From 3582b6ffe571cb96b69dc6c356ef8d946df57fe7 Mon Sep 17 00:00:00 2001
From: "Mokhtar Z. Alaya" <mokhtarzahdi.alaya@gmail.com>
Date: Mon, 6 Jan 2020 11:33:01 +0100
Subject: [PATCH 01/39] add screenkhorn: screening Sinkhorn algorithm

---
 ot/bregman.py | 288 +++++++++++++++++++++++++++++++++++++++++++++++++-
 1 file changed, 287 insertions(+), 1 deletion(-)

diff --git a/ot/bregman.py b/ot/bregman.py
index ba5c7ba29..61b860582 100644
--- a/ot/bregman.py
+++ b/ot/bregman.py
@@ -8,13 +8,15 @@
 #         Kilian Fatras <kilian.fatras@irisa.fr>
 #         Titouan Vayer <titouan.vayer@irisa.fr>
 #         Hicham Janati <hicham.janati@inria.fr>
+#         Mokhtar Z. Alaya <mokhtarzahdi.alaya@gmail.com>
 #
 # License: MIT License
 
 import numpy as np
 import warnings
 from .utils import unif, dist
-
+import bottleneck
+from scipy.optimize import fmin_l_bfgs_b
 
 def sinkhorn(a, b, M, reg, method='sinkhorn', numItermax=1000,
              stopThr=1e-9, verbose=False, log=False, **kwargs):
@@ -1787,3 +1789,287 @@ def empirical_sinkhorn_divergence(X_s, X_t, reg, a=None, b=None, metric='sqeucli
 
         sinkhorn_div = sinkhorn_loss_ab - 1 / 2 * (sinkhorn_loss_a + sinkhorn_loss_b)
         return max(0, sinkhorn_div)
+ 
+def screenkhorn(a, b, M, reg, ns_budget, nt_budget, uniform=True, restricted=True, verbose=False):
+
+    """"
+    Screening Sinkhorn Algorithm for Regularized Optimal Transport.
+
+    Parameters
+    ----------
+    a : `numpy.ndarray`, shape=(ns,)
+        samples weights in the source domain.
+
+    b : `numpy.ndarray`, shape=(nt,)
+        samples weights in the target domain.
+
+    M : `numpy.ndarray`, shape=(ns, nt)
+        Cost matrix.
+
+    reg : `float`
+        Level of the entropy regularisation.
+
+    ns_budget: `int`
+        Number budget of points to be keeped in the source domain.
+
+    nt_budget: `int`
+        Number budget of points to be keeped in the target domain.
+
+    uniform: `bool`, default=True
+        If `True`, a_i = 1. / ns and b_j = 1. / nt
+
+    restricted: `bool`, default=True
+         If `True`, a warm-start initialization for the  L-BFGS-B solver
+         using a restricted Sinkhorn algorithm with at most 5 iterations.
+
+    verbose: `bool`, default=False
+        If `True`, dispaly informations along iterations.
+
+    Returns
+    -------
+    Gsc : `numpy.ndarray`, shape=(ns, nt)
+        Screened optimal transportation matrix for the given parameters.
+
+    References:
+    -----------
+    .. [1] M. Z. Alaya, Maxime Bérar, Gilles Gasso, Alain Rakotomamonjy. Screening Sinkhorn Algorithm for Regularized
+    Optimal Transport, NeurIPS 2019.
+
+    """
+    a = np.asarray(a, dtype=np.float64)
+    b = np.asarray(b, dtype=np.float64)
+
+    # if the "autograd" package is needed for some experiments, we then have to change the instance of the cost matrix M
+    # from "ArrayBox"-type to "np.array"-type as follows:
+    if isinstance(M, np.ndarray) == False:
+        M = M._value
+
+    M = np.asarray(M, dtype=np.float64)
+    ns, nt = M.shape
+
+    # calculate the Gibbs kernel
+    K = np.empty_like(M)
+    np.divide(M, - reg, out=K)
+    np.exp(K, out=K)
+
+    def projection(u, epsilon):
+        u[np.where(u <= epsilon)] = epsilon
+        return u
+
+    # ----------------------------------------------------------------------------------------------------------------#
+    #                                          Step 1: Screening Pre-processing                                       #
+    # ----------------------------------------------------------------------------------------------------------------#
+
+    if ns_budget == ns and nt_budget == nt:
+        # full number of budget points (ns, nt) = (ns_budget, nt_budget)
+        I = list(range(ns))
+        J = list(range(nt))
+        epsilon = 0.0  
+        kappa = 1.0  
+
+        cst_u = 0.
+        cst_v = 0.
+
+        bounds_u = [(0.0, np.inf)] * ns
+        bounds_v = [(0.0, np.inf)] * nt
+        
+        a_I = a
+        b_J = b
+        K_min = K.min()
+        K_IJ = K
+        K_IJc = []
+        K_IcJ = []
+
+        vec_eps_IJc = np.zeros(nt)
+        vec_eps_IcJ = np.zeros(ns)
+
+    else:
+        # sum of rows and columns of K
+        K_sum_cols = K.sum(axis=1)
+        K_sum_rows = K.sum(axis=0)
+
+        if uniform:
+            if ns / ns_budget < 4:
+                aK_sort = np.sort(K_sum_cols)
+                epsilon_u_square = a[0] / aK_sort[ns_budget - 1]
+            else:
+                aK_sort = bottleneck.partition(K_sum_cols, ns_budget - 1)[ns_budget - 1]
+                epsilon_u_square = a[0] / aK_sort
+
+            if nt / ns_budget < 4:
+                bK_sort = np.sort(K_sum_rows)
+                epsilon_v_square = b[0] / bK_sort[ns_budget - 1]
+            else:
+                bK_sort = bottleneck.partition(K_sum_rows, nt_budget - 1)[nt_budget - 1]
+                epsilon_v_square = b[0] / bK_sort
+        else:
+            aK = a / K_sum_cols
+            bK = b / K_sum_rows
+
+            aK_sort = np.sort(aK)[::-1]
+            epsilon_u_square = aK_sort[ns_budget - 1]
+
+            bK_sort = np.sort(bK)[::-1]
+            epsilon_v_square = bK_sort[ns_budget - 1]
+
+        # active sets I and J (see Proposition .. in [1])
+        I = np.where(a >= epsilon_u_square * K_sum_cols)[0].tolist()
+        J = np.where(b >= epsilon_v_square * K_sum_rows)[0].tolist()
+
+        if len(I) != ns_budget:
+            if uniform:
+                aK = a / K_sum_cols
+                aK_sort = np.sort(aK)[::-1]
+            epsilon_u_square = aK_sort[ns_budget - 1:ns_budget + 1].mean()
+            I = np.where(a >= epsilon_u_square * K_sum_cols)[0].tolist()
+
+        if len(J) != nt_budget:
+            if uniform:
+                bK = b / K_sum_rows
+                bK_sort = np.sort(bK)[::-1]
+            epsilon_v_square = bK_sort[ns_budget - 1:ns_budget + 1].mean()
+            J = np.where(b >= epsilon_v_square * K_sum_rows)[0].tolist()
+
+        epsilon = (epsilon_u_square * epsilon_v_square) ** (1 / 4)
+        kappa = (epsilon_v_square / epsilon_u_square) ** (1 / 2)
+
+        if verbose:
+            print("Epsilon = %s\n" %epsilon)
+            print("Scaling factor = %s\n" %kappa)
+
+        if verbose:
+            print('|I_active| = %s \t |J_active| = %s ' %(len(I), len(J)))
+
+        # Ic, Jc: complementary of the active sets I and J
+        Ic = list(set(list(range(ns))) - set(I))
+        Jc = list(set(list(range(nt))) - set(J))
+
+        K_IJ = K[np.ix_(I, J)]
+        K_IcJ = K[np.ix_(Ic, J)]
+        K_IJc = K[np.ix_(I, Jc)]
+
+        K_min = K_IJ.min()
+        if K_min == 0:
+            K_min = np.finfo(float).tiny
+
+        # a_I, b_J, a_Ic, b_Jc
+        a_I = a[I]
+        b_J = b[J]
+        if not uniform:
+            a_I_min = a_I.min()
+            a_I_max = a_I.max()
+            b_J_max = b_J.max()
+            b_J_min = b_J.min()
+        else:
+            a_I_min = a_I[0]
+            a_I_max = a_I[0]
+            b_J_max = b_J[0]
+            b_J_min = b_J[0]
+
+        # box constraints in L-BFGS-B (see Proposition 1 in [1])
+        bounds_u = [(max(kappa * a_I_min / (epsilon * (nt - ns_budget) + ns_budget * (b_J_max / (
+                epsilon * ns * K_min))), epsilon / kappa), a_I_max / (epsilon * nt * K_min))] * ns_budget
+
+        bounds_v = [(max(b_J_min / (epsilon * (ns - ns_budget) + ns_budget * (a_I_max / (epsilon * nt * K_min))), \
+                         epsilon * kappa), b_J_max / (epsilon * ns * K_min))] * ns_budget
+
+        # pre-calculated constants for the objective
+        vec_eps_IJc = epsilon * kappa * (K_IJc * np.ones(nt - ns_budget).reshape((1, -1))).sum(axis=1)
+        vec_eps_IcJ = (epsilon / kappa) * (np.ones(ns - ns_budget).reshape((-1, 1)) * K_IcJ).sum(axis=0)
+
+    # initialisation
+    u0 = np.full(ns_budget, (1. / ns_budget) + epsilon / kappa)
+    v0 = np.full(nt_budget, (1. / nt_budget) + epsilon * kappa)
+
+    # pre-calculed constants for Restricted Sinkhorn (see Algorithm 2 in [1])
+    if restricted:
+        if ns_budget != ns or ns_budget != nt:
+            cst_u = kappa * epsilon * K_IJc.sum(axis=1)
+            cst_v = epsilon * K_IcJ.sum(axis=0) / kappa
+
+        cpt = 1
+        while (cpt < 5):  # 5 iterations
+            K_IJ_v = K_IJ.T @ u0 + cst_v
+            v0 = b_J / (kappa * K_IJ_v)
+            KIJ_u = K_IJ @ v0 + cst_u
+            u0 = (kappa * a_I) / KIJ_u
+            cpt += 1
+
+        u0 = projection(u0, epsilon / kappa)
+        v0 = projection(v0, epsilon * kappa)
+
+    else:
+        u0 = u0
+        v0 = v0
+
+    def restricted_sinkhorn(usc, vsc, max_iter=5):
+        """
+        Restricted Sinkhorn Algorithm as a warm-start initialized point for L-BFGS-B (see Algorithm 2 in [1]).
+        """
+        cpt = 1
+        while (cpt < max_iter):
+            K_IJ_v = K_IJ.T @ usc + cst_v
+            vsc = b_J / (kappa * K_IJ_v)
+            KIJ_u = K_IJ @ vsc + cst_u
+            usc = (kappa * a_I) / KIJ_u
+            cpt += 1
+
+        usc = projection(usc, epsilon / kappa)
+        vsc = projection(vsc, epsilon * kappa)
+
+        return usc, vsc
+
+    def screened_obj(usc, vsc):
+        part_IJ = usc @ K_IJ @ vsc - kappa * a_I @ np.log(usc) - (1. / kappa) * b_J @ np.log(vsc)
+        part_IJc = usc @ vec_eps_IJc
+        part_IcJ = vec_eps_IcJ @ vsc
+        psi_epsilon = part_IJ + part_IJc + part_IcJ
+        return psi_epsilon
+
+    def screened_grad(usc, vsc):
+        # gradients of Psi_epsilon w.r.t u and v
+        grad_u = K_IJ @ vsc + vec_eps_IJc - kappa * a_I / usc
+        grad_v = K_IJ.T @ usc + vec_eps_IcJ - (1. / kappa) * b_J / vsc
+        return grad_u, grad_v
+
+    def bfgspost(theta):
+
+        u = theta[:ns_budget]
+        v = theta[ns_budget:]
+        # objective
+        f = screened_obj(u, v)
+        # gradient
+        g_u, g_v = screened_grad(u, v)
+        g = np.hstack([g_u, g_v])
+        return f, g
+
+    #----------------------------------------------------------------------------------------------------------------#
+    #                                           Step 2: L-BFGS-B solver                                              #
+    #----------------------------------------------------------------------------------------------------------------#
+
+    u0, v0 = restricted_sinkhorn(u0, v0)
+    theta0 = np.hstack([u0, v0])
+    maxiter = 10000  # max number of iterations
+    maxfun = 10000  # max  number of function evaluations
+    pgtol = 1e-09  # final objective function accuracy
+
+    bounds = bounds_u + bounds_v  # constraint bounds
+    obj = lambda theta: bfgspost(theta)
+
+    theta, _, _ = fmin_l_bfgs_b(func=obj,
+                                x0=theta0,
+                                bounds=bounds,
+                                maxfun=maxfun,
+                                pgtol=pgtol,
+                                maxiter=maxiter)
+
+    usc = theta[:ns_budget]
+    vsc = theta[ns_budget:]
+
+    usc_full = np.full(ns, epsilon / kappa)
+    vsc_full = np.full(nt, epsilon * kappa)
+    usc_full[I] = usc
+    vsc_full[J] = vsc
+
+    Gsc = usc_full.reshape((-1, 1)) * K * vsc_full.reshape((1, -1))
+    return Gsc

From d4b403ef3bda06db101d8a7c3dba1e0be36e9c80 Mon Sep 17 00:00:00 2001
From: "Mokhtar Z. Alaya" <mokhtarzahdi.alaya@gmail.com>
Date: Tue, 7 Jan 2020 11:18:43 +0100
Subject: [PATCH 02/39] close "bottleneck" tag

---
 ot/bregman.py | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/ot/bregman.py b/ot/bregman.py
index 61b860582..58c76d006 100644
--- a/ot/bregman.py
+++ b/ot/bregman.py
@@ -15,7 +15,6 @@
 import numpy as np
 import warnings
 from .utils import unif, dist
-import bottleneck
 from scipy.optimize import fmin_l_bfgs_b
 
 def sinkhorn(a, b, M, reg, method='sinkhorn', numItermax=1000,
@@ -1893,6 +1892,7 @@ def projection(u, epsilon):
                 aK_sort = np.sort(K_sum_cols)
                 epsilon_u_square = a[0] / aK_sort[ns_budget - 1]
             else:
+                import bottleneck
                 aK_sort = bottleneck.partition(K_sum_cols, ns_budget - 1)[ns_budget - 1]
                 epsilon_u_square = a[0] / aK_sort
 
@@ -1900,6 +1900,7 @@ def projection(u, epsilon):
                 bK_sort = np.sort(K_sum_rows)
                 epsilon_v_square = b[0] / bK_sort[ns_budget - 1]
             else:
+                import bottleneck
                 bK_sort = bottleneck.partition(K_sum_rows, nt_budget - 1)[nt_budget - 1]
                 epsilon_v_square = b[0] / bK_sort
         else:

From 3979fe909c64403337ed9259de9b8673dd789a18 Mon Sep 17 00:00:00 2001
From: "Mokhtar Z. Alaya" <mokhtarzahdi.alaya@gmail.com>
Date: Tue, 7 Jan 2020 11:47:41 +0100
Subject: [PATCH 03/39] update readme

---
 README.md | 5 ++++-
 1 file changed, 4 insertions(+), 1 deletion(-)

diff --git a/README.md b/README.md
index d8bb051a7..08bacd418 100644
--- a/README.md
+++ b/README.md
@@ -180,6 +180,7 @@ The contributors to this library are
 * [Vayer Titouan](https://tvayer.github.io/)
 * [Hicham Janati](https://hichamjanati.github.io/) (Unbalanced OT)
 * [Romain Tavenard](https://rtavenar.github.io/) (1d Wasserstein)
+* [Mokhtar Z. Alaya](http://mzalaya.github.io/) (Screenkhorn)
 
 This toolbox benefit a lot from open source research and we would like to thank the following persons for providing some code (in various languages):
 
@@ -252,4 +253,6 @@ You can also post bug reports and feature requests in Github issues. Make sure t
 
 [24] Vayer, T., Chapel, L., Flamary, R., Tavenard, R. and Courty, N. (2019). [Optimal Transport for structured data with application on graphs](http://proceedings.mlr.press/v97/titouan19a.html) Proceedings of the 36th International Conference on Machine Learning (ICML).
 
-[25] Frogner C., Zhang C., Mobahi H., Araya-Polo M., Poggio T. (2019). [Learning with a Wasserstein Loss](http://cbcl.mit.edu/wasserstein/)  Advances in Neural Information Processing Systems (NIPS).
+[25] Frogner C., Zhang C., Mobahi H., Araya-Polo M., Poggio T. (2015). [Learning with a Wasserstein Loss](http://cbcl.mit.edu/wasserstein/)  Advances in Neural Information Processing Systems (NIPS).
+
+[26] Alaya M. Z., Bérar M., Gasso G., Rakotomamonjy A. (2019). Screening Sinkhorn Algorithm for Regularized Optimal Transport (https://papers.nips.cc/paper/9386-screening-sinkhorn-algorithm-for-regularized-optimal-transport) Advances in Neural Information Processing Systems (NIPS).

From 0d33c3f42b1c22768c45299589b9b699f4f9f924 Mon Sep 17 00:00:00 2001
From: "Mokhtar Z. Alaya" <mokhtarzahdi.alaya@gmail.com>
Date: Tue, 7 Jan 2020 11:49:27 +0100
Subject: [PATCH 04/39] update readme

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 08bacd418..ce59e5957 100644
--- a/README.md
+++ b/README.md
@@ -255,4 +255,4 @@ You can also post bug reports and feature requests in Github issues. Make sure t
 
 [25] Frogner C., Zhang C., Mobahi H., Araya-Polo M., Poggio T. (2015). [Learning with a Wasserstein Loss](http://cbcl.mit.edu/wasserstein/)  Advances in Neural Information Processing Systems (NIPS).
 
