])
numItermax : int, optional
Max number of iterations
stopThr : float, optional
Stop threshol on error (>0)
verbose : bool, optional
Print information along iterations
log : bool, optional
record log if True
Returns
-------
a : (d,) ndarray
Wasserstein barycenter
log : dict
log dictionary return only if log==True in parameters
References
----------
.. [4] S. Nakhostin, N. Courty, R. Flamary, D. Tuia, T. Corpetti, Supervised planetary unmixing with optimal transport, Whorkshop on Hyperspectral Image and Signal Processing : Evolution in Remote Sensing (WHISPERS), 2016.
"""
# M = M/np.median(M)
K = np.exp(-M / reg)
# M0 = M0/np.median(M0)
K0 = np.exp(-M0 / reg0)
old = h0
err = 1
cpt = 0
# log = {'niter':0, 'all_err':[]}
if log:
log = {'err': []}
while (err > stopThr and cpt < numItermax):
K = projC(K, a)
K0 = projC(K0, h0)
new = np.sum(K0, axis=1)
# we recombine the current selection from dictionnary
inv_new = np.dot(D, new)
other = np.sum(K, axis=1)
# geometric interpolation
delta = np.exp(alpha * np.log(other) + (1 - alpha) * np.log(inv_new))
K = projR(K, delta)
K0 = np.dot(np.diag(np.dot(D.T, delta / inv_new)), K0)
err = np.linalg.norm(np.sum(K0, axis=1) - old)
old = new
if log:
log['err'].append(err)
if verbose:
if cpt % 200 == 0:
print('{:5s}|{:12s}'.format('It.', 'Err') + '\n' + '-' * 19)
print('{:5d}|{:8e}|'.format(cpt, err))
cpt = cpt + 1
if log:
log['niter'] = cpt
return np.sum(K0, axis=1), log
else:
return np.sum(K0, axis=1) | python | def unmix(a, D, M, M0, h0, reg, reg0, alpha, numItermax=1000,
stopThr=1e-3, verbose=False, log=False):
# M = M/np.median(M)
K = np.exp(-M / reg)
# M0 = M0/np.median(M0)
K0 = np.exp(-M0 / reg0)
old = h0
err = 1
cpt = 0
# log = {'niter':0, 'all_err':[]}
if log:
log = {'err': []}
while (err > stopThr and cpt < numItermax):
K = projC(K, a)
K0 = projC(K0, h0)
new = np.sum(K0, axis=1)
# we recombine the current selection from dictionnary
inv_new = np.dot(D, new)
other = np.sum(K, axis=1)
# geometric interpolation
delta = np.exp(alpha * np.log(other) + (1 - alpha) * np.log(inv_new))
K = projR(K, delta)
K0 = np.dot(np.diag(np.dot(D.T, delta / inv_new)), K0)
err = np.linalg.norm(np.sum(K0, axis=1) - old)
old = new
if log:
log['err'].append(err)
if verbose:
if cpt % 200 == 0:
print('{:5s}|{:12s}'.format('It.', 'Err') + '\n' + '-' * 19)
print('{:5d}|{:8e}|'.format(cpt, err))
cpt = cpt + 1
if log:
log['niter'] = cpt
return np.sum(K0, axis=1), log
else:
return np.sum(K0, axis=1) | [
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"# M = M/n... | Compute the unmixing of an observation with a given dictionary using Wasserstein distance
The function solve the following optimization problem:
.. math::
\mathbf{h} = arg\min_\mathbf{h} (1- \\alpha) W_{M,reg}(\mathbf{a},\mathbf{Dh})+\\alpha W_{M0,reg0}(\mathbf{h}_0,\mathbf{h})
where :
- :math:`W_{M,reg}(\cdot,\cdot)` is the entropic regularized Wasserstein distance with M loss matrix (see ot.bregman.sinkhorn)
- :math:`\mathbf{a}` is an observed distribution, :math:`\mathbf{h}_0` is aprior on unmixing
- reg and :math:`\mathbf{M}` are respectively the regularization term and the cost matrix for OT data fitting
- reg0 and :math:`\mathbf{M0}` are respectively the regularization term and the cost matrix for regularization
- :math:`\\alpha`weight data fitting and regularization
The optimization problem is solved suing the algorithm described in [4]
Parameters
----------
a : np.ndarray (d)
observed distribution
D : np.ndarray (d,n)
dictionary matrix
M : np.ndarray (d,d)
loss matrix
M0 : np.ndarray (n,n)
loss matrix
h0 : np.ndarray (n,)
prior on h
reg : float
Regularization term >0 (Wasserstein data fitting)
reg0 : float
Regularization term >0 (Wasserstein reg with h0)
alpha : float
How much should we trust the prior ([0,1])
numItermax : int, optional
Max number of iterations
stopThr : float, optional
Stop threshol on error (>0)
verbose : bool, optional
Print information along iterations
log : bool, optional
record log if True
Returns
-------
a : (d,) ndarray
Wasserstein barycenter
log : dict
log dictionary return only if log==True in parameters
References
----------
.. [4] S. Nakhostin, N. Courty, R. Flamary, D. Tuia, T. Corpetti, Supervised planetary unmixing with optimal transport, Whorkshop on Hyperspectral Image and Signal Processing : Evolution in Remote Sensing (WHISPERS), 2016. | [
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240,914 | rflamary/POT | ot/bregman.py | empirical_sinkhorn | def empirical_sinkhorn(X_s, X_t, reg, a=None, b=None, metric='sqeuclidean', numIterMax=10000, stopThr=1e-9, verbose=False, log=False, **kwargs):
'''
Solve the entropic regularization optimal transport problem and return the
OT matrix from empirical data
The function solves the following optimization problem:
.. math::
\gamma = arg\min_\gamma <\gamma,M>_F + reg\cdot\Omega(\gamma)
s.t. \gamma 1 = a
\gamma^T 1= b
\gamma\geq 0
where :
- :math:`M` is the (ns,nt) metric cost matrix
- :math:`\Omega` is the entropic regularization term :math:`\Omega(\gamma)=\sum_{i,j} \gamma_{i,j}\log(\gamma_{i,j})`
- :math:`a` and :math:`b` are source and target weights (sum to 1)
Parameters
----------
X_s : np.ndarray (ns, d)
samples in the source domain
X_t : np.ndarray (nt, d)
samples in the target domain
reg : float
Regularization term >0
a : np.ndarray (ns,)
samples weights in the source domain
b : np.ndarray (nt,)
samples weights in the target domain
numItermax : int, optional
Max number of iterations
stopThr : float, optional
Stop threshol on error (>0)
verbose : bool, optional
Print information along iterations
log : bool, optional
record log if True
Returns
-------
gamma : (ns x nt) ndarray
Regularized optimal transportation matrix for the given parameters
log : dict
log dictionary return only if log==True in parameters
Examples
--------
>>> n_s = 2
>>> n_t = 2
>>> reg = 0.1
>>> X_s = np.reshape(np.arange(n_s), (n_s, 1))
>>> X_t = np.reshape(np.arange(0, n_t), (n_t, 1))
>>> emp_sinkhorn = empirical_sinkhorn(X_s, X_t, reg, verbose=False)
>>> print(emp_sinkhorn)
>>> [[4.99977301e-01 2.26989344e-05]
[2.26989344e-05 4.99977301e-01]]
References
----------
.. [2] M. Cuturi, Sinkhorn Distances : Lightspeed Computation of Optimal Transport, Advances in Neural Information Processing Systems (NIPS) 26, 2013
.. [9] Schmitzer, B. (2016). Stabilized Sparse Scaling Algorithms for Entropy Regularized Transport Problems. arXiv preprint arXiv:1610.06519.
.. [10] Chizat, L., Peyré, G., Schmitzer, B., & Vialard, F. X. (2016). Scaling algorithms for unbalanced transport problems. arXiv preprint arXiv:1607.05816.
'''
if a is None:
a = unif(np.shape(X_s)[0])
if b is None:
b = unif(np.shape(X_t)[0])
M = dist(X_s, X_t, metric=metric)
if log:
pi, log = sinkhorn(a, b, M, reg, numItermax=numIterMax, stopThr=stopThr, verbose=verbose, log=True, **kwargs)
return pi, log
else:
pi = sinkhorn(a, b, M, reg, numItermax=numIterMax, stopThr=stopThr, verbose=verbose, log=False, **kwargs)
return pi | python | def empirical_sinkhorn(X_s, X_t, reg, a=None, b=None, metric='sqeuclidean', numIterMax=10000, stopThr=1e-9, verbose=False, log=False, **kwargs):
'''
Solve the entropic regularization optimal transport problem and return the
OT matrix from empirical data
The function solves the following optimization problem:
.. math::
\gamma = arg\min_\gamma <\gamma,M>_F + reg\cdot\Omega(\gamma)
s.t. \gamma 1 = a
\gamma^T 1= b
\gamma\geq 0
where :
- :math:`M` is the (ns,nt) metric cost matrix
- :math:`\Omega` is the entropic regularization term :math:`\Omega(\gamma)=\sum_{i,j} \gamma_{i,j}\log(\gamma_{i,j})`
- :math:`a` and :math:`b` are source and target weights (sum to 1)
Parameters
----------
X_s : np.ndarray (ns, d)
samples in the source domain
X_t : np.ndarray (nt, d)
samples in the target domain
reg : float
Regularization term >0
a : np.ndarray (ns,)
samples weights in the source domain
b : np.ndarray (nt,)
samples weights in the target domain
numItermax : int, optional
Max number of iterations
stopThr : float, optional
Stop threshol on error (>0)
verbose : bool, optional
Print information along iterations
log : bool, optional
record log if True
Returns
-------
gamma : (ns x nt) ndarray
Regularized optimal transportation matrix for the given parameters
log : dict
log dictionary return only if log==True in parameters
Examples
--------
>>> n_s = 2
>>> n_t = 2
>>> reg = 0.1
>>> X_s = np.reshape(np.arange(n_s), (n_s, 1))
>>> X_t = np.reshape(np.arange(0, n_t), (n_t, 1))
>>> emp_sinkhorn = empirical_sinkhorn(X_s, X_t, reg, verbose=False)
>>> print(emp_sinkhorn)
>>> [[4.99977301e-01 2.26989344e-05]
[2.26989344e-05 4.99977301e-01]]
References
----------
.. [2] M. Cuturi, Sinkhorn Distances : Lightspeed Computation of Optimal Transport, Advances in Neural Information Processing Systems (NIPS) 26, 2013
.. [9] Schmitzer, B. (2016). Stabilized Sparse Scaling Algorithms for Entropy Regularized Transport Problems. arXiv preprint arXiv:1610.06519.
.. [10] Chizat, L., Peyré, G., Schmitzer, B., & Vialard, F. X. (2016). Scaling algorithms for unbalanced transport problems. arXiv preprint arXiv:1607.05816.
'''
if a is None:
a = unif(np.shape(X_s)[0])
if b is None:
b = unif(np.shape(X_t)[0])
M = dist(X_s, X_t, metric=metric)
if log:
pi, log = sinkhorn(a, b, M, reg, numItermax=numIterMax, stopThr=stopThr, verbose=verbose, log=True, **kwargs)
return pi, log
else:
pi = sinkhorn(a, b, M, reg, numItermax=numIterMax, stopThr=stopThr, verbose=verbose, log=False, **kwargs)
return pi | [
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OT matrix from empirical data
The function solves the following optimization problem:
.. math::
\gamma = arg\min_\gamma <\gamma,M>_F + reg\cdot\Omega(\gamma)
s.t. \gamma 1 = a
\gamma^T 1= b
\gamma\geq 0
where :
- :math:`M` is the (ns,nt) metric cost matrix
- :math:`\Omega` is the entropic regularization term :math:`\Omega(\gamma)=\sum_{i,j} \gamma_{i,j}\log(\gamma_{i,j})`
- :math:`a` and :math:`b` are source and target weights (sum to 1)
Parameters
----------
X_s : np.ndarray (ns, d)
samples in the source domain
X_t : np.ndarray (nt, d)
samples in the target domain
reg : float
Regularization term >0
a : np.ndarray (ns,)
samples weights in the source domain
b : np.ndarray (nt,)
samples weights in the target domain
numItermax : int, optional
Max number of iterations
stopThr : float, optional
Stop threshol on error (>0)
verbose : bool, optional
Print information along iterations
log : bool, optional
record log if True
Returns
-------
gamma : (ns x nt) ndarray
Regularized optimal transportation matrix for the given parameters
log : dict
log dictionary return only if log==True in parameters
Examples
--------
>>> n_s = 2
>>> n_t = 2
>>> reg = 0.1
>>> X_s = np.reshape(np.arange(n_s), (n_s, 1))
>>> X_t = np.reshape(np.arange(0, n_t), (n_t, 1))
>>> emp_sinkhorn = empirical_sinkhorn(X_s, X_t, reg, verbose=False)
>>> print(emp_sinkhorn)
>>> [[4.99977301e-01 2.26989344e-05]
[2.26989344e-05 4.99977301e-01]]
References
----------
.. [2] M. Cuturi, Sinkhorn Distances : Lightspeed Computation of Optimal Transport, Advances in Neural Information Processing Systems (NIPS) 26, 2013
.. [9] Schmitzer, B. (2016). Stabilized Sparse Scaling Algorithms for Entropy Regularized Transport Problems. arXiv preprint arXiv:1610.06519.
.. [10] Chizat, L., Peyré, G., Schmitzer, B., & Vialard, F. X. (2016). Scaling algorithms for unbalanced transport problems. arXiv preprint arXiv:1607.05816. | [
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240,915 | rflamary/POT | ot/bregman.py | empirical_sinkhorn2 | def empirical_sinkhorn2(X_s, X_t, reg, a=None, b=None, metric='sqeuclidean', numIterMax=10000, stopThr=1e-9, verbose=False, log=False, **kwargs):
'''
Solve the entropic regularization optimal transport problem from empirical
data and return the OT loss
The function solves the following optimization problem:
.. math::
W = \min_\gamma <\gamma,M>_F + reg\cdot\Omega(\gamma)
s.t. \gamma 1 = a
\gamma^T 1= b
\gamma\geq 0
where :
- :math:`M` is the (ns,nt) metric cost matrix
- :math:`\Omega` is the entropic regularization term :math:`\Omega(\gamma)=\sum_{i,j} \gamma_{i,j}\log(\gamma_{i,j})`
- :math:`a` and :math:`b` are source and target weights (sum to 1)
Parameters
----------
X_s : np.ndarray (ns, d)
samples in the source domain
X_t : np.ndarray (nt, d)
samples in the target domain
reg : float
Regularization term >0
a : np.ndarray (ns,)
samples weights in the source domain
b : np.ndarray (nt,)
samples weights in the target domain
numItermax : int, optional
Max number of iterations
stopThr : float, optional
Stop threshol on error (>0)
verbose : bool, optional
Print information along iterations
log : bool, optional
record log if True
Returns
-------
gamma : (ns x nt) ndarray
Regularized optimal transportation matrix for the given parameters
log : dict
log dictionary return only if log==True in parameters
Examples
--------
>>> n_s = 2
>>> n_t = 2
>>> reg = 0.1
>>> X_s = np.reshape(np.arange(n_s), (n_s, 1))
>>> X_t = np.reshape(np.arange(0, n_t), (n_t, 1))
>>> loss_sinkhorn = empirical_sinkhorn2(X_s, X_t, reg, verbose=False)
>>> print(loss_sinkhorn)
>>> [4.53978687e-05]
References
----------
.. [2] M. Cuturi, Sinkhorn Distances : Lightspeed Computation of Optimal Transport, Advances in Neural Information Processing Systems (NIPS) 26, 2013
.. [9] Schmitzer, B. (2016). Stabilized Sparse Scaling Algorithms for Entropy Regularized Transport Problems. arXiv preprint arXiv:1610.06519.
.. [10] Chizat, L., Peyré, G., Schmitzer, B., & Vialard, F. X. (2016). Scaling algorithms for unbalanced transport problems. arXiv preprint arXiv:1607.05816.
'''
if a is None:
a = unif(np.shape(X_s)[0])
if b is None:
b = unif(np.shape(X_t)[0])
M = dist(X_s, X_t, metric=metric)
if log:
sinkhorn_loss, log = sinkhorn2(a, b, M, reg, numItermax=numIterMax, stopThr=stopThr, verbose=verbose, log=log, **kwargs)
return sinkhorn_loss, log
else:
sinkhorn_loss = sinkhorn2(a, b, M, reg, numItermax=numIterMax, stopThr=stopThr, verbose=verbose, log=log, **kwargs)
return sinkhorn_loss | python | def empirical_sinkhorn2(X_s, X_t, reg, a=None, b=None, metric='sqeuclidean', numIterMax=10000, stopThr=1e-9, verbose=False, log=False, **kwargs):
'''
Solve the entropic regularization optimal transport problem from empirical
data and return the OT loss
The function solves the following optimization problem:
.. math::
W = \min_\gamma <\gamma,M>_F + reg\cdot\Omega(\gamma)
s.t. \gamma 1 = a
\gamma^T 1= b
\gamma\geq 0
where :
- :math:`M` is the (ns,nt) metric cost matrix
- :math:`\Omega` is the entropic regularization term :math:`\Omega(\gamma)=\sum_{i,j} \gamma_{i,j}\log(\gamma_{i,j})`
- :math:`a` and :math:`b` are source and target weights (sum to 1)
Parameters
----------
X_s : np.ndarray (ns, d)
samples in the source domain
X_t : np.ndarray (nt, d)
samples in the target domain
reg : float
Regularization term >0
a : np.ndarray (ns,)
samples weights in the source domain
b : np.ndarray (nt,)
samples weights in the target domain
numItermax : int, optional
Max number of iterations
stopThr : float, optional
Stop threshol on error (>0)
verbose : bool, optional
Print information along iterations
log : bool, optional
record log if True
Returns
-------
gamma : (ns x nt) ndarray
Regularized optimal transportation matrix for the given parameters
log : dict
log dictionary return only if log==True in parameters
Examples
--------
>>> n_s = 2
>>> n_t = 2
>>> reg = 0.1
>>> X_s = np.reshape(np.arange(n_s), (n_s, 1))
>>> X_t = np.reshape(np.arange(0, n_t), (n_t, 1))
>>> loss_sinkhorn = empirical_sinkhorn2(X_s, X_t, reg, verbose=False)
>>> print(loss_sinkhorn)
>>> [4.53978687e-05]
References
----------
.. [2] M. Cuturi, Sinkhorn Distances : Lightspeed Computation of Optimal Transport, Advances in Neural Information Processing Systems (NIPS) 26, 2013
.. [9] Schmitzer, B. (2016). Stabilized Sparse Scaling Algorithms for Entropy Regularized Transport Problems. arXiv preprint arXiv:1610.06519.
.. [10] Chizat, L., Peyré, G., Schmitzer, B., & Vialard, F. X. (2016). Scaling algorithms for unbalanced transport problems. arXiv preprint arXiv:1607.05816.
'''
if a is None:
a = unif(np.shape(X_s)[0])
if b is None:
b = unif(np.shape(X_t)[0])
M = dist(X_s, X_t, metric=metric)
if log:
sinkhorn_loss, log = sinkhorn2(a, b, M, reg, numItermax=numIterMax, stopThr=stopThr, verbose=verbose, log=log, **kwargs)
return sinkhorn_loss, log
else:
sinkhorn_loss = sinkhorn2(a, b, M, reg, numItermax=numIterMax, stopThr=stopThr, verbose=verbose, log=log, **kwargs)
return sinkhorn_loss | [
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"log... | Solve the entropic regularization optimal transport problem from empirical
data and return the OT loss
The function solves the following optimization problem:
.. math::
W = \min_\gamma <\gamma,M>_F + reg\cdot\Omega(\gamma)
s.t. \gamma 1 = a
\gamma^T 1= b
\gamma\geq 0
where :
- :math:`M` is the (ns,nt) metric cost matrix
- :math:`\Omega` is the entropic regularization term :math:`\Omega(\gamma)=\sum_{i,j} \gamma_{i,j}\log(\gamma_{i,j})`
- :math:`a` and :math:`b` are source and target weights (sum to 1)
Parameters
----------
X_s : np.ndarray (ns, d)
samples in the source domain
X_t : np.ndarray (nt, d)
samples in the target domain
reg : float
Regularization term >0
a : np.ndarray (ns,)
samples weights in the source domain
b : np.ndarray (nt,)
samples weights in the target domain
numItermax : int, optional
Max number of iterations
stopThr : float, optional
Stop threshol on error (>0)
verbose : bool, optional
Print information along iterations
log : bool, optional
record log if True
Returns
-------
gamma : (ns x nt) ndarray
Regularized optimal transportation matrix for the given parameters
log : dict
log dictionary return only if log==True in parameters
Examples
--------
>>> n_s = 2
>>> n_t = 2
>>> reg = 0.1
>>> X_s = np.reshape(np.arange(n_s), (n_s, 1))
>>> X_t = np.reshape(np.arange(0, n_t), (n_t, 1))
>>> loss_sinkhorn = empirical_sinkhorn2(X_s, X_t, reg, verbose=False)
>>> print(loss_sinkhorn)
>>> [4.53978687e-05]
References
----------
.. [2] M. Cuturi, Sinkhorn Distances : Lightspeed Computation of Optimal Transport, Advances in Neural Information Processing Systems (NIPS) 26, 2013
.. [9] Schmitzer, B. (2016). Stabilized Sparse Scaling Algorithms for Entropy Regularized Transport Problems. arXiv preprint arXiv:1610.06519.
.. [10] Chizat, L., Peyré, G., Schmitzer, B., & Vialard, F. X. (2016). Scaling algorithms for unbalanced transport problems. arXiv preprint arXiv:1607.05816. | [
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240,916 | rflamary/POT | ot/bregman.py | empirical_sinkhorn_divergence | def empirical_sinkhorn_divergence(X_s, X_t, reg, a=None, b=None, metric='sqeuclidean', numIterMax=10000, stopThr=1e-9, verbose=False, log=False, **kwargs):
'''
Compute the sinkhorn divergence loss from empirical data
The function solves the following optimization problems and return the
sinkhorn divergence :math:`S`:
.. math::
W &= \min_\gamma <\gamma,M>_F + reg\cdot\Omega(\gamma)
W_a &= \min_{\gamma_a} <\gamma_a,M_a>_F + reg\cdot\Omega(\gamma_a)
W_b &= \min_{\gamma_b} <\gamma_b,M_b>_F + reg\cdot\Omega(\gamma_b)
S &= W - 1/2 * (W_a + W_b)
.. math::
s.t. \gamma 1 = a
\gamma^T 1= b
\gamma\geq 0
\gamma_a 1 = a
\gamma_a^T 1= a
\gamma_a\geq 0
\gamma_b 1 = b
\gamma_b^T 1= b
\gamma_b\geq 0
where :
- :math:`M` (resp. :math:`M_a, M_b`) is the (ns,nt) metric cost matrix (resp (ns, ns) and (nt, nt))
- :math:`\Omega` is the entropic regularization term :math:`\Omega(\gamma)=\sum_{i,j} \gamma_{i,j}\log(\gamma_{i,j})`
- :math:`a` and :math:`b` are source and target weights (sum to 1)
Parameters
----------
X_s : np.ndarray (ns, d)
samples in the source domain
X_t : np.ndarray (nt, d)
samples in the target domain
reg : float
Regularization term >0
a : np.ndarray (ns,)
samples weights in the source domain
b : np.ndarray (nt,)
samples weights in the target domain
numItermax : int, optional
Max number of iterations
stopThr : float, optional
Stop threshol on error (>0)
verbose : bool, optional
Print information along iterations
log : bool, optional
record log if True
Returns
-------
gamma : (ns x nt) ndarray
Regularized optimal transportation matrix for the given parameters
log : dict
log dictionary return only if log==True in parameters
Examples
--------
>>> n_s = 2
>>> n_t = 4
>>> reg = 0.1
>>> X_s = np.reshape(np.arange(n_s), (n_s, 1))
>>> X_t = np.reshape(np.arange(0, n_t), (n_t, 1))
>>> emp_sinkhorn_div = empirical_sinkhorn_divergence(X_s, X_t, reg)
>>> print(emp_sinkhorn_div)
>>> [2.99977435]
References
----------
.. [23] Aude Genevay, Gabriel Peyré, Marco Cuturi, Learning Generative Models with Sinkhorn Divergences, Proceedings of the Twenty-First International Conference on Artficial Intelligence and Statistics, (AISTATS) 21, 2018
'''
if log:
sinkhorn_loss_ab, log_ab = empirical_sinkhorn2(X_s, X_t, reg, a, b, metric=metric, numIterMax=numIterMax, stopThr=1e-9, verbose=verbose, log=log, **kwargs)
sinkhorn_loss_a, log_a = empirical_sinkhorn2(X_s, X_s, reg, a, b, metric=metric, numIterMax=numIterMax, stopThr=1e-9, verbose=verbose, log=log, **kwargs)
sinkhorn_loss_b, log_b = empirical_sinkhorn2(X_t, X_t, reg, a, b, metric=metric, numIterMax=numIterMax, stopThr=1e-9, verbose=verbose, log=log, **kwargs)
sinkhorn_div = sinkhorn_loss_ab - 1 / 2 * (sinkhorn_loss_a + sinkhorn_loss_b)
log = {}
log['sinkhorn_loss_ab'] = sinkhorn_loss_ab
log['sinkhorn_loss_a'] = sinkhorn_loss_a
log['sinkhorn_loss_b'] = sinkhorn_loss_b
log['log_sinkhorn_ab'] = log_ab
log['log_sinkhorn_a'] = log_a
log['log_sinkhorn_b'] = log_b
return max(0, sinkhorn_div), log
else:
sinkhorn_loss_ab = empirical_sinkhorn2(X_s, X_t, reg, a, b, metric=metric, numIterMax=numIterMax, stopThr=1e-9, verbose=verbose, log=log, **kwargs)
sinkhorn_loss_a = empirical_sinkhorn2(X_s, X_s, reg, a, b, metric=metric, numIterMax=numIterMax, stopThr=1e-9, verbose=verbose, log=log, **kwargs)
sinkhorn_loss_b = empirical_sinkhorn2(X_t, X_t, reg, a, b, metric=metric, numIterMax=numIterMax, stopThr=1e-9, verbose=verbose, log=log, **kwargs)
sinkhorn_div = sinkhorn_loss_ab - 1 / 2 * (sinkhorn_loss_a + sinkhorn_loss_b)
return max(0, sinkhorn_div) | python | def empirical_sinkhorn_divergence(X_s, X_t, reg, a=None, b=None, metric='sqeuclidean', numIterMax=10000, stopThr=1e-9, verbose=False, log=False, **kwargs):
'''
Compute the sinkhorn divergence loss from empirical data
The function solves the following optimization problems and return the
sinkhorn divergence :math:`S`:
.. math::
W &= \min_\gamma <\gamma,M>_F + reg\cdot\Omega(\gamma)
W_a &= \min_{\gamma_a} <\gamma_a,M_a>_F + reg\cdot\Omega(\gamma_a)
W_b &= \min_{\gamma_b} <\gamma_b,M_b>_F + reg\cdot\Omega(\gamma_b)
S &= W - 1/2 * (W_a + W_b)
.. math::
s.t. \gamma 1 = a
\gamma^T 1= b
\gamma\geq 0
\gamma_a 1 = a
\gamma_a^T 1= a
\gamma_a\geq 0
\gamma_b 1 = b
\gamma_b^T 1= b
\gamma_b\geq 0
where :
- :math:`M` (resp. :math:`M_a, M_b`) is the (ns,nt) metric cost matrix (resp (ns, ns) and (nt, nt))
- :math:`\Omega` is the entropic regularization term :math:`\Omega(\gamma)=\sum_{i,j} \gamma_{i,j}\log(\gamma_{i,j})`
- :math:`a` and :math:`b` are source and target weights (sum to 1)
Parameters
----------
X_s : np.ndarray (ns, d)
samples in the source domain
X_t : np.ndarray (nt, d)
samples in the target domain
reg : float
Regularization term >0
a : np.ndarray (ns,)
samples weights in the source domain
b : np.ndarray (nt,)
samples weights in the target domain
numItermax : int, optional
Max number of iterations
stopThr : float, optional
Stop threshol on error (>0)
verbose : bool, optional
Print information along iterations
log : bool, optional
record log if True
Returns
-------
gamma : (ns x nt) ndarray
Regularized optimal transportation matrix for the given parameters
log : dict
log dictionary return only if log==True in parameters
Examples
--------
>>> n_s = 2
>>> n_t = 4
>>> reg = 0.1
>>> X_s = np.reshape(np.arange(n_s), (n_s, 1))
>>> X_t = np.reshape(np.arange(0, n_t), (n_t, 1))
>>> emp_sinkhorn_div = empirical_sinkhorn_divergence(X_s, X_t, reg)
>>> print(emp_sinkhorn_div)
>>> [2.99977435]
References
----------
.. [23] Aude Genevay, Gabriel Peyré, Marco Cuturi, Learning Generative Models with Sinkhorn Divergences, Proceedings of the Twenty-First International Conference on Artficial Intelligence and Statistics, (AISTATS) 21, 2018
'''
if log:
sinkhorn_loss_ab, log_ab = empirical_sinkhorn2(X_s, X_t, reg, a, b, metric=metric, numIterMax=numIterMax, stopThr=1e-9, verbose=verbose, log=log, **kwargs)
sinkhorn_loss_a, log_a = empirical_sinkhorn2(X_s, X_s, reg, a, b, metric=metric, numIterMax=numIterMax, stopThr=1e-9, verbose=verbose, log=log, **kwargs)
sinkhorn_loss_b, log_b = empirical_sinkhorn2(X_t, X_t, reg, a, b, metric=metric, numIterMax=numIterMax, stopThr=1e-9, verbose=verbose, log=log, **kwargs)
sinkhorn_div = sinkhorn_loss_ab - 1 / 2 * (sinkhorn_loss_a + sinkhorn_loss_b)
log = {}
log['sinkhorn_loss_ab'] = sinkhorn_loss_ab
log['sinkhorn_loss_a'] = sinkhorn_loss_a
log['sinkhorn_loss_b'] = sinkhorn_loss_b
log['log_sinkhorn_ab'] = log_ab
log['log_sinkhorn_a'] = log_a
log['log_sinkhorn_b'] = log_b
return max(0, sinkhorn_div), log
else:
sinkhorn_loss_ab = empirical_sinkhorn2(X_s, X_t, reg, a, b, metric=metric, numIterMax=numIterMax, stopThr=1e-9, verbose=verbose, log=log, **kwargs)
sinkhorn_loss_a = empirical_sinkhorn2(X_s, X_s, reg, a, b, metric=metric, numIterMax=numIterMax, stopThr=1e-9, verbose=verbose, log=log, **kwargs)
sinkhorn_loss_b = empirical_sinkhorn2(X_t, X_t, reg, a, b, metric=metric, numIterMax=numIterMax, stopThr=1e-9, verbose=verbose, log=log, **kwargs)
sinkhorn_div = sinkhorn_loss_ab - 1 / 2 * (sinkhorn_loss_a + sinkhorn_loss_b)
return max(0, sinkhorn_div) | [
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"... | Compute the sinkhorn divergence loss from empirical data
The function solves the following optimization problems and return the
sinkhorn divergence :math:`S`:
.. math::
W &= \min_\gamma <\gamma,M>_F + reg\cdot\Omega(\gamma)
W_a &= \min_{\gamma_a} <\gamma_a,M_a>_F + reg\cdot\Omega(\gamma_a)
W_b &= \min_{\gamma_b} <\gamma_b,M_b>_F + reg\cdot\Omega(\gamma_b)
S &= W - 1/2 * (W_a + W_b)
.. math::
s.t. \gamma 1 = a
\gamma^T 1= b
\gamma\geq 0
\gamma_a 1 = a
\gamma_a^T 1= a
\gamma_a\geq 0
\gamma_b 1 = b
\gamma_b^T 1= b
\gamma_b\geq 0
where :
- :math:`M` (resp. :math:`M_a, M_b`) is the (ns,nt) metric cost matrix (resp (ns, ns) and (nt, nt))
- :math:`\Omega` is the entropic regularization term :math:`\Omega(\gamma)=\sum_{i,j} \gamma_{i,j}\log(\gamma_{i,j})`
- :math:`a` and :math:`b` are source and target weights (sum to 1)
Parameters
----------
X_s : np.ndarray (ns, d)
samples in the source domain
X_t : np.ndarray (nt, d)
samples in the target domain
reg : float
Regularization term >0
a : np.ndarray (ns,)
samples weights in the source domain
b : np.ndarray (nt,)
samples weights in the target domain
numItermax : int, optional
Max number of iterations
stopThr : float, optional
Stop threshol on error (>0)
verbose : bool, optional
Print information along iterations
log : bool, optional
record log if True
Returns
-------
gamma : (ns x nt) ndarray
Regularized optimal transportation matrix for the given parameters
log : dict
log dictionary return only if log==True in parameters
Examples
--------
>>> n_s = 2
>>> n_t = 4
>>> reg = 0.1
>>> X_s = np.reshape(np.arange(n_s), (n_s, 1))
>>> X_t = np.reshape(np.arange(0, n_t), (n_t, 1))
>>> emp_sinkhorn_div = empirical_sinkhorn_divergence(X_s, X_t, reg)
>>> print(emp_sinkhorn_div)
>>> [2.99977435]
References
----------
.. [23] Aude Genevay, Gabriel Peyré, Marco Cuturi, Learning Generative Models with Sinkhorn Divergences, Proceedings of the Twenty-First International Conference on Artficial Intelligence and Statistics, (AISTATS) 21, 2018 | [
"Compute",
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] | c5108efc7b6702e1af3928bef1032e6b37734d1c | https://github.com/rflamary/POT/blob/c5108efc7b6702e1af3928bef1032e6b37734d1c/ot/bregman.py#L1483-L1599 |
240,917 | rflamary/POT | ot/lp/__init__.py | emd | def emd(a, b, M, numItermax=100000, log=False):
"""Solves the Earth Movers distance problem and returns the OT matrix
.. math::
\gamma = arg\min_\gamma <\gamma,M>_F
s.t. \gamma 1 = a
\gamma^T 1= b
\gamma\geq 0
where :
- M is the metric cost matrix
- a and b are the sample weights
Uses the algorithm proposed in [1]_
Parameters
----------
a : (ns,) ndarray, float64
Source histogram (uniform weigth if empty list)
b : (nt,) ndarray, float64
Target histogram (uniform weigth if empty list)
M : (ns,nt) ndarray, float64
loss matrix
numItermax : int, optional (default=100000)
The maximum number of iterations before stopping the optimization
algorithm if it has not converged.
log: boolean, optional (default=False)
If True, returns a dictionary containing the cost and dual
variables. Otherwise returns only the optimal transportation matrix.