-[26] Alaya M. Z., Bérar M., Gasso G., Rakotomamonjy A. (2019). Screening Sinkhorn Algorithm for Regularized Optimal Transport (https://papers.nips.cc/paper/9386-screening-sinkhorn-algorithm-for-regularized-optimal-transport) Advances in Neural Information Processing Systems (NIPS).
+[26] Alaya M. Z., Bérar M., Gasso G., Rakotomamonjy A. (2019). [Screening Sinkhorn Algorithm for Regularized Optimal Transport](https://papers.nips.cc/paper/9386-screening-sinkhorn-algorithm-for-regularized-optimal-transport) Advances in Neural Information Processing Systems (NIPS).

From e11dbadefab138a6d1d41c1e08d9c58c9b294e99 Mon Sep 17 00:00:00 2001
From: "Mokhtar Z. Alaya" <mokhtarzahdi.alaya@gmail.com>
Date: Tue, 7 Jan 2020 11:51:14 +0100
Subject: [PATCH 05/39] update README

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index ce59e5957..6bb8d245d 100644
--- a/README.md
+++ b/README.md
@@ -255,4 +255,4 @@ You can also post bug reports and feature requests in Github issues. Make sure t
 
 [25] Frogner C., Zhang C., Mobahi H., Araya-Polo M., Poggio T. (2015). [Learning with a Wasserstein Loss](http://cbcl.mit.edu/wasserstein/)  Advances in Neural Information Processing Systems (NIPS).
 
-[26] Alaya M. Z., Bérar M., Gasso G., Rakotomamonjy A. (2019). [Screening Sinkhorn Algorithm for Regularized Optimal Transport](https://papers.nips.cc/paper/9386-screening-sinkhorn-algorithm-for-regularized-optimal-transport) Advances in Neural Information Processing Systems (NIPS).
+[26] Alaya M. Z., Bérar M., Gasso G., Rakotomamonjy A. (2019). [Screening Sinkhorn Algorithm for Regularized Optimal Transport](https://papers.nips.cc/paper/9386-screening-sinkhorn-algorithm-for-regularized-optimal-transport), Advances in Neural Information Processing Systems 32 (NIPS).

From 4488a0b577075daac13fd381f09c2a1969273bd1 Mon Sep 17 00:00:00 2001
From: "Mokhtar Z. Alaya" <mokhtarzahdi.alaya@gmail.com>
Date: Tue, 7 Jan 2020 13:20:05 +0100
Subject: [PATCH 06/39] update README

---
 README.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/README.md b/README.md
index 6bb8d245d..f82099ea9 100644
--- a/README.md
+++ b/README.md
@@ -28,6 +28,7 @@ It provides the following solvers:
 * Stochastic Optimization for Large-scale Optimal Transport (semi-dual problem [18] and dual problem [19])
 * Non regularized free support Wasserstein barycenters [20].
 * Unbalanced OT with KL relaxation distance and barycenter [10, 25].
+* Screening Sinkhorn Algorithm for OT [26].
 
 Some demonstrations (both in Python and Jupyter Notebook format) are available in the examples folder.
 

From e821872581e5e62d984883d8b8f881e35160be56 Mon Sep 17 00:00:00 2001
From: "Mokhtar Z. Alaya" <mokhtarzahdi.alaya@gmail.com>
Date: Tue, 7 Jan 2020 13:22:44 +0100
Subject: [PATCH 07/39] update README

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index f82099ea9..987adf1d6 100644
--- a/README.md
+++ b/README.md
@@ -256,4 +256,4 @@ You can also post bug reports and feature requests in Github issues. Make sure t
 
 [25] Frogner C., Zhang C., Mobahi H., Araya-Polo M., Poggio T. (2015). [Learning with a Wasserstein Loss](http://cbcl.mit.edu/wasserstein/)  Advances in Neural Information Processing Systems (NIPS).
 
-[26] Alaya M. Z., Bérar M., Gasso G., Rakotomamonjy A. (2019). [Screening Sinkhorn Algorithm for Regularized Optimal Transport](https://papers.nips.cc/paper/9386-screening-sinkhorn-algorithm-for-regularized-optimal-transport), Advances in Neural Information Processing Systems 32 (NIPS).
+[26] Alaya M. Z., Bérar M., Gasso G., Rakotomamonjy A. (2019). [Screening Sinkhorn Algorithm for Regularized Optimal Transport](https://papers.nips.cc/paper/9386-screening-sinkhorn-algorithm-for-regularized-optimal-transport), Advances in Neural Information Processing Systems 33 (NIPS).

From 27b6740ea95b609ecdb103fbff7c1bbc62071ddc Mon Sep 17 00:00:00 2001
From: "Mokhtar Z. Alaya" <mokhtarzahdi.alaya@gmail.com>
Date: Tue, 7 Jan 2020 15:29:23 +0100
Subject: [PATCH 08/39] improve documentation of screenkhorn

add Exception at the beginning to check the installation of bottleneck module
---
 ot/bregman.py | 62 +++++++++++++++++++++++++++++++++++++--------------
 1 file changed, 45 insertions(+), 17 deletions(-)

diff --git a/ot/bregman.py b/ot/bregman.py
index 58c76d006..456b61f3e 100644
--- a/ot/bregman.py
+++ b/ot/bregman.py
@@ -1789,52 +1789,82 @@ def empirical_sinkhorn_divergence(X_s, X_t, reg, a=None, b=None, metric='sqeucli
         sinkhorn_div = sinkhorn_loss_ab - 1 / 2 * (sinkhorn_loss_a + sinkhorn_loss_b)
         return max(0, sinkhorn_div)
  
-def screenkhorn(a, b, M, reg, ns_budget, nt_budget, uniform=True, restricted=True, verbose=False):
+def screenkhorn(a, b, M, reg, ns_budget, nt_budget, uniform=True, restricted=True, verbose=False, log=False):
 
     """"
-    Screening Sinkhorn Algorithm for Regularized Optimal Transport.
+    Screening Sinkhorn Algorithm for Regularized Optimal Transport
+    
+    The function solves an approximate dual of Sinkhorn divergence [2] which is written as the following optimization problem:
+    
+    ..math::
+      (u, v) = \argmin_{u, v} 1_{ns}.T B(u,v) 1_{nt} - <\kappa u, a> - <v/\kappa, b> 
+      
+      where B(u,v) = \diag(e^u) K \diag(e^v), with K = e^{-M/reg} and 
+      
+      s.t. e^{u_i} >= \epsilon / \kappa, for all i in {1, ..., ns}
+      
+           e^{v_j} >= \epsilon \kappa, for all j in {1, ..., nt}
+           
+      The parameters \kappa and \epsilon are determined w.r.t the couple number budget of points (ns_budget, nt_budget), see Equation (5) in [26] 
+
 
     Parameters
     ----------
     a : `numpy.ndarray`, shape=(ns,)
-        samples weights in the source domain.
+        samples weights in the source domain
 
     b : `numpy.ndarray`, shape=(nt,)
-        samples weights in the target domain.
+        samples weights in the target domain
 
     M : `numpy.ndarray`, shape=(ns, nt)
         Cost matrix.
 
     reg : `float`
-        Level of the entropy regularisation.
+        Level of the entropy regularisation
 
     ns_budget: `int`
-        Number budget of points to be keeped in the source domain.
+        Number budget of points to be keeped in the source domain
 
     nt_budget: `int`
-        Number budget of points to be keeped in the target domain.
+        Number budget of points to be keeped in the target domain
 
     uniform: `bool`, default=True
         If `True`, a_i = 1. / ns and b_j = 1. / nt
 
     restricted: `bool`, default=True
          If `True`, a warm-start initialization for the  L-BFGS-B solver
-         using a restricted Sinkhorn algorithm with at most 5 iterations.
+         using a restricted Sinkhorn algorithm with at most 5 iterations
 
     verbose: `bool`, default=False
-        If `True`, dispaly informations along iterations.
-
+        If `True`, dispaly informations along iterations
+        
+    Dependency
+    ----------
+    To gain more efficiency, screenkhorn needs to call the "Bottleneck" package (https://pypi.org/project/Bottleneck/) in the screening pre-processing step. 
+    If Bottleneck isn't installed, the following error message appears: 
+    "Bottleneck module doesn't exist. Install it from https://pypi.org/project/Bottleneck/"
+   
+   
     Returns
     -------
-    Gsc : `numpy.ndarray`, shape=(ns, nt)
-        Screened optimal transportation matrix for the given parameters.
+    gamma : `numpy.ndarray`, shape=(ns, nt)
+        Screened optimal transportation matrix for the given parameters
+    
+    log : `dict`, default=False
+      Log dictionary return only if log==True in parameters
 
-    References:
+
+    References
     -----------
-    .. [1] M. Z. Alaya, Maxime Bérar, Gilles Gasso, Alain Rakotomamonjy. Screening Sinkhorn Algorithm for Regularized
-    Optimal Transport, NeurIPS 2019.
+    .. [26] Alaya M. Z., Bérar M., Gasso G., Rakotomamonjy A. (2019). Screening Sinkhorn Algorithm for Regularized Optimal Transport (NIPS) 33, 2019
 
     """
+    # check if bottleneck module exists
+    try:
+        import bottleneck
+    except ImportError as e:
+        print("Bottleneck module doesn't exist. Install it from https://pypi.org/project/Bottleneck/")
+      
     a = np.asarray(a, dtype=np.float64)
     b = np.asarray(b, dtype=np.float64)
 
@@ -1892,7 +1922,6 @@ def projection(u, epsilon):
                 aK_sort = np.sort(K_sum_cols)
                 epsilon_u_square = a[0] / aK_sort[ns_budget - 1]
             else:
-                import bottleneck
                 aK_sort = bottleneck.partition(K_sum_cols, ns_budget - 1)[ns_budget - 1]
                 epsilon_u_square = a[0] / aK_sort
 
@@ -1900,7 +1929,6 @@ def projection(u, epsilon):
                 bK_sort = np.sort(K_sum_rows)
                 epsilon_v_square = b[0] / bK_sort[ns_budget - 1]
             else:
-                import bottleneck
                 bK_sort = bottleneck.partition(K_sum_rows, nt_budget - 1)[nt_budget - 1]
                 epsilon_v_square = b[0] / bK_sort
         else:

From 7d603f0aa642dbe49da70ad3143fd4e9c74a22c5 Mon Sep 17 00:00:00 2001
From: "Mokhtar Z. Alaya" <mokhtarzahdi.alaya@gmail.com>
Date: Tue, 7 Jan 2020 15:34:22 +0100
Subject: [PATCH 09/39] delete "ArrayBox"-type test of dist. matrix M

---
 ot/bregman.py | 8 +-------
 1 file changed, 1 insertion(+), 7 deletions(-)

diff --git a/ot/bregman.py b/ot/bregman.py
index 456b61f3e..dedbf281e 100644
--- a/ot/bregman.py
+++ b/ot/bregman.py
@@ -1867,12 +1867,6 @@ def screenkhorn(a, b, M, reg, ns_budget, nt_budget, uniform=True, restricted=Tru
       
     a = np.asarray(a, dtype=np.float64)
     b = np.asarray(b, dtype=np.float64)
-
-    # if the "autograd" package is needed for some experiments, we then have to change the instance of the cost matrix M
-    # from "ArrayBox"-type to "np.array"-type as follows:
-    if isinstance(M, np.ndarray) == False:
-        M = M._value
-
     M = np.asarray(M, dtype=np.float64)
     ns, nt = M.shape
 
@@ -1882,7 +1876,7 @@ def screenkhorn(a, b, M, reg, ns_budget, nt_budget, uniform=True, restricted=Tru
     np.exp(K, out=K)
 
     def projection(u, epsilon):
-        u[np.where(u <= epsilon)] = epsilon
+        u[u <= epsilon] = epsilon
         return u
 
     # ----------------------------------------------------------------------------------------------------------------#

From be33a36eb1916968d9281c5a76e12e04b7ddb686 Mon Sep 17 00:00:00 2001
From: "Mokhtar Z. Alaya" <mokhtarzahdi.alaya@gmail.com>
Date: Tue, 7 Jan 2020 15:51:58 +0100
Subject: [PATCH 10/39] replace @ operator by np.dot

---
 ot/bregman.py | 26 +++++++++++++-------------
 1 file changed, 13 insertions(+), 13 deletions(-)

diff --git a/ot/bregman.py b/ot/bregman.py
index dedbf281e..4a899a6d0 100644
--- a/ot/bregman.py
+++ b/ot/bregman.py
@@ -1885,8 +1885,8 @@ def projection(u, epsilon):
 
     if ns_budget == ns and nt_budget == nt:
         # full number of budget points (ns, nt) = (ns_budget, nt_budget)
-        I = list(range(ns))
-        J = list(range(nt))
+        I = list(np.arange(ns)) 
+        J = list(np.arange(nt))
         epsilon = 0.0  
         kappa = 1.0  
 
@@ -1989,7 +1989,7 @@ def projection(u, epsilon):
             b_J_max = b_J[0]
             b_J_min = b_J[0]
 
-        # box constraints in L-BFGS-B (see Proposition 1 in [1])
+        # box constraints in L-BFGS-B (see Proposition 1 in [26])
         bounds_u = [(max(kappa * a_I_min / (epsilon * (nt - ns_budget) + ns_budget * (b_J_max / (
                 epsilon * ns * K_min))), epsilon / kappa), a_I_max / (epsilon * nt * K_min))] * ns_budget
 
@@ -2004,7 +2004,7 @@ def projection(u, epsilon):
     u0 = np.full(ns_budget, (1. / ns_budget) + epsilon / kappa)
     v0 = np.full(nt_budget, (1. / nt_budget) + epsilon * kappa)
 
-    # pre-calculed constants for Restricted Sinkhorn (see Algorithm 2 in [1])
+    # pre-calculed constants for Restricted Sinkhorn (see Algorithm 2 in [26])
     if restricted:
         if ns_budget != ns or ns_budget != nt:
             cst_u = kappa * epsilon * K_IJc.sum(axis=1)
@@ -2012,9 +2012,9 @@ def projection(u, epsilon):
 
         cpt = 1
         while (cpt < 5):  # 5 iterations
-            K_IJ_v = K_IJ.T @ u0 + cst_v
+            K_IJ_v = np.dot(K_IJ.T, u0) + cst_v
             v0 = b_J / (kappa * K_IJ_v)
-            KIJ_u = K_IJ @ v0 + cst_u
+            KIJ_u = np.dot(K_IJ, v0) + cst_u
             u0 = (kappa * a_I) / KIJ_u
             cpt += 1
 
@@ -2031,9 +2031,9 @@ def restricted_sinkhorn(usc, vsc, max_iter=5):
         """
         cpt = 1
         while (cpt < max_iter):
-            K_IJ_v = K_IJ.T @ usc + cst_v
+            K_IJ_v = np.dot(K_IJ.T, usc) + cst_v
             vsc = b_J / (kappa * K_IJ_v)
-            KIJ_u = K_IJ @ vsc + cst_u
+            KIJ_u = np.dot(K_IJ, vsc) + cst_u
             usc = (kappa * a_I) / KIJ_u
             cpt += 1
 
@@ -2043,16 +2043,16 @@ def restricted_sinkhorn(usc, vsc, max_iter=5):
         return usc, vsc
 
     def screened_obj(usc, vsc):
-        part_IJ = usc @ K_IJ @ vsc - kappa * a_I @ np.log(usc) - (1. / kappa) * b_J @ np.log(vsc)
-        part_IJc = usc @ vec_eps_IJc
-        part_IcJ = vec_eps_IcJ @ vsc
+        part_IJ = np.dot(np.dot(usc, K_IJ), vsc) - kappa * np.dot(a_I, np.log(usc)) - (1. / kappa) * np.dot(b_J, np.log(vsc))
+        part_IJc = np.dot(usc, vec_eps_IJc)
+        part_IcJ = np.dot(vec_eps_IcJ, vsc)
         psi_epsilon = part_IJ + part_IJc + part_IcJ
         return psi_epsilon
 
     def screened_grad(usc, vsc):
         # gradients of Psi_epsilon w.r.t u and v
-        grad_u = K_IJ @ vsc + vec_eps_IJc - kappa * a_I / usc
-        grad_v = K_IJ.T @ usc + vec_eps_IcJ - (1. / kappa) * b_J / vsc
+        grad_u = np.dot(K_IJ, vsc) + vec_eps_IJc - kappa * a_I / usc
+        grad_v = np.dot(K_IJ.T, usc) + vec_eps_IcJ - (1. / kappa) * b_J / vsc
         return grad_u, grad_v
 
     def bfgspost(theta):

From 69c666fc82553bed0fbbc7fc17a906eb2487ddf7 Mon Sep 17 00:00:00 2001
From: "Mokhtar Z. Alaya" <mokhtarzahdi.alaya@gmail.com>
Date: Tue, 7 Jan 2020 16:03:18 +0100
Subject: [PATCH 11/39] set default param. for LBFGS in the function's
 prototype

---
 ot/bregman.py | 18 ++++++++++++------
 1 file changed, 12 insertions(+), 6 deletions(-)

diff --git a/ot/bregman.py b/ot/bregman.py
index 4a899a6d0..12eaa65b1 100644
--- a/ot/bregman.py
+++ b/ot/bregman.py
@@ -1789,7 +1789,8 @@ def empirical_sinkhorn_divergence(X_s, X_t, reg, a=None, b=None, metric='sqeucli
         sinkhorn_div = sinkhorn_loss_ab - 1 / 2 * (sinkhorn_loss_a + sinkhorn_loss_b)
         return max(0, sinkhorn_div)
  
-def screenkhorn(a, b, M, reg, ns_budget, nt_budget, uniform=True, restricted=True, verbose=False, log=False):
+def screenkhorn(a, b, M, reg, ns_budget, nt_budget, uniform=True, restricted=True,
+                maxiter=10000, maxfun=10000, pgtol=1e-09, verbose=False, log=False):
 
     """"
     Screening Sinkhorn Algorithm for Regularized Optimal Transport
@@ -1834,6 +1835,15 @@ def screenkhorn(a, b, M, reg, ns_budget, nt_budget, uniform=True, restricted=Tru
     restricted: `bool`, default=True
          If `True`, a warm-start initialization for the  L-BFGS-B solver
          using a restricted Sinkhorn algorithm with at most 5 iterations
+         
+    maxiter : `int`, default=10000
+      Maximum number of iterations in LBFGS solver
+        
+    maxfun : `int`, default=10000
+      Maximum  number of function evaluations in LBFGS solver 
+        
+    pgtol : `float`, default=1e-09  
+      Final objective function accuracy in LBFGS solver
 
     verbose: `bool`, default=False
         If `True`, dispaly informations along iterations
@@ -2056,7 +2066,6 @@ def screened_grad(usc, vsc):
         return grad_u, grad_v
 
     def bfgspost(theta):
-
         u = theta[:ns_budget]
         v = theta[ns_budget:]
         # objective
@@ -2072,10 +2081,7 @@ def bfgspost(theta):
 
     u0, v0 = restricted_sinkhorn(u0, v0)
     theta0 = np.hstack([u0, v0])
-    maxiter = 10000  # max number of iterations
-    maxfun = 10000  # max  number of function evaluations
-    pgtol = 1e-09  # final objective function accuracy
-
+  
     bounds = bounds_u + bounds_v  # constraint bounds
     obj = lambda theta: bfgspost(theta)
 

From 05a97b44a7137ef6cb0397cca3bb2ea1f8736ac5 Mon Sep 17 00:00:00 2001
From: "Mokhtar Z. Alaya" <mokhtarzahdi.alaya@gmail.com>
Date: Tue, 7 Jan 2020 16:10:36 +0100
Subject: [PATCH 12/39] fix default values for the budget arguments

---
 ot/bregman.py | 16 ++++++++++++----
 1 file changed, 12 insertions(+), 4 deletions(-)

diff --git a/ot/bregman.py b/ot/bregman.py
index 12eaa65b1..8a203070d 100644
--- a/ot/bregman.py
+++ b/ot/bregman.py
@@ -1789,7 +1789,7 @@ def empirical_sinkhorn_divergence(X_s, X_t, reg, a=None, b=None, metric='sqeucli
         sinkhorn_div = sinkhorn_loss_ab - 1 / 2 * (sinkhorn_loss_a + sinkhorn_loss_b)
         return max(0, sinkhorn_div)
  
-def screenkhorn(a, b, M, reg, ns_budget, nt_budget, uniform=True, restricted=True,
+def screenkhorn(a, b, M, reg, ns_budget=None, nt_budget=None, uniform=True, restricted=True,
                 maxiter=10000, maxfun=10000, pgtol=1e-09, verbose=False, log=False):
 
     """"
@@ -1823,11 +1823,13 @@ def screenkhorn(a, b, M, reg, ns_budget, nt_budget, uniform=True, restricted=Tru
     reg : `float`
         Level of the entropy regularisation
 
-    ns_budget: `int`
+    ns_budget: `int`, deafult=None
         Number budget of points to be keeped in the source domain
+        If it is None then 50% of the source sample points will be keeped
 
-    nt_budget: `int`
+    nt_budget: `int`, deafult=None
         Number budget of points to be keeped in the target domain
+        If it is None then 50% of the target sample points will be keeped
 
     uniform: `bool`, default=True
         If `True`, a_i = 1. / ns and b_j = 1. / nt
@@ -1874,11 +1876,17 @@ def screenkhorn(a, b, M, reg, ns_budget, nt_budget, uniform=True, restricted=Tru
         import bottleneck
     except ImportError as e:
         print("Bottleneck module doesn't exist. Install it from https://pypi.org/project/Bottleneck/")
-      
+   
     a = np.asarray(a, dtype=np.float64)
     b = np.asarray(b, dtype=np.float64)
     M = np.asarray(M, dtype=np.float64)
     ns, nt = M.shape
+    
+    # by default, we keep only 50% of the sapmle data points
+    if ns_budget is None:
+      ns_budget = int(np.floor(0.5*ns))
+    if nt_budget is None:
+      ns_budget = int(np.floor(0.5*ns))
 
     # calculate the Gibbs kernel
     K = np.empty_like(M)

From 92b7075568207a468cc821cd6a21e130b9d89f96 Mon Sep 17 00:00:00 2001
From: "Mokhtar Z. Alaya" <mokhtarzahdi.alaya@gmail.com>
Date: Tue, 7 Jan 2020 16:21:40 +0100
Subject: [PATCH 13/39] replace reshape by numpy slicing in return

---
 ot/bregman.py | 12 ++++++++++--
 1 file changed, 10 insertions(+), 2 deletions(-)

diff --git a/ot/bregman.py b/ot/bregman.py
index 8a203070d..8cfea7e62 100644
--- a/ot/bregman.py
+++ b/ot/bregman.py
@@ -2107,6 +2107,14 @@ def bfgspost(theta):
     vsc_full = np.full(nt, epsilon * kappa)
     usc_full[I] = usc
     vsc_full[J] = vsc
+    
+    if log:
+      log['u'] = usc_full
+      log['v'] = vsc_full
+      
+    gamma = usc_full[:, None] * K * vsc_full[None, :]
 
-    Gsc = usc_full.reshape((-1, 1)) * K * vsc_full.reshape((1, -1))
-    return Gsc
+    if log:
+      return gamma, log
+    else:
+      return gamma

From cfe26140af85082197151d0dc50915c0bd71f602 Mon Sep 17 00:00:00 2001
From: "Mokhtar Z. Alaya" <mokhtarzahdi.alaya@gmail.com>
Date: Tue, 7 Jan 2020 19:00:50 +0100
Subject: [PATCH 14/39] fix definitions complementary active sets Ic, Jc

---
 ot/bregman.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/ot/bregman.py b/ot/bregman.py
index 8cfea7e62..c0634b12d 100644
--- a/ot/bregman.py
+++ b/ot/bregman.py
@@ -1982,8 +1982,8 @@ def projection(u, epsilon):
             print('|I_active| = %s \t |J_active| = %s ' %(len(I), len(J)))
 
         # Ic, Jc: complementary of the active sets I and J
-        Ic = list(set(list(range(ns))) - set(I))
-        Jc = list(set(list(range(nt))) - set(J))
+        Ic = list(set(np.arange(ns)) - set(I))
+        Jc = list(set(np.arange(nt)) - set(J))
 
         K_IJ = K[np.ix_(I, J)]
         K_IcJ = K[np.ix_(Ic, J)]

From 88fb534d83f42e45a42c0a9773ccfe338cd3a811 Mon Sep 17 00:00:00 2001
From: "Mokhtar Z. Alaya" <mokhtarzahdi.alaya@gmail.com>
Date: Tue, 7 Jan 2020 19:09:30 +0100
Subject: [PATCH 15/39] fix typos in documentation

---
 ot/bregman.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/ot/bregman.py b/ot/bregman.py
index c0634b12d..ceb7754de 100644
--- a/ot/bregman.py
+++ b/ot/bregman.py
@@ -1818,7 +1818,7 @@ def screenkhorn(a, b, M, reg, ns_budget=None, nt_budget=None, uniform=True, rest
         samples weights in the target domain
 
     M : `numpy.ndarray`, shape=(ns, nt)
-        Cost matrix.
+        Cost matrix
 
     reg : `float`
         Level of the entropy regularisation
@@ -2045,7 +2045,7 @@ def projection(u, epsilon):
 
     def restricted_sinkhorn(usc, vsc, max_iter=5):
         """
-        Restricted Sinkhorn Algorithm as a warm-start initialized point for L-BFGS-B (see Algorithm 2 in [1]).
+        Restricted Sinkhorn Algorithm as a warm-start initialized point for L-BFGS-B (see Algorithm 2 in [26])
         """
         cpt = 1
         while (cpt < max_iter):

From 45119609cbc317f59beb92382c28de6c51290c53 Mon Sep 17 00:00:00 2001
From: "Mokhtar Z. Alaya" <mokhtarzahdi.alaya@gmail.com>
Date: Wed, 8 Jan 2020 11:03:59 +0100
Subject: [PATCH 16/39] using binary indexing for definition the active sets

---
 ot/bregman.py | 44 +++++++++++++++++++++-----------------------
 1 file changed, 21 insertions(+), 23 deletions(-)

diff --git a/ot/bregman.py b/ot/bregman.py
index ceb7754de..b664ac1bc 100644
--- a/ot/bregman.py
+++ b/ot/bregman.py
@@ -1884,13 +1884,13 @@ def screenkhorn(a, b, M, reg, ns_budget=None, nt_budget=None, uniform=True, rest
     
     # by default, we keep only 50% of the sapmle data points
     if ns_budget is None:
-      ns_budget = int(np.floor(0.5*ns))
+        ns_budget = int(np.floor(0.5*ns))
     if nt_budget is None:
-      ns_budget = int(np.floor(0.5*ns))
+        nt_budget = int(np.floor(0.5*ns))
 
     # calculate the Gibbs kernel
     K = np.empty_like(M)
-    np.divide(M, - reg, out=K)
+    np.divide(M, -reg, out=K)
     np.exp(K, out=K)
 
     def projection(u, epsilon):
@@ -1898,13 +1898,13 @@ def projection(u, epsilon):
         return u
 
     # ----------------------------------------------------------------------------------------------------------------#
-    #                                          Step 1: Screening Pre-processing                                       #
+    #                                          Step 1: Screening pre-processing                                       #
     # ----------------------------------------------------------------------------------------------------------------#
 
     if ns_budget == ns and nt_budget == nt:
         # full number of budget points (ns, nt) = (ns_budget, nt_budget)
-        I = list(np.arange(ns)) 
-        J = list(np.arange(nt))
+        I = np.arange(ns) 
+        J = np.arange(nt)
         epsilon = 0.0  
         kappa = 1.0  
 
@@ -1953,37 +1953,34 @@ def projection(u, epsilon):
             bK_sort = np.sort(bK)[::-1]
             epsilon_v_square = bK_sort[ns_budget - 1]
 
-        # active sets I and J (see Proposition .. in [1])
-        I = np.where(a >= epsilon_u_square * K_sum_cols)[0].tolist()
-        J = np.where(b >= epsilon_v_square * K_sum_rows)[0].tolist()
+        # active sets I and J (see Lemma 1 in [26])
+        I = np.where(a >= epsilon_u_square * K_sum_cols)[0]
+        J = np.where(b >= epsilon_v_square * K_sum_rows)[0]
 
         if len(I) != ns_budget:
             if uniform:
                 aK = a / K_sum_cols
                 aK_sort = np.sort(aK)[::-1]
             epsilon_u_square = aK_sort[ns_budget - 1:ns_budget + 1].mean()
-            I = np.where(a >= epsilon_u_square * K_sum_cols)[0].tolist()
+            I = np.where(a >= epsilon_u_square * K_sum_cols)[0]
 
         if len(J) != nt_budget:
             if uniform:
                 bK = b / K_sum_rows
                 bK_sort = np.sort(bK)[::-1]
-            epsilon_v_square = bK_sort[ns_budget - 1:ns_budget + 1].mean()
-            J = np.where(b >= epsilon_v_square * K_sum_rows)[0].tolist()
+            epsilon_v_square = bK_sort[nt_budget - 1:nt_budget + 1].mean()
+            J = np.where(b >= epsilon_v_square * K_sum_rows)[0]
 
         epsilon = (epsilon_u_square * epsilon_v_square) ** (1 / 4)
         kappa = (epsilon_v_square / epsilon_u_square) ** (1 / 2)
-
+        
         if verbose:
             print("Epsilon = %s\n" %epsilon)
-            print("Scaling factor = %s\n" %kappa)
-
-        if verbose:
             print('|I_active| = %s \t |J_active| = %s ' %(len(I), len(J)))
 
         # Ic, Jc: complementary of the active sets I and J
-        Ic = list(set(np.arange(ns)) - set(I))
-        Jc = list(set(np.arange(nt)) - set(J))
+        Ic = np.arange(ns)[~np.isin(np.arange(ns), I)]
+        Jc = np.arange(nt)[~np.isin(np.arange(nt), J)]
 
         K_IJ = K[np.ix_(I, J)]
         K_IcJ = K[np.ix_(Ic, J)]
@@ -2109,12 +2106,13 @@ def bfgspost(theta):
     vsc_full[J] = vsc
     
     if log:
-      log['u'] = usc_full
-      log['v'] = vsc_full
+        log['u'] = usc_full
+        log['v'] = vsc_full
       
     gamma = usc_full[:, None] * K * vsc_full[None, :]
-
+    gamma = gamma / gamma.sum()
+    
     if log:
-      return gamma, log
+        return gamma, log
     else:
-      return gamma
+        return gamma

From e00f46aa2ea11f0e88a5b2005caa7518ca109357 Mon Sep 17 00:00:00 2001
From: "Mokhtar Z. Alaya" <mzalaya@Mokhtars-MacBook-Pro.local>
Date: Wed, 8 Jan 2020 18:49:16 +0100
Subject: [PATCH 17/39] fix binary indexing

---
 ot/bregman.py | 109 +++++++++++++++++++++++++-------------------------
 1 file changed, 55 insertions(+), 54 deletions(-)

diff --git a/ot/bregman.py b/ot/bregman.py
index b664ac1bc..28377b042 100644
--- a/ot/bregman.py
+++ b/ot/bregman.py
@@ -17,6 +17,7 @@
 from .utils import unif, dist
 from scipy.optimize import fmin_l_bfgs_b
 
+
 def sinkhorn(a, b, M, reg, method='sinkhorn', numItermax=1000,
              stopThr=1e-9, verbose=False, log=False, **kwargs):
     r"""
@@ -1788,24 +1789,24 @@ def empirical_sinkhorn_divergence(X_s, X_t, reg, a=None, b=None, metric='sqeucli
 
         sinkhorn_div = sinkhorn_loss_ab - 1 / 2 * (sinkhorn_loss_a + sinkhorn_loss_b)
         return max(0, sinkhorn_div)
- 
+
+
 def screenkhorn(a, b, M, reg, ns_budget=None, nt_budget=None, uniform=True, restricted=True,
                 maxiter=10000, maxfun=10000, pgtol=1e-09, verbose=False, log=False):
-
     """"
     Screening Sinkhorn Algorithm for Regularized Optimal Transport
-    
+
     The function solves an approximate dual of Sinkhorn divergence [2] which is written as the following optimization problem:
-    
+
     ..math::
       (u, v) = \argmin_{u, v} 1_{ns}.T B(u,v) 1_{nt} - <\kappa u, a> - <v/\kappa, b> 
-      
+
       where B(u,v) = \diag(e^u) K \diag(e^v), with K = e^{-M/reg} and 
-      
+
       s.t. e^{u_i} >= \epsilon / \kappa, for all i in {1, ..., ns}
-      
+
            e^{v_j} >= \epsilon \kappa, for all j in {1, ..., nt}
-           
+
       The parameters \kappa and \epsilon are determined w.r.t the couple number budget of points (ns_budget, nt_budget), see Equation (5) in [26] 
 
 
@@ -1837,31 +1838,31 @@ def screenkhorn(a, b, M, reg, ns_budget=None, nt_budget=None, uniform=True, rest
     restricted: `bool`, default=True
          If `True`, a warm-start initialization for the  L-BFGS-B solver
          using a restricted Sinkhorn algorithm with at most 5 iterations
-         
+
     maxiter : `int`, default=10000
       Maximum number of iterations in LBFGS solver
-        
+
     maxfun : `int`, default=10000
       Maximum  number of function evaluations in LBFGS solver 
-        
+
     pgtol : `float`, default=1e-09  
       Final objective function accuracy in LBFGS solver
 
     verbose: `bool`, default=False
         If `True`, dispaly informations along iterations
-        
+
     Dependency
     ----------
     To gain more efficiency, screenkhorn needs to call the "Bottleneck" package (https://pypi.org/project/Bottleneck/) in the screening pre-processing step. 
     If Bottleneck isn't installed, the following error message appears: 
     "Bottleneck module doesn't exist. Install it from https://pypi.org/project/Bottleneck/"
-   
-   
+
+
     Returns
     -------
     gamma : `numpy.ndarray`, shape=(ns, nt)
         Screened optimal transportation matrix for the given parameters
-    
+
     log : `dict`, default=False
       Log dictionary return only if log==True in parameters
 
@@ -1876,17 +1877,17 @@ def screenkhorn(a, b, M, reg, ns_budget=None, nt_budget=None, uniform=True, rest
         import bottleneck
     except ImportError as e:
         print("Bottleneck module doesn't exist. Install it from https://pypi.org/project/Bottleneck/")
-   
+
     a = np.asarray(a, dtype=np.float64)
     b = np.asarray(b, dtype=np.float64)
     M = np.asarray(M, dtype=np.float64)
     ns, nt = M.shape
-    
-    # by default, we keep only 50% of the sapmle data points
+
+    # by default, we keep only 50% of the sample data points
     if ns_budget is None:
-        ns_budget = int(np.floor(0.5*ns))
+        ns_budget = int(np.floor(0.5 * ns))
     if nt_budget is None:
-        nt_budget = int(np.floor(0.5*ns))
+        nt_budget = int(np.floor(0.5 * nt))
 
     # calculate the Gibbs kernel
     K = np.empty_like(M)
@@ -1903,20 +1904,19 @@ def projection(u, epsilon):
 
     if ns_budget == ns and nt_budget == nt:
         # full number of budget points (ns, nt) = (ns_budget, nt_budget)
-        I = np.arange(ns) 
-        J = np.arange(nt)
-        epsilon = 0.0  
-        kappa = 1.0  
+        I = np.ones(ns, dtype=bool)
+        J = np.ones(nt, dtype=bool)
+        epsilon = 0.0
+        kappa = 1.0
 
         cst_u = 0.
         cst_v = 0.
 
         bounds_u = [(0.0, np.inf)] * ns
         bounds_v = [(0.0, np.inf)] * nt
-        
+
         a_I = a
         b_J = b
-        K_min = K.min()
         K_IJ = K
         K_IJc = []
         K_IcJ = []
@@ -1937,9 +1937,9 @@ def projection(u, epsilon):
                 aK_sort = bottleneck.partition(K_sum_cols, ns_budget - 1)[ns_budget - 1]
                 epsilon_u_square = a[0] / aK_sort
 