Returns
-------
gamma: (ns x nt) ndarray
Optimal transportation matrix for the given parameters
log: dict
If input log is true, a dictionary containing the cost and dual
variables and exit status
Examples
--------
Simple example with obvious solution. The function emd accepts lists and
perform automatic conversion to numpy arrays
>>> import ot
>>> a=[.5,.5]
>>> b=[.5,.5]
>>> M=[[0.,1.],[1.,0.]]
>>> ot.emd(a,b,M)
array([[ 0.5, 0. ],
[ 0. , 0.5]])
References
----------
.. [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.
See Also
--------
ot.bregman.sinkhorn : Entropic regularized OT
ot.optim.cg : General regularized OT"""
a = np.asarray(a, dtype=np.float64)
b = np.asarray(b, dtype=np.float64)
M = np.asarray(M, dtype=np.float64)
# if empty array given then use unifor distributions
if len(a) == 0:
a = np.ones((M.shape[0],), dtype=np.float64) / M.shape[0]
if len(b) == 0:
b = np.ones((M.shape[1],), dtype=np.float64) / M.shape[1]
G, cost, u, v, result_code = emd_c(a, b, M, numItermax)
result_code_string = check_result(result_code)
if log:
log = {}
log['cost'] = cost
log['u'] = u
log['v'] = v
log['warning'] = result_code_string
log['result_code'] = result_code
return G, log
return G | python | def emd(a, b, M, numItermax=100000, log=False):
a = np.asarray(a, dtype=np.float64)
b = np.asarray(b, dtype=np.float64)
M = np.asarray(M, dtype=np.float64)
# if empty array given then use unifor distributions
if len(a) == 0:
a = np.ones((M.shape[0],), dtype=np.float64) / M.shape[0]
if len(b) == 0:
b = np.ones((M.shape[1],), dtype=np.float64) / M.shape[1]
G, cost, u, v, result_code = emd_c(a, b, M, numItermax)
result_code_string = check_result(result_code)
if log:
log = {}
log['cost'] = cost
log['u'] = u
log['v'] = v
log['warning'] = result_code_string
log['result_code'] = result_code
return G, log
return G | [
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"... | Solves the Earth Movers distance problem and returns the OT matrix
.. math::
\gamma = arg\min_\gamma <\gamma,M>_F
s.t. \gamma 1 = a
\gamma^T 1= b
\gamma\geq 0
where :
- M is the metric cost matrix
- a and b are the sample weights
Uses the algorithm proposed in [1]_
Parameters
----------
a : (ns,) ndarray, float64
Source histogram (uniform weigth if empty list)
b : (nt,) ndarray, float64
Target histogram (uniform weigth if empty list)
M : (ns,nt) ndarray, float64
loss matrix
numItermax : int, optional (default=100000)
The maximum number of iterations before stopping the optimization
algorithm if it has not converged.
log: boolean, optional (default=False)
If True, returns a dictionary containing the cost and dual
variables. Otherwise returns only the optimal transportation matrix.
Returns
-------
gamma: (ns x nt) ndarray
Optimal transportation matrix for the given parameters
log: dict
If input log is true, a dictionary containing the cost and dual
variables and exit status
Examples
--------
Simple example with obvious solution. The function emd accepts lists and
perform automatic conversion to numpy arrays
>>> import ot
>>> a=[.5,.5]
>>> b=[.5,.5]
>>> M=[[0.,1.],[1.,0.]]
>>> ot.emd(a,b,M)
array([[ 0.5, 0. ],
[ 0. , 0.5]])
References
----------
.. [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.
See Also
--------
ot.bregman.sinkhorn : Entropic regularized OT
ot.optim.cg : General regularized OT | [
"Solves",
"the",
"Earth",
"Movers",
"distance",
"problem",
"and",
"returns",
"the",
"OT",
"matrix"
] | c5108efc7b6702e1af3928bef1032e6b37734d1c | https://github.com/rflamary/POT/blob/c5108efc7b6702e1af3928bef1032e6b37734d1c/ot/lp/__init__.py#L25-L113 |
240,918 | rflamary/POT | ot/lp/__init__.py | emd2 | def emd2(a, b, M, processes=multiprocessing.cpu_count(),
numItermax=100000, log=False, return_matrix=False):
"""Solves the Earth Movers distance problem and returns the loss
.. math::
\gamma = arg\min_\gamma <\gamma,M>_F
s.t. \gamma 1 = a
\gamma^T 1= b
\gamma\geq 0
where :
- M is the metric cost matrix
- a and b are the sample weights
Uses the algorithm proposed in [1]_
Parameters
----------
a : (ns,) ndarray, float64
Source histogram (uniform weigth if empty list)
b : (nt,) ndarray, float64
Target histogram (uniform weigth if empty list)
M : (ns,nt) ndarray, float64
loss matrix
numItermax : int, optional (default=100000)
The maximum number of iterations before stopping the optimization
algorithm if it has not converged.
log: boolean, optional (default=False)
If True, returns a dictionary containing the cost and dual
variables. Otherwise returns only the optimal transportation cost.
return_matrix: boolean, optional (default=False)
If True, returns the optimal transportation matrix in the log.
Returns
-------
gamma: (ns x nt) ndarray
Optimal transportation matrix for the given parameters
log: dict
If input log is true, a dictionary containing the cost and dual
variables and exit status
Examples
--------
Simple example with obvious solution. The function emd accepts lists and
perform automatic conversion to numpy arrays
>>> import ot
>>> a=[.5,.5]
>>> b=[.5,.5]
>>> M=[[0.,1.],[1.,0.]]
>>> ot.emd2(a,b,M)
0.0
References
----------
.. [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.
See Also
--------
ot.bregman.sinkhorn : Entropic regularized OT
ot.optim.cg : General regularized OT"""
a = np.asarray(a, dtype=np.float64)
b = np.asarray(b, dtype=np.float64)
M = np.asarray(M, dtype=np.float64)
# if empty array given then use unifor distributions
if len(a) == 0:
a = np.ones((M.shape[0],), dtype=np.float64) / M.shape[0]
if len(b) == 0:
b = np.ones((M.shape[1],), dtype=np.float64) / M.shape[1]
if log or return_matrix:
def f(b):
G, cost, u, v, resultCode = emd_c(a, b, M, numItermax)
result_code_string = check_result(resultCode)
log = {}
if return_matrix:
log['G'] = G
log['u'] = u
log['v'] = v
log['warning'] = result_code_string
log['result_code'] = resultCode
return [cost, log]
else:
def f(b):
G, cost, u, v, result_code = emd_c(a, b, M, numItermax)
check_result(result_code)
return cost
if len(b.shape) == 1:
return f(b)
nb = b.shape[1]
res = parmap(f, [b[:, i] for i in range(nb)], processes)
return res | python | def emd2(a, b, M, processes=multiprocessing.cpu_count(),
numItermax=100000, log=False, return_matrix=False):
a = np.asarray(a, dtype=np.float64)
b = np.asarray(b, dtype=np.float64)
M = np.asarray(M, dtype=np.float64)
# if empty array given then use unifor distributions
if len(a) == 0:
a = np.ones((M.shape[0],), dtype=np.float64) / M.shape[0]
if len(b) == 0:
b = np.ones((M.shape[1],), dtype=np.float64) / M.shape[1]
if log or return_matrix:
def f(b):
G, cost, u, v, resultCode = emd_c(a, b, M, numItermax)
result_code_string = check_result(resultCode)
log = {}
if return_matrix:
log['G'] = G
log['u'] = u
log['v'] = v
log['warning'] = result_code_string
log['result_code'] = resultCode
return [cost, log]
else:
def f(b):
G, cost, u, v, result_code = emd_c(a, b, M, numItermax)
check_result(result_code)
return cost
if len(b.shape) == 1:
return f(b)
nb = b.shape[1]
res = parmap(f, [b[:, i] for i in range(nb)], processes)
return res | [
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"asarr... | Solves the Earth Movers distance problem and returns the loss
.. math::
\gamma = arg\min_\gamma <\gamma,M>_F
s.t. \gamma 1 = a
\gamma^T 1= b
\gamma\geq 0
where :
- M is the metric cost matrix
- a and b are the sample weights
Uses the algorithm proposed in [1]_
Parameters
----------
a : (ns,) ndarray, float64
Source histogram (uniform weigth if empty list)
b : (nt,) ndarray, float64
Target histogram (uniform weigth if empty list)
M : (ns,nt) ndarray, float64
loss matrix
numItermax : int, optional (default=100000)
The maximum number of iterations before stopping the optimization
algorithm if it has not converged.
log: boolean, optional (default=False)
If True, returns a dictionary containing the cost and dual
variables. Otherwise returns only the optimal transportation cost.
return_matrix: boolean, optional (default=False)
If True, returns the optimal transportation matrix in the log.
Returns
-------
gamma: (ns x nt) ndarray
Optimal transportation matrix for the given parameters
log: dict
If input log is true, a dictionary containing the cost and dual
variables and exit status
Examples
--------
Simple example with obvious solution. The function emd accepts lists and
perform automatic conversion to numpy arrays
>>> import ot
>>> a=[.5,.5]
>>> b=[.5,.5]
>>> M=[[0.,1.],[1.,0.]]
>>> ot.emd2(a,b,M)
0.0
References
----------
.. [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.
See Also
--------
ot.bregman.sinkhorn : Entropic regularized OT
ot.optim.cg : General regularized OT | [
"Solves",
"the",
"Earth",
"Movers",
"distance",
"problem",
"and",
"returns",
"the",
"loss"
] | c5108efc7b6702e1af3928bef1032e6b37734d1c | https://github.com/rflamary/POT/blob/c5108efc7b6702e1af3928bef1032e6b37734d1c/ot/lp/__init__.py#L116-L219 |
240,919 | rflamary/POT | ot/da.py | sinkhorn_l1l2_gl | def sinkhorn_l1l2_gl(a, labels_a, b, M, reg, eta=0.1, numItermax=10,
numInnerItermax=200, stopInnerThr=1e-9, verbose=False,
log=False):
"""
Solve the entropic regularization optimal transport problem with group
lasso regularization
The function solves the following optimization problem:
.. math::
\gamma = arg\min_\gamma <\gamma,M>_F + reg\cdot\Omega_e(\gamma)+
\eta \Omega_g(\gamma)
s.t. \gamma 1 = a
\gamma^T 1= b
\gamma\geq 0
where :
- M is the (ns,nt) metric cost matrix
- :math:`\Omega_e` is the entropic regularization term
:math:`\Omega_e(\gamma)=\sum_{i,j} \gamma_{i,j}\log(\gamma_{i,j})`
- :math:`\Omega_g` is the group lasso regulaization term
:math:`\Omega_g(\gamma)=\sum_{i,c} \|\gamma_{i,\mathcal{I}_c}\|^2`
where :math:`\mathcal{I}_c` are the index of samples from class
c in the source domain.
- a and b are source and target weights (sum to 1)
The algorithm used for solving the problem is the generalised conditional
gradient as proposed in [5]_ [7]_
Parameters
----------
a : np.ndarray (ns,)
samples weights in the source domain
labels_a : np.ndarray (ns,)
labels of samples in the source domain
b : np.ndarray (nt,)
samples in the target domain
M : np.ndarray (ns,nt)
loss matrix
reg : float
Regularization term for entropic regularization >0
eta : float, optional
Regularization term for group lasso regularization >0
numItermax : int, optional
Max number of iterations
numInnerItermax : int, optional
Max number of iterations (inner sinkhorn solver)
stopInnerThr : float, optional
Stop threshold on error (inner sinkhorn solver) (>0)
verbose : bool, optional
Print information along iterations
log : bool, optional
record log if True
Returns
-------
gamma : (ns x nt) ndarray
Optimal transportation matrix for the given parameters
log : dict
log dictionary return only if log==True in parameters
References
----------
.. [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
.. [7] Rakotomamonjy, A., Flamary, R., & Courty, N. (2015).
Generalized conditional gradient: analysis of convergence and
applications. arXiv preprint arXiv:1510.06567.
See Also
--------
ot.optim.gcg : Generalized conditional gradient for OT problems
"""
lstlab = np.unique(labels_a)
def f(G):
res = 0
for i in range(G.shape[1]):
for lab in lstlab:
temp = G[labels_a == lab, i]
res += np.linalg.norm(temp)
return res
def df(G):
W = np.zeros(G.shape)
for i in range(G.shape[1]):
for lab in lstlab:
temp = G[labels_a == lab, i]
n = np.linalg.norm(temp)
if n:
W[labels_a == lab, i] = temp / n
return W
return gcg(a, b, M, reg, eta, f, df, G0=None, numItermax=numItermax,
numInnerItermax=numInnerItermax, stopThr=stopInnerThr,
verbose=verbose, log=log) | python | def sinkhorn_l1l2_gl(a, labels_a, b, M, reg, eta=0.1, numItermax=10,
numInnerItermax=200, stopInnerThr=1e-9, verbose=False,
log=False):
lstlab = np.unique(labels_a)
def f(G):
res = 0
for i in range(G.shape[1]):
for lab in lstlab:
temp = G[labels_a == lab, i]
res += np.linalg.norm(temp)
return res
def df(G):
W = np.zeros(G.shape)
for i in range(G.shape[1]):
for lab in lstlab:
temp = G[labels_a == lab, i]
n = np.linalg.norm(temp)
if n:
W[labels_a == lab, i] = temp / n
return W
return gcg(a, b, M, reg, eta, f, df, G0=None, numItermax=numItermax,
numInnerItermax=numInnerItermax, stopThr=stopInnerThr,
verbose=verbose, log=log) | [
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lasso regularization
The function solves the following optimization problem:
.. math::
\gamma = arg\min_\gamma <\gamma,M>_F + reg\cdot\Omega_e(\gamma)+
\eta \Omega_g(\gamma)
s.t. \gamma 1 = a
\gamma^T 1= b
\gamma\geq 0
where :
- M is the (ns,nt) metric cost matrix
- :math:`\Omega_e` is the entropic regularization term
:math:`\Omega_e(\gamma)=\sum_{i,j} \gamma_{i,j}\log(\gamma_{i,j})`
- :math:`\Omega_g` is the group lasso regulaization term
:math:`\Omega_g(\gamma)=\sum_{i,c} \|\gamma_{i,\mathcal{I}_c}\|^2`
where :math:`\mathcal{I}_c` are the index of samples from class
c in the source domain.
- a and b are source and target weights (sum to 1)
The algorithm used for solving the problem is the generalised conditional
gradient as proposed in [5]_ [7]_
Parameters
----------
a : np.ndarray (ns,)
samples weights in the source domain
labels_a : np.ndarray (ns,)
labels of samples in the source domain
b : np.ndarray (nt,)
samples in the target domain
M : np.ndarray (ns,nt)
loss matrix
reg : float
Regularization term for entropic regularization >0
eta : float, optional
Regularization term for group lasso regularization >0
numItermax : int, optional
Max number of iterations
numInnerItermax : int, optional
Max number of iterations (inner sinkhorn solver)
stopInnerThr : float, optional
Stop threshold on error (inner sinkhorn solver) (>0)
verbose : bool, optional
Print information along iterations
log : bool, optional
record log if True
Returns
-------
gamma : (ns x nt) ndarray
Optimal transportation matrix for the given parameters
log : dict
log dictionary return only if log==True in parameters
References
----------
.. [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
.. [7] Rakotomamonjy, A., Flamary, R., & Courty, N. (2015).
Generalized conditional gradient: analysis of convergence and
applications. arXiv preprint arXiv:1510.06567.
See Also
--------
ot.optim.gcg : Generalized conditional gradient for OT problems | [
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240,920 | rflamary/POT | ot/da.py | OT_mapping_linear | def OT_mapping_linear(xs, xt, reg=1e-6, ws=None,
wt=None, bias=True, log=False):
""" return OT linear operator between samples
The function estimates the optimal linear operator that aligns the two
empirical distributions. This is equivalent to estimating the closed
form mapping between two Gaussian distributions :math:`N(\mu_s,\Sigma_s)`
and :math:`N(\mu_t,\Sigma_t)` as proposed in [14] and discussed in remark 2.29 in [15].
The linear operator from source to target :math:`M`
.. math::
M(x)=Ax+b
where :
.. math::
A=\Sigma_s^{-1/2}(\Sigma_s^{1/2}\Sigma_t\Sigma_s^{1/2})^{1/2}
\Sigma_s^{-1/2}
.. math::
b=\mu_t-A\mu_s
Parameters
----------
xs : np.ndarray (ns,d)
samples in the source domain
xt : np.ndarray (nt,d)
samples in the target domain
reg : float,optional
regularization added to the diagonals of convariances (>0)
ws : np.ndarray (ns,1), optional
weights for the source samples
wt : np.ndarray (ns,1), optional
weights for the target samples
bias: boolean, optional
estimate bias b else b=0 (default:True)
log : bool, optional
record log if True
Returns
-------
A : (d x d) ndarray
Linear operator
b : (1 x d) ndarray
bias
log : dict
log dictionary return only if log==True in parameters
References
----------
.. [14] Knott, M. and Smith, C. S. "On the optimal mapping of
distributions", Journal of Optimization Theory and Applications
Vol 43, 1984
.. [15] Peyré, G., & Cuturi, M. (2017). "Computational Optimal
Transport", 2018.
"""
d = xs.shape[1]
if bias:
mxs = xs.mean(0, keepdims=True)
mxt = xt.mean(0, keepdims=True)
xs = xs - mxs
xt = xt - mxt
else:
mxs = np.zeros((1, d))
mxt = np.zeros((1, d))
if ws is None:
ws = np.ones((xs.shape[0], 1)) / xs.shape[0]
if wt is None:
wt = np.ones((xt.shape[0], 1)) / xt.shape[0]
Cs = (xs * ws).T.dot(xs) / ws.sum() + reg * np.eye(d)
Ct = (xt * wt).T.dot(xt) / wt.sum() + reg * np.eye(d)
Cs12 = linalg.sqrtm(Cs)
Cs_12 = linalg.inv(Cs12)
M0 = linalg.sqrtm(Cs12.dot(Ct.dot(Cs12)))
A = Cs_12.dot(M0.dot(Cs_12))
b = mxt - mxs.dot(A)
if log:
log = {}
log['Cs'] = Cs
log['Ct'] = Ct
log['Cs12'] = Cs12
log['Cs_12'] = Cs_12
return A, b, log
else:
return A, b | python | def OT_mapping_linear(xs, xt, reg=1e-6, ws=None,
wt=None, bias=True, log=False):
d = xs.shape[1]
if bias:
mxs = xs.mean(0, keepdims=True)
mxt = xt.mean(0, keepdims=True)
xs = xs - mxs
xt = xt - mxt
else:
mxs = np.zeros((1, d))
mxt = np.zeros((1, d))
if ws is None:
ws = np.ones((xs.shape[0], 1)) / xs.shape[0]
if wt is None:
wt = np.ones((xt.shape[0], 1)) / xt.shape[0]
Cs = (xs * ws).T.dot(xs) / ws.sum() + reg * np.eye(d)
Ct = (xt * wt).T.dot(xt) / wt.sum() + reg * np.eye(d)
Cs12 = linalg.sqrtm(Cs)
Cs_12 = linalg.inv(Cs12)
M0 = linalg.sqrtm(Cs12.dot(Ct.dot(Cs12)))
A = Cs_12.dot(M0.dot(Cs_12))
b = mxt - mxs.dot(A)
if log:
log = {}
log['Cs'] = Cs
log['Ct'] = Ct
log['Cs12'] = Cs12
log['Cs_12'] = Cs_12
return A, b, log
else:
return A, b | [
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The function estimates the optimal linear operator that aligns the two
empirical distributions. This is equivalent to estimating the closed
form mapping between two Gaussian distributions :math:`N(\mu_s,\Sigma_s)`
and :math:`N(\mu_t,\Sigma_t)` as proposed in [14] and discussed in remark 2.29 in [15].
The linear operator from source to target :math:`M`
.. math::
M(x)=Ax+b
where :
.. math::
A=\Sigma_s^{-1/2}(\Sigma_s^{1/2}\Sigma_t\Sigma_s^{1/2})^{1/2}
\Sigma_s^{-1/2}
.. math::
b=\mu_t-A\mu_s
Parameters
----------
xs : np.ndarray (ns,d)
samples in the source domain
xt : np.ndarray (nt,d)
samples in the target domain
reg : float,optional
regularization added to the diagonals of convariances (>0)
ws : np.ndarray (ns,1), optional
weights for the source samples
wt : np.ndarray (ns,1), optional
weights for the target samples
bias: boolean, optional
estimate bias b else b=0 (default:True)
log : bool, optional
record log if True
Returns
-------
A : (d x d) ndarray
Linear operator
b : (1 x d) ndarray
bias
log : dict
log dictionary return only if log==True in parameters
References
----------
.. [14] Knott, M. and Smith, C. S. "On the optimal mapping of
distributions", Journal of Optimization Theory and Applications
Vol 43, 1984
.. [15] Peyré, G., & Cuturi, M. (2017). "Computational Optimal
Transport", 2018. | [
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240,921 | rflamary/POT | ot/gpu/utils.py | euclidean_distances | def euclidean_distances(a, b, squared=False, to_numpy=True):
"""
Compute the pairwise euclidean distance between matrices a and b.
If the input matrix are in numpy format, they will be uploaded to the
GPU first which can incur significant time overhead.
Parameters
----------
a : np.ndarray (n, f)
first matrix
b : np.ndarray (m, f)
second matrix
to_numpy : boolean, optional (default True)
If true convert back the GPU array result to numpy format.
squared : boolean, optional (default False)
if True, return squared euclidean distance matrix
Returns
-------
c : (n x m) np.ndarray or cupy.ndarray
pairwise euclidean distance distance matrix
"""
a, b = to_gpu(a, b)
a2 = np.sum(np.square(a), 1)
b2 = np.sum(np.square(b), 1)
c = -2 * np.dot(a, b.T)
c += a2[:, None]
c += b2[None, :]
if not squared:
np.sqrt(c, out=c)
if to_numpy:
return to_np(c)
else:
return c | python | def euclidean_distances(a, b, squared=False, to_numpy=True):
a, b = to_gpu(a, b)
a2 = np.sum(np.square(a), 1)
b2 = np.sum(np.square(b), 1)
c = -2 * np.dot(a, b.T)
c += a2[:, None]
c += b2[None, :]
if not squared:
np.sqrt(c, out=c)
if to_numpy:
return to_np(c)
else:
return c | [
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b : np.ndarray (m, f)
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240,922 | rflamary/POT | ot/gpu/utils.py | dist | def dist(x1, x2=None, metric='sqeuclidean', to_numpy=True):
"""Compute distance between samples in x1 and x2 on gpu
Parameters
----------
x1 : np.array (n1,d)
matrix with n1 samples of size d
x2 : np.array (n2,d), optional
matrix with n2 samples of size d (if None then x2=x1)
metric : str
Metric from 'sqeuclidean', 'euclidean',
Returns
-------
M : np.array (n1,n2)
distance matrix computed with given metric
"""
if x2 is None:
x2 = x1
if metric == "sqeuclidean":
return euclidean_distances(x1, x2, squared=True, to_numpy=to_numpy)
elif metric == "euclidean":
return euclidean_distances(x1, x2, squared=False, to_numpy=to_numpy)
else:
raise NotImplementedError | python | def dist(x1, x2=None, metric='sqeuclidean', to_numpy=True):
if x2 is None:
x2 = x1
if metric == "sqeuclidean":
return euclidean_distances(x1, x2, squared=True, to_numpy=to_numpy)
elif metric == "euclidean":
return euclidean_distances(x1, x2, squared=False, to_numpy=to_numpy)
else:
raise NotImplementedError | [
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240,923 | rflamary/POT | ot/gpu/utils.py | to_gpu | def to_gpu(*args):
""" Upload numpy arrays to GPU and return them"""
if len(args) > 1:
return (cp.asarray(x) for x in args)
else:
return cp.asarray(args[0]) | python | def to_gpu(*args):
if len(args) > 1:
return (cp.asarray(x) for x in args)
else:
return cp.asarray(args[0]) | [
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240,924 | rflamary/POT | ot/gpu/utils.py | to_np | def to_np(*args):
""" convert GPU arras to numpy and return them"""
if len(args) > 1:
return (cp.asnumpy(x) for x in args)
else:
return cp.asnumpy(args[0]) | python | def to_np(*args):
if len(args) > 1:
return (cp.asnumpy(x) for x in args)
else:
return cp.asnumpy(args[0]) | [
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240,925 | rflamary/POT | ot/lp/cvx.py | scipy_sparse_to_spmatrix | def scipy_sparse_to_spmatrix(A):
"""Efficient conversion from scipy sparse matrix to cvxopt sparse matrix"""
coo = A.tocoo()
SP = spmatrix(coo.data.tolist(), coo.row.tolist(), coo.col.tolist(), size=A.shape)
return SP | python | def scipy_sparse_to_spmatrix(A):
coo = A.tocoo()
SP = spmatrix(coo.data.tolist(), coo.row.tolist(), coo.col.tolist(), size=A.shape)
return SP | [
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240,926 | rflamary/POT | ot/optim.py | line_search_armijo | def line_search_armijo(f, xk, pk, gfk, old_fval,
args=(), c1=1e-4, alpha0=0.99):
"""
Armijo linesearch function that works with matrices
find an approximate minimum of f(xk+alpha*pk) that satifies the
armijo conditions.
Parameters
----------
f : function
loss function
xk : np.ndarray
initial position
pk : np.ndarray
descent direction
gfk : np.ndarray
gradient of f at xk
old_fval : float
loss value at xk
args : tuple, optional
arguments given to f
c1 : float, optional
c1 const in armijo rule (>0)
alpha0 : float, optional
initial step (>0)
Returns
-------
alpha : float
step that satisfy armijo conditions
fc : int
nb of function call
fa : float
loss value at step alpha
"""
xk = np.atleast_1d(xk)
fc = [0]
def phi(alpha1):
fc[0] += 1
return f(xk + alpha1 * pk, *args)
if old_fval is None:
phi0 = phi(0.)
else:
phi0 = old_fval
derphi0 = np.sum(pk * gfk) # Quickfix for matrices
alpha, phi1 = scalar_search_armijo(
phi, phi0, derphi0, c1=c1, alpha0=alpha0)
return alpha, fc[0], phi1 | python | def line_search_armijo(f, xk, pk, gfk, old_fval,
args=(), c1=1e-4, alpha0=0.99):
xk = np.atleast_1d(xk)
fc = [0]
def phi(alpha1):
fc[0] += 1
return f(xk + alpha1 * pk, *args)
if old_fval is None:
phi0 = phi(0.)
else:
phi0 = old_fval
derphi0 = np.sum(pk * gfk) # Quickfix for matrices
alpha, phi1 = scalar_search_armijo(
phi, phi0, derphi0, c1=c1, alpha0=alpha0)
return alpha, fc[0], phi1 | [
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find an approximate minimum of f(xk+alpha*pk) that satifies the
armijo conditions.