-            if nt / ns_budget < 4:
+            if nt / nt_budget < 4:
                 bK_sort = np.sort(K_sum_rows)
-                epsilon_v_square = b[0] / bK_sort[ns_budget - 1]
+                epsilon_v_square = b[0] / bK_sort[nt_budget - 1]
             else:
                 bK_sort = bottleneck.partition(K_sum_rows, nt_budget - 1)[nt_budget - 1]
                 epsilon_v_square = b[0] / bK_sort
@@ -1951,36 +1951,37 @@ def projection(u, epsilon):
             epsilon_u_square = aK_sort[ns_budget - 1]
 
             bK_sort = np.sort(bK)[::-1]
-            epsilon_v_square = bK_sort[ns_budget - 1]
+            epsilon_v_square = bK_sort[nt_budget - 1]
 
         # active sets I and J (see Lemma 1 in [26])
-        I = np.where(a >= epsilon_u_square * K_sum_cols)[0]
-        J = np.where(b >= epsilon_v_square * K_sum_rows)[0]
+        I = a >= epsilon_u_square * K_sum_cols
+        J = b >= epsilon_v_square * K_sum_rows
 
-        if len(I) != ns_budget:
+        if sum(I) != ns_budget:
             if uniform:
                 aK = a / K_sum_cols
                 aK_sort = np.sort(aK)[::-1]
             epsilon_u_square = aK_sort[ns_budget - 1:ns_budget + 1].mean()
-            I = np.where(a >= epsilon_u_square * K_sum_cols)[0]
+            I = a >= epsilon_u_square * K_sum_cols
 
-        if len(J) != nt_budget:
+        if sum(J) != nt_budget:
             if uniform:
                 bK = b / K_sum_rows
                 bK_sort = np.sort(bK)[::-1]
             epsilon_v_square = bK_sort[nt_budget - 1:nt_budget + 1].mean()
-            J = np.where(b >= epsilon_v_square * K_sum_rows)[0]
+            J = b >= epsilon_v_square * K_sum_rows
 
         epsilon = (epsilon_u_square * epsilon_v_square) ** (1 / 4)
         kappa = (epsilon_v_square / epsilon_u_square) ** (1 / 2)
-        
+
         if verbose:
-            print("Epsilon = %s\n" %epsilon)
-            print('|I_active| = %s \t |J_active| = %s ' %(len(I), len(J)))
+            print("epsilon = %s\n" % epsilon)
+            print("kappa= %s\n" % kappa)
+            print('|I_active| = %s \t |J_active| = %s ' % (sum(I), sum(J)))
 
         # Ic, Jc: complementary of the active sets I and J
-        Ic = np.arange(ns)[~np.isin(np.arange(ns), I)]
-        Jc = np.arange(nt)[~np.isin(np.arange(nt), J)]
+        Ic = ~I
+        Jc = ~J
 
         K_IJ = K[np.ix_(I, J)]
         K_IcJ = K[np.ix_(Ic, J)]
@@ -2005,23 +2006,23 @@ def projection(u, epsilon):
             b_J_min = b_J[0]
 
         # box constraints in L-BFGS-B (see Proposition 1 in [26])
-        bounds_u = [(max(kappa * a_I_min / (epsilon * (nt - ns_budget) + ns_budget * (b_J_max / (
-                epsilon * ns * K_min))), epsilon / kappa), a_I_max / (epsilon * nt * K_min))] * ns_budget
+        bounds_u = [(max(a_I_min / ((nt - nt_budget) * epsilon + nt_budget * (b_J_max / (
+            ns * epsilon * kappa * K_min))), epsilon / kappa), a_I_max / (nt * epsilon * K_min))] * ns_budget
 
-        bounds_v = [(max(b_J_min / (epsilon * (ns - ns_budget) + ns_budget * (a_I_max / (epsilon * nt * K_min))), \
-                         epsilon * kappa), b_J_max / (epsilon * ns * K_min))] * ns_budget
+        bounds_v = [(max(b_J_min / ((ns - ns_budget) * epsilon + ns_budget * (kappa * a_I_max / (nt * epsilon * K_min))),
+                         epsilon * kappa), b_J_max / (ns * epsilon * K_min))] * nt_budget
 
         # pre-calculated constants for the objective
-        vec_eps_IJc = epsilon * kappa * (K_IJc * np.ones(nt - ns_budget).reshape((1, -1))).sum(axis=1)
+        vec_eps_IJc = epsilon * kappa * (K_IJc * np.ones(nt - nt_budget).reshape((1, -1))).sum(axis=1)
         vec_eps_IcJ = (epsilon / kappa) * (np.ones(ns - ns_budget).reshape((-1, 1)) * K_IcJ).sum(axis=0)
 
     # initialisation
     u0 = np.full(ns_budget, (1. / ns_budget) + epsilon / kappa)
     v0 = np.full(nt_budget, (1. / nt_budget) + epsilon * kappa)
 
-    # pre-calculed constants for Restricted Sinkhorn (see Algorithm 2 in [26])
+    # pre-calculed constants for Restricted Sinkhorn (see Algorithm 1 in supplementary of [26])
     if restricted:
-        if ns_budget != ns or ns_budget != nt:
+        if ns_budget != ns or nt_budget != nt:
             cst_u = kappa * epsilon * K_IJc.sum(axis=1)
             cst_v = epsilon * K_IcJ.sum(axis=0) / kappa
 
@@ -2042,7 +2043,7 @@ def projection(u, epsilon):
 
     def restricted_sinkhorn(usc, vsc, max_iter=5):
         """
-        Restricted Sinkhorn Algorithm as a warm-start initialized point for L-BFGS-B (see Algorithm 2 in [26])
+        Restricted Sinkhorn Algorithm as a warm-start initialized point for L-BFGS-B (see Algorithm 1 in supplementary of [26])
         """
         cpt = 1
         while (cpt < max_iter):
@@ -2086,9 +2087,9 @@ def bfgspost(theta):
 
     u0, v0 = restricted_sinkhorn(u0, v0)
     theta0 = np.hstack([u0, v0])
-  
+
     bounds = bounds_u + bounds_v  # constraint bounds
-    obj = lambda theta: bfgspost(theta)
+    def obj(theta): return bfgspost(theta)
 
     theta, _, _ = fmin_l_bfgs_b(func=obj,
                                 x0=theta0,
@@ -2104,15 +2105,15 @@ def bfgspost(theta):
     vsc_full = np.full(nt, epsilon * kappa)
     usc_full[I] = usc
     vsc_full[J] = vsc
-    
+
     if log:
         log['u'] = usc_full
         log['v'] = vsc_full
-      
+
     gamma = usc_full[:, None] * K * vsc_full[None, :]
     gamma = gamma / gamma.sum()
-    
+
     if log:
         return gamma, log
     else:
-        return gamma
+        return gamma
\ No newline at end of file

From 3e77515b4f19cf1c37b2f971a54b2fe5efe9daef Mon Sep 17 00:00:00 2001
From: "Mokhtar Z. Alaya" <mzalaya@Mokhtars-MacBook-Pro.local>
Date: Wed, 8 Jan 2020 18:54:07 +0100
Subject: [PATCH 18/39] add illustration for screenkhorn

---
 examples/plot_screenkhorn_1D.py     | 103 ++++++++++++++
 notebooks/plot_screenkhorn_1D.ipynb | 207 ++++++++++++++++++++++++++++
 2 files changed, 310 insertions(+)
 create mode 100644 examples/plot_screenkhorn_1D.py
 create mode 100644 notebooks/plot_screenkhorn_1D.ipynb

diff --git a/examples/plot_screenkhorn_1D.py b/examples/plot_screenkhorn_1D.py
new file mode 100644
index 000000000..e0d7bfd35
--- /dev/null
+++ b/examples/plot_screenkhorn_1D.py
@@ -0,0 +1,103 @@
+#!/usr/bin/env python
+# coding: utf-8
+
+# In[ ]:
+
+
+get_ipython().run_line_magic('matplotlib', 'inline')
+
+
+# 
+# # 1D Screened optimal transport
+# 
+# 
+# This example illustrates the computation of Screenkhorn: Screening Sinkhorn Algorithm for Optimal transport.
+# 
+# 
+
+# In[13]:
+
+
+# Author: Mokhtar Z. Alaya <mokhtarzahdi.alaya@gmail.com>
+#
+# License: MIT License
+
+import numpy as np
+import matplotlib.pylab as pl
+import ot
+import ot.plot
+from ot.datasets import make_1D_gauss as gauss
+from ot.bregman import screenkhorn
+
+
+# Generate data
+# -------------
+# 
+# 
+
+# In[14]:
+
+
+#%% parameters
+
+n = 100  # nb bins
+
+# bin positions
+x = np.arange(n, dtype=np.float64)
+
+# Gaussian distributions
+a = gauss(n, m=20, s=5)  # m= mean, s= std
+b = gauss(n, m=60, s=10)
+
+# loss matrix
+M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)))
+M /= M.max()
+
+
+# Plot distributions and loss matrix
+# ----------------------------------
+# 
+# 
+
+# In[15]:
+
+
+#%% plot the distributions
+
+pl.figure(1, figsize=(6.4, 3))
+pl.plot(x, a, 'b', label='Source distribution')
+pl.plot(x, b, 'r', label='Target distribution')
+pl.legend()
+
+# plot distributions and loss matrix
+
+pl.figure(2, figsize=(5, 5))
+ot.plot.plot1D_mat(a, b, M, 'Cost matrix M')
+
+
+# Solve Screened Sinkhorn
+# --------------
+# 
+# 
+
+# In[21]:
+
+
+# Screenkhorn
+
+lambd = 1e-2 # entropy parameter
+ns_budget = 30 # budget number of points to be keeped in the source distribution
+nt_budget = 30 # budget number of points to be keeped in the target distribution
+
+Gsc = screenkhorn(a, b, M, lambd, ns_budget, nt_budget, uniform=False, restricted=True, verbose=True)
+pl.figure(4, figsize=(5, 5))
+ot.plot.plot1D_mat(a, b, Gs, 'OT matrix Screenkhorn')
+
+pl.show()
+
+
+# In[ ]:
+
+
+
+
diff --git a/notebooks/plot_screenkhorn_1D.ipynb b/notebooks/plot_screenkhorn_1D.ipynb
new file mode 100644
index 000000000..612634671
--- /dev/null
+++ b/notebooks/plot_screenkhorn_1D.ipynb
@@ -0,0 +1,207 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "%matplotlib inline"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "\n",
+    "# 1D Screened optimal transport\n",
+    "\n",
+    "\n",
+    "This example illustrates the computation of Screenkhorn: Screening Sinkhorn Algorithm for Optimal transport.\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Author: Mokhtar Z. Alaya <mokhtarzahdi.alaya@gmail.com>\n",
+    "#\n",
+    "# License: MIT License\n",
+    "\n",
+    "import numpy as np\n",
+    "import matplotlib.pylab as pl\n",
+    "import ot\n",
+    "import ot.plot\n",
+    "from ot.datasets import make_1D_gauss as gauss\n",
+    "from ot.bregman import screenkhorn"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Generate data\n",
+    "-------------\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "#%% parameters\n",
+    "\n",
+    "n = 100  # nb bins\n",
+    "\n",
+    "# bin positions\n",
+    "x = np.arange(n, dtype=np.float64)\n",
+    "\n",
+    "# Gaussian distributions\n",
+    "a = gauss(n, m=20, s=5)  # m= mean, s= std\n",
+    "b = gauss(n, m=60, s=10)\n",
+    "\n",
+    "# loss matrix\n",
+    "M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)))\n",
+    "M /= M.max()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Plot distributions and loss matrix\n",
+    "----------------------------------\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 460.8x216 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 360x360 with 3 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "#%% plot the distributions\n",
+    "\n",
+    "pl.figure(1, figsize=(6.4, 3))\n",
+    "pl.plot(x, a, 'b', label='Source distribution')\n",
+    "pl.plot(x, b, 'r', label='Target distribution')\n",
+    "pl.legend()\n",
+    "\n",
+    "# plot distributions and loss matrix\n",
+    "\n",
+    "pl.figure(2, figsize=(5, 5))\n",
+    "ot.plot.plot1D_mat(a, b, M, 'Cost matrix M')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Solve Screened Sinkhorn\n",
+    "--------------\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epsilon = 0.014767606916367452\n",
+      "\n",
+      "Kappa = 3.3854408965782907\n",
+      "\n",
+      "|I_active| = 30 \t |J_active| = 30 \n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 360x360 with 3 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# Screenkhorn\n",
+    "\n",
+    "lambd = 1e-2 # entropy parameter\n",
+    "ns_budget = 30 # budget number of points to be keeped in the source distribution\n",
+    "nt_budget = 30 # budget number of points to be keeped in the target distribution\n",
+    "\n",
+    "Gsc = screenkhorn(a, b, M, lambd, ns_budget, nt_budget, uniform=False, restricted=True, verbose=True)\n",
+    "pl.figure(4, figsize=(5, 5))\n",
+    "ot.plot.plot1D_mat(a, b, Gs, 'OT matrix Screenkhorn')\n",
+    "\n",
+    "pl.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.7.4"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 1
+}

From 112a2d46b80b91af399ee12c3711ba61d7aef977 Mon Sep 17 00:00:00 2001
From: "Mokhtar Z. Alaya" <mzalaya@Mokhtars-MacBook-Pro.local>
Date: Wed, 8 Jan 2020 19:28:09 +0100
Subject: [PATCH 19/39] plot_screenkhorn_1D.ipynb

---
 notebooks/plot_screenkhorn_1D.ipynb | 207 ----------------------------
 1 file changed, 207 deletions(-)
 delete mode 100644 notebooks/plot_screenkhorn_1D.ipynb