Parameters
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f : function
loss function
xk : np.ndarray
initial position
pk : np.ndarray
descent direction
gfk : np.ndarray
gradient of f at xk
old_fval : float
loss value at xk
args : tuple, optional
arguments given to f
c1 : float, optional
c1 const in armijo rule (>0)
alpha0 : float, optional
initial step (>0)
Returns
-------
alpha : float
step that satisfy armijo conditions
fc : int
nb of function call
fa : float
loss value at step alpha | [
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240,927 | rflamary/POT | ot/optim.py | cg | def cg(a, b, M, reg, f, df, G0=None, numItermax=200,
stopThr=1e-9, verbose=False, log=False):
"""
Solve the general regularized OT problem with conditional gradient
The function solves the following optimization problem:
.. math::
\gamma = arg\min_\gamma <\gamma,M>_F + reg*f(\gamma)
s.t. \gamma 1 = a
\gamma^T 1= b
\gamma\geq 0
where :
- M is the (ns,nt) metric cost matrix
- :math:`f` is the regularization term ( and df is its gradient)
- a and b are source and target weights (sum to 1)
The algorithm used for solving the problem is conditional gradient as discussed in [1]_
Parameters
----------
a : np.ndarray (ns,)
samples weights in the source domain
b : np.ndarray (nt,)
samples in the target domain
M : np.ndarray (ns,nt)
loss matrix
reg : float
Regularization term >0
G0 : np.ndarray (ns,nt), optional
initial guess (default is indep joint density)
numItermax : int, optional
Max number of iterations
stopThr : float, optional
Stop threshol on error (>0)
verbose : bool, optional
Print information along iterations
log : bool, optional
record log if True
Returns
-------
gamma : (ns x nt) ndarray
Optimal transportation matrix for the given parameters
log : dict
log dictionary return only if log==True in parameters
References
----------
.. [1] Ferradans, S., Papadakis, N., Peyré, G., & Aujol, J. F. (2014). Regularized discrete optimal transport. SIAM Journal on Imaging Sciences, 7(3), 1853-1882.
See Also
--------
ot.lp.emd : Unregularized optimal ransport
ot.bregman.sinkhorn : Entropic regularized optimal transport
"""
loop = 1
if log:
log = {'loss': []}
if G0 is None:
G = np.outer(a, b)
else:
G = G0
def cost(G):
return np.sum(M * G) + reg * f(G)
f_val = cost(G)
if log:
log['loss'].append(f_val)
it = 0
if verbose:
print('{:5s}|{:12s}|{:8s}'.format(
'It.', 'Loss', 'Delta loss') + '\n' + '-' * 32)
print('{:5d}|{:8e}|{:8e}'.format(it, f_val, 0))
while loop:
it += 1
old_fval = f_val
# problem linearization
Mi = M + reg * df(G)
# set M positive
Mi += Mi.min()
# solve linear program
Gc = emd(a, b, Mi)
deltaG = Gc - G
# line search
alpha, fc, f_val = line_search_armijo(cost, G, deltaG, Mi, f_val)
G = G + alpha * deltaG
# test convergence
if it >= numItermax:
loop = 0
delta_fval = (f_val - old_fval) / abs(f_val)
if abs(delta_fval) < stopThr:
loop = 0
if log:
log['loss'].append(f_val)
if verbose:
if it % 20 == 0:
print('{:5s}|{:12s}|{:8s}'.format(
'It.', 'Loss', 'Delta loss') + '\n' + '-' * 32)
print('{:5d}|{:8e}|{:8e}'.format(it, f_val, delta_fval))
if log:
return G, log
else:
return G | python | def cg(a, b, M, reg, f, df, G0=None, numItermax=200,
stopThr=1e-9, verbose=False, log=False):
loop = 1
if log:
log = {'loss': []}
if G0 is None:
G = np.outer(a, b)
else:
G = G0
def cost(G):
return np.sum(M * G) + reg * f(G)
f_val = cost(G)
if log:
log['loss'].append(f_val)
it = 0
if verbose:
print('{:5s}|{:12s}|{:8s}'.format(
'It.', 'Loss', 'Delta loss') + '\n' + '-' * 32)
print('{:5d}|{:8e}|{:8e}'.format(it, f_val, 0))
while loop:
it += 1
old_fval = f_val
# problem linearization
Mi = M + reg * df(G)
# set M positive
Mi += Mi.min()
# solve linear program
Gc = emd(a, b, Mi)
deltaG = Gc - G
# line search
alpha, fc, f_val = line_search_armijo(cost, G, deltaG, Mi, f_val)
G = G + alpha * deltaG
# test convergence
if it >= numItermax:
loop = 0
delta_fval = (f_val - old_fval) / abs(f_val)
if abs(delta_fval) < stopThr:
loop = 0
if log:
log['loss'].append(f_val)
if verbose:
if it % 20 == 0:
print('{:5s}|{:12s}|{:8s}'.format(
'It.', 'Loss', 'Delta loss') + '\n' + '-' * 32)
print('{:5d}|{:8e}|{:8e}'.format(it, f_val, delta_fval))
if log:
return G, log
else:
return G | [
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The function solves the following optimization problem:
.. math::
\gamma = arg\min_\gamma <\gamma,M>_F + reg*f(\gamma)
s.t. \gamma 1 = a
\gamma^T 1= b
\gamma\geq 0
where :
- M is the (ns,nt) metric cost matrix
- :math:`f` is the regularization term ( and df is its gradient)
- a and b are source and target weights (sum to 1)
The algorithm used for solving the problem is conditional gradient as discussed in [1]_
Parameters
----------
a : np.ndarray (ns,)
samples weights in the source domain
b : np.ndarray (nt,)
samples in the target domain
M : np.ndarray (ns,nt)
loss matrix
reg : float
Regularization term >0
G0 : np.ndarray (ns,nt), optional
initial guess (default is indep joint density)
numItermax : int, optional
Max number of iterations
stopThr : float, optional
Stop threshol on error (>0)
verbose : bool, optional
Print information along iterations
log : bool, optional
record log if True
Returns
-------
gamma : (ns x nt) ndarray
Optimal transportation matrix for the given parameters
log : dict
log dictionary return only if log==True in parameters
References
----------
.. [1] Ferradans, S., Papadakis, N., Peyré, G., & Aujol, J. F. (2014). Regularized discrete optimal transport. SIAM Journal on Imaging Sciences, 7(3), 1853-1882.
See Also
--------
ot.lp.emd : Unregularized optimal ransport
ot.bregman.sinkhorn : Entropic regularized optimal transport | [
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240,928 | rflamary/POT | ot/optim.py | gcg | def gcg(a, b, M, reg1, reg2, f, df, G0=None, numItermax=10,
numInnerItermax=200, stopThr=1e-9, verbose=False, log=False):
"""
Solve the general regularized OT problem with the generalized conditional gradient
The function solves the following optimization problem:
.. math::
\gamma = arg\min_\gamma <\gamma,M>_F + reg1\cdot\Omega(\gamma) + reg2\cdot f(\gamma)
s.t. \gamma 1 = a
\gamma^T 1= b
\gamma\geq 0
where :
- M is the (ns,nt) metric cost matrix
- :math:`\Omega` is the entropic regularization term :math:`\Omega(\gamma)=\sum_{i,j} \gamma_{i,j}\log(\gamma_{i,j})`
- :math:`f` is the regularization term ( and df is its gradient)
- a and b are source and target weights (sum to 1)
The algorithm used for solving the problem is the generalized conditional gradient as discussed in [5,7]_
Parameters
----------
a : np.ndarray (ns,)
samples weights in the source domain
b : np.ndarray (nt,)
samples in the target domain
M : np.ndarray (ns,nt)
loss matrix
reg1 : float
Entropic Regularization term >0
reg2 : float
Second Regularization term >0
G0 : np.ndarray (ns,nt), optional
initial guess (default is indep joint density)
numItermax : int, optional
Max number of iterations
numInnerItermax : int, optional
Max number of iterations of Sinkhorn
stopThr : float, optional
Stop threshol on error (>0)
verbose : bool, optional
Print information along iterations
log : bool, optional
record log if True
Returns
-------
gamma : (ns x nt) ndarray
Optimal transportation matrix for the given parameters
log : dict
log dictionary return only if log==True in parameters
References
----------
.. [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
.. [7] Rakotomamonjy, A., Flamary, R., & Courty, N. (2015). Generalized conditional gradient: analysis of convergence and applications. arXiv preprint arXiv:1510.06567.
See Also
--------
ot.optim.cg : conditional gradient
"""
loop = 1
if log:
log = {'loss': []}
if G0 is None:
G = np.outer(a, b)
else:
G = G0
def cost(G):
return np.sum(M * G) + reg1 * np.sum(G * np.log(G)) + reg2 * f(G)
f_val = cost(G)
if log:
log['loss'].append(f_val)
it = 0
if verbose:
print('{:5s}|{:12s}|{:8s}'.format(
'It.', 'Loss', 'Delta loss') + '\n' + '-' * 32)
print('{:5d}|{:8e}|{:8e}'.format(it, f_val, 0))
while loop:
it += 1
old_fval = f_val
# problem linearization
Mi = M + reg2 * df(G)
# solve linear program with Sinkhorn
# Gc = sinkhorn_stabilized(a,b, Mi, reg1, numItermax = numInnerItermax)
Gc = sinkhorn(a, b, Mi, reg1, numItermax=numInnerItermax)
deltaG = Gc - G
# line search
dcost = Mi + reg1 * (1 + np.log(G)) # ??
alpha, fc, f_val = line_search_armijo(cost, G, deltaG, dcost, f_val)
G = G + alpha * deltaG
# test convergence
if it >= numItermax:
loop = 0
delta_fval = (f_val - old_fval) / abs(f_val)
if abs(delta_fval) < stopThr:
loop = 0
if log:
log['loss'].append(f_val)
if verbose:
if it % 20 == 0:
print('{:5s}|{:12s}|{:8s}'.format(
'It.', 'Loss', 'Delta loss') + '\n' + '-' * 32)
print('{:5d}|{:8e}|{:8e}'.format(it, f_val, delta_fval))
if log:
return G, log
else:
return G | python | def gcg(a, b, M, reg1, reg2, f, df, G0=None, numItermax=10,
numInnerItermax=200, stopThr=1e-9, verbose=False, log=False):
loop = 1
if log:
log = {'loss': []}
if G0 is None:
G = np.outer(a, b)
else:
G = G0
def cost(G):
return np.sum(M * G) + reg1 * np.sum(G * np.log(G)) + reg2 * f(G)
f_val = cost(G)
if log:
log['loss'].append(f_val)
it = 0
if verbose:
print('{:5s}|{:12s}|{:8s}'.format(
'It.', 'Loss', 'Delta loss') + '\n' + '-' * 32)
print('{:5d}|{:8e}|{:8e}'.format(it, f_val, 0))
while loop:
it += 1
old_fval = f_val
# problem linearization
Mi = M + reg2 * df(G)
# solve linear program with Sinkhorn
# Gc = sinkhorn_stabilized(a,b, Mi, reg1, numItermax = numInnerItermax)
Gc = sinkhorn(a, b, Mi, reg1, numItermax=numInnerItermax)
deltaG = Gc - G
# line search
dcost = Mi + reg1 * (1 + np.log(G)) # ??
alpha, fc, f_val = line_search_armijo(cost, G, deltaG, dcost, f_val)
G = G + alpha * deltaG
# test convergence
if it >= numItermax:
loop = 0
delta_fval = (f_val - old_fval) / abs(f_val)
if abs(delta_fval) < stopThr:
loop = 0
if log:
log['loss'].append(f_val)
if verbose:
if it % 20 == 0:
print('{:5s}|{:12s}|{:8s}'.format(
'It.', 'Loss', 'Delta loss') + '\n' + '-' * 32)
print('{:5d}|{:8e}|{:8e}'.format(it, f_val, delta_fval))
if log:
return G, log
else:
return G | [
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",",... | Solve the general regularized OT problem with the generalized conditional gradient
The function solves the following optimization problem:
.. math::
\gamma = arg\min_\gamma <\gamma,M>_F + reg1\cdot\Omega(\gamma) + reg2\cdot f(\gamma)
s.t. \gamma 1 = a
\gamma^T 1= b
\gamma\geq 0
where :
- M is the (ns,nt) metric cost matrix
- :math:`\Omega` is the entropic regularization term :math:`\Omega(\gamma)=\sum_{i,j} \gamma_{i,j}\log(\gamma_{i,j})`
- :math:`f` is the regularization term ( and df is its gradient)
- a and b are source and target weights (sum to 1)
The algorithm used for solving the problem is the generalized conditional gradient as discussed in [5,7]_
Parameters
----------
a : np.ndarray (ns,)
samples weights in the source domain
b : np.ndarray (nt,)
samples in the target domain
M : np.ndarray (ns,nt)
loss matrix
reg1 : float
Entropic Regularization term >0
reg2 : float
Second Regularization term >0
G0 : np.ndarray (ns,nt), optional
initial guess (default is indep joint density)
numItermax : int, optional
Max number of iterations
numInnerItermax : int, optional
Max number of iterations of Sinkhorn
stopThr : float, optional
Stop threshol on error (>0)
verbose : bool, optional
Print information along iterations
log : bool, optional
record log if True
Returns
-------
gamma : (ns x nt) ndarray
Optimal transportation matrix for the given parameters
log : dict
log dictionary return only if log==True in parameters
References
----------
.. [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
.. [7] Rakotomamonjy, A., Flamary, R., & Courty, N. (2015). Generalized conditional gradient: analysis of convergence and applications. arXiv preprint arXiv:1510.06567.
See Also
--------
ot.optim.cg : conditional gradient | [
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240,929 | rflamary/POT | ot/smooth.py | projection_simplex | def projection_simplex(V, z=1, axis=None):
""" Projection of x onto the simplex, scaled by z
P(x; z) = argmin_{y >= 0, sum(y) = z} ||y - x||^2
z: float or array
If array, len(z) must be compatible with V
axis: None or int
- axis=None: project V by P(V.ravel(); z)
- axis=1: project each V[i] by P(V[i]; z[i])
- axis=0: project each V[:, j] by P(V[:, j]; z[j])
"""
if axis == 1:
n_features = V.shape[1]
U = np.sort(V, axis=1)[:, ::-1]
z = np.ones(len(V)) * z
cssv = np.cumsum(U, axis=1) - z[:, np.newaxis]
ind = np.arange(n_features) + 1
cond = U - cssv / ind > 0
rho = np.count_nonzero(cond, axis=1)
theta = cssv[np.arange(len(V)), rho - 1] / rho
return np.maximum(V - theta[:, np.newaxis], 0)
elif axis == 0:
return projection_simplex(V.T, z, axis=1).T
else:
V = V.ravel().reshape(1, -1)
return projection_simplex(V, z, axis=1).ravel() | python | def projection_simplex(V, z=1, axis=None):
if axis == 1:
n_features = V.shape[1]
U = np.sort(V, axis=1)[:, ::-1]
z = np.ones(len(V)) * z
cssv = np.cumsum(U, axis=1) - z[:, np.newaxis]
ind = np.arange(n_features) + 1
cond = U - cssv / ind > 0
rho = np.count_nonzero(cond, axis=1)
theta = cssv[np.arange(len(V)), rho - 1] / rho
return np.maximum(V - theta[:, np.newaxis], 0)
elif axis == 0:
return projection_simplex(V.T, z, axis=1).T
else:
V = V.ravel().reshape(1, -1)
return projection_simplex(V, z, axis=1).ravel() | [
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P(x; z) = argmin_{y >= 0, sum(y) = z} ||y - x||^2
z: float or array
If array, len(z) must be compatible with V
axis: None or int
- axis=None: project V by P(V.ravel(); z)
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240,930 | rflamary/POT | ot/smooth.py | dual_obj_grad | def dual_obj_grad(alpha, beta, a, b, C, regul):
"""
Compute objective value and gradients of dual objective.
Parameters
----------
alpha: array, shape = len(a)
beta: array, shape = len(b)
Current iterate of dual potentials.
a: array, shape = len(a)
b: array, shape = len(b)
Input histograms (should be non-negative and sum to 1).
C: array, shape = len(a) x len(b)
Ground cost matrix.
regul: Regularization object
Should implement a delta_Omega(X) method.
Returns
-------
obj: float
Objective value (higher is better).
grad_alpha: array, shape = len(a)
Gradient w.r.t. alpha.
grad_beta: array, shape = len(b)
Gradient w.r.t. beta.
"""
obj = np.dot(alpha, a) + np.dot(beta, b)
grad_alpha = a.copy()
grad_beta = b.copy()
# X[:, j] = alpha + beta[j] - C[:, j]
X = alpha[:, np.newaxis] + beta - C
# val.shape = len(b)
# G.shape = len(a) x len(b)
val, G = regul.delta_Omega(X)
obj -= np.sum(val)
grad_alpha -= G.sum(axis=1)
grad_beta -= G.sum(axis=0)
return obj, grad_alpha, grad_beta | python | def dual_obj_grad(alpha, beta, a, b, C, regul):
obj = np.dot(alpha, a) + np.dot(beta, b)
grad_alpha = a.copy()
grad_beta = b.copy()
# X[:, j] = alpha + beta[j] - C[:, j]
X = alpha[:, np.newaxis] + beta - C
# val.shape = len(b)
# G.shape = len(a) x len(b)
val, G = regul.delta_Omega(X)
obj -= np.sum(val)
grad_alpha -= G.sum(axis=1)
grad_beta -= G.sum(axis=0)
return obj, grad_alpha, grad_beta | [
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Parameters
----------
alpha: array, shape = len(a)
beta: array, shape = len(b)
Current iterate of dual potentials.
a: array, shape = len(a)
b: array, shape = len(b)
Input histograms (should be non-negative and sum to 1).
C: array, shape = len(a) x len(b)
Ground cost matrix.
regul: Regularization object
Should implement a delta_Omega(X) method.
Returns
-------
obj: float
Objective value (higher is better).
grad_alpha: array, shape = len(a)
Gradient w.r.t. alpha.
grad_beta: array, shape = len(b)
Gradient w.r.t. beta. | [
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240,931 | rflamary/POT | ot/smooth.py | solve_dual | def solve_dual(a, b, C, regul, method="L-BFGS-B", tol=1e-3, max_iter=500,
verbose=False):
"""
Solve the "smoothed" dual objective.
Parameters
----------
a: array, shape = len(a)
b: array, shape = len(b)
Input histograms (should be non-negative and sum to 1).
C: array, shape = len(a) x len(b)
Ground cost matrix.
regul: Regularization object
Should implement a delta_Omega(X) method.
method: str
Solver to be used (passed to `scipy.optimize.minimize`).
tol: float
Tolerance parameter.
max_iter: int
Maximum number of iterations.
Returns
-------
alpha: array, shape = len(a)
beta: array, shape = len(b)
Dual potentials.
"""
def _func(params):
# Unpack alpha and beta.
alpha = params[:len(a)]
beta = params[len(a):]
obj, grad_alpha, grad_beta = dual_obj_grad(alpha, beta, a, b, C, regul)
# Pack grad_alpha and grad_beta.
grad = np.concatenate((grad_alpha, grad_beta))
# We need to maximize the dual.
return -obj, -grad
# Unfortunately, `minimize` only supports functions whose argument is a
# vector. So, we need to concatenate alpha and beta.
alpha_init = np.zeros(len(a))
beta_init = np.zeros(len(b))
params_init = np.concatenate((alpha_init, beta_init))
res = minimize(_func, params_init, method=method, jac=True,
tol=tol, options=dict(maxiter=max_iter, disp=verbose))
alpha = res.x[:len(a)]
beta = res.x[len(a):]
return alpha, beta, res | python | def solve_dual(a, b, C, regul, method="L-BFGS-B", tol=1e-3, max_iter=500,
verbose=False):
def _func(params):
# Unpack alpha and beta.
alpha = params[:len(a)]
beta = params[len(a):]
obj, grad_alpha, grad_beta = dual_obj_grad(alpha, beta, a, b, C, regul)
# Pack grad_alpha and grad_beta.
grad = np.concatenate((grad_alpha, grad_beta))
# We need to maximize the dual.
return -obj, -grad
# Unfortunately, `minimize` only supports functions whose argument is a
# vector. So, we need to concatenate alpha and beta.
alpha_init = np.zeros(len(a))
beta_init = np.zeros(len(b))
params_init = np.concatenate((alpha_init, beta_init))
res = minimize(_func, params_init, method=method, jac=True,
tol=tol, options=dict(maxiter=max_iter, disp=verbose))
alpha = res.x[:len(a)]
beta = res.x[len(a):]
return alpha, beta, res | [
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b: array, shape = len(b)
Input histograms (should be non-negative and sum to 1).
C: array, shape = len(a) x len(b)
Ground cost matrix.
regul: Regularization object
Should implement a delta_Omega(X) method.
method: str
Solver to be used (passed to `scipy.optimize.minimize`).
tol: float
Tolerance parameter.
max_iter: int
Maximum number of iterations.
Returns
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alpha: array, shape = len(a)
beta: array, shape = len(b)
Dual potentials. | [
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240,932 | rflamary/POT | ot/smooth.py | semi_dual_obj_grad | def semi_dual_obj_grad(alpha, a, b, C, regul):
"""
Compute objective value and gradient of semi-dual objective.
Parameters
----------
alpha: array, shape = len(a)
Current iterate of semi-dual potentials.
a: array, shape = len(a)
b: array, shape = len(b)
Input histograms (should be non-negative and sum to 1).
C: array, shape = len(a) x len(b)
Ground cost matrix.
regul: Regularization object
Should implement a max_Omega(X) method.
Returns
-------
obj: float
Objective value (higher is better).
grad: array, shape = len(a)
Gradient w.r.t. alpha.
"""
obj = np.dot(alpha, a)
grad = a.copy()
# X[:, j] = alpha - C[:, j]
X = alpha[:, np.newaxis] - C
# val.shape = len(b)
# G.shape = len(a) x len(b)
val, G = regul.max_Omega(X, b)
obj -= np.dot(b, val)
grad -= np.dot(G, b)
return obj, grad | python | def semi_dual_obj_grad(alpha, a, b, C, regul):
obj = np.dot(alpha, a)
grad = a.copy()
# X[:, j] = alpha - C[:, j]
X = alpha[:, np.newaxis] - C
# val.shape = len(b)
# G.shape = len(a) x len(b)
val, G = regul.max_Omega(X, b)
obj -= np.dot(b, val)
grad -= np.dot(G, b)
return obj, grad | [
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alpha: array, shape = len(a)
Current iterate of semi-dual potentials.
a: array, shape = len(a)
b: array, shape = len(b)
Input histograms (should be non-negative and sum to 1).
C: array, shape = len(a) x len(b)
Ground cost matrix.
regul: Regularization object
Should implement a max_Omega(X) method.
Returns
-------
obj: float
Objective value (higher is better).
grad: array, shape = len(a)
Gradient w.r.t. alpha. | [
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240,933 | rflamary/POT | ot/smooth.py | solve_semi_dual | def solve_semi_dual(a, b, C, regul, method="L-BFGS-B", tol=1e-3, max_iter=500,
verbose=False):
"""
Solve the "smoothed" semi-dual objective.
Parameters
----------
a: array, shape = len(a)
b: array, shape = len(b)
Input histograms (should be non-negative and sum to 1).
C: array, shape = len(a) x len(b)
Ground cost matrix.
regul: Regularization object
Should implement a max_Omega(X) method.
method: str
Solver to be used (passed to `scipy.optimize.minimize`).
tol: float
Tolerance parameter.
max_iter: int
Maximum number of iterations.
Returns
-------
alpha: array, shape = len(a)
Semi-dual potentials.
"""
def _func(alpha):
obj, grad = semi_dual_obj_grad(alpha, a, b, C, regul)
# We need to maximize the semi-dual.
return -obj, -grad
alpha_init = np.zeros(len(a))
res = minimize(_func, alpha_init, method=method, jac=True,
tol=tol, options=dict(maxiter=max_iter, disp=verbose))
return res.x, res | python | def solve_semi_dual(a, b, C, regul, method="L-BFGS-B", tol=1e-3, max_iter=500,
verbose=False):
def _func(alpha):
obj, grad = semi_dual_obj_grad(alpha, a, b, C, regul)
# We need to maximize the semi-dual.
return -obj, -grad
alpha_init = np.zeros(len(a))
res = minimize(_func, alpha_init, method=method, jac=True,
tol=tol, options=dict(maxiter=max_iter, disp=verbose))
return res.x, res | [
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b: array, shape = len(b)
Input histograms (should be non-negative and sum to 1).
C: array, shape = len(a) x len(b)
Ground cost matrix.
regul: Regularization object
Should implement a max_Omega(X) method.
method: str
Solver to be used (passed to `scipy.optimize.minimize`).
tol: float
Tolerance parameter.
max_iter: int
Maximum number of iterations.
Returns
-------
alpha: array, shape = len(a)
Semi-dual potentials. | [
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240,934 | rflamary/POT | ot/smooth.py | get_plan_from_dual | def get_plan_from_dual(alpha, beta, C, regul):
"""
Retrieve optimal transportation plan from optimal dual potentials.
Parameters
----------
alpha: array, shape = len(a)
beta: array, shape = len(b)
Optimal dual potentials.
C: array, shape = len(a) x len(b)
Ground cost matrix.
regul: Regularization object
Should implement a delta_Omega(X) method.
Returns
-------
T: array, shape = len(a) x len(b)
Optimal transportation plan.
"""
X = alpha[:, np.newaxis] + beta - C
return regul.delta_Omega(X)[1] | python | def get_plan_from_dual(alpha, beta, C, regul):
X = alpha[:, np.newaxis] + beta - C
return regul.delta_Omega(X)[1] | [
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Parameters
----------
alpha: array, shape = len(a)
beta: array, shape = len(b)
Optimal dual potentials.
C: array, shape = len(a) x len(b)
Ground cost matrix.
regul: Regularization object
Should implement a delta_Omega(X) method.
Returns
-------
T: array, shape = len(a) x len(b)
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240,935 | rflamary/POT | ot/smooth.py | get_plan_from_semi_dual | def get_plan_from_semi_dual(alpha, b, C, regul):
"""
Retrieve optimal transportation plan from optimal semi-dual potentials.
Parameters
----------
alpha: array, shape = len(a)
Optimal semi-dual potentials.
b: array, shape = len(b)
Second input histogram (should be non-negative and sum to 1).
C: array, shape = len(a) x len(b)
Ground cost matrix.
regul: Regularization object
Should implement a delta_Omega(X) method.
Returns
-------
T: array, shape = len(a) x len(b)
Optimal transportation plan.
"""
X = alpha[:, np.newaxis] - C
return regul.max_Omega(X, b)[1] * b | python | def get_plan_from_semi_dual(alpha, b, C, regul):
X = alpha[:, np.newaxis] - C
return regul.max_Omega(X, b)[1] * b | [
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Parameters
----------
alpha: array, shape = len(a)
Optimal semi-dual potentials.
b: array, shape = len(b)
Second input histogram (should be non-negative and sum to 1).
C: array, shape = len(a) x len(b)
Ground cost matrix.
regul: Regularization object
Should implement a delta_Omega(X) method.
Returns
-------
T: array, shape = len(a) x len(b)
Optimal transportation plan. | [
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240,936 | rflamary/POT | ot/smooth.py | smooth_ot_dual | def smooth_ot_dual(a, b, M, reg, reg_type='l2', method="L-BFGS-B", stopThr=1e-9,
numItermax=500, verbose=False, log=False):
r"""
Solve the regularized OT problem in the dual and return the OT matrix
The function solves the smooth relaxed dual formulation (7) in [17]_ :
.. math::
\max_{\alpha,\beta}\quad a^T\alpha+b^T\beta-\sum_j\delta_\Omega(\alpha+\beta_j-\mathbf{m}_j)
where :
- :math:`\mathbf{m}_j` is the jth column of the cost matrix
- :math:`\delta_\Omega` is the convex conjugate of the regularization term :math:`\Omega`
- a and b are source and target weights (sum to 1)
The OT matrix can is reconstructed from the gradient of :math:`\delta_\Omega`
(See [17]_ Proposition 1).
The optimization algorithm is using gradient decent (L-BFGS by default).
Parameters
----------
a : np.ndarray (ns,)
samples weights in the source domain
b : np.ndarray (nt,) or np.ndarray (nt,nbb)
samples in the target domain, compute sinkhorn with multiple targets
and fixed M if b is a matrix (return OT loss + dual variables in log)
M : np.ndarray (ns,nt)
loss matrix
reg : float
Regularization term >0
reg_type : str
Regularization type, can be the following (default ='l2'):
- 'kl' : Kullback Leibler (~ Neg-entropy used in sinkhorn [2]_)
- 'l2' : Squared Euclidean regularization
method : str
Solver to use for scipy.optimize.minimize
numItermax : int, optional
Max number of iterations
stopThr : float, optional
Stop threshol on error (>0)
verbose : bool, optional
Print information along iterations
log : bool, optional
record log if True
Returns
-------
gamma : (ns x nt) ndarray
Optimal transportation matrix for the given parameters
log : dict
log dictionary return only if log==True in parameters
References
----------
.. [2] M. Cuturi, Sinkhorn Distances : Lightspeed Computation of Optimal Transport, Advances in Neural Information Processing Systems (NIPS) 26, 2013
.. [17] Blondel, M., Seguy, V., & Rolet, A. (2018). Smooth and Sparse Optimal Transport. Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics (AISTATS).