diff --git a/notebooks/plot_screenkhorn_1D.ipynb b/notebooks/plot_screenkhorn_1D.ipynb
deleted file mode 100644
index 612634671..000000000
--- a/notebooks/plot_screenkhorn_1D.ipynb
+++ /dev/null
@@ -1,207 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "%matplotlib inline"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "\n",
-    "# 1D Screened optimal transport\n",
-    "\n",
-    "\n",
-    "This example illustrates the computation of Screenkhorn: Screening Sinkhorn Algorithm for Optimal transport.\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 13,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# Author: Mokhtar Z. Alaya <mokhtarzahdi.alaya@gmail.com>\n",
-    "#\n",
-    "# License: MIT License\n",
-    "\n",
-    "import numpy as np\n",
-    "import matplotlib.pylab as pl\n",
-    "import ot\n",
-    "import ot.plot\n",
-    "from ot.datasets import make_1D_gauss as gauss\n",
-    "from ot.bregman import screenkhorn"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Generate data\n",
-    "-------------\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 14,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "#%% parameters\n",
-    "\n",
-    "n = 100  # nb bins\n",
-    "\n",
-    "# bin positions\n",
-    "x = np.arange(n, dtype=np.float64)\n",
-    "\n",
-    "# Gaussian distributions\n",
-    "a = gauss(n, m=20, s=5)  # m= mean, s= std\n",
-    "b = gauss(n, m=60, s=10)\n",
-    "\n",
-    "# loss matrix\n",
-    "M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)))\n",
-    "M /= M.max()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Plot distributions and loss matrix\n",
-    "----------------------------------\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 15,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 460.8x216 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 360x360 with 3 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "#%% plot the distributions\n",
-    "\n",
-    "pl.figure(1, figsize=(6.4, 3))\n",
-    "pl.plot(x, a, 'b', label='Source distribution')\n",
-    "pl.plot(x, b, 'r', label='Target distribution')\n",
-    "pl.legend()\n",
-    "\n",
-    "# plot distributions and loss matrix\n",
-    "\n",
-    "pl.figure(2, figsize=(5, 5))\n",
-    "ot.plot.plot1D_mat(a, b, M, 'Cost matrix M')"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Solve Screened Sinkhorn\n",
-    "--------------\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 21,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Epsilon = 0.014767606916367452\n",
-      "\n",
-      "Kappa = 3.3854408965782907\n",
-      "\n",
-      "|I_active| = 30 \t |J_active| = 30 \n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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d7Oc/TxtLufnc52CPPbxN+NVXU0eThBKwyEC65hq46Saf92EoLzU/EMx8zbiWFu8ZMQwnbVcCFhkob70F3/wm7LCDT8koHW26qfcJnjULrr02dTSDTglYZCCE4HMfLFniC1PmcqkjKl/HHw8NDb6S8iuvpI5mUCkBiwyEc8+Fv/7VZ//6wAdSR1Peqqvhj3+Epib40pegtTV1RINGCVikvz3wgE+0s88+3gQh3dt8c/9P6+674bTTUkczaJSARfrTggWw776wzjpw2WWVvdJFfzv0UJ+e87TT4LrrUkczKIbBTNAig2TlSvjsZ2HRIvjnPz0JS89lvSKeecaT8SabwHbbpY5qQKkCFukPTU0+0GL2bPj9732hTVl9I0bAn//sw5X33rviJ+xRAhbpq5YWOPhg+J//gfPO8wEG0nvrruvTdprB7rvD88+njmjAKAGL9MWyZZ5w//QnOOss70olfTd1qk/U09gIH/kIPPRQ6ogGhBKwSG+98QbstptXvueeC8cdlzqiyjJtGtx1l/eh3nVXuOWW1BH1OyVgkd64/XaYPh0efdTbLL/2tdQRVaZp0+Dee33mtL33hv/8z4qaPU0JWGR1LF0KJ5wAH/84jBvnN90+85nUUVW2SZO8V8mhh8KPfgQzZsDjj6eOql8oAYv0RGsr/OEPsNVW3tZ79NHwr3/B+9+fOrLhYfRoX9L+97+HJ5/0Xibf/rbPtzGEKQGLrMry5T6gYuut4ZBDvG/vvfd6b4dRo1JHN/x86Uvw9NP+d/HLX3rTxMknw8svp46sV5SARUq1tMDf/gZf/zpssIFPqlNb66Oz5syBnXZKHeHwtvbacOmlPpn7Jz/p8yxvson/+Xe/g8WLU0fYYxaG4Ryc0lFDQ0OYM2dO6jDSWLrUuzn9618+F8Fdd/ksZvX1Pqz4q1/1rlAaVlye5s2Diy6CK67w2dRyOZ8C9GMfgw9+0GdaW3/9Afn7M7O5IYSGXr9eCVigwhJwayusWOHNB0uX+uOdd3yI8JtvevexefP8a+szz8D8+YXXTpninf/32ssfamYYOkLw/0RnzYI774T77y/MrLbmmt63eMoU2GgjmDjRB3yMHw9jx/rzY8b433d9vc/Q1oOErQQs/aKhvj7M2WyzwXvD0n932X7x8RA6Ptra/NHaWni0tPijudk77nfXTcnMfwE32shn4dpyS58ysqEB1luvf39OSWf5cnj4YZg714c0P/20/6c7b57/O1kVM6ir86anmhpPyLlc4bHJJnDHHX1OwJqMR1xdHQxmAoaOFUa2X3zcrP0jlytsix81Nf4YMcJ/lpEj/TFmjD/GjvVuY+us4/MMVOuffsWrr4edd/ZHsRC8nfiNN+Dtt/2b0bvv+jel5cv929PKlZ6km5r8P/aWlsJ/+G1t/TbRkv4Vitt0U7j++tRRiAw8M/8PeezY1JGoF4SISCpKwCIiiegmnABgZkuBp1PH0Y21gXIf+jQUYoShEedQiHFqCGFMb1+sNmDJPN2Xu7mDwczmKMb+MRTiHCox9uX1aoIQEUlECVhEJBElYMlcmDqAHlCM/WcoxFnxMeomnIhIIqqARUQSUQIWEUlECXiYM7O9zOxpM3vOzE5OHU/GzDY0s7+Z2ZNm9riZfSseH2dmt5nZs3GbfDypmeXM7EEzuzHuTzGz2THGa8ysNnF8a5nZdWb2VPw8dy63z9HMjo9/z4+Z2VVmNqIcPkczu9TM3jSzx4qOdfrZmft1/F16xMy26+76SsDDmJnlgHOBvYH3AQeZ2fvSRpXXApwYQtgK2An4eoztZOCOEMLmwB1xP7VvAU8W7Z8BnBVjfAf4SpKoCn4F3BxC2BKYjsdaNp+jmW0AfBNoCCFMA3LAFymPz/FyYK+SY119dnsDm8fHTOC8bq8eQtBjmD6AnYFbiva/B3wvdVxdxHoDsCc+Wm9iPDYRH0CSMq5J8ZdwN+BGwPDRW9WdfcYJ4lsDeJF4w73oeNl8jsAGwCvAOHxw2I3AJ8rlcwQmA49199kBFwAHdXZeVw9VwMNb9g8/Mz8eKytmNhnYFpgNrBtCWAAQt/0zL2DvnQ2cBLTF/fHA4hBCNilx6s90E2AhcFlsJrnYzEZRRp9jCOFV4ExgHrAAWALMpbw+x2JdfXar/fukBDy8dTblf1n1SzSz0cCfgONCCO+mjqeYmX0KeDOEMLf4cCenpvxMq4HtgPNCCNsCyyiPZpu82Ia6LzAFWB8YhX+dL1VW/zY7sdp/90rAw9t8YMOi/UnAa4li6cDMavDke2UIIZus+A0zmxifnwi8mSo+4EPAZ8zsJeBqvBnibGAtM8vmWUn9mc4H5ocQZsf96/CEXE6f4x7AiyGEhSGEZuB6YBfK63Ms1tVnt9q/T0rAw9u/gM3j3eZa/MbHrMQxAX5HGbgEeDKE8Muip2YBh8U/H4a3DScRQvheCGFSCGEy/tndGUL4N+BvwP7xtNQxvg68YmZT46HdgScoo88Rb3rYyczq4997FmPZfI4luvrsZgGHxt4QOwFLsqaKLqVqeNejPB7APsAzwPPAD1LHUxTXh/Gvb48AD8XHPngb6x3As3E7LnWsMd4ZwI3xz5sA9wPPAdcCdYlj2waYEz/LvwBjy+1zBE4FngIeA34P1JXD5whchbdLN+MV7le6+uzwJohz4+/So3ivjlVeX0ORRUQS6VMTRLl24hcRGQp6XQHHTvzP4H0z5+PtiQeFEJ7ov/BERCpXX1bE2BF4LoTwAoCZXY13JekyAa+99tph8uTJfXhL6auFC+Gdd2CLLdofH/vAlDQBiQxht7Vd21nXsx7rSwLurNPxB0tPMrOZ+LA8NtpoI+bM6dMKHtJH3/kOnHsulP417Fl1QJqARIaxvrQB96jTcQjhwhBCQwihYcKECX14O+kPLS1QU5M6ChGBviXgsu7EL51rbITapHNziUimLwm4bDvxS9eWL4f6+tRRiAj0oQ04hNBiZscCt+DTx10aQni83yKTAfHeezB6dOooRAT6dhOOEMJNwE39FIsMgrffhvHjU0chItDHBCxDz+uvw9Zbp46izFmfehb1jUamDiuajGcYaWuDF1+EKeryK1IWVAEPIy+84L0gSgdhDFs9rXRtMOuUtu5PyahaHvJUAQ8j//iHb3fZJW0cIuJUAQ8js2bBOuvAVluljiSxrirfLipdq1pFpdxddVz62rZuqtbQ9XuF0tda/okuXqAKudypAh4mFizwBHzYYVClv3WRsqAKeJg49VQviI46KnUkCfWw8u1Q8WbPd1IJW3bN0v/VetuTIqta2zqpaksr2qwiLqma85WyKuSyp1poGPi//4MLLoDjjoPNN08djYhklIAr3OOPwwEHwCabwGmnpY5GRIqpCaKCPfYY7LYbVFfDTTfBqFGpI0pkdZseSpocOm1mKDlWOKfza3QbS5fNC4XmA4vHQmkzRZf77ZsoOtzE66rLm5omBo0q4ArU1ga//S3stJMn37vugqlTu32ZiAwyVcAV5sUX4cgj4c474ROfgIsvhkmTUkdV3rqtfHO5eLxQr1iuqv1rsv14rmXnZtvsWqWVclfy1WtRNdra6peIx0JrrGDbWtu9xuJ5IW6za1iskPOv6+rmXWeVsariAaEKuEI8+6z3cJg6Ff71L7joIvjf/1XyFSlnqoCHuIcegp/+FK691le6OOooOPlk2HDD7l87bHUzeKJDm2/Wzpsrel1WFVf7r5DFbf411f58KKmM85VyfI+Qf68uYmktqjyzKjRf+frWWmKlm22ztuCWlnh+a8l+W/vj2fmdVMbddmlTZdwnSsBD0Pz5cPXV8Mc/woMPwpgxvtbbccfBeuuljk5EekoJeIhYtAiuu86T7t13e+Gxww5w1llw+OGw1lqpI6wAXfRY6NAWDB0r3xrfhlj55vdrcp1vYyUc4nuGXNZG3HV4WS8IWrO2Xt9WtcRKuDmrdLP9lnZbsv1YCYfm5ni9Lirm4j932aNCFXFfKAGXqZYWX7n4llvg1lth9mz/XZg6FU45BQ4+GDbbLHWUItIXSsBl5OWXPdneeivcfjssXuxFWEODt+t+7nOw7bZp5wsfkrKqLPvgsnbM0rbgrKrLlXzAVSU9GOjYTpyvfGt9yelQ679abSPiNla+bbV+fmvcttX6ddqqY2UZQwpVnVTE2Y+R9XaIP0ZVS6yEm+O2yZ/INbbF417FVq2MFXBTrHSbvALOV8qNTf42WSVMcbVcUh3n26NjjwtVxL2iBJxISws8+ijcc48/7r3Xu5CB91z43Oe8G9nuu2sJIZFKpQQ8SN55B+67r5BwZ8+GZcv8uYkT4UMfgm99Cz7+cdhyS1W5Za+0P29WCWfbrOKN29aRvm0ZGSvgOt+21PnrW2v9Mm3ZtqQi9veI23wlHLexKM1XwLFpt7rR93NxW70iVsYrs61XtVUr4rYxVsQrmwrvGatksvbibL+0vbhk22XvCVXE7SgBD4DFi713wty58MADvn3mGX8ul4Pp0+GII3xi9F12gY02UsIVGY6UgPto0aJCks22zz9feH7DDWH77eHQQz3Z7rCDloVPpou24NAW+/lWxf14p986zKnQSZ/c0v2sDTe2I4dYybbVZJWub5tH+ral3s9vifutdfEt47a1tvA+ITYzh5Km69JKONfk16pq9G2u0Y9Xr/AXVi/3/ZoV3l5ds6w1HvdtbkWhDbhquVfDtjJWx7GdON9e3Ny+HTmUVsbZ/BX5jhVqIy6mBNxD2YKWDz/c/vHSS4VzJk/2ZPvlL/t2u+1gwoRUEYtIuVMC7sSyZX6DrDjRPvooLF3qz1dV+cKWH/wgHHOMJ9rttoNx49LGLf2krX0jazanQvFE7aEqzvnQ2r5t00r66ObPz0a+5bJeD348q4hbR/h+82h/XetI37aNLKoY62KFWht7N1RlpW+sMmMl39Qa36Mxxhi3Vcv9+Zpl/nz18rh9z4/XvlcdtzX5t6xe5o3SNe/FduLlzXHbGK8d24tXxjK7q4o4++y66zUBw6oqHtYJOAQfVVZa1T77bOHfwBprwAc+4E0I06fDNtvA1ltDfX3a2EVk6Bs2CbixEZ54omOyXbSocM6UKZ5kDz7Yt9One7OCbpBVmF62BednEQMs135+BWuOvR+y0XL50WhxW1IZWzbfQhZCfFlbLD6zyjc3pjn/niPrvcpcY+RKAEbXePU5sjpWpbFib4uNxCta/GLvNXsVu3SlNywvX+bl9sql/nxuqb95zVIPpvbdwoi/mqV+rbql1XG/pt02tyyriP09LKuEs8q4tPdEd70m/CegnQquiCsyAS9f7pPUzJ3ro8keeACeeqrQc2bkSHj/++Hzny8k2g98wKtdEZHBMuQT8IoVXslmyXbOHK90swme1l3Xb4h95jOFZLvZZu2H9csw1V0lTKzO4untvgg1W/vnsnkjYj/gqmzWs+qsX3D7kW+5pqzPbnxdLAitpPiryhXmZRhV51XlhJHegXz9+iW+X+s3J9bMrQCgJl6sNUa8PHateCd2uViwck3fLveKY+F7vlTKe0tGAtC4uDb/nrVL/BpNS6ra7dfFKrn23dKKOFbCWRvxiqwLRqyIs0q4Ke5nn33Rt4su55uowEp4yCXg117zRSbvussHMzz2WOHbzIQJPmz3s5/17fbbw/rrqwlBRMpT2SfgBQs82WaPbEDDGmv4kjuf+pQn2oYGH8KrZCurbTUr4WL5gV4lFXBpRZyLvR+qs/7BcdtaE3s7xH7CbfleEXHEXHPhq1pza/sOwCOrvIpcu/o9ADasfRuAcTnfH2VN7c5fGfzXfWGrV76vNPkY95dW+vb5sd5n8pV318y/ZvFir46bFnkVXbvYY2h+J7YXj/LtiPrYwyJWxjWxR0VV7FFRtdzbrfOVcPYNoXRkHUW9TrLPvS37uSuvbbjsEnAIvqLD737nE9I8/bQfX2MN2HVXmDkTZszw3ghqRhCRoaxsEvBbb8Hvfw+XXurNCiNH+oq+Rx5ZSLjVZROtVKQeVsLQsRq2kuPZfla7WRfVWrD4j9razw/cFivk5upCe+y7Ob/GwhqvFteo9Tbf8TXeJtwaez9kle+6Od+OiX2Wc7GCXBneAGBRrW9fGzEGgGfqfTb/p0cXZvV/emrvfKwAABKISURBVMy6AMwb4xNOLx3tFXFLfU3cxhF9ca6LESNi/HGui5o4F0YubquWxb7J+RVDYltxU6G3R5ftwxXYNtxtSjOzDYHfAevhP/GFIYRfmdk44BpgMvAS8IUQwjurG8C8efDtb8Nf/uI9VnbcES64AA48ENZcs/vXi4gMVT2pKVuAE0MID5jZGGCumd0GHA7cEUL4qZmdDJwMfHd13vytt2DPPb2d99hjfQjvtGmr+yOI9LNuKmEobp/M5osoqcZKViLOKuBc6Yi5bDBbHBpnsZ3X2uJ8Dq2FdrbG2JvhjeCVSVusCNtKJofIxYvW2FsAjIi9IuqrvP/v6Lhds8qPj6vyXhTjcj5JxDrV7+avlVXXa9VOBOD5Om8vXjjC25FX1HmF3lZbMt9xbNOui/u1sRdITewVkq+ES1ePhvyouZDNV4xvs/kk8v20K6BtuNsEHEJYACyIf15qZk8CGwD7AjPiaVcAd7EaCbix0W+gzZvnbb0f+tBqRi4iMsStVquqmU0GtgVmA+vG5EwIYYGZrdPFa2YCMwE22mij/PHXX/c+uw0NPkOYSNnpUEkVKq0Oo+ay6iyr1rKKuKRCziriqriCcU1LtmqFV5K5Jv+VzMXeD1VNhcqwqsmPNTZ6Bfv6St9f1uivXdzk/XjfHuPttG/We5W6Re3rAKxfHSvdeMkRFnssxPbncVXettxcXRgemvXGyMcQq+uqOP/Em+bv0Zjz6rytw1p32X5cIy9eria2cedK192jqCrOjmXbbHWOrnpJ5Fc6yb65lH8lvOr1uYuY2WjgT8BxIYR3uzs/E0K4MITQEEJomFA0NdjGG8OFF3pf3sMP9+YIEZHhpEcJ2Mxq8OR7ZQjh+nj4DTObGJ+fCLy5um/+5S/DT34CV13lAya+8AW4+eb2i7KKiFSqnvSCMOAS4MkQwi+LnpoFHAb8NG5v6E0A3/sefPrTcMkl3g3t2mt9QMXhh8N++6m/r5SRdl9p2zc9ZFNCdlh6J3/TLX5dzr4+xyaIXNxmS8pnTRFVjd7Nq3pl4Vd0ZX5Cdf+K3RgnwHkvDnp4cqk3TSxYy7uVPb+Gf+PMupVNHuEDNbIBGxNy/kV2hGWDIGKTRih0fctu6I3J+UCKCbU+yOPdkd7csXKMv/fiOAVmc4s3RVTF/exmomVNNqHzlFNV1ASR77oXt50OBW93fOg2RfSkAv4QcAiwm5k9FB/74Il3TzN7Ftgz7vfKtGlw1lnw6quegKdNg9NP9/bh8eM9Qf/iFz6pjqpjEakUPekF8Q86/ueT2b0/g6mrg/3390c2BPlvf/PtjTf6OWuu6SPiZszwnhPTp8OIEf0ZhUgPdHGDrsPw5dJuavlpGON+vLFUlS0N3xQryDh1ZPWKQjVavdyr4qZl2XDfOFHOu3Ei9iX+i/DOmnHynbV87asX1vSVAiaM9i5lE+u98p04wifzGRvXKKqPgyJyRcNMmuM8mUtaveJd0VaIB6AmF6fNrPGfq7nO97Mllqqy5ZHipENVLdnkQ/EmYycT2IeSrnvZjcuQ7dPeUK6Ey3Zs2cSJcNBB/gCvjrNJeO66C/76Vz9eXe0VczYfREODTzVZV5cqchGRninbBFxqgw18ovSDD/b9V1+F++8vTEH55z97OzJATY0n4Swhb7edr2KhSlkGTL66Wr224fwkNPmJ3UsWv1xRqCSqlseq+L32U0A2xwlwGhfHdtgxsSJew//BLx/jr3thjLcNvzzGB1PUj/J23TEjvPItneAdup/kPesC19ba/kZN1t2sdKL5/BJMcdsyIg7IaC4aTBHfo6q1fde9/MT4+TdpXxEPxUp4yCTgUhts4NNOfvazvh8CvPxyISHPnQv//d/e1Q38Rt7UqYU5gbPlhdZbr+v3EBEZSEM2AZcy8+WDJk/2NmTwpPzCC37zLluC6B//8G5vmXXWaZ+Up0+HLbf0KlpktXXVNpxVxFmbcNYWnHXxyfZjWzAllTBALv45W/4ntyxOERknRa8d7b/OLaP8mk2jYyU8Olab2fP1vl0+yivk9+pjjHHRz6q6wp3uqjgBUDbgJJsQpy1Wl63ZQJFs4c/YU6MqFtHZRPNZeZqtxBRKpuXMJqwH8pPYk03YU5MN087a0WNFnMsq3bifLXxqJYNkyrgSrpgE3Bkz2HRTfxxwQOH4okXwyCPt14b7zW98eDRAbS28730dE/P48Wl+DhGpTBWdgLsybpz3opgxo3Csudkney9OyjffDFdcUThngw0KTRdZUt588/bziIi009OKuC1b+DPrJ5xVwoWJyvNV8cq4/E9cALMqLgOUi23CbfW+Xzcyq3i9kmyOlXFz7KEQVyjKTyXZWhcn1Cm6gd1aG+OKhXrJvD9UZ0VlVtBnvR5iMZPLttkSTC3Z+dnipB2r0NLqOD9MOQ5rtmx4c1tsP84+u9L29SHQZXVYJuDO1NT4jbqtty7c6AN4442OKynfemvh3sno0Z6Qt9/eb/Ztv723NWvuYhHpjtJEN9ZdFz7+cX9ksiXuH3oIHnzQb/hddJGvxgw+mfw22xQS8vbbw1ZbqV1Z6L4izm/bj5yDQlWcn6Yxax+uzZb9idvYSyI3wivh6rrYRhwr4tYR2dYryZaRsT23LlbGdYWetlnvhWzJpA6VcHZqflpN31a1xIo3W4Eobqsb47Sc+UVJYyXcUvhc8n2Cs44RpeuMlU7SU9V+f7XbgiFZe7AScC/U1cG22/rjiCP8WGurL580d67f9Js715svzj3Xnx850ieb32UXf+y8s9qURYY7JeB+ksv5jbv3vQ8OOcSPtbXBs896Mr7/frjnHvj5zwvNF1OnFhLyLrt47wu1Jw8z+XbLbD5La7ebbyOGjj0nmkuWeI+9BbL2L1sep7aMk6ZXxeerY8Ucan2/LVbEbTVZW3DhH2E2wXp+0dDqGF9WTOarz+znibtt7SecL1TEWQUcp7XMts1FlX78s+Wn9CyZ2rMMei/0FyXgAVRV5Ul26tRCu/Ly5d5P+Z57/DFrFlx2mT83fjzssUehyWPSpHSxi8jAUwIeZPX1PpfFrrv6fgheJd97r897ceutcM01/tz73ldIxrvuCqNGpYtbBsmqJoEvrYqz6jP2iw3ZaLpctuBl7CXQ2H4peIs3IyxWylllnPW3ra4pSguxT26I1XFbtp/LeiZkFXEX08VkFXF+CaZs7ofYdzerdjupgLMeINnMcZTMCZH/rNq6qIjzn0/JcStpC4ZkfYP1hTcxM9hiCzjsMLj8ch9i/cgjcOaZXgGffz7ss493ndt3X0/O2c0+ERnaVAGXGTOfx+L974cTT4QVK+Dvf4ebbvKpOmfN8q5v++3nzRp77KHeFRWt04qsi/kmSnpQ5Cu9XGwrrsqq1zjPRC4bcRbTQKyYq4r7UFa1H5VWFbf549k1rH3f3a7kezjk++qWzBJH0Yi30sq3ZN6MfE+R0oo401VlXEZUAZe5kSO9CeLss30B0zvvhC9+0afn3GcfHxxyyinw9tupIxWR1WVhENs8Ghoawpw5cwbt/SpZY6OP1Lv0Uq+KR42CmTO9at5gg9W/3p5VB3R/kpS3Dv1ls36wXRzPqteSRTCteAma7M/ZNapy7V+bH6WWa7/fVZtwprRHQ3EeyireruZQDtk3gJJeEqUVcf49suuVzEzXmdXMh7e1XdvND7pqqoCHqLo6bxO+4QZ49FGfFe7Xv4YpU+CEE9ROLDIUqA24Akyb5uvpnXaaL3J61lneRHH55d6/WIaJ7kbZZaxk3ol8X95sCfnC/BP5eRhKquQQ963DaLSq9vuFC/UwZjpUrpTO9ZBVvCX73Va+ZUgVcAWZMsWHRN95p/fR//CHvX24gvqti1QUVcAV6GMf865sxx4Lp57qzRFnnNF1ESIVqsv/edu3gXbZmwI6qWTbV7j5VShK/3GVVMy90qFXQ0mlmz/eedtuh8q3H9t++4sScIUaM8abIEaN8uHPtbXw4x+njkpEiikBVzAznwxo5UpvG957b19JWoa5rqq9kvkoig/ldVYlQ9e9HqyLVs5V9ZLors22i0q2y7berirfMmibUxtwhTPz3hEbbQRHHlmYt0VE0lMFPAyMHg2/+pWPnvvLX+ALX0gdkZS1VVWGnVTJxYc7sC6uNRCrVayqjbfdeekr34wq4GHi05+GjTeGCy5IHYmIZJSAh4mqKjj0UJ9xbcmS1NGICCgBDysf/ah/+7r33tSRyJAXQg8fbYP36GmMZUQJeBjZcUffPvBA2jhExOkm3DAyZowvMvrii6kjkWGjzCrOcqMKeJjZeGOf1lJE0lMCHmbGj4dFi1JHISKgBDzsjB0L77yTOgoRgdVIwGaWM7MHzezGuD/FzGab2bNmdo2Z1Q5cmNJf6us1V7BIuVidCvhbwJNF+2cAZ4UQNgfeAb7Sn4HJwBg50teZE5H0epSAzWwS8Eng4rhvwG7AdfGUK4D9BiJA6V81NYU1DUUkrZ5WwGcDJ1GYSHQ8sDiEkP0qzwd6sRKZDLbqap+sXUTS6zYBm9mngDdDCHOLD3dyaqcd/sxsppnNMbM5Cxcu7GWY0l9yucKKLiKSVk8q4A8BnzGzl4Cr8aaHs4G1zCwbyDEJeK2zF4cQLgwhNIQQGiZMmNAPIUtfVFUVFpkVkbS6TcAhhO+FECaFECYDXwTuDCH8G/A3YP942mHADQMWpfQbMw1OEikXfekH/F3gBDN7Dm8TvqR/QpKBpAQsUj5Way6IEMJdwF3xzy8AO/Z/SDKQtDCnSPnQSDgRkUSUgIcZVcAi5UMJWEQkESVgEZFElIBFRBJRAhYRSUQJWEQkESVgEZFElIBFRBJRAhYRSUQJWEQkESVgEZFElIBFRBJRAhYRSUQJWEQkESVgEZFElIBFRBJRAhYRSUQJWEQkESVgEZFElIBFRBJRAhYRSUQJWEQkESVgEZFElIBFRBJRAhYRSUQJWEQkESVgEZFElIBFRBJRAhYRSUQJWEQkESVgEZFElIBFRBLpUQI2s7XM7Doze8rMnjSznc1snJndZmbPxu3YgQ5WRKSS9LQC/hVwcwhhS2A68CRwMnBHCGFz4I64LyIiPdRtAjazNYBdgUsAQghNIYTFwL7AFfG0K4D9BipIEZFK1JMKeBNgIXCZmT1oZheb2Shg3RDCAoC4XaezF5vZTDObY2ZzFi5c2G+Bi4gMdT1JwNXAdsB5IYRtgWWsRnNDCOHCEEJDCKFhwoQJvQxTRKTy9CQBzwfmhxBmx/3r8IT8hplNBIjbNwcmRBGRytRtAg4hvA68YmZT46HdgSeAWcBh8dhhwA0DEqGISIWq7uF53wCuNLNa4AXgCDx5/7eZfQWYBxwwMCGKiFSmHiXgEMJDQEMnT+3ev+GIiAwfGgknIpKIErCISCJKwCIiiSgBi4gkogQsIpKIErCISCJKwCIiiSgBi4gkogQsIpKIErCISCJKwCIiiSgBi4gkogQsIpKIErCISCJKwCIiiSgBi4gkogQsIpKIErCISCJKwCIiiSgBi4gkogQsIpKIErCISCJKwCIiiSgBi4gkogQsIpKIErCISCJKwCIiiSgBi4gkogQsIpKIErCISCJKwCIiiSgBi4gk0qMEbGbHm9njZvaYmV1lZiPMbIqZzTazZ83sGjOrHehgRUQqSbcJ2Mw2AL4JNIQQpgE54IvAGcBZIYTNgXeArwxkoCIilaanTRDVwEgzqwbqgQXAbsB18fkrgP36PzwRkcrVbQIOIbwKnAnMwxPvEmAusDiE0BJPmw9s0NnrzWymmc0xszkLFy7sn6hFRCpAT5ogxgL7AlOA9YFRwN6dnBo6e30I4cIQQkMIoWHChAl9iVVEpKL0pAliD+DFEMLCEEIzcD2wC7BWbJIAmAS8NkAxiohUpJ4k4HnATmZWb2YG7A48AfwN2D+ecxhww8CEKCJSmXrSBjwbv9n2APBofM2FwHeBE8zsOWA8cMkAxikiUnGquz8FQgg/BH5YcvgFYMd+j0hEZJjQSDgRkUSUgEVEElECFhFJRAlYRCQRJWARkUSUgEVEElECFhFJRAlYRCQRJWARkUSUgEVEElECFhFJRAlYRCQRJWARkUSUgEVEElECFhFJRAlYRCQRJWARkUSUgEVEElECFhFJRAlYRCQRJWARkUSUgEVEElECFhFJRAlYRCQRJWARkUSUgEVEElECFhFJRAlYRCQRJWARkUSUgEVEElECFhFJRAlYRCQRJWARkUSUgEVEErEQwuC9mdlC4OVBe0NZHRuHECakDkJkOBnUBCwiIgVqghARSUQJWEQkESVgEZFElIBFRBJRAhYRSUQJWEQkESVgEZFElIBFRBJRAhYRSeT/AQ6KGRM5MOlWAAAAAElFTkSuQmCC\n",
-      "text/plain": [
-       "<Figure size 360x360 with 3 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "# Screenkhorn\n",
-    "\n",
-    "lambd = 1e-2 # entropy parameter\n",
-    "ns_budget = 30 # budget number of points to be keeped in the source distribution\n",
-    "nt_budget = 30 # budget number of points to be keeped in the target distribution\n",
-    "\n",
-    "Gsc = screenkhorn(a, b, M, lambd, ns_budget, nt_budget, uniform=False, restricted=True, verbose=True)\n",
-    "pl.figure(4, figsize=(5, 5))\n",
-    "ot.plot.plot1D_mat(a, b, Gs, 'OT matrix Screenkhorn')\n",
-    "\n",
-    "pl.show()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "Python 3",
-   "language": "python",
-   "name": "python3"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.7.4"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 1
-}