See Also
--------
ot.lp.emd : Unregularized OT
ot.sinhorn : Entropic regularized OT
ot.optim.cg : General regularized OT
"""
if reg_type.lower() in ['l2', 'squaredl2']:
regul = SquaredL2(gamma=reg)
elif reg_type.lower() in ['entropic', 'negentropy', 'kl']:
regul = NegEntropy(gamma=reg)
else:
raise NotImplementedError('Unknown regularization')
# solve dual
alpha, beta, res = solve_dual(a, b, M, regul, max_iter=numItermax,
tol=stopThr, verbose=verbose)
# reconstruct transport matrix
G = get_plan_from_dual(alpha, beta, M, regul)
if log:
log = {'alpha': alpha, 'beta': beta, 'res': res}
return G, log
else:
return G | python | def smooth_ot_dual(a, b, M, reg, reg_type='l2', method="L-BFGS-B", stopThr=1e-9,
numItermax=500, verbose=False, log=False):
r"""
Solve the regularized OT problem in the dual and return the OT matrix
The function solves the smooth relaxed dual formulation (7) in [17]_ :
.. math::
\max_{\alpha,\beta}\quad a^T\alpha+b^T\beta-\sum_j\delta_\Omega(\alpha+\beta_j-\mathbf{m}_j)
where :
- :math:`\mathbf{m}_j` is the jth column of the cost matrix
- :math:`\delta_\Omega` is the convex conjugate of the regularization term :math:`\Omega`
- a and b are source and target weights (sum to 1)
The OT matrix can is reconstructed from the gradient of :math:`\delta_\Omega`
(See [17]_ Proposition 1).
The optimization algorithm is using gradient decent (L-BFGS by default).
Parameters
----------
a : np.ndarray (ns,)
samples weights in the source domain
b : np.ndarray (nt,) or np.ndarray (nt,nbb)
samples in the target domain, compute sinkhorn with multiple targets
and fixed M if b is a matrix (return OT loss + dual variables in log)
M : np.ndarray (ns,nt)
loss matrix
reg : float
Regularization term >0
reg_type : str
Regularization type, can be the following (default ='l2'):
- 'kl' : Kullback Leibler (~ Neg-entropy used in sinkhorn [2]_)
- 'l2' : Squared Euclidean regularization
method : str
Solver to use for scipy.optimize.minimize
numItermax : int, optional
Max number of iterations
stopThr : float, optional
Stop threshol on error (>0)
verbose : bool, optional
Print information along iterations
log : bool, optional
record log if True
Returns
-------
gamma : (ns x nt) ndarray
Optimal transportation matrix for the given parameters
log : dict
log dictionary return only if log==True in parameters
References
----------
.. [2] M. Cuturi, Sinkhorn Distances : Lightspeed Computation of Optimal Transport, Advances in Neural Information Processing Systems (NIPS) 26, 2013
.. [17] Blondel, M., Seguy, V., & Rolet, A. (2018). Smooth and Sparse Optimal Transport. Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics (AISTATS).
See Also
--------
ot.lp.emd : Unregularized OT
ot.sinhorn : Entropic regularized OT
ot.optim.cg : General regularized OT
"""
if reg_type.lower() in ['l2', 'squaredl2']:
regul = SquaredL2(gamma=reg)
elif reg_type.lower() in ['entropic', 'negentropy', 'kl']:
regul = NegEntropy(gamma=reg)
else:
raise NotImplementedError('Unknown regularization')
# solve dual
alpha, beta, res = solve_dual(a, b, M, regul, max_iter=numItermax,
tol=stopThr, verbose=verbose)
# reconstruct transport matrix
G = get_plan_from_dual(alpha, beta, M, regul)
if log:
log = {'alpha': alpha, 'beta': beta, 'res': res}
return G, log
else:
return G | [
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Solve the regularized OT problem in the dual and return the OT matrix
The function solves the smooth relaxed dual formulation (7) in [17]_ :
.. math::
\max_{\alpha,\beta}\quad a^T\alpha+b^T\beta-\sum_j\delta_\Omega(\alpha+\beta_j-\mathbf{m}_j)
where :
- :math:`\mathbf{m}_j` is the jth column of the cost matrix
- :math:`\delta_\Omega` is the convex conjugate of the regularization term :math:`\Omega`
- a and b are source and target weights (sum to 1)
The OT matrix can is reconstructed from the gradient of :math:`\delta_\Omega`
(See [17]_ Proposition 1).
The optimization algorithm is using gradient decent (L-BFGS by default).
Parameters
----------
a : np.ndarray (ns,)
samples weights in the source domain
b : np.ndarray (nt,) or np.ndarray (nt,nbb)
samples in the target domain, compute sinkhorn with multiple targets
and fixed M if b is a matrix (return OT loss + dual variables in log)
M : np.ndarray (ns,nt)
loss matrix
reg : float
Regularization term >0
reg_type : str
Regularization type, can be the following (default ='l2'):
- 'kl' : Kullback Leibler (~ Neg-entropy used in sinkhorn [2]_)
- 'l2' : Squared Euclidean regularization
method : str
Solver to use for scipy.optimize.minimize
numItermax : int, optional
Max number of iterations
stopThr : float, optional
Stop threshol on error (>0)
verbose : bool, optional
Print information along iterations
log : bool, optional
record log if True
Returns
-------
gamma : (ns x nt) ndarray
Optimal transportation matrix for the given parameters
log : dict
log dictionary return only if log==True in parameters
References
----------
.. [2] M. Cuturi, Sinkhorn Distances : Lightspeed Computation of Optimal Transport, Advances in Neural Information Processing Systems (NIPS) 26, 2013
.. [17] Blondel, M., Seguy, V., & Rolet, A. (2018). Smooth and Sparse Optimal Transport. Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics (AISTATS).
See Also
--------
ot.lp.emd : Unregularized OT
ot.sinhorn : Entropic regularized OT
ot.optim.cg : General regularized OT | [
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240,937 | rflamary/POT | ot/smooth.py | smooth_ot_semi_dual | def smooth_ot_semi_dual(a, b, M, reg, reg_type='l2', method="L-BFGS-B", stopThr=1e-9,
numItermax=500, verbose=False, log=False):
r"""
Solve the regularized OT problem in the semi-dual and return the OT matrix
The function solves the smooth relaxed dual formulation (10) in [17]_ :
.. math::
\max_{\alpha}\quad a^T\alpha-OT_\Omega^*(\alpha,b)
where :
.. math::
OT_\Omega^*(\alpha,b)=\sum_j b_j
- :math:`\mathbf{m}_j` is the jth column of the cost matrix
- :math:`OT_\Omega^*(\alpha,b)` is defined in Eq. (9) in [17]
- a and b are source and target weights (sum to 1)
The OT matrix can is reconstructed using [17]_ Proposition 2.
The optimization algorithm is using gradient decent (L-BFGS by default).
Parameters
----------
a : np.ndarray (ns,)
samples weights in the source domain
b : np.ndarray (nt,) or np.ndarray (nt,nbb)
samples in the target domain, compute sinkhorn with multiple targets
and fixed M if b is a matrix (return OT loss + dual variables in log)
M : np.ndarray (ns,nt)
loss matrix
reg : float
Regularization term >0
reg_type : str
Regularization type, can be the following (default ='l2'):
- 'kl' : Kullback Leibler (~ Neg-entropy used in sinkhorn [2]_)
- 'l2' : Squared Euclidean regularization
method : str
Solver to use for scipy.optimize.minimize
numItermax : int, optional
Max number of iterations
stopThr : float, optional
Stop threshol on error (>0)
verbose : bool, optional
Print information along iterations
log : bool, optional
record log if True
Returns
-------
gamma : (ns x nt) ndarray
Optimal transportation matrix for the given parameters
log : dict
log dictionary return only if log==True in parameters
References
----------
.. [2] M. Cuturi, Sinkhorn Distances : Lightspeed Computation of Optimal Transport, Advances in Neural Information Processing Systems (NIPS) 26, 2013
.. [17] Blondel, M., Seguy, V., & Rolet, A. (2018). Smooth and Sparse Optimal Transport. Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics (AISTATS).
See Also
--------
ot.lp.emd : Unregularized OT
ot.sinhorn : Entropic regularized OT
ot.optim.cg : General regularized OT
"""
if reg_type.lower() in ['l2', 'squaredl2']:
regul = SquaredL2(gamma=reg)
elif reg_type.lower() in ['entropic', 'negentropy', 'kl']:
regul = NegEntropy(gamma=reg)
else:
raise NotImplementedError('Unknown regularization')
# solve dual
alpha, res = solve_semi_dual(a, b, M, regul, max_iter=numItermax,
tol=stopThr, verbose=verbose)
# reconstruct transport matrix
G = get_plan_from_semi_dual(alpha, b, M, regul)
if log:
log = {'alpha': alpha, 'res': res}
return G, log
else:
return G | python | def smooth_ot_semi_dual(a, b, M, reg, reg_type='l2', method="L-BFGS-B", stopThr=1e-9,
numItermax=500, verbose=False, log=False):
r"""
Solve the regularized OT problem in the semi-dual and return the OT matrix
The function solves the smooth relaxed dual formulation (10) in [17]_ :
.. math::
\max_{\alpha}\quad a^T\alpha-OT_\Omega^*(\alpha,b)
where :
.. math::
OT_\Omega^*(\alpha,b)=\sum_j b_j
- :math:`\mathbf{m}_j` is the jth column of the cost matrix
- :math:`OT_\Omega^*(\alpha,b)` is defined in Eq. (9) in [17]
- a and b are source and target weights (sum to 1)
The OT matrix can is reconstructed using [17]_ Proposition 2.
The optimization algorithm is using gradient decent (L-BFGS by default).
Parameters
----------
a : np.ndarray (ns,)
samples weights in the source domain
b : np.ndarray (nt,) or np.ndarray (nt,nbb)
samples in the target domain, compute sinkhorn with multiple targets
and fixed M if b is a matrix (return OT loss + dual variables in log)
M : np.ndarray (ns,nt)
loss matrix
reg : float
Regularization term >0
reg_type : str
Regularization type, can be the following (default ='l2'):
- 'kl' : Kullback Leibler (~ Neg-entropy used in sinkhorn [2]_)
- 'l2' : Squared Euclidean regularization
method : str
Solver to use for scipy.optimize.minimize
numItermax : int, optional
Max number of iterations
stopThr : float, optional
Stop threshol on error (>0)
verbose : bool, optional
Print information along iterations
log : bool, optional
record log if True
Returns
-------
gamma : (ns x nt) ndarray
Optimal transportation matrix for the given parameters
log : dict
log dictionary return only if log==True in parameters
References
----------
.. [2] M. Cuturi, Sinkhorn Distances : Lightspeed Computation of Optimal Transport, Advances in Neural Information Processing Systems (NIPS) 26, 2013
.. [17] Blondel, M., Seguy, V., & Rolet, A. (2018). Smooth and Sparse Optimal Transport. Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics (AISTATS).
See Also
--------
ot.lp.emd : Unregularized OT
ot.sinhorn : Entropic regularized OT
ot.optim.cg : General regularized OT
"""
if reg_type.lower() in ['l2', 'squaredl2']:
regul = SquaredL2(gamma=reg)
elif reg_type.lower() in ['entropic', 'negentropy', 'kl']:
regul = NegEntropy(gamma=reg)
else:
raise NotImplementedError('Unknown regularization')
# solve dual
alpha, res = solve_semi_dual(a, b, M, regul, max_iter=numItermax,
tol=stopThr, verbose=verbose)
# reconstruct transport matrix
G = get_plan_from_semi_dual(alpha, b, M, regul)
if log:
log = {'alpha': alpha, 'res': res}
return G, log
else:
return G | [
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Solve the regularized OT problem in the semi-dual and return the OT matrix
The function solves the smooth relaxed dual formulation (10) in [17]_ :
.. math::
\max_{\alpha}\quad a^T\alpha-OT_\Omega^*(\alpha,b)
where :
.. math::
OT_\Omega^*(\alpha,b)=\sum_j b_j
- :math:`\mathbf{m}_j` is the jth column of the cost matrix
- :math:`OT_\Omega^*(\alpha,b)` is defined in Eq. (9) in [17]
- a and b are source and target weights (sum to 1)
The OT matrix can is reconstructed using [17]_ Proposition 2.
The optimization algorithm is using gradient decent (L-BFGS by default).
Parameters
----------
a : np.ndarray (ns,)
samples weights in the source domain
b : np.ndarray (nt,) or np.ndarray (nt,nbb)
samples in the target domain, compute sinkhorn with multiple targets
and fixed M if b is a matrix (return OT loss + dual variables in log)
M : np.ndarray (ns,nt)
loss matrix
reg : float
Regularization term >0
reg_type : str
Regularization type, can be the following (default ='l2'):
- 'kl' : Kullback Leibler (~ Neg-entropy used in sinkhorn [2]_)
- 'l2' : Squared Euclidean regularization
method : str
Solver to use for scipy.optimize.minimize
numItermax : int, optional
Max number of iterations
stopThr : float, optional
Stop threshol on error (>0)
verbose : bool, optional
Print information along iterations
log : bool, optional
record log if True
Returns
-------
gamma : (ns x nt) ndarray
Optimal transportation matrix for the given parameters
log : dict
log dictionary return only if log==True in parameters
References
----------
.. [2] M. Cuturi, Sinkhorn Distances : Lightspeed Computation of Optimal Transport, Advances in Neural Information Processing Systems (NIPS) 26, 2013
.. [17] Blondel, M., Seguy, V., & Rolet, A. (2018). Smooth and Sparse Optimal Transport. Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics (AISTATS).
See Also
--------
ot.lp.emd : Unregularized OT
ot.sinhorn : Entropic regularized OT
ot.optim.cg : General regularized OT | [
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240,938 | rflamary/POT | ot/utils.py | kernel | def kernel(x1, x2, method='gaussian', sigma=1, **kwargs):
"""Compute kernel matrix"""
if method.lower() in ['gaussian', 'gauss', 'rbf']:
K = np.exp(-dist(x1, x2) / (2 * sigma**2))
return K | python | def kernel(x1, x2, method='gaussian', sigma=1, **kwargs):
if method.lower() in ['gaussian', 'gauss', 'rbf']:
K = np.exp(-dist(x1, x2) / (2 * sigma**2))
return K | [
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240,939 | rflamary/POT | ot/utils.py | clean_zeros | def clean_zeros(a, b, M):
""" Remove all components with zeros weights in a and b
"""
M2 = M[a > 0, :][:, b > 0].copy() # copy force c style matrix (froemd)
a2 = a[a > 0]
b2 = b[b > 0]
return a2, b2, M2 | python | def clean_zeros(a, b, M):
M2 = M[a > 0, :][:, b > 0].copy() # copy force c style matrix (froemd)
a2 = a[a > 0]
b2 = b[b > 0]
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240,940 | rflamary/POT | ot/utils.py | dist | def dist(x1, x2=None, metric='sqeuclidean'):
"""Compute distance between samples in x1 and x2 using function scipy.spatial.distance.cdist
Parameters
----------
x1 : np.array (n1,d)
matrix with n1 samples of size d
x2 : np.array (n2,d), optional
matrix with n2 samples of size d (if None then x2=x1)
metric : str, fun, optional
name of the metric to be computed (full list in the doc of scipy), If a string,
the distance function can be 'braycurtis', 'canberra', 'chebyshev', 'cityblock',
'correlation', 'cosine', 'dice', 'euclidean', 'hamming', 'jaccard', 'kulsinski',
'mahalanobis', 'matching', 'minkowski', 'rogerstanimoto', 'russellrao', 'seuclidean',
'sokalmichener', 'sokalsneath', 'sqeuclidean', 'wminkowski', 'yule'.
Returns
-------
M : np.array (n1,n2)
distance matrix computed with given metric
"""
if x2 is None:
x2 = x1
if metric == "sqeuclidean":
return euclidean_distances(x1, x2, squared=True)
return cdist(x1, x2, metric=metric) | python | def dist(x1, x2=None, metric='sqeuclidean'):
if x2 is None:
x2 = x1
if metric == "sqeuclidean":
return euclidean_distances(x1, x2, squared=True)
return cdist(x1, x2, metric=metric) | [
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x1 : np.array (n1,d)
matrix with n1 samples of size d
x2 : np.array (n2,d), optional
matrix with n2 samples of size d (if None then x2=x1)
metric : str, fun, optional
name of the metric to be computed (full list in the doc of scipy), If a string,
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M : np.array (n1,n2)
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240,941 | rflamary/POT | ot/utils.py | cost_normalization | def cost_normalization(C, norm=None):
""" Apply normalization to the loss matrix
Parameters
----------
C : np.array (n1, n2)
The cost matrix to normalize.
norm : str
type of normalization from 'median','max','log','loglog'. Any other
value do not normalize.
Returns
-------
C : np.array (n1, n2)
The input cost matrix normalized according to given norm.
"""
if norm == "median":
C /= float(np.median(C))
elif norm == "max":
C /= float(np.max(C))
elif norm == "log":
C = np.log(1 + C)
elif norm == "loglog":
C = np.log(1 + np.log(1 + C))
return C | python | def cost_normalization(C, norm=None):
if norm == "median":
C /= float(np.median(C))
elif norm == "max":
C /= float(np.max(C))
elif norm == "log":
C = np.log(1 + C)
elif norm == "loglog":
C = np.log(1 + np.log(1 + C))
return C | [
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The cost matrix to normalize.
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240,942 | rflamary/POT | ot/utils.py | parmap | def parmap(f, X, nprocs=multiprocessing.cpu_count()):
""" paralell map for multiprocessing """
q_in = multiprocessing.Queue(1)
q_out = multiprocessing.Queue()
proc = [multiprocessing.Process(target=fun, args=(f, q_in, q_out))
for _ in range(nprocs)]
for p in proc:
p.daemon = True
p.start()
sent = [q_in.put((i, x)) for i, x in enumerate(X)]
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res = [q_out.get() for _ in range(len(sent))]
[p.join() for p in proc]
return [x for i, x in sorted(res)] | python | def parmap(f, X, nprocs=multiprocessing.cpu_count()):
q_in = multiprocessing.Queue(1)
q_out = multiprocessing.Queue()
proc = [multiprocessing.Process(target=fun, args=(f, q_in, q_out))
for _ in range(nprocs)]
for p in proc:
p.daemon = True
p.start()
sent = [q_in.put((i, x)) for i, x in enumerate(X)]
[q_in.put((None, None)) for _ in range(nprocs)]
res = [q_out.get() for _ in range(len(sent))]
[p.join() for p in proc]
return [x for i, x in sorted(res)] | [
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240,943 | rflamary/POT | ot/utils.py | _is_deprecated | def _is_deprecated(func):
"""Helper to check if func is wraped by our deprecated decorator"""
if sys.version_info < (3, 5):
raise NotImplementedError("This is only available for python3.5 "
"or above")
closures = getattr(func, '__closure__', [])
if closures is None:
closures = []
is_deprecated = ('deprecated' in ''.join([c.cell_contents
for c in closures
if isinstance(c.cell_contents, str)]))
return is_deprecated | python | def _is_deprecated(func):
if sys.version_info < (3, 5):
raise NotImplementedError("This is only available for python3.5 "
"or above")
closures = getattr(func, '__closure__', [])
if closures is None:
closures = []
is_deprecated = ('deprecated' in ''.join([c.cell_contents
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240,944 | rflamary/POT | ot/utils.py | deprecated._decorate_fun | def _decorate_fun(self, fun):
"""Decorate function fun"""
msg = "Function %s is deprecated" % fun.__name__
if self.extra:
msg += "; %s" % self.extra
def wrapped(*args, **kwargs):
warnings.warn(msg, category=DeprecationWarning)
return fun(*args, **kwargs)
wrapped.__name__ = fun.__name__
wrapped.__dict__ = fun.__dict__
wrapped.__doc__ = self._update_doc(fun.__doc__)
return wrapped | python | def _decorate_fun(self, fun):
msg = "Function %s is deprecated" % fun.__name__
if self.extra:
msg += "; %s" % self.extra
def wrapped(*args, **kwargs):
warnings.warn(msg, category=DeprecationWarning)
return fun(*args, **kwargs)
wrapped.__name__ = fun.__name__
wrapped.__dict__ = fun.__dict__
wrapped.__doc__ = self._update_doc(fun.__doc__)
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240,945 | rflamary/POT | ot/dr.py | split_classes | def split_classes(X, y):
"""split samples in X by classes in y
"""
lstsclass = np.unique(y)
return [X[y == i, :].astype(np.float32) for i in lstsclass] | python | def split_classes(X, y):
lstsclass = np.unique(y)
return [X[y == i, :].astype(np.float32) for i in lstsclass] | [
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240,946 | rflamary/POT | ot/dr.py | fda | def fda(X, y, p=2, reg=1e-16):
"""
Fisher Discriminant Analysis
Parameters
----------
X : numpy.ndarray (n,d)
Training samples
y : np.ndarray (n,)
labels for training samples
p : int, optional
size of dimensionnality reduction
reg : float, optional
Regularization term >0 (ridge regularization)
Returns
-------
P : (d x p) ndarray
Optimal transportation matrix for the given parameters
proj : fun
projection function including mean centering
"""
mx = np.mean(X)
X -= mx.reshape((1, -1))
# data split between classes
d = X.shape[1]
xc = split_classes(X, y)
nc = len(xc)
p = min(nc - 1, p)
Cw = 0
for x in xc:
Cw += np.cov(x, rowvar=False)
Cw /= nc
mxc = np.zeros((d, nc))
for i in range(nc):
mxc[:, i] = np.mean(xc[i])
mx0 = np.mean(mxc, 1)
Cb = 0
for i in range(nc):
Cb += (mxc[:, i] - mx0).reshape((-1, 1)) * \
(mxc[:, i] - mx0).reshape((1, -1))
w, V = linalg.eig(Cb, Cw + reg * np.eye(d))
idx = np.argsort(w.real)
Popt = V[:, idx[-p:]]
def proj(X):
return (X - mx.reshape((1, -1))).dot(Popt)
return Popt, proj | python | def fda(X, y, p=2, reg=1e-16):
mx = np.mean(X)
X -= mx.reshape((1, -1))
# data split between classes
d = X.shape[1]
xc = split_classes(X, y)
nc = len(xc)
p = min(nc - 1, p)
Cw = 0
for x in xc:
Cw += np.cov(x, rowvar=False)
Cw /= nc
mxc = np.zeros((d, nc))
for i in range(nc):
mxc[:, i] = np.mean(xc[i])
mx0 = np.mean(mxc, 1)
Cb = 0
for i in range(nc):
Cb += (mxc[:, i] - mx0).reshape((-1, 1)) * \
(mxc[:, i] - mx0).reshape((1, -1))
w, V = linalg.eig(Cb, Cw + reg * np.eye(d))
idx = np.argsort(w.real)
Popt = V[:, idx[-p:]]
def proj(X):
return (X - mx.reshape((1, -1))).dot(Popt)
return Popt, proj | [
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Training samples
y : np.ndarray (n,)
labels for training samples
p : int, optional
size of dimensionnality reduction
reg : float, optional
Regularization term >0 (ridge regularization)
Returns
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P : (d x p) ndarray
Optimal transportation matrix for the given parameters
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projection function including mean centering | [
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240,947 | rflamary/POT | ot/stochastic.py | sag_entropic_transport | def sag_entropic_transport(a, b, M, reg, numItermax=10000, lr=None):
'''
Compute the SAG algorithm to solve the regularized discrete measures
optimal transport max problem
The function solves the following optimization problem:
.. math::
\gamma = arg\min_\gamma <\gamma,M>_F + reg\cdot\Omega(\gamma)
s.t. \gamma 1 = a
\gamma^T 1 = b
\gamma \geq 0
Where :
- M is the (ns,nt) metric cost matrix
- :math:`\Omega` is the entropic regularization term with :math:`\Omega(\gamma)=\sum_{i,j} \gamma_{i,j}\log(\gamma_{i,j})`
- a and b are source and target weights (sum to 1)
The algorithm used for solving the problem is the SAG algorithm
as proposed in [18]_ [alg.1]
Parameters
----------
a : np.ndarray(ns,),
source measure
b : np.ndarray(nt,),
target measure
M : np.ndarray(ns, nt),
cost matrix
reg : float number,
Regularization term > 0
numItermax : int number
number of iteration
lr : float number
learning rate
Returns
-------
v : np.ndarray(nt,)
dual variable
Examples
--------
>>> n_source = 7
>>> n_target = 4
>>> reg = 1
>>> numItermax = 300000
>>> a = ot.utils.unif(n_source)
>>> b = ot.utils.unif(n_target)
>>> rng = np.random.RandomState(0)
>>> X_source = rng.randn(n_source, 2)
>>> Y_target = rng.randn(n_target, 2)
>>> M = ot.dist(X_source, Y_target)
>>> method = "ASGD"
>>> asgd_pi = stochastic.solve_semi_dual_entropic(a, b, M, reg,
method, numItermax)
>>> print(asgd_pi)
References
----------
[Genevay et al., 2016] :
Stochastic Optimization for Large-scale Optimal Transport,
Advances in Neural Information Processing Systems (2016),
arXiv preprint arxiv:1605.08527.
'''
if lr is None:
lr = 1. / max(a / reg)
n_source = np.shape(M)[0]
n_target = np.shape(M)[1]
cur_beta = np.zeros(n_target)
stored_gradient = np.zeros((n_source, n_target))
sum_stored_gradient = np.zeros(n_target)
for _ in range(numItermax):
i = np.random.randint(n_source)
cur_coord_grad = a[i] * coordinate_grad_semi_dual(b, M, reg,
cur_beta, i)
sum_stored_gradient += (cur_coord_grad - stored_gradient[i])
stored_gradient[i] = cur_coord_grad
cur_beta += lr * (1. / n_source) * sum_stored_gradient
return cur_beta | python | def sag_entropic_transport(a, b, M, reg, numItermax=10000, lr=None):
'''
Compute the SAG algorithm to solve the regularized discrete measures
optimal transport max problem
The function solves the following optimization problem:
.. math::
\gamma = arg\min_\gamma <\gamma,M>_F + reg\cdot\Omega(\gamma)
s.t. \gamma 1 = a
\gamma^T 1 = b
\gamma \geq 0
Where :
- M is the (ns,nt) metric cost matrix
- :math:`\Omega` is the entropic regularization term with :math:`\Omega(\gamma)=\sum_{i,j} \gamma_{i,j}\log(\gamma_{i,j})`
- a and b are source and target weights (sum to 1)
The algorithm used for solving the problem is the SAG algorithm
as proposed in [18]_ [alg.1]
Parameters
----------
a : np.ndarray(ns,),
source measure
b : np.ndarray(nt,),
target measure
M : np.ndarray(ns, nt),
cost matrix
reg : float number,
Regularization term > 0
numItermax : int number
number of iteration
lr : float number
learning rate
Returns
-------
v : np.ndarray(nt,)
dual variable
Examples
--------
>>> n_source = 7
>>> n_target = 4
>>> reg = 1
>>> numItermax = 300000
>>> a = ot.utils.unif(n_source)
>>> b = ot.utils.unif(n_target)
>>> rng = np.random.RandomState(0)
>>> X_source = rng.randn(n_source, 2)
>>> Y_target = rng.randn(n_target, 2)
>>> M = ot.dist(X_source, Y_target)
>>> method = "ASGD"
>>> asgd_pi = stochastic.solve_semi_dual_entropic(a, b, M, reg,
method, numItermax)
>>> print(asgd_pi)
References
----------
[Genevay et al., 2016] :
Stochastic Optimization for Large-scale Optimal Transport,
Advances in Neural Information Processing Systems (2016),
arXiv preprint arxiv:1605.08527.
'''
if lr is None:
lr = 1. / max(a / reg)
n_source = np.shape(M)[0]
n_target = np.shape(M)[1]
cur_beta = np.zeros(n_target)
stored_gradient = np.zeros((n_source, n_target))
sum_stored_gradient = np.zeros(n_target)
for _ in range(numItermax):
i = np.random.randint(n_source)
cur_coord_grad = a[i] * coordinate_grad_semi_dual(b, M, reg,
cur_beta, i)
sum_stored_gradient += (cur_coord_grad - stored_gradient[i])
stored_gradient[i] = cur_coord_grad
cur_beta += lr * (1. / n_source) * sum_stored_gradient
return cur_beta | [
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optimal transport max problem
The function solves the following optimization problem:
.. math::
\gamma = arg\min_\gamma <\gamma,M>_F + reg\cdot\Omega(\gamma)
s.t. \gamma 1 = a
\gamma^T 1 = b
\gamma \geq 0
Where :
- M is the (ns,nt) metric cost matrix
- :math:`\Omega` is the entropic regularization term with :math:`\Omega(\gamma)=\sum_{i,j} \gamma_{i,j}\log(\gamma_{i,j})`
- a and b are source and target weights (sum to 1)
The algorithm used for solving the problem is the SAG algorithm
as proposed in [18]_ [alg.1]
Parameters
----------
a : np.ndarray(ns,),
source measure
b : np.ndarray(nt,),
target measure
M : np.ndarray(ns, nt),
cost matrix
reg : float number,
Regularization term > 0
numItermax : int number
number of iteration
lr : float number
learning rate
Returns
-------
v : np.ndarray(nt,)
dual variable
Examples
--------
>>> n_source = 7
>>> n_target = 4
>>> reg = 1
>>> numItermax = 300000
>>> a = ot.utils.unif(n_source)
>>> b = ot.utils.unif(n_target)
>>> rng = np.random.RandomState(0)
>>> X_source = rng.randn(n_source, 2)
>>> Y_target = rng.randn(n_target, 2)
>>> M = ot.dist(X_source, Y_target)
>>> method = "ASGD"
>>> asgd_pi = stochastic.solve_semi_dual_entropic(a, b, M, reg,
method, numItermax)
>>> print(asgd_pi)
References
----------
[Genevay et al., 2016] :
Stochastic Optimization for Large-scale Optimal Transport,
Advances in Neural Information Processing Systems (2016),
arXiv preprint arxiv:1605.08527. | [
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240,948 | rflamary/POT | ot/stochastic.py | averaged_sgd_entropic_transport | def averaged_sgd_entropic_transport(a, b, M, reg, numItermax=300000, lr=None):
'''
Compute the ASGD algorithm to solve the regularized semi continous measures optimal transport max problem
The function solves the following optimization problem:
.. math::
\gamma = arg\min_\gamma <\gamma,M>_F + reg\cdot\Omega(\gamma)
s.t. \gamma 1 = a
\gamma^T 1= b
\gamma \geq 0
Where :
- M is the (ns,nt) metric cost matrix
- :math:`\Omega` is the entropic regularization term with :math:`\Omega(\gamma)=\sum_{i,j} \gamma_{i,j}\log(\gamma_{i,j})`
- a and b are source and target weights (sum to 1)
The algorithm used for solving the problem is the ASGD algorithm
as proposed in [18]_ [alg.2]
Parameters
----------
b : np.ndarray(nt,)
target measure
M : np.ndarray(ns, nt)
cost matrix
reg : float number
Regularization term > 0
numItermax : int number
number of iteration
lr : float number
learning rate
Returns
-------
ave_v : np.ndarray(nt,)
dual variable
Examples
--------
>>> n_source = 7
>>> n_target = 4
>>> reg = 1
>>> numItermax = 300000
>>> a = ot.utils.unif(n_source)
>>> b = ot.utils.unif(n_target)
>>> rng = np.random.RandomState(0)
>>> X_source = rng.randn(n_source, 2)
>>> Y_target = rng.randn(n_target, 2)
>>> M = ot.dist(X_source, Y_target)
>>> method = "ASGD"
>>> asgd_pi = stochastic.solve_semi_dual_entropic(a, b, M, reg,
method, numItermax)
>>> print(asgd_pi)
References
----------
[Genevay et al., 2016] :
Stochastic Optimization for Large-scale Optimal Transport,
Advances in Neural Information Processing Systems (2016),
arXiv preprint arxiv:1605.08527.
'''
if lr is None:
lr = 1. / max(a / reg)
n_source = np.shape(M)[0]
n_target = np.shape(M)[1]
cur_beta = np.zeros(n_target)
ave_beta = np.zeros(n_target)
for cur_iter in range(numItermax):
k = cur_iter + 1
i = np.random.randint(n_source)
cur_coord_grad = coordinate_grad_semi_dual(b, M, reg, cur_beta, i)
cur_beta += (lr / np.sqrt(k)) * cur_coord_grad
ave_beta = (1. / k) * cur_beta + (1 - 1. / k) * ave_beta
return ave_beta | python | def averaged_sgd_entropic_transport(a, b, M, reg, numItermax=300000, lr=None):
'''
Compute the ASGD algorithm to solve the regularized semi continous measures optimal transport max problem
The function solves the following optimization problem:
.. math::
\gamma = arg\min_\gamma <\gamma,M>_F + reg\cdot\Omega(\gamma)
s.t. \gamma 1 = a
\gamma^T 1= b
\gamma \geq 0
Where :
- M is the (ns,nt) metric cost matrix
- :math:`\Omega` is the entropic regularization term with :math:`\Omega(\gamma)=\sum_{i,j} \gamma_{i,j}\log(\gamma_{i,j})`
- a and b are source and target weights (sum to 1)
The algorithm used for solving the problem is the ASGD algorithm
as proposed in [18]_ [alg.2]
Parameters
----------
b : np.ndarray(nt,)
target measure
M : np.ndarray(ns, nt)
cost matrix
reg : float number
Regularization term > 0
numItermax : int number
number of iteration
lr : float number
learning rate
Returns
-------
ave_v : np.ndarray(nt,)
dual variable
Examples
--------
>>> n_source = 7
>>> n_target = 4
>>> reg = 1
>>> numItermax = 300000
>>> a = ot.utils.unif(n_source)
>>> b = ot.utils.unif(n_target)
>>> rng = np.random.RandomState(0)
>>> X_source = rng.randn(n_source, 2)
>>> Y_target = rng.randn(n_target, 2)
>>> M = ot.dist(X_source, Y_target)
>>> method = "ASGD"
>>> asgd_pi = stochastic.solve_semi_dual_entropic(a, b, M, reg,
method, numItermax)
>>> print(asgd_pi)
References
----------
[Genevay et al., 2016] :
Stochastic Optimization for Large-scale Optimal Transport,
Advances in Neural Information Processing Systems (2016),
arXiv preprint arxiv:1605.08527.
'''
if lr is None:
lr = 1. / max(a / reg)
n_source = np.shape(M)[0]
n_target = np.shape(M)[1]
cur_beta = np.zeros(n_target)
ave_beta = np.zeros(n_target)
for cur_iter in range(numItermax):
k = cur_iter + 1
i = np.random.randint(n_source)
cur_coord_grad = coordinate_grad_semi_dual(b, M, reg, cur_beta, i)
cur_beta += (lr / np.sqrt(k)) * cur_coord_grad
ave_beta = (1. / k) * cur_beta + (1 - 1. / k) * ave_beta
return ave_beta | [
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The function solves the following optimization problem:
.. math::
\gamma = arg\min_\gamma <\gamma,M>_F + reg\cdot\Omega(\gamma)
s.t. \gamma 1 = a
\gamma^T 1= b
\gamma \geq 0
Where :
- M is the (ns,nt) metric cost matrix
- :math:`\Omega` is the entropic regularization term with :math:`\Omega(\gamma)=\sum_{i,j} \gamma_{i,j}\log(\gamma_{i,j})`
- a and b are source and target weights (sum to 1)
The algorithm used for solving the problem is the ASGD algorithm
as proposed in [18]_ [alg.2]
Parameters
----------
b : np.ndarray(nt,)
target measure
M : np.ndarray(ns, nt)
cost matrix
reg : float number
Regularization term > 0
numItermax : int number
number of iteration
lr : float number
learning rate
Returns
-------
ave_v : np.ndarray(nt,)
dual variable
Examples
--------
>>> n_source = 7
>>> n_target = 4
>>> reg = 1
>>> numItermax = 300000
>>> a = ot.utils.unif(n_source)
>>> b = ot.utils.unif(n_target)
>>> rng = np.random.RandomState(0)
>>> X_source = rng.randn(n_source, 2)
>>> Y_target = rng.randn(n_target, 2)
>>> M = ot.dist(X_source, Y_target)
>>> method = "ASGD"
>>> asgd_pi = stochastic.solve_semi_dual_entropic(a, b, M, reg,
method, numItermax)
>>> print(asgd_pi)
References
----------
[Genevay et al., 2016] :
Stochastic Optimization for Large-scale Optimal Transport,
Advances in Neural Information Processing Systems (2016),
arXiv preprint arxiv:1605.08527. | [
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240,949 | rflamary/POT | ot/stochastic.py | c_transform_entropic | def c_transform_entropic(b, M, reg, beta):
'''
The goal is to recover u from the c-transform.
The function computes the c_transform of a dual variable from the other
dual variable:
.. math::
u = v^{c,reg} = -reg \sum_j exp((v - M)/reg) b_j
Where :
- M is the (ns,nt) metric cost matrix
- u, v are dual variables in R^IxR^J
- reg is the regularization term
It is used to recover an optimal u from optimal v solving the semi dual
problem, see Proposition 2.1 of [18]_
Parameters
----------
b : np.ndarray(nt,)
target measure
M : np.ndarray(ns, nt)
cost matrix
reg : float
regularization term > 0
v : np.ndarray(nt,)
dual variable
Returns
-------
u : np.ndarray(ns,)
dual variable
Examples
--------
>>> n_source = 7
>>> n_target = 4
>>> reg = 1
>>> numItermax = 300000
>>> a = ot.utils.unif(n_source)
>>> b = ot.utils.unif(n_target)
>>> rng = np.random.RandomState(0)
>>> X_source = rng.randn(n_source, 2)
>>> Y_target = rng.randn(n_target, 2)
>>> M = ot.dist(X_source, Y_target)
>>> method = "ASGD"
>>> asgd_pi = stochastic.solve_semi_dual_entropic(a, b, M, reg,
method, numItermax)
>>> print(asgd_pi)
References
----------
[Genevay et al., 2016] :
Stochastic Optimization for Large-scale Optimal Transport,
Advances in Neural Information Processing Systems (2016),
arXiv preprint arxiv:1605.08527.
'''
n_source = np.shape(M)[0]
alpha = np.zeros(n_source)
for i in range(n_source):
r = M[i, :] - beta
min_r = np.min(r)
exp_beta = np.exp(-(r - min_r) / reg) * b
alpha[i] = min_r - reg * np.log(np.sum(exp_beta))
return alpha | python | def c_transform_entropic(b, M, reg, beta):
'''
The goal is to recover u from the c-transform.
The function computes the c_transform of a dual variable from the other
dual variable:
.. math::
u = v^{c,reg} = -reg \sum_j exp((v - M)/reg) b_j
Where :
- M is the (ns,nt) metric cost matrix
- u, v are dual variables in R^IxR^J
- reg is the regularization term
It is used to recover an optimal u from optimal v solving the semi dual
problem, see Proposition 2.1 of [18]_
Parameters
----------
b : np.ndarray(nt,)
target measure
M : np.ndarray(ns, nt)
cost matrix
reg : float
regularization term > 0
v : np.ndarray(nt,)
dual variable
Returns
-------
u : np.ndarray(ns,)
dual variable
Examples
--------
>>> n_source = 7
>>> n_target = 4
>>> reg = 1
>>> numItermax = 300000
>>> a = ot.utils.unif(n_source)
>>> b = ot.utils.unif(n_target)
>>> rng = np.random.RandomState(0)
>>> X_source = rng.randn(n_source, 2)
>>> Y_target = rng.randn(n_target, 2)
>>> M = ot.dist(X_source, Y_target)
>>> method = "ASGD"
>>> asgd_pi = stochastic.solve_semi_dual_entropic(a, b, M, reg,
method, numItermax)
>>> print(asgd_pi)
References
----------
[Genevay et al., 2016] :
Stochastic Optimization for Large-scale Optimal Transport,
Advances in Neural Information Processing Systems (2016),
arXiv preprint arxiv:1605.08527.
'''
n_source = np.shape(M)[0]
alpha = np.zeros(n_source)
for i in range(n_source):
r = M[i, :] - beta
min_r = np.min(r)
exp_beta = np.exp(-(r - min_r) / reg) * b
alpha[i] = min_r - reg * np.log(np.sum(exp_beta))
return alpha | [
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The function computes the c_transform of a dual variable from the other
dual variable:
.. math::
u = v^{c,reg} = -reg \sum_j exp((v - M)/reg) b_j
Where :
- M is the (ns,nt) metric cost matrix
- u, v are dual variables in R^IxR^J
- reg is the regularization term
It is used to recover an optimal u from optimal v solving the semi dual
problem, see Proposition 2.1 of [18]_
Parameters
----------
b : np.ndarray(nt,)
target measure
M : np.ndarray(ns, nt)
cost matrix
reg : float
regularization term > 0
v : np.ndarray(nt,)
dual variable
Returns
-------
u : np.ndarray(ns,)
dual variable
Examples
--------
>>> n_source = 7
>>> n_target = 4
>>> reg = 1
>>> numItermax = 300000
>>> a = ot.utils.unif(n_source)
>>> b = ot.utils.unif(n_target)
>>> rng = np.random.RandomState(0)
>>> X_source = rng.randn(n_source, 2)
>>> Y_target = rng.randn(n_target, 2)
>>> M = ot.dist(X_source, Y_target)
>>> method = "ASGD"
>>> asgd_pi = stochastic.solve_semi_dual_entropic(a, b, M, reg,
method, numItermax)
>>> print(asgd_pi)
References
----------
[Genevay et al., 2016] :
Stochastic Optimization for Large-scale Optimal Transport,
Advances in Neural Information Processing Systems (2016),
arXiv preprint arxiv:1605.08527. | [
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240,950 | rflamary/POT | ot/stochastic.py | solve_semi_dual_entropic | def solve_semi_dual_entropic(a, b, M, reg, method, numItermax=10000, lr=None,
log=False):
'''
Compute the transportation matrix to solve the regularized discrete
measures optimal transport max problem
The function solves the following optimization problem:
.. math::
\gamma = arg\min_\gamma <\gamma,M>_F + reg\cdot\Omega(\gamma)
s.t. \gamma 1 = a
\gamma^T 1= b
\gamma \geq 0
Where :
- M is the (ns,nt) metric cost matrix
- :math:`\Omega` is the entropic regularization term with :math:`\Omega(\gamma)=\sum_{i,j} \gamma_{i,j}\log(\gamma_{i,j})`
- a and b are source and target weights (sum to 1)
The algorithm used for solving the problem is the SAG or ASGD algorithms
as proposed in [18]_
Parameters
----------
a : np.ndarray(ns,)
source measure
b : np.ndarray(nt,)
target measure
M : np.ndarray(ns, nt)
cost matrix
reg : float number
Regularization term > 0
methode : str
used method (SAG or ASGD)
numItermax : int number
number of iteration
lr : float number
learning rate
n_source : int number
size of the source measure
n_target : int number
size of the target measure
log : bool, optional
record log if True
Returns
-------
pi : np.ndarray(ns, nt)
transportation matrix
log : dict
log dictionary return only if log==True in parameters
Examples
--------
>>> n_source = 7
>>> n_target = 4
>>> reg = 1
>>> numItermax = 300000
>>> a = ot.utils.unif(n_source)
>>> b = ot.utils.unif(n_target)
>>> rng = np.random.RandomState(0)
>>> X_source = rng.randn(n_source, 2)
>>> Y_target = rng.randn(n_target, 2)
>>> M = ot.dist(X_source, Y_target)
>>> method = "ASGD"
>>> asgd_pi = stochastic.solve_semi_dual_entropic(a, b, M, reg,
method, numItermax)
>>> print(asgd_pi)
References
----------
[Genevay et al., 2016] :
Stochastic Optimization for Large-scale Optimal Transport,
Advances in Neural Information Processing Systems (2016),
arXiv preprint arxiv:1605.08527.
'''
if method.lower() == "sag":
opt_beta = sag_entropic_transport(a, b, M, reg, numItermax, lr)
elif method.lower() == "asgd":
opt_beta = averaged_sgd_entropic_transport(a, b, M, reg, numItermax, lr)
else:
print("Please, select your method between SAG and ASGD")
return None
opt_alpha = c_transform_entropic(b, M, reg, opt_beta)
pi = (np.exp((opt_alpha[:, None] + opt_beta[None, :] - M[:, :]) / reg) *
a[:, None] * b[None, :])
if log:
log = {}
log['alpha'] = opt_alpha
log['beta'] = opt_beta
return pi, log
else:
return pi | python | def solve_semi_dual_entropic(a, b, M, reg, method, numItermax=10000, lr=None,
log=False):
'''
Compute the transportation matrix to solve the regularized discrete
measures optimal transport max problem
The function solves the following optimization problem:
.. math::
\gamma = arg\min_\gamma <\gamma,M>_F + reg\cdot\Omega(\gamma)
s.t. \gamma 1 = a
\gamma^T 1= b
\gamma \geq 0
Where :
- M is the (ns,nt) metric cost matrix
- :math:`\Omega` is the entropic regularization term with :math:`\Omega(\gamma)=\sum_{i,j} \gamma_{i,j}\log(\gamma_{i,j})`
- a and b are source and target weights (sum to 1)
The algorithm used for solving the problem is the SAG or ASGD algorithms
as proposed in [18]_
Parameters
----------
a : np.ndarray(ns,)
source measure
b : np.ndarray(nt,)
target measure
M : np.ndarray(ns, nt)
cost matrix
reg : float number
Regularization term > 0
methode : str
used method (SAG or ASGD)
numItermax : int number
number of iteration
lr : float number
learning rate
n_source : int number
size of the source measure
n_target : int number
size of the target measure
log : bool, optional
record log if True
Returns
-------
pi : np.ndarray(ns, nt)
transportation matrix
log : dict
log dictionary return only if log==True in parameters
Examples
--------
>>> n_source = 7
>>> n_target = 4
>>> reg = 1
>>> numItermax = 300000
>>> a = ot.utils.unif(n_source)
>>> b = ot.utils.unif(n_target)
>>> rng = np.random.RandomState(0)
>>> X_source = rng.randn(n_source, 2)
>>> Y_target = rng.randn(n_target, 2)
>>> M = ot.dist(X_source, Y_target)
>>> method = "ASGD"
>>> asgd_pi = stochastic.solve_semi_dual_entropic(a, b, M, reg,
method, numItermax)
>>> print(asgd_pi)
References
----------
[Genevay et al., 2016] :
Stochastic Optimization for Large-scale Optimal Transport,
Advances in Neural Information Processing Systems (2016),
arXiv preprint arxiv:1605.08527.
'''
if method.lower() == "sag":
opt_beta = sag_entropic_transport(a, b, M, reg, numItermax, lr)
elif method.lower() == "asgd":
opt_beta = averaged_sgd_entropic_transport(a, b, M, reg, numItermax, lr)
else:
print("Please, select your method between SAG and ASGD")
return None
opt_alpha = c_transform_entropic(b, M, reg, opt_beta)
pi = (np.exp((opt_alpha[:, None] + opt_beta[None, :] - M[:, :]) / reg) *
a[:, None] * b[None, :])
if log:
log = {}
log['alpha'] = opt_alpha
log['beta'] = opt_beta
return pi, log
else:
return pi | [
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measures optimal transport max problem
The function solves the following optimization problem:
.. math::
\gamma = arg\min_\gamma <\gamma,M>_F + reg\cdot\Omega(\gamma)
s.t. \gamma 1 = a
\gamma^T 1= b
\gamma \geq 0
Where :
- M is the (ns,nt) metric cost matrix
- :math:`\Omega` is the entropic regularization term with :math:`\Omega(\gamma)=\sum_{i,j} \gamma_{i,j}\log(\gamma_{i,j})`
- a and b are source and target weights (sum to 1)
The algorithm used for solving the problem is the SAG or ASGD algorithms
as proposed in [18]_
Parameters
----------
a : np.ndarray(ns,)
source measure
b : np.ndarray(nt,)
target measure
M : np.ndarray(ns, nt)
cost matrix
reg : float number
Regularization term > 0
methode : str
used method (SAG or ASGD)
numItermax : int number
number of iteration
lr : float number
learning rate
n_source : int number
size of the source measure
n_target : int number
size of the target measure
log : bool, optional
record log if True
Returns
-------
pi : np.ndarray(ns, nt)
transportation matrix
log : dict
log dictionary return only if log==True in parameters
Examples
--------
>>> n_source = 7
>>> n_target = 4
>>> reg = 1
>>> numItermax = 300000
>>> a = ot.utils.unif(n_source)
>>> b = ot.utils.unif(n_target)
>>> rng = np.random.RandomState(0)
>>> X_source = rng.randn(n_source, 2)
>>> Y_target = rng.randn(n_target, 2)
>>> M = ot.dist(X_source, Y_target)
>>> method = "ASGD"
>>> asgd_pi = stochastic.solve_semi_dual_entropic(a, b, M, reg,
method, numItermax)
>>> print(asgd_pi)
References
----------
[Genevay et al., 2016] :
Stochastic Optimization for Large-scale Optimal Transport,
Advances in Neural Information Processing Systems (2016),
arXiv preprint arxiv:1605.08527. | [
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240,951 | rflamary/POT | ot/stochastic.py | batch_grad_dual | def batch_grad_dual(a, b, M, reg, alpha, beta, batch_size, batch_alpha,
batch_beta):
'''
Computes the partial gradient of the dual optimal transport problem.
For each (i,j) in a batch of coordinates, the partial gradients are :
.. math::
\partial_{u_i} F = u_i * b_s/l_{v} - \sum_{j \in B_v} exp((u_i + v_j - M_{i,j})/reg) * a_i * b_j
\partial_{v_j} F = v_j * b_s/l_{u} - \sum_{i \in B_u} exp((u_i + v_j - M_{i,j})/reg) * a_i * b_j
Where :
- M is the (ns,nt) metric cost matrix
- u, v are dual variables in R^ixR^J
- reg is the regularization term
- :math:`B_u` and :math:`B_v` are lists of index
- :math:`b_s` is the size of the batchs :math:`B_u` and :math:`B_v`
- :math:`l_u` and :math:`l_v` are the lenghts of :math:`B_u` and :math:`B_v`
- a and b are source and target weights (sum to 1)
The algorithm used for solving the dual problem is the SGD algorithm
as proposed in [19]_ [alg.1]
Parameters
----------
a : np.ndarray(ns,)
source measure
b : np.ndarray(nt,)
target measure
M : np.ndarray(ns, nt)
cost matrix
reg : float number
Regularization term > 0
alpha : np.ndarray(ns,)
dual variable
beta : np.ndarray(nt,)
dual variable
batch_size : int number
size of the batch
batch_alpha : np.ndarray(bs,)
batch of index of alpha
batch_beta : np.ndarray(bs,)
batch of index of beta
Returns
-------
grad : np.ndarray(ns,)
partial grad F
Examples
--------
>>> n_source = 7
>>> n_target = 4
>>> reg = 1
>>> numItermax = 20000
>>> lr = 0.1
>>> batch_size = 3
>>> log = True
>>> a = ot.utils.unif(n_source)
>>> b = ot.utils.unif(n_target)
>>> rng = np.random.RandomState(0)
>>> X_source = rng.randn(n_source, 2)
>>> Y_target = rng.randn(n_target, 2)
>>> M = ot.dist(X_source, Y_target)
>>> sgd_dual_pi, log = stochastic.solve_dual_entropic(a, b, M, reg,
batch_size,
numItermax, lr, log)
>>> print(log['alpha'], log['beta'])
>>> print(sgd_dual_pi)
References
----------
[Seguy et al., 2018] :
International Conference on Learning Representation (2018),
arXiv preprint arxiv:1711.02283.
'''
G = - (np.exp((alpha[batch_alpha, None] + beta[None, batch_beta] -
M[batch_alpha, :][:, batch_beta]) / reg) *
a[batch_alpha, None] * b[None, batch_beta])
grad_beta = np.zeros(np.shape(M)[1])
grad_alpha = np.zeros(np.shape(M)[0])
grad_beta[batch_beta] = (b[batch_beta] * len(batch_alpha) / np.shape(M)[0]
+ G.sum(0))
grad_alpha[batch_alpha] = (a[batch_alpha] * len(batch_beta)
/ np.shape(M)[1] + G.sum(1))
return grad_alpha, grad_beta | python | def batch_grad_dual(a, b, M, reg, alpha, beta, batch_size, batch_alpha,
batch_beta):
'''
Computes the partial gradient of the dual optimal transport problem.
For each (i,j) in a batch of coordinates, the partial gradients are :
.. math::
\partial_{u_i} F = u_i * b_s/l_{v} - \sum_{j \in B_v} exp((u_i + v_j - M_{i,j})/reg) * a_i * b_j
\partial_{v_j} F = v_j * b_s/l_{u} - \sum_{i \in B_u} exp((u_i + v_j - M_{i,j})/reg) * a_i * b_j
Where :
- M is the (ns,nt) metric cost matrix
- u, v are dual variables in R^ixR^J
- reg is the regularization term
- :math:`B_u` and :math:`B_v` are lists of index
- :math:`b_s` is the size of the batchs :math:`B_u` and :math:`B_v`
- :math:`l_u` and :math:`l_v` are the lenghts of :math:`B_u` and :math:`B_v`
- a and b are source and target weights (sum to 1)
The algorithm used for solving the dual problem is the SGD algorithm
as proposed in [19]_ [alg.1]
Parameters
----------
a : np.ndarray(ns,)
source measure
b : np.ndarray(nt,)
target measure
M : np.ndarray(ns, nt)
cost matrix
reg : float number
Regularization term > 0
alpha : np.ndarray(ns,)
dual variable
beta : np.ndarray(nt,)
dual variable
batch_size : int number
size of the batch
batch_alpha : np.ndarray(bs,)
batch of index of alpha
batch_beta : np.ndarray(bs,)
batch of index of beta
Returns
-------
grad : np.ndarray(ns,)
partial grad F
Examples
--------
>>> n_source = 7
>>> n_target = 4
>>> reg = 1
>>> numItermax = 20000
>>> lr = 0.1
>>> batch_size = 3
>>> log = True
>>> a = ot.utils.unif(n_source)
>>> b = ot.utils.unif(n_target)
>>> rng = np.random.RandomState(0)
>>> X_source = rng.randn(n_source, 2)
>>> Y_target = rng.randn(n_target, 2)
>>> M = ot.dist(X_source, Y_target)
>>> sgd_dual_pi, log = stochastic.solve_dual_entropic(a, b, M, reg,
batch_size,
numItermax, lr, log)
>>> print(log['alpha'], log['beta'])
>>> print(sgd_dual_pi)
References
----------
[Seguy et al., 2018] :
International Conference on Learning Representation (2018),
arXiv preprint arxiv:1711.02283.
'''
G = - (np.exp((alpha[batch_alpha, None] + beta[None, batch_beta] -
M[batch_alpha, :][:, batch_beta]) / reg) *
a[batch_alpha, None] * b[None, batch_beta])
grad_beta = np.zeros(np.shape(M)[1])
grad_alpha = np.zeros(np.shape(M)[0])
grad_beta[batch_beta] = (b[batch_beta] * len(batch_alpha) / np.shape(M)[0]
+ G.sum(0))
grad_alpha[batch_alpha] = (a[batch_alpha] * len(batch_beta)
/ np.shape(M)[1] + G.sum(1))
return grad_alpha, grad_beta | [
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"... | Computes the partial gradient of the dual optimal transport problem.
For each (i,j) in a batch of coordinates, the partial gradients are :
.. math::
\partial_{u_i} F = u_i * b_s/l_{v} - \sum_{j \in B_v} exp((u_i + v_j - M_{i,j})/reg) * a_i * b_j
\partial_{v_j} F = v_j * b_s/l_{u} - \sum_{i \in B_u} exp((u_i + v_j - M_{i,j})/reg) * a_i * b_j
Where :
- M is the (ns,nt) metric cost matrix
- u, v are dual variables in R^ixR^J
- reg is the regularization term
- :math:`B_u` and :math:`B_v` are lists of index
- :math:`b_s` is the size of the batchs :math:`B_u` and :math:`B_v`
- :math:`l_u` and :math:`l_v` are the lenghts of :math:`B_u` and :math:`B_v`
- a and b are source and target weights (sum to 1)
The algorithm used for solving the dual problem is the SGD algorithm
as proposed in [19]_ [alg.1]
Parameters
----------
a : np.ndarray(ns,)
source measure
b : np.ndarray(nt,)
target measure
M : np.ndarray(ns, nt)
cost matrix
reg : float number
Regularization term > 0
alpha : np.ndarray(ns,)
dual variable
beta : np.ndarray(nt,)
dual variable
batch_size : int number
size of the batch
batch_alpha : np.ndarray(bs,)
batch of index of alpha
batch_beta : np.ndarray(bs,)
batch of index of beta
Returns
-------
grad : np.ndarray(ns,)
partial grad F
Examples
--------
>>> n_source = 7
>>> n_target = 4
>>> reg = 1
>>> numItermax = 20000
>>> lr = 0.1
>>> batch_size = 3
>>> log = True
>>> a = ot.utils.unif(n_source)
>>> b = ot.utils.unif(n_target)
>>> rng = np.random.RandomState(0)
>>> X_source = rng.randn(n_source, 2)
>>> Y_target = rng.randn(n_target, 2)
>>> M = ot.dist(X_source, Y_target)
>>> sgd_dual_pi, log = stochastic.solve_dual_entropic(a, b, M, reg,
batch_size,
numItermax, lr, log)
>>> print(log['alpha'], log['beta'])
>>> print(sgd_dual_pi)
References
----------
[Seguy et al., 2018] :
International Conference on Learning Representation (2018),
arXiv preprint arxiv:1711.02283. | [
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] | c5108efc7b6702e1af3928bef1032e6b37734d1c | https://github.com/rflamary/POT/blob/c5108efc7b6702e1af3928bef1032e6b37734d1c/ot/stochastic.py#L452-L547 |
240,952 | rflamary/POT | ot/stochastic.py | sgd_entropic_regularization | def sgd_entropic_regularization(a, b, M, reg, batch_size, numItermax, lr):
'''
Compute the sgd algorithm to solve the regularized discrete measures
optimal transport dual problem
The function solves the following optimization problem:
.. math::
\gamma = arg\min_\gamma <\gamma,M>_F + reg\cdot\Omega(\gamma)
s.t. \gamma 1 = a
\gamma^T 1= b
\gamma \geq 0
Where :
- M is the (ns,nt) metric cost matrix
- :math:`\Omega` is the entropic regularization term with :math:`\Omega(\gamma)=\sum_{i,j} \gamma_{i,j}\log(\gamma_{i,j})`
- a and b are source and target weights (sum to 1)
Parameters
----------
a : np.ndarray(ns,)
source measure
b : np.ndarray(nt,)
target measure
M : np.ndarray(ns, nt)
cost matrix
reg : float number
Regularization term > 0
batch_size : int number
size of the batch
numItermax : int number
number of iteration
lr : float number
learning rate
Returns
-------
alpha : np.ndarray(ns,)
dual variable
beta : np.ndarray(nt,)
dual variable
Examples
--------
>>> n_source = 7
>>> n_target = 4
>>> reg = 1
>>> numItermax = 20000
>>> lr = 0.1
>>> batch_size = 3
>>> log = True
>>> a = ot.utils.unif(n_source)
>>> b = ot.utils.unif(n_target)
>>> rng = np.random.RandomState(0)
>>> X_source = rng.randn(n_source, 2)
>>> Y_target = rng.randn(n_target, 2)
>>> M = ot.dist(X_source, Y_target)
>>> sgd_dual_pi, log = stochastic.solve_dual_entropic(a, b, M, reg,
batch_size,
numItermax, lr, log)
>>> print(log['alpha'], log['beta'])
>>> print(sgd_dual_pi)
References
----------
[Seguy et al., 2018] :
International Conference on Learning Representation (2018),
arXiv preprint arxiv:1711.02283.