From 73de2854ef8564521e082ea706ba2ed5ab44786e Mon Sep 17 00:00:00 2001
From: "Mokhtar Z. Alaya" <mzalaya@Mokhtars-MacBook-Pro.local>
Date: Fri, 10 Jan 2020 06:05:54 +0100
Subject: [PATCH 20/39] improve documentation

---
 examples/plot_screenkhorn_1D.py | 45 +++++++++++++++------------------
 ot/bregman.py                   | 12 ++++-----
 2 files changed, 26 insertions(+), 31 deletions(-)

diff --git a/examples/plot_screenkhorn_1D.py b/examples/plot_screenkhorn_1D.py
index e0d7bfd35..22a9ddc47 100644
--- a/examples/plot_screenkhorn_1D.py
+++ b/examples/plot_screenkhorn_1D.py
@@ -4,16 +4,22 @@
 # In[ ]:
 
 
+from ot.bregman import screenkhorn
+from ot.datasets import make_1D_gauss as gauss
+import ot.plot
+import ot
+import matplotlib.pylab as pl
+import numpy as np
 get_ipython().run_line_magic('matplotlib', 'inline')
 
 
-# 
+#
 # # 1D Screened optimal transport
-# 
-# 
+#
+#
 # This example illustrates the computation of Screenkhorn: Screening Sinkhorn Algorithm for Optimal transport.
-# 
-# 
+#
+#
 
 # In[13]:
 
@@ -22,18 +28,11 @@
 #
 # License: MIT License
 
-import numpy as np
-import matplotlib.pylab as pl
-import ot
-import ot.plot
-from ot.datasets import make_1D_gauss as gauss
-from ot.bregman import screenkhorn
-
 
 # Generate data
 # -------------
-# 
-# 
+#
+#
 
 # In[14]:
 
@@ -56,8 +55,8 @@
 
 # Plot distributions and loss matrix
 # ----------------------------------
-# 
-# 
+#
+#
 
 # In[15]:
 
@@ -77,17 +76,17 @@
 
 # Solve Screened Sinkhorn
 # --------------
-# 
-# 
+#
+#
 
 # In[21]:
 
 
 # Screenkhorn
 
-lambd = 1e-2 # entropy parameter
-ns_budget = 30 # budget number of points to be keeped in the source distribution
-nt_budget = 30 # budget number of points to be keeped in the target distribution
+lambd = 1e-2  # entropy parameter
+ns_budget = 30  # budget number of points to be keeped in the source distribution
+nt_budget = 30  # budget number of points to be keeped in the target distribution
 
 Gsc = screenkhorn(a, b, M, lambd, ns_budget, nt_budget, uniform=False, restricted=True, verbose=True)
 pl.figure(4, figsize=(5, 5))
@@ -97,7 +96,3 @@
 
 
 # In[ ]:
-
-
-
-
diff --git a/ot/bregman.py b/ot/bregman.py
index 28377b042..4f24cf430 100644
--- a/ot/bregman.py
+++ b/ot/bregman.py
@@ -1791,7 +1791,7 @@ def empirical_sinkhorn_divergence(X_s, X_t, reg, a=None, b=None, metric='sqeucli
         return max(0, sinkhorn_div)
 
 
-def screenkhorn(a, b, M, reg, ns_budget=None, nt_budget=None, uniform=True, restricted=True,
+def screenkhorn(a, b, M, reg, ns_budget=None, nt_budget=None, uniform=False, restricted=True,
                 maxiter=10000, maxfun=10000, pgtol=1e-09, verbose=False, log=False):
     """"
     Screening Sinkhorn Algorithm for Regularized Optimal Transport
@@ -1824,18 +1824,18 @@ def screenkhorn(a, b, M, reg, ns_budget=None, nt_budget=None, uniform=True, rest
     reg : `float`
         Level of the entropy regularisation
 
-    ns_budget: `int`, deafult=None
+    ns_budget : `int`, deafult=None
         Number budget of points to be keeped in the source domain
         If it is None then 50% of the source sample points will be keeped
 
-    nt_budget: `int`, deafult=None
+    nt_budget : `int`, deafult=None
         Number budget of points to be keeped in the target domain
         If it is None then 50% of the target sample points will be keeped
 
-    uniform: `bool`, default=True
-        If `True`, a_i = 1. / ns and b_j = 1. / nt
+    uniform : `bool`, default=False
+        If `True`, the source and target distribution are supposed to be uniform, namely a_i = 1 / ns and b_j = 1 / nt.
 
-    restricted: `bool`, default=True
+    restricted : `bool`, default=True
          If `True`, a warm-start initialization for the  L-BFGS-B solver
          using a restricted Sinkhorn algorithm with at most 5 iterations
 

From 5a70afeaa1671e4af010009d47bdea1073967e1e Mon Sep 17 00:00:00 2001
From: "Mokhtar Z. Alaya" <mzalaya@sct-18-1bee-1581.univ-rouen.fr>
Date: Fri, 10 Jan 2020 11:52:37 +0100
Subject: [PATCH 21/39] update screenkhorn example

---
 examples/plot_screenkhorn_1D.py | 66 ++++++++++-----------------------
 ot/bregman.py                   |  8 ++--
 2 files changed, 23 insertions(+), 51 deletions(-)

diff --git a/examples/plot_screenkhorn_1D.py b/examples/plot_screenkhorn_1D.py
index 22a9ddc47..0eb64b0b7 100644
--- a/examples/plot_screenkhorn_1D.py
+++ b/examples/plot_screenkhorn_1D.py
@@ -1,41 +1,26 @@
-#!/usr/bin/env python
-# coding: utf-8
-
-# In[ ]:
-
-
-from ot.bregman import screenkhorn
-from ot.datasets import make_1D_gauss as gauss
-import ot.plot
-import ot
-import matplotlib.pylab as pl
-import numpy as np
-get_ipython().run_line_magic('matplotlib', 'inline')
-
-
-#
-# # 1D Screened optimal transport
-#
-#
-# This example illustrates the computation of Screenkhorn: Screening Sinkhorn Algorithm for Optimal transport.
-#
-#
-
-# In[13]:
+# -*- coding: utf-8 -*-
+"""
+===============================
+1D Screened optimal transport
+===============================
 
+This example illustrates the computation of Screenkhorn:
+Screening Sinkhorn Algorithm for Optimal transport.
+"""
 
 # Author: Mokhtar Z. Alaya <mokhtarzahdi.alaya@gmail.com>
 #
 # License: MIT License
 
+import numpy as np
+import matplotlib.pylab as pl
+import ot.plot
+from ot.datasets import make_1D_gauss as gauss
+from ot.bregman import screenkhorn
 
+##############################################################################
 # Generate data
 # -------------
-#
-#
-
-# In[14]:
-
 
 #%% parameters
 
@@ -52,14 +37,9 @@
 M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)))
 M /= M.max()
 
-
+##############################################################################
 # Plot distributions and loss matrix
 # ----------------------------------
-#
-#
-
-# In[15]:
-
 
 #%% plot the distributions
 
@@ -73,14 +53,9 @@
 pl.figure(2, figsize=(5, 5))
 ot.plot.plot1D_mat(a, b, M, 'Cost matrix M')
 
-
+##############################################################################
 # Solve Screened Sinkhorn
-# --------------
-#
-#
-
-# In[21]:
-
+# -----------------------
 
 # Screenkhorn
 
@@ -90,9 +65,6 @@
 
 Gsc = screenkhorn(a, b, M, lambd, ns_budget, nt_budget, uniform=False, restricted=True, verbose=True)
 pl.figure(4, figsize=(5, 5))
-ot.plot.plot1D_mat(a, b, Gs, 'OT matrix Screenkhorn')
-
-pl.show()
-
+ot.plot.plot1D_mat(a, b, Gsc, 'OT matrix Screenkhorn')
 
-# In[ ]:
+pl.show()
\ No newline at end of file
diff --git a/ot/bregman.py b/ot/bregman.py
index 4f24cf430..95b27e451 100644
--- a/ot/bregman.py
+++ b/ot/bregman.py
@@ -1793,13 +1793,13 @@ def empirical_sinkhorn_divergence(X_s, X_t, reg, a=None, b=None, metric='sqeucli
 
 def screenkhorn(a, b, M, reg, ns_budget=None, nt_budget=None, uniform=False, restricted=True,
                 maxiter=10000, maxfun=10000, pgtol=1e-09, verbose=False, log=False):
-    """"
+    r""""
     Screening Sinkhorn Algorithm for Regularized Optimal Transport
 