'''
n_source = np.shape(M)[0]
n_target = np.shape(M)[1]
cur_alpha = np.zeros(n_source)
cur_beta = np.zeros(n_target)
for cur_iter in range(numItermax):
k = np.sqrt(cur_iter + 1)
batch_alpha = np.random.choice(n_source, batch_size, replace=False)
batch_beta = np.random.choice(n_target, batch_size, replace=False)
update_alpha, update_beta = batch_grad_dual(a, b, M, reg, cur_alpha,
cur_beta, batch_size,
batch_alpha, batch_beta)
cur_alpha[batch_alpha] += (lr / k) * update_alpha[batch_alpha]
cur_beta[batch_beta] += (lr / k) * update_beta[batch_beta]
return cur_alpha, cur_beta | python | def sgd_entropic_regularization(a, b, M, reg, batch_size, numItermax, lr):
'''
Compute the sgd algorithm to solve the regularized discrete measures
optimal transport dual problem
The function solves the following optimization problem:
.. math::
\gamma = arg\min_\gamma <\gamma,M>_F + reg\cdot\Omega(\gamma)
s.t. \gamma 1 = a
\gamma^T 1= b
\gamma \geq 0
Where :
- M is the (ns,nt) metric cost matrix
- :math:`\Omega` is the entropic regularization term with :math:`\Omega(\gamma)=\sum_{i,j} \gamma_{i,j}\log(\gamma_{i,j})`
- a and b are source and target weights (sum to 1)
Parameters
----------
a : np.ndarray(ns,)
source measure
b : np.ndarray(nt,)
target measure
M : np.ndarray(ns, nt)
cost matrix
reg : float number
Regularization term > 0
batch_size : int number
size of the batch
numItermax : int number
number of iteration
lr : float number
learning rate
Returns
-------
alpha : np.ndarray(ns,)
dual variable
beta : np.ndarray(nt,)
dual variable
Examples
--------
>>> n_source = 7
>>> n_target = 4
>>> reg = 1
>>> numItermax = 20000
>>> lr = 0.1
>>> batch_size = 3
>>> log = True
>>> a = ot.utils.unif(n_source)
>>> b = ot.utils.unif(n_target)
>>> rng = np.random.RandomState(0)
>>> X_source = rng.randn(n_source, 2)
>>> Y_target = rng.randn(n_target, 2)
>>> M = ot.dist(X_source, Y_target)
>>> sgd_dual_pi, log = stochastic.solve_dual_entropic(a, b, M, reg,
batch_size,
numItermax, lr, log)
>>> print(log['alpha'], log['beta'])
>>> print(sgd_dual_pi)
References
----------
[Seguy et al., 2018] :
International Conference on Learning Representation (2018),
arXiv preprint arxiv:1711.02283.
'''
n_source = np.shape(M)[0]
n_target = np.shape(M)[1]
cur_alpha = np.zeros(n_source)
cur_beta = np.zeros(n_target)
for cur_iter in range(numItermax):
k = np.sqrt(cur_iter + 1)
batch_alpha = np.random.choice(n_source, batch_size, replace=False)
batch_beta = np.random.choice(n_target, batch_size, replace=False)
update_alpha, update_beta = batch_grad_dual(a, b, M, reg, cur_alpha,
cur_beta, batch_size,
batch_alpha, batch_beta)
cur_alpha[batch_alpha] += (lr / k) * update_alpha[batch_alpha]
cur_beta[batch_beta] += (lr / k) * update_beta[batch_beta]
return cur_alpha, cur_beta | [
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optimal transport dual problem
The function solves the following optimization problem:
.. math::
\gamma = arg\min_\gamma <\gamma,M>_F + reg\cdot\Omega(\gamma)
s.t. \gamma 1 = a
\gamma^T 1= b
\gamma \geq 0
Where :
- M is the (ns,nt) metric cost matrix
- :math:`\Omega` is the entropic regularization term with :math:`\Omega(\gamma)=\sum_{i,j} \gamma_{i,j}\log(\gamma_{i,j})`
- a and b are source and target weights (sum to 1)
Parameters
----------
a : np.ndarray(ns,)
source measure
b : np.ndarray(nt,)
target measure
M : np.ndarray(ns, nt)
cost matrix
reg : float number
Regularization term > 0
batch_size : int number
size of the batch
numItermax : int number
number of iteration
lr : float number
learning rate
Returns
-------
alpha : np.ndarray(ns,)
dual variable
beta : np.ndarray(nt,)
dual variable
Examples
--------
>>> n_source = 7
>>> n_target = 4
>>> reg = 1
>>> numItermax = 20000
>>> lr = 0.1
>>> batch_size = 3
>>> log = True
>>> a = ot.utils.unif(n_source)
>>> b = ot.utils.unif(n_target)
>>> rng = np.random.RandomState(0)
>>> X_source = rng.randn(n_source, 2)
>>> Y_target = rng.randn(n_target, 2)
>>> M = ot.dist(X_source, Y_target)
>>> sgd_dual_pi, log = stochastic.solve_dual_entropic(a, b, M, reg,
batch_size,
numItermax, lr, log)
>>> print(log['alpha'], log['beta'])
>>> print(sgd_dual_pi)
References
----------
[Seguy et al., 2018] :
International Conference on Learning Representation (2018),
arXiv preprint arxiv:1711.02283. | [
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240,953 | rflamary/POT | ot/stochastic.py | solve_dual_entropic | def solve_dual_entropic(a, b, M, reg, batch_size, numItermax=10000, lr=1,
log=False):
'''
Compute the transportation matrix to solve the regularized discrete measures
optimal transport dual problem
The function solves the following optimization problem:
.. math::
\gamma = arg\min_\gamma <\gamma,M>_F + reg\cdot\Omega(\gamma)
s.t. \gamma 1 = a
\gamma^T 1= b
\gamma \geq 0
Where :
- M is the (ns,nt) metric cost matrix
- :math:`\Omega` is the entropic regularization term :math:`\Omega(\gamma)=\sum_{i,j} \gamma_{i,j}\log(\gamma_{i,j})`
- a and b are source and target weights (sum to 1)
Parameters
----------
a : np.ndarray(ns,)
source measure
b : np.ndarray(nt,)
target measure
M : np.ndarray(ns, nt)
cost matrix
reg : float number
Regularization term > 0
batch_size : int number
size of the batch
numItermax : int number
number of iteration
lr : float number
learning rate
log : bool, optional
record log if True
Returns
-------
pi : np.ndarray(ns, nt)
transportation matrix
log : dict
log dictionary return only if log==True in parameters
Examples
--------
>>> n_source = 7
>>> n_target = 4
>>> reg = 1
>>> numItermax = 20000
>>> lr = 0.1
>>> batch_size = 3
>>> log = True
>>> a = ot.utils.unif(n_source)
>>> b = ot.utils.unif(n_target)
>>> rng = np.random.RandomState(0)
>>> X_source = rng.randn(n_source, 2)
>>> Y_target = rng.randn(n_target, 2)
>>> M = ot.dist(X_source, Y_target)
>>> sgd_dual_pi, log = stochastic.solve_dual_entropic(a, b, M, reg,
batch_size,
numItermax, lr, log)
>>> print(log['alpha'], log['beta'])
>>> print(sgd_dual_pi)
References
----------
[Seguy et al., 2018] :
International Conference on Learning Representation (2018),
arXiv preprint arxiv:1711.02283.
'''
opt_alpha, opt_beta = sgd_entropic_regularization(a, b, M, reg, batch_size,
numItermax, lr)
pi = (np.exp((opt_alpha[:, None] + opt_beta[None, :] - M[:, :]) / reg) *
a[:, None] * b[None, :])
if log:
log = {}
log['alpha'] = opt_alpha
log['beta'] = opt_beta
return pi, log
else:
return pi | python | def solve_dual_entropic(a, b, M, reg, batch_size, numItermax=10000, lr=1,
log=False):
'''
Compute the transportation matrix to solve the regularized discrete measures
optimal transport dual problem
The function solves the following optimization problem:
.. math::
\gamma = arg\min_\gamma <\gamma,M>_F + reg\cdot\Omega(\gamma)
s.t. \gamma 1 = a
\gamma^T 1= b
\gamma \geq 0
Where :
- M is the (ns,nt) metric cost matrix
- :math:`\Omega` is the entropic regularization term :math:`\Omega(\gamma)=\sum_{i,j} \gamma_{i,j}\log(\gamma_{i,j})`
- a and b are source and target weights (sum to 1)
Parameters
----------
a : np.ndarray(ns,)
source measure
b : np.ndarray(nt,)
target measure
M : np.ndarray(ns, nt)
cost matrix
reg : float number
Regularization term > 0
batch_size : int number
size of the batch
numItermax : int number
number of iteration
lr : float number
learning rate
log : bool, optional
record log if True
Returns
-------
pi : np.ndarray(ns, nt)
transportation matrix
log : dict
log dictionary return only if log==True in parameters
Examples
--------
>>> n_source = 7
>>> n_target = 4
>>> reg = 1
>>> numItermax = 20000
>>> lr = 0.1
>>> batch_size = 3
>>> log = True
>>> a = ot.utils.unif(n_source)
>>> b = ot.utils.unif(n_target)
>>> rng = np.random.RandomState(0)
>>> X_source = rng.randn(n_source, 2)
>>> Y_target = rng.randn(n_target, 2)
>>> M = ot.dist(X_source, Y_target)
>>> sgd_dual_pi, log = stochastic.solve_dual_entropic(a, b, M, reg,
batch_size,
numItermax, lr, log)
>>> print(log['alpha'], log['beta'])
>>> print(sgd_dual_pi)
References
----------
[Seguy et al., 2018] :
International Conference on Learning Representation (2018),
arXiv preprint arxiv:1711.02283.
'''
opt_alpha, opt_beta = sgd_entropic_regularization(a, b, M, reg, batch_size,
numItermax, lr)
pi = (np.exp((opt_alpha[:, None] + opt_beta[None, :] - M[:, :]) / reg) *
a[:, None] * b[None, :])
if log:
log = {}
log['alpha'] = opt_alpha
log['beta'] = opt_beta
return pi, log
else:
return pi | [
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The function solves the following optimization problem:
.. math::
\gamma = arg\min_\gamma <\gamma,M>_F + reg\cdot\Omega(\gamma)
s.t. \gamma 1 = a
\gamma^T 1= b
\gamma \geq 0
Where :
- M is the (ns,nt) metric cost matrix
- :math:`\Omega` is the entropic regularization term :math:`\Omega(\gamma)=\sum_{i,j} \gamma_{i,j}\log(\gamma_{i,j})`
- a and b are source and target weights (sum to 1)
Parameters
----------
a : np.ndarray(ns,)
source measure
b : np.ndarray(nt,)
target measure
M : np.ndarray(ns, nt)
cost matrix
reg : float number
Regularization term > 0
batch_size : int number
size of the batch
numItermax : int number
number of iteration
lr : float number
learning rate
log : bool, optional
record log if True
Returns
-------
pi : np.ndarray(ns, nt)
transportation matrix
log : dict
log dictionary return only if log==True in parameters
Examples
--------
>>> n_source = 7
>>> n_target = 4
>>> reg = 1
>>> numItermax = 20000
>>> lr = 0.1
>>> batch_size = 3
>>> log = True
>>> a = ot.utils.unif(n_source)
>>> b = ot.utils.unif(n_target)
>>> rng = np.random.RandomState(0)
>>> X_source = rng.randn(n_source, 2)
>>> Y_target = rng.randn(n_target, 2)
>>> M = ot.dist(X_source, Y_target)
>>> sgd_dual_pi, log = stochastic.solve_dual_entropic(a, b, M, reg,
batch_size,
numItermax, lr, log)
>>> print(log['alpha'], log['beta'])
>>> print(sgd_dual_pi)
References
----------
[Seguy et al., 2018] :
International Conference on Learning Representation (2018),
arXiv preprint arxiv:1711.02283. | [
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240,954 | PyCQA/pyflakes | pyflakes/reporter.py | Reporter.flake | def flake(self, message):
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Simplest required implementation of collections.Counter. Required as 2.6
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240,956 | PyCQA/pyflakes | pyflakes/checker.py | Importation.source_statement | def source_statement(self):
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240,957 | PyCQA/pyflakes | pyflakes/checker.py | Checker.CLASSDEF | def CLASSDEF(self, node):
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240,958 | PyCQA/pyflakes | pyflakes/api.py | isPythonFile | def isPythonFile(filename):
"""Return True if filename points to a Python file."""
if filename.endswith('.py'):
return True
# Avoid obvious Emacs backup files
if filename.endswith("~"):
return False
max_bytes = 128
try:
with open(filename, 'rb') as f:
text = f.read(max_bytes)
if not text:
return False
except IOError:
return False
first_line = text.splitlines()[0]
return PYTHON_SHEBANG_REGEX.match(first_line) | python | def isPythonFile(filename):
if filename.endswith('.py'):
return True
# Avoid obvious Emacs backup files
if filename.endswith("~"):
return False
max_bytes = 128
try:
with open(filename, 'rb') as f:
text = f.read(max_bytes)
if not text:
return False
except IOError:
return False
first_line = text.splitlines()[0]
return PYTHON_SHEBANG_REGEX.match(first_line) | [
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240,959 | PyCQA/pyflakes | pyflakes/api.py | _exitOnSignal | def _exitOnSignal(sigName, message):
"""Handles a signal with sys.exit.
Some of these signals (SIGPIPE, for example) don't exist or are invalid on
Windows. So, ignore errors that might arise.
"""
import signal
try:
sigNumber = getattr(signal, sigName)
except AttributeError:
# the signal constants defined in the signal module are defined by
# whether the C library supports them or not. So, SIGPIPE might not
# even be defined.
return
def handler(sig, f):
sys.exit(message)
try:
signal.signal(sigNumber, handler)
except ValueError:
# It's also possible the signal is defined, but then it's invalid. In
# this case, signal.signal raises ValueError.
pass | python | def _exitOnSignal(sigName, message):
import signal
try:
sigNumber = getattr(signal, sigName)
except AttributeError:
# the signal constants defined in the signal module are defined by
# whether the C library supports them or not. So, SIGPIPE might not
# even be defined.
return
def handler(sig, f):
sys.exit(message)
try:
signal.signal(sigNumber, handler)
except ValueError:
# It's also possible the signal is defined, but then it's invalid. In
# this case, signal.signal raises ValueError.
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240,960 | jazzband/django-model-utils | model_utils/managers.py | InheritanceQuerySetMixin._get_subclasses_recurse | def _get_subclasses_recurse(self, model, levels=None):
"""
Given a Model class, find all related objects, exploring children
recursively, returning a `list` of strings representing the
relations for select_related
"""
related_objects = [
f for f in model._meta.get_fields()
if isinstance(f, OneToOneRel)]
rels = [
rel for rel in related_objects
if isinstance(rel.field, OneToOneField)
and issubclass(rel.field.model, model)
and model is not rel.field.model
and rel.parent_link
]
subclasses = []
if levels:
levels -= 1
for rel in rels:
if levels or levels is None:
for subclass in self._get_subclasses_recurse(
rel.field.model, levels=levels):
subclasses.append(
rel.get_accessor_name() + LOOKUP_SEP + subclass)
subclasses.append(rel.get_accessor_name())
return subclasses | python | def _get_subclasses_recurse(self, model, levels=None):
related_objects = [
f for f in model._meta.get_fields()
if isinstance(f, OneToOneRel)]
rels = [
rel for rel in related_objects
if isinstance(rel.field, OneToOneField)
and issubclass(rel.field.model, model)
and model is not rel.field.model
and rel.parent_link
]
subclasses = []
if levels:
levels -= 1
for rel in rels:
if levels or levels is None:
for subclass in self._get_subclasses_recurse(
rel.field.model, levels=levels):
subclasses.append(
rel.get_accessor_name() + LOOKUP_SEP + subclass)
subclasses.append(rel.get_accessor_name())
return subclasses | [
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240,961 | jazzband/django-model-utils | model_utils/managers.py | InheritanceQuerySetMixin._get_ancestors_path | def _get_ancestors_path(self, model, levels=None):
"""
Serves as an opposite to _get_subclasses_recurse, instead walking from
the Model class up the Model's ancestry and constructing the desired
select_related string backwards.
"""
if not issubclass(model, self.model):
raise ValueError(
"%r is not a subclass of %r" % (model, self.model))
ancestry = []
# should be a OneToOneField or None
parent_link = model._meta.get_ancestor_link(self.model)
if levels:
levels -= 1
while parent_link is not None:
related = parent_link.remote_field
ancestry.insert(0, related.get_accessor_name())
if levels or levels is None:
parent_model = related.model
parent_link = parent_model._meta.get_ancestor_link(
self.model)
else:
parent_link = None
return LOOKUP_SEP.join(ancestry) | python | def _get_ancestors_path(self, model, levels=None):
if not issubclass(model, self.model):
raise ValueError(
"%r is not a subclass of %r" % (model, self.model))
ancestry = []
# should be a OneToOneField or None
parent_link = model._meta.get_ancestor_link(self.model)
if levels:
levels -= 1
while parent_link is not None:
related = parent_link.remote_field
ancestry.insert(0, related.get_accessor_name())
if levels or levels is None:
parent_model = related.model
parent_link = parent_model._meta.get_ancestor_link(
self.model)
else:
parent_link = None
return LOOKUP_SEP.join(ancestry) | [
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240,962 | jazzband/django-model-utils | model_utils/managers.py | SoftDeletableManagerMixin.get_queryset | def get_queryset(self):
"""
Return queryset limited to not removed entries.
"""
kwargs = {'model': self.model, 'using': self._db}
if hasattr(self, '_hints'):
kwargs['hints'] = self._hints
return self._queryset_class(**kwargs).filter(is_removed=False) | python | def get_queryset(self):
kwargs = {'model': self.model, 'using': self._db}
if hasattr(self, '_hints'):
kwargs['hints'] = self._hints
return self._queryset_class(**kwargs).filter(is_removed=False) | [
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240,963 | jazzband/django-model-utils | model_utils/tracker.py | FieldInstanceTracker.previous | def previous(self, field):
"""Returns currently saved value of given field"""
# handle deferred fields that have not yet been loaded from the database
if self.instance.pk and field in self.deferred_fields and field not in self.saved_data:
# if the field has not been assigned locally, simply fetch and un-defer the value
if field not in self.instance.__dict__:
self.get_field_value(field)
# if the field has been assigned locally, store the local value, fetch the database value,
# store database value to saved_data, and restore the local value
else:
current_value = self.get_field_value(field)
self.instance.refresh_from_db(fields=[field])
self.saved_data[field] = deepcopy(self.get_field_value(field))
setattr(self.instance, self.field_map[field], current_value)
return self.saved_data.get(field) | python | def previous(self, field):
# handle deferred fields that have not yet been loaded from the database
if self.instance.pk and field in self.deferred_fields and field not in self.saved_data:
# if the field has not been assigned locally, simply fetch and un-defer the value
if field not in self.instance.__dict__:
self.get_field_value(field)
# if the field has been assigned locally, store the local value, fetch the database value,
# store database value to saved_data, and restore the local value
else:
current_value = self.get_field_value(field)
self.instance.refresh_from_db(fields=[field])
self.saved_data[field] = deepcopy(self.get_field_value(field))
setattr(self.instance, self.field_map[field], current_value)
return self.saved_data.get(field) | [
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240,964 | jazzband/django-model-utils | model_utils/tracker.py | FieldTracker.get_field_map | def get_field_map(self, cls):
"""Returns dict mapping fields names to model attribute names"""
field_map = dict((field, field) for field in self.fields)
all_fields = dict((f.name, f.attname) for f in cls._meta.fields)
field_map.update(**dict((k, v) for (k, v) in all_fields.items()
if k in field_map))
return field_map | python | def get_field_map(self, cls):
field_map = dict((field, field) for field in self.fields)
all_fields = dict((f.name, f.attname) for f in cls._meta.fields)
field_map.update(**dict((k, v) for (k, v) in all_fields.items()
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return field_map | [
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240,965 | jazzband/django-model-utils | model_utils/models.py | add_status_query_managers | def add_status_query_managers(sender, **kwargs):
"""
Add a Querymanager for each status item dynamically.
"""
if not issubclass(sender, StatusModel):
return
if django.VERSION >= (1, 10):
# First, get current manager name...
default_manager = sender._meta.default_manager
for value, display in getattr(sender, 'STATUS', ()):
if _field_exists(sender, value):
raise ImproperlyConfigured(
"StatusModel: Model '%s' has a field named '%s' which "
"conflicts with a status of the same name."
% (sender.__name__, value)
)
sender.add_to_class(value, QueryManager(status=value))
if django.VERSION >= (1, 10):
# ...then, put it back, as add_to_class is modifying the default manager!
sender._meta.default_manager_name = default_manager.name | python | def add_status_query_managers(sender, **kwargs):
if not issubclass(sender, StatusModel):
return
if django.VERSION >= (1, 10):
# First, get current manager name...
default_manager = sender._meta.default_manager
for value, display in getattr(sender, 'STATUS', ()):
if _field_exists(sender, value):
raise ImproperlyConfigured(
"StatusModel: Model '%s' has a field named '%s' which "
"conflicts with a status of the same name."
% (sender.__name__, value)
)
sender.add_to_class(value, QueryManager(status=value))
if django.VERSION >= (1, 10):
# ...then, put it back, as add_to_class is modifying the default manager!
sender._meta.default_manager_name = default_manager.name | [
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240,966 | jazzband/django-model-utils | model_utils/models.py | add_timeframed_query_manager | def add_timeframed_query_manager(sender, **kwargs):
"""
Add a QueryManager for a specific timeframe.
"""
if not issubclass(sender, TimeFramedModel):
return
if _field_exists(sender, 'timeframed'):
raise ImproperlyConfigured(
"Model '%s' has a field named 'timeframed' "
"which conflicts with the TimeFramedModel manager."
% sender.__name__
)
sender.add_to_class('timeframed', QueryManager(
(models.Q(start__lte=now) | models.Q(start__isnull=True)) &
(models.Q(end__gte=now) | models.Q(end__isnull=True))
)) | python | def add_timeframed_query_manager(sender, **kwargs):
if not issubclass(sender, TimeFramedModel):
return
if _field_exists(sender, 'timeframed'):
raise ImproperlyConfigured(
"Model '%s' has a field named 'timeframed' "
"which conflicts with the TimeFramedModel manager."
% sender.__name__
)
sender.add_to_class('timeframed', QueryManager(
(models.Q(start__lte=now) | models.Q(start__isnull=True)) &
(models.Q(end__gte=now) | models.Q(end__isnull=True))
)) | [
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240,967 | invoice-x/invoice2data | src/invoice2data/input/tesseract4.py | to_text | def to_text(path, language='fra'):
"""Wraps Tesseract 4 OCR with custom language model.
Parameters
----------
path : str
path of electronic invoice in JPG or PNG format
Returns
-------
extracted_str : str
returns extracted text from image in JPG or PNG format
"""
import subprocess
from distutils import spawn
import tempfile
import time
# Check for dependencies. Needs Tesseract and Imagemagick installed.
if not spawn.find_executable('tesseract'):
raise EnvironmentError('tesseract not installed.')
if not spawn.find_executable('convert'):
raise EnvironmentError('imagemagick not installed.')
if not spawn.find_executable('gs'):
raise EnvironmentError('ghostscript not installed.')
with tempfile.NamedTemporaryFile(suffix='.tiff') as tf:
# Step 1: Convert to TIFF
gs_cmd = [
'gs',
'-q',
'-dNOPAUSE',
'-r600x600',
'-sDEVICE=tiff24nc',
'-sOutputFile=' + tf.name,
path,
'-c',
'quit',
]
subprocess.Popen(gs_cmd)
time.sleep(3)
# Step 2: Enhance TIFF
magick_cmd = [
'convert',
tf.name,
'-colorspace',
'gray',
'-type',
'grayscale',
'-contrast-stretch',
'0',
'-sharpen',
'0x1',
'tiff:-',
]
p1 = subprocess.Popen(magick_cmd, stdout=subprocess.PIPE)
tess_cmd = ['tesseract', '-l', language, '--oem', '1', '--psm', '3', 'stdin', 'stdout']
p2 = subprocess.Popen(tess_cmd, stdin=p1.stdout, stdout=subprocess.PIPE)
out, err = p2.communicate()
extracted_str = out
return extracted_str | python | def to_text(path, language='fra'):
import subprocess
from distutils import spawn
import tempfile
import time
# Check for dependencies. Needs Tesseract and Imagemagick installed.
if not spawn.find_executable('tesseract'):
raise EnvironmentError('tesseract not installed.')
if not spawn.find_executable('convert'):
raise EnvironmentError('imagemagick not installed.')
if not spawn.find_executable('gs'):
raise EnvironmentError('ghostscript not installed.')
with tempfile.NamedTemporaryFile(suffix='.tiff') as tf:
# Step 1: Convert to TIFF
gs_cmd = [
'gs',
'-q',
'-dNOPAUSE',
'-r600x600',
'-sDEVICE=tiff24nc',
'-sOutputFile=' + tf.name,
path,
'-c',
'quit',
]
subprocess.Popen(gs_cmd)
time.sleep(3)
# Step 2: Enhance TIFF
magick_cmd = [
'convert',
tf.name,
'-colorspace',
'gray',
'-type',
'grayscale',
'-contrast-stretch',
'0',
'-sharpen',
'0x1',
'tiff:-',
]
p1 = subprocess.Popen(magick_cmd, stdout=subprocess.PIPE)
tess_cmd = ['tesseract', '-l', language, '--oem', '1', '--psm', '3', 'stdin', 'stdout']
p2 = subprocess.Popen(tess_cmd, stdin=p1.stdout, stdout=subprocess.PIPE)
out, err = p2.communicate()
extracted_str = out
return extracted_str | [
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Parameters
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path : str
path of electronic invoice in JPG or PNG format
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extracted_str : str
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] | d97fdc5db9c1844fd77fa64f8ea7c42fefd0ba20 | https://github.com/invoice-x/invoice2data/blob/d97fdc5db9c1844fd77fa64f8ea7c42fefd0ba20/src/invoice2data/input/tesseract4.py#L2-L69 |
240,968 | invoice-x/invoice2data | src/invoice2data/input/gvision.py | to_text | def to_text(path, bucket_name='cloud-vision-84893', language='fr'):
"""Sends PDF files to Google Cloud Vision for OCR.
Before using invoice2data, make sure you have the auth json path set as
env var GOOGLE_APPLICATION_CREDENTIALS
Parameters
----------
path : str
path of electronic invoice in JPG or PNG format
bucket_name : str
name of bucket to use for file storage and results cache.
Returns
-------
extracted_str : str
returns extracted text from image in JPG or PNG format
"""
"""OCR with PDF/TIFF as source files on GCS"""
import os
from google.cloud import vision
from google.cloud import storage
from google.protobuf import json_format
# Supported mime_types are: 'application/pdf' and 'image/tiff'
mime_type = 'application/pdf'
path_dir, filename = os.path.split(path)
result_blob_basename = filename.replace('.pdf', '').replace('.PDF', '')
result_blob_name = result_blob_basename + '/output-1-to-1.json'
result_blob_uri = 'gs://{}/{}/'.format(bucket_name, result_blob_basename)
input_blob_uri = 'gs://{}/{}'.format(bucket_name, filename)
# Upload file to gcloud if it doesn't exist yet
storage_client = storage.Client()
bucket = storage_client.get_bucket(bucket_name)
if bucket.get_blob(filename) is None:
blob = bucket.blob(filename)
blob.upload_from_filename(path)
# See if result already exists
# TODO: upload as hash, not filename
result_blob = bucket.get_blob(result_blob_name)
if result_blob is None:
# How many pages should be grouped into each json output file.
batch_size = 10
client = vision.ImageAnnotatorClient()
feature = vision.types.Feature(type=vision.enums.Feature.Type.DOCUMENT_TEXT_DETECTION)
gcs_source = vision.types.GcsSource(uri=input_blob_uri)
input_config = vision.types.InputConfig(gcs_source=gcs_source, mime_type=mime_type)
gcs_destination = vision.types.GcsDestination(uri=result_blob_uri)
output_config = vision.types.OutputConfig(
gcs_destination=gcs_destination, batch_size=batch_size
)
async_request = vision.types.AsyncAnnotateFileRequest(
features=[feature], input_config=input_config, output_config=output_config
)
operation = client.async_batch_annotate_files(requests=[async_request])
print('Waiting for the operation to finish.')
operation.result(timeout=180)
# Get result after OCR is completed
result_blob = bucket.get_blob(result_blob_name)
json_string = result_blob.download_as_string()
response = json_format.Parse(json_string, vision.types.AnnotateFileResponse())
# The actual response for the first page of the input file.
first_page_response = response.responses[0]
annotation = first_page_response.full_text_annotation
return annotation.text.encode('utf-8') | python | def to_text(path, bucket_name='cloud-vision-84893', language='fr'):
"""OCR with PDF/TIFF as source files on GCS"""
import os
from google.cloud import vision
from google.cloud import storage
from google.protobuf import json_format
# Supported mime_types are: 'application/pdf' and 'image/tiff'
mime_type = 'application/pdf'
path_dir, filename = os.path.split(path)
result_blob_basename = filename.replace('.pdf', '').replace('.PDF', '')
result_blob_name = result_blob_basename + '/output-1-to-1.json'
result_blob_uri = 'gs://{}/{}/'.format(bucket_name, result_blob_basename)
input_blob_uri = 'gs://{}/{}'.format(bucket_name, filename)
# Upload file to gcloud if it doesn't exist yet
storage_client = storage.Client()
bucket = storage_client.get_bucket(bucket_name)
if bucket.get_blob(filename) is None:
blob = bucket.blob(filename)
blob.upload_from_filename(path)
# See if result already exists
# TODO: upload as hash, not filename
result_blob = bucket.get_blob(result_blob_name)
if result_blob is None:
# How many pages should be grouped into each json output file.
batch_size = 10
client = vision.ImageAnnotatorClient()
feature = vision.types.Feature(type=vision.enums.Feature.Type.DOCUMENT_TEXT_DETECTION)
gcs_source = vision.types.GcsSource(uri=input_blob_uri)
input_config = vision.types.InputConfig(gcs_source=gcs_source, mime_type=mime_type)
gcs_destination = vision.types.GcsDestination(uri=result_blob_uri)
output_config = vision.types.OutputConfig(
gcs_destination=gcs_destination, batch_size=batch_size
)
async_request = vision.types.AsyncAnnotateFileRequest(
features=[feature], input_config=input_config, output_config=output_config
)
operation = client.async_batch_annotate_files(requests=[async_request])
print('Waiting for the operation to finish.')
operation.result(timeout=180)
# Get result after OCR is completed
result_blob = bucket.get_blob(result_blob_name)
json_string = result_blob.download_as_string()
response = json_format.Parse(json_string, vision.types.AnnotateFileResponse())
# The actual response for the first page of the input file.
first_page_response = response.responses[0]
annotation = first_page_response.full_text_annotation
return annotation.text.encode('utf-8') | [
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Before using invoice2data, make sure you have the auth json path set as
env var GOOGLE_APPLICATION_CREDENTIALS
Parameters
----------
path : str
path of electronic invoice in JPG or PNG format
bucket_name : str
name of bucket to use for file storage and results cache.
Returns
-------
extracted_str : str
returns extracted text from image in JPG or PNG format | [
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240,969 | invoice-x/invoice2data | src/invoice2data/output/to_csv.py | write_to_file | def write_to_file(data, path):
"""Export extracted fields to csv
Appends .csv to path if missing and generates csv file in specified directory, if not then in root
Parameters
----------
data : dict
Dictionary of extracted fields
path : str
directory to save generated csv file
Notes
----
Do give file name to the function parameter path.