     The function solves an approximate dual of Sinkhorn divergence [2] which is written as the following optimization problem:
 
     ..math::
-      (u, v) = \argmin_{u, v} 1_{ns}.T B(u,v) 1_{nt} - <\kappa u, a> - <v/\kappa, b> 
+      (u, v) = \argmin_{u, v} 1_{ns}^\top B(u,v) 1_{nt} - <\kappa u, a> - <v/\kappa, b>
 
       where B(u,v) = \diag(e^u) K \diag(e^v), with K = e^{-M/reg} and 
 
@@ -1853,8 +1853,8 @@ def screenkhorn(a, b, M, reg, ns_budget=None, nt_budget=None, uniform=False, res
 
     Dependency
     ----------
-    To gain more efficiency, screenkhorn needs to call the "Bottleneck" package (https://pypi.org/project/Bottleneck/) in the screening pre-processing step. 
-    If Bottleneck isn't installed, the following error message appears: 
+    To gain more efficiency, screenkhorn needs to call the "Bottleneck" package (https://pypi.org/project/Bottleneck/)
+    in the screening pre-processing step. If Bottleneck isn't installed, the following error message appears:
     "Bottleneck module doesn't exist. Install it from https://pypi.org/project/Bottleneck/"
 
 

From cadd301c4de54332378159ab55a02a48beb1d753 Mon Sep 17 00:00:00 2001
From: "Mokhtar Z. Alaya" <mzalaya@sct-18-1bee-1581.univ-rouen.fr>
Date: Fri, 10 Jan 2020 12:00:08 +0100
Subject: [PATCH 22/39] improve doc

---
 ot/bregman.py | 16 ++++++++--------
 1 file changed, 8 insertions(+), 8 deletions(-)

diff --git a/ot/bregman.py b/ot/bregman.py
index 95b27e451..0f0222663 100644
--- a/ot/bregman.py
+++ b/ot/bregman.py
@@ -1799,15 +1799,15 @@ def screenkhorn(a, b, M, reg, ns_budget=None, nt_budget=None, uniform=False, res
     The function solves an approximate dual of Sinkhorn divergence [2] which is written as the following optimization problem:
 
     ..math::
-      (u, v) = \argmin_{u, v} 1_{ns}^\top B(u,v) 1_{nt} - <\kappa u, a> - <v/\kappa, b>
+      (u, v) = \argmin_{u, v} 1_{ns}^T B(u,v) 1_{nt} - <\kappa u, a> - <v/\kappa, b>
 
-      where B(u,v) = \diag(e^u) K \diag(e^v), with K = e^{-M/reg} and 
+      where B(u,v) = \diag(e^u) K \diag(e^v), with K = e^{-M/reg} and
 
-      s.t. e^{u_i} >= \epsilon / \kappa, for all i in {1, ..., ns}
+      s.t. e^{u_i} \geq \epsilon / \kappa, for all i \in {1, ..., ns}
 
-           e^{v_j} >= \epsilon \kappa, for all j in {1, ..., nt}
+           e^{v_j} \geq \epsilon \kappa, for all j \in {1, ..., nt}
 
-      The parameters \kappa and \epsilon are determined w.r.t the couple number budget of points (ns_budget, nt_budget), see Equation (5) in [26] 
+      The parameters \kappa and \epsilon are determined w.r.t the couple number budget of points (ns_budget, nt_budget), see Equation (5) in [26]
 
 
     Parameters
@@ -1843,9 +1843,9 @@ def screenkhorn(a, b, M, reg, ns_budget=None, nt_budget=None, uniform=False, res
       Maximum number of iterations in LBFGS solver
 
     maxfun : `int`, default=10000
-      Maximum  number of function evaluations in LBFGS solver 
+      Maximum  number of function evaluations in LBFGS solver
 
-    pgtol : `float`, default=1e-09  
+    pgtol : `float`, default=1e-09
       Final objective function accuracy in LBFGS solver
 
     verbose: `bool`, default=False
@@ -2116,4 +2116,4 @@ def obj(theta): return bfgspost(theta)
     if log:
         return gamma, log
     else:
-        return gamma
\ No newline at end of file
+        return gamma

From 0461fb539b23d90d772fe5c4dd75463f915a1da5 Mon Sep 17 00:00:00 2001
From: "Mokhtar Z. Alaya" <mzalaya@sct-18-1bee-1581.univ-rouen.fr>
Date: Fri, 10 Jan 2020 12:17:45 +0100
Subject: [PATCH 23/39] improve doc

---
 ot/bregman.py | 9 +++++----
 1 file changed, 5 insertions(+), 4 deletions(-)

diff --git a/ot/bregman.py b/ot/bregman.py
index 0f0222663..16012b591 100644
--- a/ot/bregman.py
+++ b/ot/bregman.py
@@ -1833,7 +1833,7 @@ def screenkhorn(a, b, M, reg, ns_budget=None, nt_budget=None, uniform=False, res
         If it is None then 50% of the target sample points will be keeped
 
     uniform : `bool`, default=False
-        If `True`, the source and target distribution are supposed to be uniform, namely a_i = 1 / ns and b_j = 1 / nt.
+        If `True`, the source and target distribution are supposed to be uniform, i.e., a_i = 1 / ns and b_j = 1 / nt
 
     restricted : `bool`, default=True
          If `True`, a warm-start initialization for the  L-BFGS-B solver
@@ -1848,8 +1848,9 @@ def screenkhorn(a, b, M, reg, ns_budget=None, nt_budget=None, uniform=False, res
     pgtol : `float`, default=1e-09
       Final objective function accuracy in LBFGS solver
 
-    verbose: `bool`, default=False
-        If `True`, dispaly informations along iterations
+    verbose : `bool`, default=False
+        If `True`, dispaly informations about the cardinals of the active sets and the paramerters kappa
+        and epsilon
 
     Dependency
     ----------
@@ -2116,4 +2117,4 @@ def obj(theta): return bfgspost(theta)
     if log:
         return gamma, log
     else:
-        return gamma
+        return gamma
\ No newline at end of file

From 365adbccc73f7fea28811b16cbbbdbb77761e55c Mon Sep 17 00:00:00 2001
From: "Mokhtar Z. Alaya" <mzalaya@sct-18-1bee-1581.univ-rouen.fr>
Date: Fri, 10 Jan 2020 13:01:42 +0100
Subject: [PATCH 24/39] add simple test for screenkhorn

---
 test/test_bregman.py | 11 +++++++++++
 1 file changed, 11 insertions(+)

diff --git a/test/test_bregman.py b/test/test_bregman.py
index f70df10cc..eb74a9f8e 100644
--- a/test/test_bregman.py
+++ b/test/test_bregman.py
@@ -337,3 +337,14 @@ def test_implemented_methods():
         ot.bregman.sinkhorn(a, b, M, epsilon, method=method)
         with pytest.raises(ValueError):
             ot.bregman.sinkhorn2(a, b, M, epsilon, method=method)
+
+def test_screenkhorn():
+    # test screenkhorn
+    rng = np.random.RandomState(0)
+    n = 100
+    a = ot.unif(n)
+    b = ot.unif(n)
+
+    x = rng.randn(n, 2)
+    M = ot.dist(x, x)
+    G_screen = ot.bregman.screenkhorn(a, b, M, 1e-1)
\ No newline at end of file

From 18242437e73aba9cf131fafc1571e376b57f25f6 Mon Sep 17 00:00:00 2001
From: "Mokhtar Z. Alaya" <mzalaya@Mokhtars-MacBook-Pro.local>
Date: Mon, 13 Jan 2020 09:50:49 +0100
Subject: [PATCH 25/39] fix simple test of screenkhorn in test/

---
 test/test_bregman.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/test/test_bregman.py b/test/test_bregman.py
index eb74a9f8e..bc8f6aef4 100644
--- a/test/test_bregman.py
+++ b/test/test_bregman.py
@@ -347,4 +347,4 @@ def test_screenkhorn():
 
     x = rng.randn(n, 2)
     M = ot.dist(x, x)
-    G_screen = ot.bregman.screenkhorn(a, b, M, 1e-1)
\ No newline at end of file
+    G_screen = ot.bregman.screenkhorn(a, b, M, 1e-2, uniform=True, verbose=True)
\ No newline at end of file

From 4918d2c619aaa654c524c9c5dc7f4dc82b838f82 Mon Sep 17 00:00:00 2001
From: "Mokhtar Z. Alaya" <mzalaya@sct-18-1bee-1581.univ-rouen.fr>
Date: Thu, 16 Jan 2020 16:44:40 +0100
Subject: [PATCH 26/39] update readme

---
 README.md            | 2 +-
 test/test_bregman.py | 3 ++-
 2 files changed, 3 insertions(+), 2 deletions(-)

diff --git a/README.md b/README.md
index 987adf1d6..c115776b7 100644
--- a/README.md
+++ b/README.md
@@ -256,4 +256,4 @@ You can also post bug reports and feature requests in Github issues. Make sure t
 
 [25] Frogner C., Zhang C., Mobahi H., Araya-Polo M., Poggio T. (2015). [Learning with a Wasserstein Loss](http://cbcl.mit.edu/wasserstein/)  Advances in Neural Information Processing Systems (NIPS).
 
-[26] Alaya M. Z., Bérar M., Gasso G., Rakotomamonjy A. (2019). [Screening Sinkhorn Algorithm for Regularized Optimal Transport](https://papers.nips.cc/paper/9386-screening-sinkhorn-algorithm-for-regularized-optimal-transport), Advances in Neural Information Processing Systems 33 (NIPS).
+[26] Alaya M. Z., Bérar M., Gasso G., Rakotomamonjy A. (2019). [Screening Sinkhorn Algorithm for Regularized Optimal Transport](https://papers.nips.cc/paper/9386-screening-sinkhorn-algorithm-for-regularized-optimal-transport), Advances in Neural Information Processing Systems 33 (NeurIPS).
diff --git a/test/test_bregman.py b/test/test_bregman.py
index bc8f6aef4..52e9fb242 100644
--- a/test/test_bregman.py
+++ b/test/test_bregman.py
@@ -338,6 +338,7 @@ def test_implemented_methods():
         with pytest.raises(ValueError):
             ot.bregman.sinkhorn2(a, b, M, epsilon, method=method)
 
+
 def test_screenkhorn():
     # test screenkhorn
     rng = np.random.RandomState(0)
@@ -347,4 +348,4 @@ def test_screenkhorn():
 
     x = rng.randn(n, 2)
     M = ot.dist(x, x)
-    G_screen = ot.bregman.screenkhorn(a, b, M, 1e-2, uniform=True, verbose=True)
\ No newline at end of file
+    G_screen = ot.bregman.screenkhorn(a, b, M, 1e-2, uniform=True, verbose=True)

From 936b5e1eb965e1d8c71b7b26cfa5238face1aaa3 Mon Sep 17 00:00:00 2001
From: "Mokhtar Z. Alaya" <mzalaya@sct-18-1bee-1581.univ-rouen.fr>
Date: Thu, 16 Jan 2020 17:13:01 +0100
Subject: [PATCH 27/39] update

---
 .idea/POT.iml        | 11 +++++++++++
 test/test_bregman.py |  2 +-
 2 files changed, 12 insertions(+), 1 deletion(-)
 create mode 100644 .idea/POT.iml

diff --git a/.idea/POT.iml b/.idea/POT.iml
new file mode 100644
index 000000000..671160631
--- /dev/null
+++ b/.idea/POT.iml
@@ -0,0 +1,11 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<module type="PYTHON_MODULE" version="4">
+  <component name="NewModuleRootManager">
+    <content url="file://$MODULE_DIR$" />
+    <orderEntry type="inheritedJdk" />
+    <orderEntry type="sourceFolder" forTests="false" />
+  </component>
+  <component name="TestRunnerService">
+    <option name="PROJECT_TEST_RUNNER" value="Unittests" />
+  </component>
+</module>
\ No newline at end of file
diff --git a/test/test_bregman.py b/test/test_bregman.py
index 52e9fb242..bcec09503 100644
--- a/test/test_bregman.py
+++ b/test/test_bregman.py
@@ -348,4 +348,4 @@ def test_screenkhorn():
 
     x = rng.randn(n, 2)
     M = ot.dist(x, x)
-    G_screen = ot.bregman.screenkhorn(a, b, M, 1e-2, uniform=True, verbose=True)
+    G_screen = ot.bregman.screenkhorn(a, b, M, 1e-2, uniform=True, verbose=True)
\ No newline at end of file

From 0f753104856b7c69c6e126b2564353c1e8ccbf77 Mon Sep 17 00:00:00 2001
From: "Mokhtar Z. Alaya" <mzalaya@Mokhtars-iMac.local>
Date: Sat, 18 Jan 2020 06:52:42 +0100
Subject: [PATCH 28/39] clean

---
 .idea/POT.iml                   |  3 +-
 examples/plot_screenkhorn_1D.py | 28 +++++++++++++----
 ot/bregman.py                   | 56 ++++++++++++++++++---------------
 3 files changed, 55 insertions(+), 32 deletions(-)

diff --git a/.idea/POT.iml b/.idea/POT.iml
index 671160631..7c9d48f0f 100644
--- a/.idea/POT.iml
+++ b/.idea/POT.iml
@@ -6,6 +6,7 @@
     <orderEntry type="sourceFolder" forTests="false" />
   </component>
   <component name="TestRunnerService">
-    <option name="PROJECT_TEST_RUNNER" value="Unittests" />
+    <option name="projectConfiguration" value="pytest" />
+    <option name="PROJECT_TEST_RUNNER" value="pytest" />
   </component>
 </module>
\ No newline at end of file
diff --git a/examples/plot_screenkhorn_1D.py b/examples/plot_screenkhorn_1D.py
index 0eb64b0b7..103d54cdd 100644
--- a/examples/plot_screenkhorn_1D.py
+++ b/examples/plot_screenkhorn_1D.py
@@ -14,6 +14,7 @@
 
 import numpy as np
 import matplotlib.pylab as pl
+import time
 import ot.plot
 from ot.datasets import make_1D_gauss as gauss
 from ot.bregman import screenkhorn
@@ -54,17 +55,32 @@
 ot.plot.plot1D_mat(a, b, M, 'Cost matrix M')
 
 ##############################################################################
-# Solve Screened Sinkhorn
+# Solve Screenkhorn
 # -----------------------
 
 # Screenkhorn
-
-lambd = 1e-2  # entropy parameter
+lambd = 1e-3  # entropy parameter
 ns_budget = 30  # budget number of points to be keeped in the source distribution
 nt_budget = 30  # budget number of points to be keeped in the target distribution
 
-Gsc = screenkhorn(a, b, M, lambd, ns_budget, nt_budget, uniform=False, restricted=True, verbose=True)
+tic = time.time()
+G_screen = screenkhorn(a, b, M, lambd, ns_budget, nt_budget, uniform=False, restricted=True, verbose=True)
+tac_screen = time.time() - tic
+
+# Sinkhorn
+tic = time.time()
+G_sink = ot.sinkhorn(a, b, M, lambd, verbose=False)
+tac_sink = time.time() - tic
+
+
 pl.figure(4, figsize=(5, 5))
-ot.plot.plot1D_mat(a, b, Gsc, 'OT matrix Screenkhorn')
+ot.plot.plot1D_mat(a, b, G_screen, 'OT matrix Screenkhorn')
 
-pl.show()
\ No newline at end of file
+pl.show()
+
+##############################################################################
+# Time complexity
+# -----------------------
+print("Sinkhorn time complexity: %s\n" % tac_sink)
+print("Screenkhorn time complexity: %s\n" % tac_screen)
+print("Time_Sinkhorn / Time_Screenkhorn: %s\n" % (tac_sink / tac_screen))
diff --git a/ot/bregman.py b/ot/bregman.py
index 16012b591..aff9f8c9c 100644
--- a/ot/bregman.py
+++ b/ot/bregman.py
@@ -1876,7 +1876,7 @@ def screenkhorn(a, b, M, reg, ns_budget=None, nt_budget=None, uniform=False, res
     # check if bottleneck module exists
     try:
         import bottleneck
-    except ImportError as e:
+    except ImportError:
         print("Bottleneck module doesn't exist. Install it from https://pypi.org/project/Bottleneck/")
 
     a = np.asarray(a, dtype=np.float64)
@@ -1905,8 +1905,8 @@ def projection(u, epsilon):
 
     if ns_budget == ns and nt_budget == nt:
         # full number of budget points (ns, nt) = (ns_budget, nt_budget)
-        I = np.ones(ns, dtype=bool)
-        J = np.ones(nt, dtype=bool)
+        Isel = np.ones(ns, dtype=bool)
+        Jsel = np.ones(nt, dtype=bool)
         epsilon = 0.0
         kappa = 1.0
 
@@ -1955,46 +1955,48 @@ def projection(u, epsilon):
             epsilon_v_square = bK_sort[nt_budget - 1]
 
         # active sets I and J (see Lemma 1 in [26])
-        I = a >= epsilon_u_square * K_sum_cols
-        J = b >= epsilon_v_square * K_sum_rows
+        Isel = a >= epsilon_u_square * K_sum_cols
+        Jsel = b >= epsilon_v_square * K_sum_rows
 
-        if sum(I) != ns_budget:
+        if sum(Isel) != ns_budget:
             if uniform:
                 aK = a / K_sum_cols
                 aK_sort = np.sort(aK)[::-1]
             epsilon_u_square = aK_sort[ns_budget - 1:ns_budget + 1].mean()
-            I = a >= epsilon_u_square * K_sum_cols
+            Isel = a >= epsilon_u_square * K_sum_cols
+            ns_budget = sum(Isel)
 