Examples
--------
>>> from invoice2data.output import to_csv
>>> to_csv.write_to_file(data, "/exported_csv/invoice.csv")
>>> to_csv.write_to_file(data, "invoice.csv")
"""
if path.endswith('.csv'):
filename = path
else:
filename = path + '.csv'
if sys.version_info[0] < 3:
openfile = open(filename, "wb")
else:
openfile = open(filename, "w", newline='')
with openfile as csv_file:
writer = csv.writer(csv_file, delimiter=',')
for line in data:
first_row = []
for k, v in line.items():
first_row.append(k)
writer.writerow(first_row)
for line in data:
csv_items = []
for k, v in line.items():
# first_row.append(k)
if k == 'date':
v = v.strftime('%d/%m/%Y')
csv_items.append(v)
writer.writerow(csv_items) | python | def write_to_file(data, path):
if path.endswith('.csv'):
filename = path
else:
filename = path + '.csv'
if sys.version_info[0] < 3:
openfile = open(filename, "wb")
else:
openfile = open(filename, "w", newline='')
with openfile as csv_file:
writer = csv.writer(csv_file, delimiter=',')
for line in data:
first_row = []
for k, v in line.items():
first_row.append(k)
writer.writerow(first_row)
for line in data:
csv_items = []
for k, v in line.items():
# first_row.append(k)
if k == 'date':
v = v.strftime('%d/%m/%Y')
csv_items.append(v)
writer.writerow(csv_items) | [
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Appends .csv to path if missing and generates csv file in specified directory, if not then in root
Parameters
----------
data : dict
Dictionary of extracted fields
path : str
directory to save generated csv file
Notes
----
Do give file name to the function parameter path.
Examples
--------
>>> from invoice2data.output import to_csv
>>> to_csv.write_to_file(data, "/exported_csv/invoice.csv")
>>> to_csv.write_to_file(data, "invoice.csv") | [
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240,970 | invoice-x/invoice2data | src/invoice2data/input/tesseract.py | to_text | def to_text(path):
"""Wraps Tesseract OCR.
Parameters
----------
path : str
path of electronic invoice in JPG or PNG format
Returns
-------
extracted_str : str
returns extracted text from image in JPG or PNG format
"""
import subprocess
from distutils import spawn
# Check for dependencies. Needs Tesseract and Imagemagick installed.
if not spawn.find_executable('tesseract'):
raise EnvironmentError('tesseract not installed.')
if not spawn.find_executable('convert'):
raise EnvironmentError('imagemagick not installed.')
# convert = "convert -density 350 %s -depth 8 tiff:-" % (path)
convert = ['convert', '-density', '350', path, '-depth', '8', 'png:-']
p1 = subprocess.Popen(convert, stdout=subprocess.PIPE)
tess = ['tesseract', 'stdin', 'stdout']
p2 = subprocess.Popen(tess, stdin=p1.stdout, stdout=subprocess.PIPE)
out, err = p2.communicate()
extracted_str = out
return extracted_str | python | def to_text(path):
import subprocess
from distutils import spawn
# Check for dependencies. Needs Tesseract and Imagemagick installed.
if not spawn.find_executable('tesseract'):
raise EnvironmentError('tesseract not installed.')
if not spawn.find_executable('convert'):
raise EnvironmentError('imagemagick not installed.')
# convert = "convert -density 350 %s -depth 8 tiff:-" % (path)
convert = ['convert', '-density', '350', path, '-depth', '8', 'png:-']
p1 = subprocess.Popen(convert, stdout=subprocess.PIPE)
tess = ['tesseract', 'stdin', 'stdout']
p2 = subprocess.Popen(tess, stdin=p1.stdout, stdout=subprocess.PIPE)
out, err = p2.communicate()
extracted_str = out
return extracted_str | [
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Parameters
----------
path : str
path of electronic invoice in JPG or PNG format
Returns
-------
extracted_str : str
returns extracted text from image in JPG or PNG format | [
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240,971 | invoice-x/invoice2data | src/invoice2data/extract/plugins/tables.py | extract | def extract(self, content, output):
"""Try to extract tables from an invoice"""
for table in self['tables']:
# First apply default options.
plugin_settings = DEFAULT_OPTIONS.copy()
plugin_settings.update(table)
table = plugin_settings
# Validate settings
assert 'start' in table, 'Table start regex missing'
assert 'end' in table, 'Table end regex missing'
assert 'body' in table, 'Table body regex missing'
start = re.search(table['start'], content)
end = re.search(table['end'], content)
if not start or not end:
logger.warning('no table body found - start %s, end %s', start, end)
continue
table_body = content[start.end(): end.start()]
for line in re.split(table['line_separator'], table_body):
# if the line has empty lines in it , skip them
if not line.strip('').strip('\n') or not line:
continue
match = re.search(table['body'], line)
if match:
for field, value in match.groupdict().items():
# If a field name already exists, do not overwrite it
if field in output:
continue
if field.startswith('date') or field.endswith('date'):
output[field] = self.parse_date(value)
if not output[field]:
logger.error("Date parsing failed on date '%s'", value)
return None
elif field.startswith('amount'):
output[field] = self.parse_number(value)
else:
output[field] = value
logger.debug('ignoring *%s* because it doesn\'t match anything', line) | python | def extract(self, content, output):
for table in self['tables']:
# First apply default options.
plugin_settings = DEFAULT_OPTIONS.copy()
plugin_settings.update(table)
table = plugin_settings
# Validate settings
assert 'start' in table, 'Table start regex missing'
assert 'end' in table, 'Table end regex missing'
assert 'body' in table, 'Table body regex missing'
start = re.search(table['start'], content)
end = re.search(table['end'], content)
if not start or not end:
logger.warning('no table body found - start %s, end %s', start, end)
continue
table_body = content[start.end(): end.start()]
for line in re.split(table['line_separator'], table_body):
# if the line has empty lines in it , skip them
if not line.strip('').strip('\n') or not line:
continue
match = re.search(table['body'], line)
if match:
for field, value in match.groupdict().items():
# If a field name already exists, do not overwrite it
if field in output:
continue
if field.startswith('date') or field.endswith('date'):
output[field] = self.parse_date(value)
if not output[field]:
logger.error("Date parsing failed on date '%s'", value)
return None
elif field.startswith('amount'):
output[field] = self.parse_number(value)
else:
output[field] = value
logger.debug('ignoring *%s* because it doesn\'t match anything', line) | [
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240,972 | invoice-x/invoice2data | src/invoice2data/input/pdftotext.py | to_text | def to_text(path):
"""Wrapper around Poppler pdftotext.
Parameters
----------
path : str
path of electronic invoice in PDF
Returns
-------
out : str
returns extracted text from pdf
Raises
------
EnvironmentError:
If pdftotext library is not found
"""
import subprocess
from distutils import spawn # py2 compat
if spawn.find_executable("pdftotext"): # shutil.which('pdftotext'):
out, err = subprocess.Popen(
["pdftotext", '-layout', '-enc', 'UTF-8', path, '-'], stdout=subprocess.PIPE
).communicate()
return out
else:
raise EnvironmentError(
'pdftotext not installed. Can be downloaded from https://poppler.freedesktop.org/'
) | python | def to_text(path):
import subprocess
from distutils import spawn # py2 compat
if spawn.find_executable("pdftotext"): # shutil.which('pdftotext'):
out, err = subprocess.Popen(
["pdftotext", '-layout', '-enc', 'UTF-8', path, '-'], stdout=subprocess.PIPE
).communicate()
return out
else:
raise EnvironmentError(
'pdftotext not installed. Can be downloaded from https://poppler.freedesktop.org/'
) | [
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Parameters
----------
path : str
path of electronic invoice in PDF
Returns
-------
out : str
returns extracted text from pdf
Raises
------
EnvironmentError:
If pdftotext library is not found | [
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240,973 | invoice-x/invoice2data | src/invoice2data/extract/invoice_template.py | InvoiceTemplate.prepare_input | def prepare_input(self, extracted_str):
"""
Input raw string and do transformations, as set in template file.
"""
# Remove withspace
if self.options['remove_whitespace']:
optimized_str = re.sub(' +', '', extracted_str)
else:
optimized_str = extracted_str
# Remove accents
if self.options['remove_accents']:
optimized_str = unidecode(optimized_str)
# convert to lower case
if self.options['lowercase']:
optimized_str = optimized_str.lower()
# specific replace
for replace in self.options['replace']:
assert len(replace) == 2, 'A replace should be a list of 2 items'
optimized_str = optimized_str.replace(replace[0], replace[1])
return optimized_str | python | def prepare_input(self, extracted_str):
# Remove withspace
if self.options['remove_whitespace']:
optimized_str = re.sub(' +', '', extracted_str)
else:
optimized_str = extracted_str
# Remove accents
if self.options['remove_accents']:
optimized_str = unidecode(optimized_str)
# convert to lower case
if self.options['lowercase']:
optimized_str = optimized_str.lower()
# specific replace
for replace in self.options['replace']:
assert len(replace) == 2, 'A replace should be a list of 2 items'
optimized_str = optimized_str.replace(replace[0], replace[1])
return optimized_str | [
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240,974 | invoice-x/invoice2data | src/invoice2data/extract/invoice_template.py | InvoiceTemplate.matches_input | def matches_input(self, optimized_str):
"""See if string matches keywords set in template file"""
if all([keyword in optimized_str for keyword in self['keywords']]):
logger.debug('Matched template %s', self['template_name'])
return True | python | def matches_input(self, optimized_str):
if all([keyword in optimized_str for keyword in self['keywords']]):
logger.debug('Matched template %s', self['template_name'])
return True | [
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240,975 | invoice-x/invoice2data | src/invoice2data/extract/invoice_template.py | InvoiceTemplate.parse_date | def parse_date(self, value):
"""Parses date and returns date after parsing"""
res = dateparser.parse(
value, date_formats=self.options['date_formats'], languages=self.options['languages']
)
logger.debug("result of date parsing=%s", res)
return res | python | def parse_date(self, value):
res = dateparser.parse(
value, date_formats=self.options['date_formats'], languages=self.options['languages']
)
logger.debug("result of date parsing=%s", res)
return res | [
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240,976 | invoice-x/invoice2data | src/invoice2data/output/to_json.py | write_to_file | def write_to_file(data, path):
"""Export extracted fields to json
Appends .json to path if missing and generates json file in specified directory, if not then in root
Parameters
----------
data : dict
Dictionary of extracted fields
path : str
directory to save generated json file
Notes
----
Do give file name to the function parameter path.
Examples
--------
>>> from invoice2data.output import to_json
>>> to_json.write_to_file(data, "/exported_json/invoice.json")
>>> to_json.write_to_file(data, "invoice.json")
"""
if path.endswith('.json'):
filename = path
else:
filename = path + '.json'
with codecs.open(filename, "w", encoding='utf-8') as json_file:
for line in data:
line['date'] = line['date'].strftime('%d/%m/%Y')
print(type(json))
print(json)
json.dump(
data, json_file, indent=4, sort_keys=True, default=myconverter, ensure_ascii=False
) | python | def write_to_file(data, path):
if path.endswith('.json'):
filename = path
else:
filename = path + '.json'
with codecs.open(filename, "w", encoding='utf-8') as json_file:
for line in data:
line['date'] = line['date'].strftime('%d/%m/%Y')
print(type(json))
print(json)
json.dump(
data, json_file, indent=4, sort_keys=True, default=myconverter, ensure_ascii=False
) | [
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"... | Export extracted fields to json
Appends .json to path if missing and generates json file in specified directory, if not then in root
Parameters
----------
data : dict
Dictionary of extracted fields
path : str
directory to save generated json file
Notes
----
Do give file name to the function parameter path.
Examples
--------
>>> from invoice2data.output import to_json
>>> to_json.write_to_file(data, "/exported_json/invoice.json")
>>> to_json.write_to_file(data, "invoice.json") | [
"Export",
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] | d97fdc5db9c1844fd77fa64f8ea7c42fefd0ba20 | https://github.com/invoice-x/invoice2data/blob/d97fdc5db9c1844fd77fa64f8ea7c42fefd0ba20/src/invoice2data/output/to_json.py#L12-L47 |
240,977 | invoice-x/invoice2data | src/invoice2data/main.py | create_parser | def create_parser():
"""Returns argument parser """
parser = argparse.ArgumentParser(
description='Extract structured data from PDF files and save to CSV or JSON.'
)
parser.add_argument(
'--input-reader',
choices=input_mapping.keys(),
default='pdftotext',
help='Choose text extraction function. Default: pdftotext',
)
parser.add_argument(
'--output-format',
choices=output_mapping.keys(),
default='none',
help='Choose output format. Default: none',
)
parser.add_argument(
'--output-name',
'-o',
dest='output_name',
default='invoices-output',
help='Custom name for output file. Extension is added based on chosen format.',
)
parser.add_argument(
'--debug', dest='debug', action='store_true', help='Enable debug information.'
)
parser.add_argument(
'--copy', '-c', dest='copy', help='Copy and rename processed PDFs to specified folder.'
)
parser.add_argument(
'--move', '-m', dest='move', help='Move and rename processed PDFs to specified folder.'
)
parser.add_argument(
'--filename-format',
dest='filename',
default="{date} {invoice_number} {desc}.pdf",
help='Filename format to use when moving or copying processed PDFs.'
'Default: "{date} {invoice_number} {desc}.pdf"',
)
parser.add_argument(
'--template-folder',
'-t',
dest='template_folder',
help='Folder containing invoice templates in yml file. Always adds built-in templates.',
)
parser.add_argument(
'--exclude-built-in-templates',
dest='exclude_built_in_templates',
default=False,
help='Ignore built-in templates.',
action="store_true",
)
parser.add_argument(
'input_files', type=argparse.FileType('r'), nargs='+', help='File or directory to analyze.'
)
return parser | python | def create_parser():
parser = argparse.ArgumentParser(
description='Extract structured data from PDF files and save to CSV or JSON.'
)
parser.add_argument(
'--input-reader',
choices=input_mapping.keys(),
default='pdftotext',
help='Choose text extraction function. Default: pdftotext',
)
parser.add_argument(
'--output-format',
choices=output_mapping.keys(),
default='none',
help='Choose output format. Default: none',
)
parser.add_argument(
'--output-name',
'-o',
dest='output_name',
default='invoices-output',
help='Custom name for output file. Extension is added based on chosen format.',
)
parser.add_argument(
'--debug', dest='debug', action='store_true', help='Enable debug information.'
)
parser.add_argument(
'--copy', '-c', dest='copy', help='Copy and rename processed PDFs to specified folder.'
)
parser.add_argument(
'--move', '-m', dest='move', help='Move and rename processed PDFs to specified folder.'
)
parser.add_argument(
'--filename-format',
dest='filename',
default="{date} {invoice_number} {desc}.pdf",
help='Filename format to use when moving or copying processed PDFs.'
'Default: "{date} {invoice_number} {desc}.pdf"',
)
parser.add_argument(
'--template-folder',
'-t',
dest='template_folder',
help='Folder containing invoice templates in yml file. Always adds built-in templates.',
)
parser.add_argument(
'--exclude-built-in-templates',
dest='exclude_built_in_templates',
default=False,
help='Ignore built-in templates.',
action="store_true",
)
parser.add_argument(
'input_files', type=argparse.FileType('r'), nargs='+', help='File or directory to analyze.'
)
return parser | [
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240,978 | invoice-x/invoice2data | src/invoice2data/main.py | main | def main(args=None):
"""Take folder or single file and analyze each."""
if args is None:
parser = create_parser()
args = parser.parse_args()
if args.debug:
logging.basicConfig(level=logging.DEBUG)
else:
logging.basicConfig(level=logging.INFO)
input_module = input_mapping[args.input_reader]
output_module = output_mapping[args.output_format]
templates = []
# Load templates from external folder if set.
if args.template_folder:
templates += read_templates(os.path.abspath(args.template_folder))
# Load internal templates, if not disabled.
if not args.exclude_built_in_templates:
templates += read_templates()
output = []
for f in args.input_files:
res = extract_data(f.name, templates=templates, input_module=input_module)
if res:
logger.info(res)
output.append(res)
if args.copy:
filename = args.filename.format(
date=res['date'].strftime('%Y-%m-%d'),
invoice_number=res['invoice_number'],
desc=res['desc'],
)
shutil.copyfile(f.name, join(args.copy, filename))
if args.move:
filename = args.filename.format(
date=res['date'].strftime('%Y-%m-%d'),
invoice_number=res['invoice_number'],
desc=res['desc'],
)
shutil.move(f.name, join(args.move, filename))
f.close()
if output_module is not None:
output_module.write_to_file(output, args.output_name) | python | def main(args=None):
if args is None:
parser = create_parser()
args = parser.parse_args()
if args.debug:
logging.basicConfig(level=logging.DEBUG)
else:
logging.basicConfig(level=logging.INFO)
input_module = input_mapping[args.input_reader]
output_module = output_mapping[args.output_format]
templates = []
# Load templates from external folder if set.
if args.template_folder:
templates += read_templates(os.path.abspath(args.template_folder))
# Load internal templates, if not disabled.
if not args.exclude_built_in_templates:
templates += read_templates()
output = []
for f in args.input_files:
res = extract_data(f.name, templates=templates, input_module=input_module)
if res:
logger.info(res)
output.append(res)
if args.copy:
filename = args.filename.format(
date=res['date'].strftime('%Y-%m-%d'),
invoice_number=res['invoice_number'],
desc=res['desc'],
)
shutil.copyfile(f.name, join(args.copy, filename))
if args.move:
filename = args.filename.format(
date=res['date'].strftime('%Y-%m-%d'),
invoice_number=res['invoice_number'],
desc=res['desc'],
)
shutil.move(f.name, join(args.move, filename))
f.close()
if output_module is not None:
output_module.write_to_file(output, args.output_name) | [
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240,979 | invoice-x/invoice2data | src/invoice2data/output/to_xml.py | write_to_file | def write_to_file(data, path):
"""Export extracted fields to xml
Appends .xml to path if missing and generates xml file in specified directory, if not then in root
Parameters
----------
data : dict
Dictionary of extracted fields
path : str
directory to save generated xml file
Notes
----
Do give file name to the function parameter path.
Only `date`, `desc`, `amount` and `currency` are exported
Examples
--------
>>> from invoice2data.output import to_xml
>>> to_xml.write_to_file(data, "/exported_xml/invoice.xml")
>>> to_xml.write_to_file(data, "invoice.xml")
"""
if path.endswith('.xml'):
filename = path
else:
filename = path + '.xml'
tag_data = ET.Element('data')
xml_file = open(filename, "w")
i = 0
for line in data:
i += 1
tag_item = ET.SubElement(tag_data, 'item')
tag_date = ET.SubElement(tag_item, 'date')
tag_desc = ET.SubElement(tag_item, 'desc')
tag_currency = ET.SubElement(tag_item, 'currency')
tag_amount = ET.SubElement(tag_item, 'amount')
tag_item.set('id', str(i))
tag_date.text = line['date'].strftime('%d/%m/%Y')
tag_desc.text = line['desc']
tag_currency.text = line['currency']
tag_amount.text = str(line['amount'])
xml_file.write(prettify(tag_data))
xml_file.close() | python | def write_to_file(data, path):
if path.endswith('.xml'):
filename = path
else:
filename = path + '.xml'
tag_data = ET.Element('data')
xml_file = open(filename, "w")
i = 0
for line in data:
i += 1
tag_item = ET.SubElement(tag_data, 'item')
tag_date = ET.SubElement(tag_item, 'date')
tag_desc = ET.SubElement(tag_item, 'desc')
tag_currency = ET.SubElement(tag_item, 'currency')
tag_amount = ET.SubElement(tag_item, 'amount')
tag_item.set('id', str(i))
tag_date.text = line['date'].strftime('%d/%m/%Y')
tag_desc.text = line['desc']
tag_currency.text = line['currency']
tag_amount.text = str(line['amount'])
xml_file.write(prettify(tag_data))
xml_file.close() | [
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")... | Export extracted fields to xml
Appends .xml to path if missing and generates xml file in specified directory, if not then in root
Parameters
----------
data : dict
Dictionary of extracted fields
path : str
directory to save generated xml file
Notes
----
Do give file name to the function parameter path.
Only `date`, `desc`, `amount` and `currency` are exported
Examples
--------
>>> from invoice2data.output import to_xml
>>> to_xml.write_to_file(data, "/exported_xml/invoice.xml")
>>> to_xml.write_to_file(data, "invoice.xml") | [
"Export",
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"to",
"xml"
] | d97fdc5db9c1844fd77fa64f8ea7c42fefd0ba20 | https://github.com/invoice-x/invoice2data/blob/d97fdc5db9c1844fd77fa64f8ea7c42fefd0ba20/src/invoice2data/output/to_xml.py#L12-L59 |
240,980 | invoice-x/invoice2data | src/invoice2data/extract/loader.py | read_templates | def read_templates(folder=None):
"""
Load yaml templates from template folder. Return list of dicts.
Use built-in templates if no folder is set.
Parameters
----------
folder : str
user defined folder where they stores their files, if None uses built-in templates
Returns
-------
output : Instance of `InvoiceTemplate`
template which match based on keywords
Examples
--------
>>> read_template("home/duskybomb/invoice-templates/")
InvoiceTemplate([('issuer', 'OYO'), ('fields', OrderedDict([('amount', 'GrandTotalRs(\\d+)'),
('date', 'Date:(\\d{1,2}\\/\\d{1,2}\\/\\d{1,4})'), ('invoice_number', '([A-Z0-9]+)CashatHotel')])),
('keywords', ['OYO', 'Oravel', 'Stays']), ('options', OrderedDict([('currency', 'INR'), ('decimal_separator', '.'),
('remove_whitespace', True)])), ('template_name', 'com.oyo.invoice.yml')])
After reading the template you can use the result as an instance of `InvoiceTemplate` to extract fields from
`extract_data()`
>>> my_template = InvoiceTemplate([('issuer', 'OYO'), ('fields', OrderedDict([('amount', 'GrandTotalRs(\\d+)'),
('date', 'Date:(\\d{1,2}\\/\\d{1,2}\\/\\d{1,4})'), ('invoice_number', '([A-Z0-9]+)CashatHotel')])),
('keywords', ['OYO', 'Oravel', 'Stays']), ('options', OrderedDict([('currency', 'INR'), ('decimal_separator', '.'),
('remove_whitespace', True)])), ('template_name', 'com.oyo.invoice.yml')])
>>> extract_data("invoice2data/test/pdfs/oyo.pdf", my_template, pdftotext)
{'issuer': 'OYO', 'amount': 1939.0, 'date': datetime.datetime(2017, 12, 31, 0, 0), 'invoice_number': 'IBZY2087',
'currency': 'INR', 'desc': 'Invoice IBZY2087 from OYO'}
"""
output = []
if folder is None:
folder = pkg_resources.resource_filename(__name__, 'templates')
for path, subdirs, files in os.walk(folder):
for name in sorted(files):
if name.endswith('.yml'):
with open(os.path.join(path, name), 'rb') as f:
encoding = chardet.detect(f.read())['encoding']
with codecs.open(os.path.join(path, name), encoding=encoding) as template_file:
tpl = ordered_load(template_file.read())
tpl['template_name'] = name
# Test if all required fields are in template:
assert 'keywords' in tpl.keys(), 'Missing keywords field.'
# Keywords as list, if only one.
if type(tpl['keywords']) is not list:
tpl['keywords'] = [tpl['keywords']]
output.append(InvoiceTemplate(tpl))
return output | python | def read_templates(folder=None):
output = []
if folder is None:
folder = pkg_resources.resource_filename(__name__, 'templates')
for path, subdirs, files in os.walk(folder):
for name in sorted(files):
if name.endswith('.yml'):
with open(os.path.join(path, name), 'rb') as f:
encoding = chardet.detect(f.read())['encoding']
with codecs.open(os.path.join(path, name), encoding=encoding) as template_file:
tpl = ordered_load(template_file.read())
tpl['template_name'] = name
# Test if all required fields are in template:
assert 'keywords' in tpl.keys(), 'Missing keywords field.'
# Keywords as list, if only one.
if type(tpl['keywords']) is not list:
tpl['keywords'] = [tpl['keywords']]
output.append(InvoiceTemplate(tpl))
return output | [
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Use built-in templates if no folder is set.
Parameters
----------
folder : str
user defined folder where they stores their files, if None uses built-in templates
Returns
-------
output : Instance of `InvoiceTemplate`
template which match based on keywords
Examples
--------
>>> read_template("home/duskybomb/invoice-templates/")
InvoiceTemplate([('issuer', 'OYO'), ('fields', OrderedDict([('amount', 'GrandTotalRs(\\d+)'),
('date', 'Date:(\\d{1,2}\\/\\d{1,2}\\/\\d{1,4})'), ('invoice_number', '([A-Z0-9]+)CashatHotel')])),
('keywords', ['OYO', 'Oravel', 'Stays']), ('options', OrderedDict([('currency', 'INR'), ('decimal_separator', '.'),
('remove_whitespace', True)])), ('template_name', 'com.oyo.invoice.yml')])
After reading the template you can use the result as an instance of `InvoiceTemplate` to extract fields from
`extract_data()`
>>> my_template = InvoiceTemplate([('issuer', 'OYO'), ('fields', OrderedDict([('amount', 'GrandTotalRs(\\d+)'),
('date', 'Date:(\\d{1,2}\\/\\d{1,2}\\/\\d{1,4})'), ('invoice_number', '([A-Z0-9]+)CashatHotel')])),
('keywords', ['OYO', 'Oravel', 'Stays']), ('options', OrderedDict([('currency', 'INR'), ('decimal_separator', '.'),
('remove_whitespace', True)])), ('template_name', 'com.oyo.invoice.yml')])
>>> extract_data("invoice2data/test/pdfs/oyo.pdf", my_template, pdftotext)
{'issuer': 'OYO', 'amount': 1939.0, 'date': datetime.datetime(2017, 12, 31, 0, 0), 'invoice_number': 'IBZY2087',
'currency': 'INR', 'desc': 'Invoice IBZY2087 from OYO'} | [
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] | d97fdc5db9c1844fd77fa64f8ea7c42fefd0ba20 | https://github.com/invoice-x/invoice2data/blob/d97fdc5db9c1844fd77fa64f8ea7c42fefd0ba20/src/invoice2data/extract/loader.py#L39-L99 |
240,981 | invoice-x/invoice2data | src/invoice2data/input/pdfminer_wrapper.py | to_text | def to_text(path):
"""Wrapper around `pdfminer`.
Parameters
----------
path : str
path of electronic invoice in PDF
Returns
-------
str : str
returns extracted text from pdf
"""
try:
# python 2
from StringIO import StringIO
import sys
reload(sys) # noqa: F821
sys.setdefaultencoding('utf8')
except ImportError:
from io import StringIO
from pdfminer.pdfinterp import PDFResourceManager, PDFPageInterpreter
from pdfminer.converter import TextConverter
from pdfminer.layout import LAParams
from pdfminer.pdfpage import PDFPage
rsrcmgr = PDFResourceManager()
retstr = StringIO()
codec = 'utf-8'
laparams = LAParams()
laparams.all_texts = True
device = TextConverter(rsrcmgr, retstr, codec=codec, laparams=laparams)
with open(path, 'rb') as fp:
interpreter = PDFPageInterpreter(rsrcmgr, device)
password = ""
maxpages = 0
caching = True
pagenos = set()
pages = PDFPage.get_pages(
fp,
pagenos,
maxpages=maxpages,
password=password,
caching=caching,
check_extractable=True,
)
for page in pages:
interpreter.process_page(page)
device.close()
str = retstr.getvalue()
retstr.close()
return str.encode('utf-8') | python | def to_text(path):
try:
# python 2
from StringIO import StringIO
import sys
reload(sys) # noqa: F821
sys.setdefaultencoding('utf8')
except ImportError:
from io import StringIO
from pdfminer.pdfinterp import PDFResourceManager, PDFPageInterpreter
from pdfminer.converter import TextConverter
from pdfminer.layout import LAParams
from pdfminer.pdfpage import PDFPage
rsrcmgr = PDFResourceManager()
retstr = StringIO()
codec = 'utf-8'
laparams = LAParams()
laparams.all_texts = True
device = TextConverter(rsrcmgr, retstr, codec=codec, laparams=laparams)
with open(path, 'rb') as fp:
interpreter = PDFPageInterpreter(rsrcmgr, device)
password = ""
maxpages = 0
caching = True
pagenos = set()
pages = PDFPage.get_pages(
fp,
pagenos,
maxpages=maxpages,
password=password,
caching=caching,
check_extractable=True,
)
for page in pages:
interpreter.process_page(page)
device.close()
str = retstr.getvalue()
retstr.close()
return str.encode('utf-8') | [
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Parameters
----------
path : str
path of electronic invoice in PDF
Returns
-------
str : str
returns extracted text from pdf | [
"Wrapper",
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] | d97fdc5db9c1844fd77fa64f8ea7c42fefd0ba20 | https://github.com/invoice-x/invoice2data/blob/d97fdc5db9c1844fd77fa64f8ea7c42fefd0ba20/src/invoice2data/input/pdfminer_wrapper.py#L2-L57 |
240,982 | SALib/SALib | src/SALib/analyze/ff.py | analyze | def analyze(problem, X, Y, second_order=False, print_to_console=False,
seed=None):
"""Perform a fractional factorial analysis
Returns a dictionary with keys 'ME' (main effect) and 'IE' (interaction
effect). The techniques bulks out the number of parameters with dummy
parameters to the nearest 2**n. Any results involving dummy parameters
could indicate a problem with the model runs.
Arguments
---------
problem: dict
The problem definition
X: numpy.matrix
The NumPy matrix containing the model inputs
Y: numpy.array
The NumPy array containing the model outputs
second_order: bool, default=False
Include interaction effects
print_to_console: bool, default=False
Print results directly to console
Returns
-------
Si: dict
A dictionary of sensitivity indices, including main effects ``ME``,
and interaction effects ``IE`` (if ``second_order`` is True)
Examples
--------
>>> X = sample(problem)
>>> Y = X[:, 0] + (0.1 * X[:, 1]) + ((1.2 * X[:, 2]) * (0.2 + X[:, 0]))
>>> analyze(problem, X, Y, second_order=True, print_to_console=True)
"""
if seed:
np.random.seed(seed)
problem = extend_bounds(problem)
num_vars = problem['num_vars']
X = generate_contrast(problem)
main_effect = (1. / (2 * num_vars)) * np.dot(Y, X)
Si = ResultDict((k, [None] * num_vars)
for k in ['names', 'ME'])
Si['ME'] = main_effect
Si['names'] = problem['names']
if print_to_console:
print("Parameter ME")
for j in range(num_vars):
print("%s %f" % (problem['names'][j], Si['ME'][j]))
if second_order:
interaction_names, interaction_effects = interactions(problem,
Y,
print_to_console)
Si['interaction_names'] = interaction_names
Si['IE'] = interaction_effects
Si.to_df = MethodType(to_df, Si)
return Si | python | def analyze(problem, X, Y, second_order=False, print_to_console=False,
seed=None):
if seed:
np.random.seed(seed)
problem = extend_bounds(problem)
num_vars = problem['num_vars']
X = generate_contrast(problem)
main_effect = (1. / (2 * num_vars)) * np.dot(Y, X)
Si = ResultDict((k, [None] * num_vars)
for k in ['names', 'ME'])
Si['ME'] = main_effect
Si['names'] = problem['names']
if print_to_console:
print("Parameter ME")
for j in range(num_vars):
print("%s %f" % (problem['names'][j], Si['ME'][j]))
if second_order:
interaction_names, interaction_effects = interactions(problem,
Y,
print_to_console)
Si['interaction_names'] = interaction_names
Si['IE'] = interaction_effects
Si.to_df = MethodType(to_df, Si)
return Si | [
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Returns a dictionary with keys 'ME' (main effect) and 'IE' (interaction
effect). The techniques bulks out the number of parameters with dummy
parameters to the nearest 2**n. Any results involving dummy parameters
could indicate a problem with the model runs.
Arguments
---------
problem: dict
The problem definition
X: numpy.matrix
The NumPy matrix containing the model inputs
Y: numpy.array
The NumPy array containing the model outputs
second_order: bool, default=False
Include interaction effects
print_to_console: bool, default=False
Print results directly to console
Returns
-------
Si: dict
A dictionary of sensitivity indices, including main effects ``ME``,
and interaction effects ``IE`` (if ``second_order`` is True)
Examples
--------
>>> X = sample(problem)
>>> Y = X[:, 0] + (0.1 * X[:, 1]) + ((1.2 * X[:, 2]) * (0.2 + X[:, 0]))
>>> analyze(problem, X, Y, second_order=True, print_to_console=True) | [
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240,983 | SALib/SALib | src/SALib/analyze/ff.py | to_df | def to_df(self):
'''Conversion method to Pandas DataFrame. To be attached to ResultDict.
Returns
-------
main_effect, inter_effect: tuple
A tuple of DataFrames for main effects and interaction effects.
The second element (for interactions) will be `None` if not available.
'''
names = self['names']
main_effect = self['ME']
interactions = self.get('IE', None)
inter_effect = None
if interactions:
interaction_names = self.get('interaction_names')
names = [name for name in names if not isinstance(name, list)]
inter_effect = pd.DataFrame({'IE': interactions},
index=interaction_names)
main_effect = pd.DataFrame({'ME': main_effect}, index=names)
return main_effect, inter_effect | python | def to_df(self):
'''Conversion method to Pandas DataFrame. To be attached to ResultDict.
Returns
-------
main_effect, inter_effect: tuple
A tuple of DataFrames for main effects and interaction effects.
The second element (for interactions) will be `None` if not available.
'''
names = self['names']
main_effect = self['ME']
interactions = self.get('IE', None)
inter_effect = None
if interactions:
interaction_names = self.get('interaction_names')
names = [name for name in names if not isinstance(name, list)]
inter_effect = pd.DataFrame({'IE': interactions},
index=interaction_names)
main_effect = pd.DataFrame({'ME': main_effect}, index=names)
return main_effect, inter_effect | [
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240,984 | SALib/SALib | src/SALib/analyze/ff.py | interactions | def interactions(problem, Y, print_to_console=False):
"""Computes the second order effects
Computes the second order effects (interactions) between
all combinations of pairs of input factors
Arguments
---------
problem: dict
The problem definition
Y: numpy.array
The NumPy array containing the model outputs
print_to_console: bool, default=False
Print results directly to console
Returns
-------
ie_names: list
The names of the interaction pairs
IE: list
The sensitivity indices for the pairwise interactions
"""
names = problem['names']
num_vars = problem['num_vars']
X = generate_contrast(problem)
ie_names = []
IE = []
for col in range(X.shape[1]):
for col_2 in range(col):
x = X[:, col] * X[:, col_2]
var_names = (names[col_2], names[col])
ie_names.append(var_names)
IE.append((1. / (2 * num_vars)) * np.dot(Y, x))
if print_to_console:
[print('%s %f' % (n, i)) for (n, i) in zip(ie_names, IE)]
return ie_names, IE | python | def interactions(problem, Y, print_to_console=False):
names = problem['names']
num_vars = problem['num_vars']
X = generate_contrast(problem)
ie_names = []
IE = []
for col in range(X.shape[1]):
for col_2 in range(col):
x = X[:, col] * X[:, col_2]
var_names = (names[col_2], names[col])
ie_names.append(var_names)
IE.append((1. / (2 * num_vars)) * np.dot(Y, x))
if print_to_console:
[print('%s %f' % (n, i)) for (n, i) in zip(ie_names, IE)]
return ie_names, IE | [
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Computes the second order effects (interactions) between
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Arguments
---------
problem: dict
The problem definition
Y: numpy.array
The NumPy array containing the model outputs
print_to_console: bool, default=False
Print results directly to console
Returns
-------
ie_names: list
The names of the interaction pairs
IE: list
The sensitivity indices for the pairwise interactions | [
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240,985 | SALib/SALib | src/SALib/util/__init__.py | avail_approaches | def avail_approaches(pkg):
'''Create list of available modules.
Arguments
---------
pkg : module
module to inspect
Returns
---------
method : list
A list of available submodules
'''
methods = [modname for importer, modname, ispkg in
pkgutil.walk_packages(path=pkg.__path__)
if modname not in
['common_args', 'directions', 'sobol_sequence']]
return methods | python | def avail_approaches(pkg):
'''Create list of available modules.
Arguments
---------
pkg : module
module to inspect
Returns
---------
method : list
A list of available submodules
'''
methods = [modname for importer, modname, ispkg in
pkgutil.walk_packages(path=pkg.__path__)
if modname not in
['common_args', 'directions', 'sobol_sequence']]
return methods | [
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Arguments
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pkg : module
module to inspect
Returns
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method : list
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240,986 | SALib/SALib | src/SALib/util/__init__.py | scale_samples | def scale_samples(params, bounds):
'''Rescale samples in 0-to-1 range to arbitrary bounds
Arguments
---------
bounds : list
list of lists of dimensions `num_params`-by-2
params : numpy.ndarray
numpy array of dimensions `num_params`-by-:math:`N`,
where :math:`N` is the number of samples
'''
# Check bounds are legal (upper bound is greater than lower bound)
b = np.array(bounds)
lower_bounds = b[:, 0]
upper_bounds = b[:, 1]
if np.any(lower_bounds >= upper_bounds):
raise ValueError("Bounds are not legal")
# This scales the samples in-place, by using the optional output
# argument for the numpy ufunctions
# The calculation is equivalent to:
# sample * (upper_bound - lower_bound) + lower_bound
np.add(np.multiply(params,
(upper_bounds - lower_bounds),
out=params),
lower_bounds,
out=params) | python | def scale_samples(params, bounds):
'''Rescale samples in 0-to-1 range to arbitrary bounds
Arguments
---------
bounds : list
list of lists of dimensions `num_params`-by-2
params : numpy.ndarray
numpy array of dimensions `num_params`-by-:math:`N`,
where :math:`N` is the number of samples
'''
# Check bounds are legal (upper bound is greater than lower bound)
b = np.array(bounds)
lower_bounds = b[:, 0]
upper_bounds = b[:, 1]
if np.any(lower_bounds >= upper_bounds):
raise ValueError("Bounds are not legal")
# This scales the samples in-place, by using the optional output
# argument for the numpy ufunctions
# The calculation is equivalent to:
# sample * (upper_bound - lower_bound) + lower_bound
np.add(np.multiply(params,
(upper_bounds - lower_bounds),
out=params),
lower_bounds,
out=params) | [
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numpy array of dimensions `num_params`-by-:math:`N`,
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240,987 | SALib/SALib | src/SALib/util/__init__.py | nonuniform_scale_samples | def nonuniform_scale_samples(params, bounds, dists):
"""Rescale samples in 0-to-1 range to other distributions
Arguments
---------
problem : dict
problem definition including bounds
params : numpy.ndarray
numpy array of dimensions num_params-by-N,
where N is the number of samples
dists : list
list of distributions, one for each parameter
unif: uniform with lower and upper bounds
triang: triangular with width (scale) and location of peak
location of peak is in percentage of width
lower bound assumed to be zero
norm: normal distribution with mean and standard deviation
lognorm: lognormal with ln-space mean and standard deviation
"""
b = np.array(bounds)
# initializing matrix for converted values
conv_params = np.zeros_like(params)
# loop over the parameters
for i in range(conv_params.shape[1]):
# setting first and second arguments for distributions
b1 = b[i][0]
b2 = b[i][1]
if dists[i] == 'triang':
# checking for correct parameters
if b1 <= 0 or b2 <= 0 or b2 >= 1:
raise ValueError('''Triangular distribution: Scale must be
greater than zero; peak on interval [0,1]''')
else:
conv_params[:, i] = sp.stats.triang.ppf(
params[:, i], c=b2, scale=b1, loc=0)
elif dists[i] == 'unif':
if b1 >= b2:
raise ValueError('''Uniform distribution: lower bound
must be less than upper bound''')
else:
conv_params[:, i] = params[:, i] * (b2 - b1) + b1
elif dists[i] == 'norm':
if b2 <= 0:
raise ValueError('''Normal distribution: stdev must be > 0''')
else:
conv_params[:, i] = sp.stats.norm.ppf(
params[:, i], loc=b1, scale=b2)
# lognormal distribution (ln-space, not base-10)
# paramters are ln-space mean and standard deviation
elif dists[i] == 'lognorm':
# checking for valid parameters
if b2 <= 0:
raise ValueError(
'''Lognormal distribution: stdev must be > 0''')
else:
conv_params[:, i] = np.exp(
sp.stats.norm.ppf(params[:, i], loc=b1, scale=b2))
else:
valid_dists = ['unif', 'triang', 'norm', 'lognorm']
raise ValueError('Distributions: choose one of %s' %
", ".join(valid_dists))
return conv_params | python | def nonuniform_scale_samples(params, bounds, dists):
b = np.array(bounds)
# initializing matrix for converted values
conv_params = np.zeros_like(params)
# loop over the parameters
for i in range(conv_params.shape[1]):
# setting first and second arguments for distributions
b1 = b[i][0]
b2 = b[i][1]
if dists[i] == 'triang':
# checking for correct parameters
if b1 <= 0 or b2 <= 0 or b2 >= 1:
raise ValueError('''Triangular distribution: Scale must be
greater than zero; peak on interval [0,1]''')
else:
conv_params[:, i] = sp.stats.triang.ppf(
params[:, i], c=b2, scale=b1, loc=0)
elif dists[i] == 'unif':
if b1 >= b2:
raise ValueError('''Uniform distribution: lower bound
must be less than upper bound''')
else:
conv_params[:, i] = params[:, i] * (b2 - b1) + b1
elif dists[i] == 'norm':
if b2 <= 0:
raise ValueError('''Normal distribution: stdev must be > 0''')
else:
conv_params[:, i] = sp.stats.norm.ppf(
params[:, i], loc=b1, scale=b2)
# lognormal distribution (ln-space, not base-10)
# paramters are ln-space mean and standard deviation
elif dists[i] == 'lognorm':
# checking for valid parameters
if b2 <= 0:
raise ValueError(
'''Lognormal distribution: stdev must be > 0''')
else:
conv_params[:, i] = np.exp(
sp.stats.norm.ppf(params[:, i], loc=b1, scale=b2))
else:
valid_dists = ['unif', 'triang', 'norm', 'lognorm']
raise ValueError('Distributions: choose one of %s' %
", ".join(valid_dists))
return conv_params | [
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Arguments
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problem : dict
problem definition including bounds
params : numpy.ndarray
numpy array of dimensions num_params-by-N,
where N is the number of samples
dists : list
list of distributions, one for each parameter
unif: uniform with lower and upper bounds
triang: triangular with width (scale) and location of peak
location of peak is in percentage of width
lower bound assumed to be zero
norm: normal distribution with mean and standard deviation
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240,988 | SALib/SALib | src/SALib/util/__init__.py | read_param_file | def read_param_file(filename, delimiter=None):
"""Unpacks a parameter file into a dictionary
Reads a parameter file of format::
Param1,0,1,Group1,dist1
Param2,0,1,Group2,dist2
Param3,0,1,Group3,dist3
(Group and Dist columns are optional)
Returns a dictionary containing:
- names - the names of the parameters
- bounds - a list of lists of lower and upper bounds
- num_vars - a scalar indicating the number of variables
(the length of names)
- groups - a list of group names (strings) for each variable
- dists - a list of distributions for the problem,
None if not specified or all uniform
Arguments
---------
filename : str
The path to the parameter file
delimiter : str, default=None
The delimiter used in the file to distinguish between columns
"""
names = []
bounds = []
groups = []
dists = []
num_vars = 0
fieldnames = ['name', 'lower_bound', 'upper_bound', 'group', 'dist']
with open(filename, 'rU') as csvfile:
dialect = csv.Sniffer().sniff(csvfile.read(1024), delimiters=delimiter)
csvfile.seek(0)
reader = csv.DictReader(
csvfile, fieldnames=fieldnames, dialect=dialect)
for row in reader:
if row['name'].strip().startswith('#'):
pass
else:
num_vars += 1
names.append(row['name'])
bounds.append(
[float(row['lower_bound']), float(row['upper_bound'])])
# If the fourth column does not contain a group name, use
# the parameter name
if row['group'] is None:
groups.append(row['name'])
elif row['group'] is 'NA':
groups.append(row['name'])
else:
groups.append(row['group'])
# If the fifth column does not contain a distribution
# use uniform
if row['dist'] is None:
dists.append('unif')
else:
dists.append(row['dist'])
if groups == names:
groups = None
elif len(set(groups)) == 1:
raise ValueError('''Only one group defined, results will not be
meaningful''')
# setting dists to none if all are uniform
# because non-uniform scaling is not needed
if all([d == 'unif' for d in dists]):
dists = None
return {'names': names, 'bounds': bounds, 'num_vars': num_vars,
'groups': groups, 'dists': dists} | python | def read_param_file(filename, delimiter=None):
names = []
bounds = []
groups = []
dists = []
num_vars = 0
fieldnames = ['name', 'lower_bound', 'upper_bound', 'group', 'dist']
with open(filename, 'rU') as csvfile:
dialect = csv.Sniffer().sniff(csvfile.read(1024), delimiters=delimiter)
csvfile.seek(0)
reader = csv.DictReader(
csvfile, fieldnames=fieldnames, dialect=dialect)
for row in reader:
if row['name'].strip().startswith('#'):
pass
else:
num_vars += 1
names.append(row['name'])
bounds.append(
[float(row['lower_bound']), float(row['upper_bound'])])
# If the fourth column does not contain a group name, use
# the parameter name
if row['group'] is None:
groups.append(row['name'])
elif row['group'] is 'NA':
groups.append(row['name'])
else:
groups.append(row['group'])
# If the fifth column does not contain a distribution
# use uniform
if row['dist'] is None:
dists.append('unif')
else:
dists.append(row['dist'])
if groups == names:
groups = None
elif len(set(groups)) == 1:
raise ValueError('''Only one group defined, results will not be
meaningful''')
# setting dists to none if all are uniform
# because non-uniform scaling is not needed
if all([d == 'unif' for d in dists]):
dists = None
return {'names': names, 'bounds': bounds, 'num_vars': num_vars,
'groups': groups, 'dists': dists} | [
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(Group and Dist columns are optional)
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- dists - a list of distributions for the problem,
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240,989 | SALib/SALib | src/SALib/util/__init__.py | compute_groups_matrix | def compute_groups_matrix(groups):
"""Generate matrix which notes factor membership of groups
Computes a k-by-g matrix which notes factor membership of groups
where:
k is the number of variables (factors)
g is the number of groups
Also returns a g-length list of unique group_names whose positions
correspond to the order of groups in the k-by-g matrix
Arguments
---------
groups : list
Group names corresponding to each variable
Returns
-------
tuple
containing group matrix assigning parameters to
groups and a list of unique group names
"""
if not groups:
return None
num_vars = len(groups)
# Get a unique set of the group names
unique_group_names = list(OrderedDict.fromkeys(groups))
number_of_groups = len(unique_group_names)
indices = dict([(x, i) for (i, x) in enumerate(unique_group_names)])
output = np.zeros((num_vars, number_of_groups), dtype=np.int)
for parameter_row, group_membership in enumerate(groups):
group_index = indices[group_membership]
output[parameter_row, group_index] = 1
return output, unique_group_names | python | def compute_groups_matrix(groups):
if not groups:
return None
num_vars = len(groups)
# Get a unique set of the group names
unique_group_names = list(OrderedDict.fromkeys(groups))
number_of_groups = len(unique_group_names)
indices = dict([(x, i) for (i, x) in enumerate(unique_group_names)])
output = np.zeros((num_vars, number_of_groups), dtype=np.int)
for parameter_row, group_membership in enumerate(groups):
group_index = indices[group_membership]
output[parameter_row, group_index] = 1
return output, unique_group_names | [
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Computes a k-by-g matrix which notes factor membership of groups
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k is the number of variables (factors)
g is the number of groups
Also returns a g-length list of unique group_names whose positions
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Arguments
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groups : list
Group names corresponding to each variable
Returns
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tuple
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240,990 | SALib/SALib | src/SALib/util/__init__.py | requires_gurobipy | def requires_gurobipy(_has_gurobi):
'''
Decorator function which takes a boolean _has_gurobi as an argument.
Use decorate any functions which require gurobi.
Raises an import error at runtime if gurobi is not present.
Note that all runtime errors should be avoided in the working code,
using brute force options as preference.
'''
def _outer_wrapper(wrapped_function):
def _wrapper(*args, **kwargs):
if _has_gurobi:
result = wrapped_function(*args, **kwargs)
else:
warn("Gurobi not available", ImportWarning)
result = None
return result
return _wrapper
return _outer_wrapper | python | def requires_gurobipy(_has_gurobi):
'''
Decorator function which takes a boolean _has_gurobi as an argument.
Use decorate any functions which require gurobi.
Raises an import error at runtime if gurobi is not present.
Note that all runtime errors should be avoided in the working code,
using brute force options as preference.
'''
def _outer_wrapper(wrapped_function):
def _wrapper(*args, **kwargs):
if _has_gurobi:
result = wrapped_function(*args, **kwargs)
else:
warn("Gurobi not available", ImportWarning)
result = None
return result
return _wrapper
return _outer_wrapper | [
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240,991 | SALib/SALib | src/SALib/analyze/morris.py | compute_grouped_sigma | def compute_grouped_sigma(ungrouped_sigma, group_matrix):
'''
Returns sigma for the groups of parameter values in the
argument ungrouped_metric where the group consists of no more than
one parameter
'''
group_matrix = np.array(group_matrix, dtype=np.bool)
sigma_masked = np.ma.masked_array(ungrouped_sigma * group_matrix.T,
mask=(group_matrix ^ 1).T)
sigma_agg = np.ma.mean(sigma_masked, axis=1)
sigma = np.zeros(group_matrix.shape[1], dtype=np.float)
np.copyto(sigma, sigma_agg, where=group_matrix.sum(axis=0) == 1)
np.copyto(sigma, np.NAN, where=group_matrix.sum(axis=0) != 1)
return sigma | python | def compute_grouped_sigma(ungrouped_sigma, group_matrix):
'''
Returns sigma for the groups of parameter values in the
argument ungrouped_metric where the group consists of no more than
one parameter
'''
group_matrix = np.array(group_matrix, dtype=np.bool)
sigma_masked = np.ma.masked_array(ungrouped_sigma * group_matrix.T,
mask=(group_matrix ^ 1).T)
sigma_agg = np.ma.mean(sigma_masked, axis=1)
sigma = np.zeros(group_matrix.shape[1], dtype=np.float)
np.copyto(sigma, sigma_agg, where=group_matrix.sum(axis=0) == 1)
np.copyto(sigma, np.NAN, where=group_matrix.sum(axis=0) != 1)
return sigma | [
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240,992 | SALib/SALib | src/SALib/analyze/morris.py | compute_grouped_metric | def compute_grouped_metric(ungrouped_metric, group_matrix):
'''
Computes the mean value for the groups of parameter values in the
argument ungrouped_metric
'''
group_matrix = np.array(group_matrix, dtype=np.bool)
mu_star_masked = np.ma.masked_array(ungrouped_metric * group_matrix.T,
mask=(group_matrix ^ 1).T)
mean_of_mu_star = np.ma.mean(mu_star_masked, axis=1)
return mean_of_mu_star | python | def compute_grouped_metric(ungrouped_metric, group_matrix):
'''
Computes the mean value for the groups of parameter values in the
argument ungrouped_metric
'''
group_matrix = np.array(group_matrix, dtype=np.bool)
mu_star_masked = np.ma.masked_array(ungrouped_metric * group_matrix.T,
mask=(group_matrix ^ 1).T)
mean_of_mu_star = np.ma.mean(mu_star_masked, axis=1)
return mean_of_mu_star | [
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240,993 | SALib/SALib | src/SALib/analyze/morris.py | compute_mu_star_confidence | def compute_mu_star_confidence(ee, num_trajectories, num_resamples,
conf_level):
'''
Uses bootstrapping where the elementary effects are resampled with
replacement to produce a histogram of resampled mu_star metrics.
This resample is used to produce a confidence interval.
'''
ee_resampled = np.zeros([num_trajectories])
mu_star_resampled = np.zeros([num_resamples])
if not 0 < conf_level < 1:
raise ValueError("Confidence level must be between 0-1.")
resample_index = np.random.randint(
len(ee), size=(num_resamples, num_trajectories))
ee_resampled = ee[resample_index]
# Compute average of the absolute values over each of the resamples
mu_star_resampled = np.average(np.abs(ee_resampled), axis=1)
return norm.ppf(0.5 + conf_level / 2) * mu_star_resampled.std(ddof=1) | python | def compute_mu_star_confidence(ee, num_trajectories, num_resamples,
conf_level):
'''
Uses bootstrapping where the elementary effects are resampled with
replacement to produce a histogram of resampled mu_star metrics.
This resample is used to produce a confidence interval.
'''
ee_resampled = np.zeros([num_trajectories])
mu_star_resampled = np.zeros([num_resamples])
if not 0 < conf_level < 1:
raise ValueError("Confidence level must be between 0-1.")
resample_index = np.random.randint(
len(ee), size=(num_resamples, num_trajectories))
ee_resampled = ee[resample_index]
# Compute average of the absolute values over each of the resamples
mu_star_resampled = np.average(np.abs(ee_resampled), axis=1)
return norm.ppf(0.5 + conf_level / 2) * mu_star_resampled.std(ddof=1) | [
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240,994 | SALib/SALib | src/SALib/sample/morris/gurobi.py | timestamp | def timestamp(num_params, p_levels, k_choices, N):
"""
Returns a uniform timestamp with parameter values for file identification
"""
string = "_v%s_l%s_gs%s_k%s_N%s_%s.txt" % (num_params,
p_levels,
k_choices,
N,
dt.strftime(dt.now(),
"%d%m%y%H%M%S"))
return string | python | def timestamp(num_params, p_levels, k_choices, N):
string = "_v%s_l%s_gs%s_k%s_N%s_%s.txt" % (num_params,
p_levels,
k_choices,
N,
dt.strftime(dt.now(),
"%d%m%y%H%M%S"))
return string | [
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240,995 | SALib/SALib | src/SALib/sample/morris/brute.py | BruteForce.brute_force_most_distant | def brute_force_most_distant(self, input_sample, num_samples,
num_params, k_choices,
num_groups=None):
"""Use brute force method to find most distant trajectories
Arguments
---------
input_sample : numpy.ndarray
num_samples : int
The number of samples to generate
num_params : int
The number of parameters
k_choices : int
The number of optimal trajectories
num_groups : int, default=None
The number of groups
Returns
-------
list
"""
scores = self.find_most_distant(input_sample,
num_samples,
num_params,
k_choices,
num_groups)
maximum_combo = self.find_maximum(scores, num_samples, k_choices)
return maximum_combo | python | def brute_force_most_distant(self, input_sample, num_samples,
num_params, k_choices,
num_groups=None):
scores = self.find_most_distant(input_sample,
num_samples,
num_params,
k_choices,
num_groups)
maximum_combo = self.find_maximum(scores, num_samples, k_choices)
return maximum_combo | [
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The number of samples to generate
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The number of parameters
k_choices : int
The number of optimal trajectories
num_groups : int, default=None
The number of groups
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240,996 | SALib/SALib | src/SALib/sample/morris/brute.py | BruteForce.find_most_distant | def find_most_distant(self, input_sample, num_samples,
num_params, k_choices, num_groups=None):
"""
Finds the 'k_choices' most distant choices from the
'num_samples' trajectories contained in 'input_sample'
Arguments
---------
input_sample : numpy.ndarray
num_samples : int
The number of samples to generate
num_params : int
The number of parameters
k_choices : int
The number of optimal trajectories
num_groups : int, default=None
The number of groups
Returns
-------
numpy.ndarray
"""
# Now evaluate the (N choose k_choices) possible combinations
if nchoosek(num_samples, k_choices) >= sys.maxsize:
raise ValueError("Number of combinations is too large")
number_of_combinations = int(nchoosek(num_samples, k_choices))
# First compute the distance matrix for each possible pairing
# of trajectories and store in a shared-memory array
distance_matrix = self.compute_distance_matrix(input_sample,
num_samples,
num_params,
num_groups)
# Initialise the output array
chunk = int(1e6)
if chunk > number_of_combinations:
chunk = number_of_combinations
counter = 0
# Generate a list of all the possible combinations
combo_gen = combinations(list(range(num_samples)), k_choices)
scores = np.zeros(number_of_combinations, dtype=np.float32)
# Generate the pairwise indices once
pairwise = np.array(
[y for y in combinations(list(range(k_choices)), 2)])
for combos in self.grouper(chunk, combo_gen):
scores[(counter * chunk):((counter + 1) * chunk)] \
= self.mappable(combos, pairwise, distance_matrix)
counter += 1
return scores | python | def find_most_distant(self, input_sample, num_samples,
num_params, k_choices, num_groups=None):
# Now evaluate the (N choose k_choices) possible combinations
if nchoosek(num_samples, k_choices) >= sys.maxsize:
raise ValueError("Number of combinations is too large")
number_of_combinations = int(nchoosek(num_samples, k_choices))
# First compute the distance matrix for each possible pairing
# of trajectories and store in a shared-memory array
distance_matrix = self.compute_distance_matrix(input_sample,
num_samples,
num_params,
num_groups)
# Initialise the output array
chunk = int(1e6)
if chunk > number_of_combinations:
chunk = number_of_combinations
counter = 0
# Generate a list of all the possible combinations
combo_gen = combinations(list(range(num_samples)), k_choices)
scores = np.zeros(number_of_combinations, dtype=np.float32)
# Generate the pairwise indices once
pairwise = np.array(
[y for y in combinations(list(range(k_choices)), 2)])
for combos in self.grouper(chunk, combo_gen):
scores[(counter * chunk):((counter + 1) * chunk)] \
= self.mappable(combos, pairwise, distance_matrix)
counter += 1
return scores | [
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The number of parameters
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The number of optimal trajectories
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The number of groups
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240,997 | SALib/SALib | src/SALib/sample/morris/brute.py | BruteForce.mappable | def mappable(combos, pairwise, distance_matrix):
'''
Obtains scores from the distance_matrix for each pairwise combination
held in the combos array
Arguments
----------
combos : numpy.ndarray
pairwise : numpy.ndarray
distance_matrix : numpy.ndarray
'''
combos = np.array(combos)
# Create a list of all pairwise combination for each combo in combos
combo_list = combos[:, pairwise[:, ]]
addresses = tuple([combo_list[:, :, 1], combo_list[:, :, 0]])
all_distances = distance_matrix[addresses]
new_scores = np.sqrt(
np.einsum('ij,ij->i', all_distances, all_distances))
return new_scores | python | def mappable(combos, pairwise, distance_matrix):
'''
Obtains scores from the distance_matrix for each pairwise combination
held in the combos array
Arguments
----------
combos : numpy.ndarray
pairwise : numpy.ndarray
distance_matrix : numpy.ndarray
'''
combos = np.array(combos)
# Create a list of all pairwise combination for each combo in combos
combo_list = combos[:, pairwise[:, ]]
addresses = tuple([combo_list[:, :, 1], combo_list[:, :, 0]])
all_distances = distance_matrix[addresses]
new_scores = np.sqrt(
np.einsum('ij,ij->i', all_distances, all_distances))
return new_scores | [
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240,998 | SALib/SALib | src/SALib/sample/morris/brute.py | BruteForce.find_maximum | def find_maximum(self, scores, N, k_choices):
"""Finds the `k_choices` maximum scores from `scores`
Arguments
---------
scores : numpy.ndarray
N : int
k_choices : int
Returns
-------
list
"""
if not isinstance(scores, np.ndarray):
raise TypeError("Scores input is not a numpy array")
index_of_maximum = int(scores.argmax())
maximum_combo = self.nth(combinations(
list(range(N)), k_choices), index_of_maximum, None)
return sorted(maximum_combo) | python | def find_maximum(self, scores, N, k_choices):
if not isinstance(scores, np.ndarray):
raise TypeError("Scores input is not a numpy array")
index_of_maximum = int(scores.argmax())
maximum_combo = self.nth(combinations(
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return sorted(maximum_combo) | [
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240,999 | SALib/SALib | src/SALib/sample/morris/brute.py | BruteForce.nth | def nth(iterable, n, default=None):
"""Returns the nth item or a default value
Arguments
---------
iterable : iterable
n : int
default : default=None
The default value to return
"""
if type(n) != int:
raise TypeError("n is not an integer")
return next(islice(iterable, n, None), default) | python | def nth(iterable, n, default=None):
if type(n) != int:
raise TypeError("n is not an integer")
return next(islice(iterable, n, None), default) | [
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Arguments
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iterable : iterable
n : int
default : default=None
The default value to return | [
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