-        if sum(J) != nt_budget:
+        if sum(Jsel) != nt_budget:
             if uniform:
                 bK = b / K_sum_rows
                 bK_sort = np.sort(bK)[::-1]
             epsilon_v_square = bK_sort[nt_budget - 1:nt_budget + 1].mean()
-            J = b >= epsilon_v_square * K_sum_rows
+            Jsel = b >= epsilon_v_square * K_sum_rows
+            nt_budget = sum(Jsel)
 
         epsilon = (epsilon_u_square * epsilon_v_square) ** (1 / 4)
         kappa = (epsilon_v_square / epsilon_u_square) ** (1 / 2)
 
         if verbose:
             print("epsilon = %s\n" % epsilon)
-            print("kappa= %s\n" % kappa)
-            print('|I_active| = %s \t |J_active| = %s ' % (sum(I), sum(J)))
+            print("kappa = %s\n" % kappa)
+            print('Cardinality of selected points: |Isel| = %s \t |Jsel| = %s \n' % (sum(Isel), sum(Jsel)))
 
         # Ic, Jc: complementary of the active sets I and J
-        Ic = ~I
-        Jc = ~J
+        Ic = ~Isel
+        Jc = ~Jsel
 
-        K_IJ = K[np.ix_(I, J)]
-        K_IcJ = K[np.ix_(Ic, J)]
-        K_IJc = K[np.ix_(I, Jc)]
+        K_IJ = K[np.ix_(Isel, Jsel)]
+        K_IcJ = K[np.ix_(Ic, Jsel)]
+        K_IJc = K[np.ix_(Isel, Jc)]
 
         K_min = K_IJ.min()
         if K_min == 0:
             K_min = np.finfo(float).tiny
 
         # a_I, b_J, a_Ic, b_Jc
-        a_I = a[I]
-        b_J = b[J]
+        a_I = a[Isel]
+        b_J = b[Jsel]
         if not uniform:
             a_I_min = a_I.min()
             a_I_max = a_I.max()
@@ -2028,7 +2030,7 @@ def projection(u, epsilon):
             cst_v = epsilon * K_IcJ.sum(axis=0) / kappa
 
         cpt = 1
-        while (cpt < 5):  # 5 iterations
+        while cpt < 5:  # 5 iterations
             K_IJ_v = np.dot(K_IJ.T, u0) + cst_v
             v0 = b_J / (kappa * K_IJ_v)
             KIJ_u = np.dot(K_IJ, v0) + cst_u
@@ -2047,7 +2049,7 @@ def restricted_sinkhorn(usc, vsc, max_iter=5):
         Restricted Sinkhorn Algorithm as a warm-start initialized point for L-BFGS-B (see Algorithm 1 in supplementary of [26])
         """
         cpt = 1
-        while (cpt < max_iter):
+        while cpt < max_iter:
             K_IJ_v = np.dot(K_IJ.T, usc) + cst_v
             vsc = b_J / (kappa * K_IJ_v)
             KIJ_u = np.dot(K_IJ, vsc) + cst_u
@@ -2067,7 +2069,7 @@ def screened_obj(usc, vsc):
         return psi_epsilon
 
     def screened_grad(usc, vsc):
-        # gradients of Psi_epsilon w.r.t u and v
+        # gradients of Psi_(kappa,epsilon) w.r.t u and v
         grad_u = np.dot(K_IJ, vsc) + vec_eps_IJc - kappa * a_I / usc
         grad_v = np.dot(K_IJ.T, usc) + vec_eps_IcJ - (1. / kappa) * b_J / vsc
         return grad_u, grad_v
@@ -2090,7 +2092,9 @@ def bfgspost(theta):
     theta0 = np.hstack([u0, v0])
 
     bounds = bounds_u + bounds_v  # constraint bounds
-    def obj(theta): return bfgspost(theta)
+
+    def obj(theta):
+        return bfgspost(theta)
 
     theta, _, _ = fmin_l_bfgs_b(func=obj,
                                 x0=theta0,
@@ -2104,13 +2108,15 @@ def obj(theta): return bfgspost(theta)
 
     usc_full = np.full(ns, epsilon / kappa)
     vsc_full = np.full(nt, epsilon * kappa)
-    usc_full[I] = usc
-    vsc_full[J] = vsc
+    usc_full[Isel] = usc
+    vsc_full[Jsel] = vsc
 
     if log:
+        log = {}
         log['u'] = usc_full
         log['v'] = vsc_full
-
+        log['Isel'] = Isel
+        log['Jsel'] = Jsel
     gamma = usc_full[:, None] * K * vsc_full[None, :]
     gamma = gamma / gamma.sum()
 

From 55e4f76095e5cea22429846fc9d1a790d7eb691b Mon Sep 17 00:00:00 2001
From: "Mokhtar Z. Alaya" <mzalaya@Mokhtars-iMac.local>
Date: Sat, 18 Jan 2020 06:56:31 +0100
Subject: [PATCH 29/39] remove .idea/POT.iml

---
 .idea/POT.iml | 12 ------------
 1 file changed, 12 deletions(-)
 delete mode 100644 .idea/POT.iml

diff --git a/.idea/POT.iml b/.idea/POT.iml
deleted file mode 100644
index 7c9d48f0f..000000000
--- a/.idea/POT.iml
+++ /dev/null
@@ -1,12 +0,0 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<module type="PYTHON_MODULE" version="4">
-  <component name="NewModuleRootManager">
-    <content url="file://$MODULE_DIR$" />
-    <orderEntry type="inheritedJdk" />
-    <orderEntry type="sourceFolder" forTests="false" />
-  </component>
-  <component name="TestRunnerService">
-    <option name="projectConfiguration" value="pytest" />
-    <option name="PROJECT_TEST_RUNNER" value="pytest" />
-  </component>
-</module>
\ No newline at end of file

From 3be0c215143e16c59ddd3be902416e91c3292937 Mon Sep 17 00:00:00 2001
From: "Mokhtar Z. Alaya" <mzalaya@Mokhtars-iMac.local>
Date: Sat, 18 Jan 2020 07:15:09 +0100
Subject: [PATCH 30/39] clean

---
 examples/plot_screenkhorn_1D.py | 2 +-
 test/test_bregman.py            | 5 ++++-
 2 files changed, 5 insertions(+), 2 deletions(-)

diff --git a/examples/plot_screenkhorn_1D.py b/examples/plot_screenkhorn_1D.py
index 103d54cdd..7c0de82d8 100644
--- a/examples/plot_screenkhorn_1D.py
+++ b/examples/plot_screenkhorn_1D.py
@@ -59,7 +59,7 @@
 # -----------------------
 
 # Screenkhorn
-lambd = 1e-3  # entropy parameter
+lambd = 1e-03  # entropy parameter
 ns_budget = 30  # budget number of points to be keeped in the source distribution
 nt_budget = 30  # budget number of points to be keeped in the target distribution
 
diff --git a/test/test_bregman.py b/test/test_bregman.py
index bcec09503..2398d457b 100644
--- a/test/test_bregman.py
+++ b/test/test_bregman.py
@@ -348,4 +348,7 @@ def test_screenkhorn():
 
     x = rng.randn(n, 2)
     M = ot.dist(x, x)
-    G_screen = ot.bregman.screenkhorn(a, b, M, 1e-2, uniform=True, verbose=True)
\ No newline at end of file
+    G_sink = ot.sinkhorn(a, b, M, 1e-03)
+    G_screen = ot.bregman.screenkhorn(a, b, M, 1e-03, uniform=True, verbose=True)
+    np.testing.assert_allclose(G_sink.sum(0), G_screen.sum(0), atol=1e-02)
+    np.testing.assert_allclose(G_sink.sum(1), G_screen.sum(1), atol=1e-02)
\ No newline at end of file

From b3fb1ef40a482f0989686b79373060d764b62d38 Mon Sep 17 00:00:00 2001
From: "Mokhtar Z. Alaya" <mzalaya@Mokhtars-iMac.local>
Date: Sat, 18 Jan 2020 07:45:34 +0100
Subject: [PATCH 31/39] clean

---
 ot/bregman.py        | 3 ++-
 test/test_bregman.py | 8 ++++----
 2 files changed, 6 insertions(+), 5 deletions(-)

diff --git a/ot/bregman.py b/ot/bregman.py
index aff9f8c9c..c304b5d04 100644
--- a/ot/bregman.py
+++ b/ot/bregman.py
@@ -2117,10 +2117,11 @@ def obj(theta):
         log['v'] = vsc_full
         log['Isel'] = Isel
         log['Jsel'] = Jsel
+
     gamma = usc_full[:, None] * K * vsc_full[None, :]
     gamma = gamma / gamma.sum()
 
     if log:
         return gamma, log
     else:
-        return gamma
\ No newline at end of file
+        return gamma
diff --git a/test/test_bregman.py b/test/test_bregman.py
index 2398d457b..e376715d4 100644
--- a/test/test_bregman.py
+++ b/test/test_bregman.py
@@ -348,7 +348,7 @@ def test_screenkhorn():
 
     x = rng.randn(n, 2)
     M = ot.dist(x, x)
-    G_sink = ot.sinkhorn(a, b, M, 1e-03)
-    G_screen = ot.bregman.screenkhorn(a, b, M, 1e-03, uniform=True, verbose=True)
-    np.testing.assert_allclose(G_sink.sum(0), G_screen.sum(0), atol=1e-02)
-    np.testing.assert_allclose(G_sink.sum(1), G_screen.sum(1), atol=1e-02)
\ No newline at end of file
+    G_s = ot.sinkhorn(a, b, M, 1e-03)
+    G_sc = ot.bregman.screenkhorn(a, b, M, 1e-03, uniform=True, verbose=True)
+    np.testing.assert_allclose(G_s.sum(0), G_sc.sum(0), atol=1e-02)
+    np.testing.assert_allclose(G_s.sum(1), G_sc.sum(1), atol=1e-02)
\ No newline at end of file

From 7f7b1c547b54b394db975f4ff9d0287904a7b820 Mon Sep 17 00:00:00 2001
From: "Mokhtar Z. Alaya" <mzalaya@Mokhtars-iMac.local>
Date: Sat, 18 Jan 2020 09:04:48 +0100
Subject: [PATCH 32/39] make autopep

---
 test/test_bregman.py | 19 +++++++++----------
 1 file changed, 9 insertions(+), 10 deletions(-)

diff --git a/test/test_bregman.py b/test/test_bregman.py
index e376715d4..fd0679b2b 100644
--- a/test/test_bregman.py
+++ b/test/test_bregman.py
@@ -106,7 +106,6 @@ def test_sinkhorn_variants_log():
 
 @pytest.mark.parametrize("method", ["sinkhorn", "sinkhorn_stabilized"])
 def test_barycenter(method):
-
     n_bins = 100  # nb bins
 
     # Gaussian distributions
@@ -133,7 +132,6 @@ def test_barycenter(method):
 
 
 def test_barycenter_stabilization():
-
     n_bins = 100  # nb bins
 
     # Gaussian distributions
@@ -161,7 +159,6 @@ def test_barycenter_stabilization():
 
 
 def test_wasserstein_bary_2d():
-
     size = 100  # size of a square image
     a1 = np.random.randn(size, size)
     a1 += a1.min()
@@ -185,7 +182,6 @@ def test_wasserstein_bary_2d():
 
 
 def test_unmix():
-
     n_bins = 50  # nb bins
 
     # Gaussian distributions
@@ -207,7 +203,7 @@ def test_unmix():
 
     # wasserstein
     reg = 1e-3
-    um = ot.bregman.unmix(a, D, M, M0, h0, reg, 1, alpha=0.01,)
+    um = ot.bregman.unmix(a, D, M, M0, h0, reg, 1, alpha=0.01, )
 
     np.testing.assert_allclose(1, np.sum(um), rtol=1e-03, atol=1e-03)
     np.testing.assert_allclose([0.5, 0.5], um, rtol=1e-03, atol=1e-03)
@@ -256,7 +252,7 @@ def test_empirical_sinkhorn():
 
 
 def test_empirical_sinkhorn_divergence():
-    #Test sinkhorn divergence
+    # Test sinkhorn divergence
     n = 10
     a = ot.unif(n)
     b = ot.unif(n)
@@ -348,7 +344,10 @@ def test_screenkhorn():
 
     x = rng.randn(n, 2)
     M = ot.dist(x, x)
-    G_s = ot.sinkhorn(a, b, M, 1e-03)
-    G_sc = ot.bregman.screenkhorn(a, b, M, 1e-03, uniform=True, verbose=True)
-    np.testing.assert_allclose(G_s.sum(0), G_sc.sum(0), atol=1e-02)
-    np.testing.assert_allclose(G_s.sum(1), G_sc.sum(1), atol=1e-02)
\ No newline at end of file
+    # sinkhorn
+    G_sink = ot.sinkhorn(a, b, M, 1e-03)
+    # screenkhorn
+    G_screen = ot.bregman.screenkhorn(a, b, M, 1e-03, uniform=True, verbose=True)
+    # check marginals
+    np.testing.assert_allclose(G_sink.sum(0), G_screen.sum(0), atol=1e-02)
+    np.testing.assert_allclose(G_s.sum(1), G_screen.sum(1), atol=1e-02)

From a1747a10e80751eacca4273af61083a853fb9dd4 Mon Sep 17 00:00:00 2001
From: "Mokhtar Z. Alaya" <mzalaya@Mokhtars-iMac.local>
Date: Sat, 18 Jan 2020 09:12:55 +0100
Subject: [PATCH 33/39] make autopep

---
 test/test_bregman.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/test/test_bregman.py b/test/test_bregman.py
index fd0679b2b..f54ba9fdc 100644
--- a/test/test_bregman.py
+++ b/test/test_bregman.py
@@ -350,4 +350,4 @@ def test_screenkhorn():
     G_screen = ot.bregman.screenkhorn(a, b, M, 1e-03, uniform=True, verbose=True)
     # check marginals
     np.testing.assert_allclose(G_sink.sum(0), G_screen.sum(0), atol=1e-02)
-    np.testing.assert_allclose(G_s.sum(1), G_screen.sum(1), atol=1e-02)
+    np.testing.assert_allclose(G_sink.sum(1), G_screen.sum(1), atol=1e-02)

From 7c25e0725e357e4beecc3bfb6f1468a5b5140e74 Mon Sep 17 00:00:00 2001
From: "Mokhtar Z. Alaya" <mzalaya@Mokhtars-iMac.local>
Date: Sat, 18 Jan 2020 09:35:14 +0100
Subject: [PATCH 34/39] clean

---
 examples/plot_screenkhorn_1D.py | 22 ++--------------------
 1 file changed, 2 insertions(+), 20 deletions(-)

diff --git a/examples/plot_screenkhorn_1D.py b/examples/plot_screenkhorn_1D.py
index 7c0de82d8..bfd374e41 100644
--- a/examples/plot_screenkhorn_1D.py
+++ b/examples/plot_screenkhorn_1D.py
@@ -14,7 +14,6 @@
 
 import numpy as np
 import matplotlib.pylab as pl
-import time
 import ot.plot
 from ot.datasets import make_1D_gauss as gauss
 from ot.bregman import screenkhorn
@@ -59,28 +58,11 @@
 # -----------------------
 
 # Screenkhorn
-lambd = 1e-03  # entropy parameter
+lambd = 2e-03  # entropy parameter
 ns_budget = 30  # budget number of points to be keeped in the source distribution
 nt_budget = 30  # budget number of points to be keeped in the target distribution
 
-tic = time.time()
 G_screen = screenkhorn(a, b, M, lambd, ns_budget, nt_budget, uniform=False, restricted=True, verbose=True)
-tac_screen = time.time() - tic
-
-# Sinkhorn
-tic = time.time()
-G_sink = ot.sinkhorn(a, b, M, lambd, verbose=False)
-tac_sink = time.time() - tic
-
-
 pl.figure(4, figsize=(5, 5))
 ot.plot.plot1D_mat(a, b, G_screen, 'OT matrix Screenkhorn')
-
-pl.show()
-
-##############################################################################
-# Time complexity
-# -----------------------
-print("Sinkhorn time complexity: %s\n" % tac_sink)
-print("Screenkhorn time complexity: %s\n" % tac_screen)
-print("Time_Sinkhorn / Time_Screenkhorn: %s\n" % (tac_sink / tac_screen))
+pl.show()
\ No newline at end of file

From b6fa567fcb8eaef0699cc8d8ca087ad9c1fb05de Mon Sep 17 00:00:00 2001
From: "Mokhtar Z. Alaya" <mzalaya@Mokhtars-iMac.local>
Date: Sat, 18 Jan 2020 09:48:00 +0100
Subject: [PATCH 35/39] clean

---
 examples/plot_screenkhorn_1D.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/examples/plot_screenkhorn_1D.py b/examples/plot_screenkhorn_1D.py
index bfd374e41..840ead848 100644
--- a/examples/plot_screenkhorn_1D.py
+++ b/examples/plot_screenkhorn_1D.py
@@ -65,4 +65,4 @@
 G_screen = screenkhorn(a, b, M, lambd, ns_budget, nt_budget, uniform=False, restricted=True, verbose=True)
 pl.figure(4, figsize=(5, 5))
 ot.plot.plot1D_mat(a, b, G_screen, 'OT matrix Screenkhorn')
-pl.show()
\ No newline at end of file
+pl.show()

From e92b7075decc2b6b55a5b395768f733a577591ea Mon Sep 17 00:00:00 2001
From: "Mokhtar Z. Alaya" <mzalaya@Mokhtars-MacBook-Pro.local>
Date: Fri, 24 Jan 2020 01:39:26 +0100
Subject: [PATCH 36/39] add a warning for non installed Botteleneck module

---
 ot/bregman.py | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/ot/bregman.py b/ot/bregman.py
index c304b5d04..2707b7c54 100644
--- a/ot/bregman.py
+++ b/ot/bregman.py
@@ -1877,7 +1877,8 @@ def screenkhorn(a, b, M, reg, ns_budget=None, nt_budget=None, uniform=False, res
     try:
         import bottleneck
     except ImportError:
-        print("Bottleneck module doesn't exist. Install it from https://pypi.org/project/Bottleneck/")
+        warnings.warn("Bottleneck module is not installed. Install it from https://pypi.org/project/Bottleneck/ for better performance.")
+        bottleneck = np
 
     a = np.asarray(a, dtype=np.float64)
     b = np.asarray(b, dtype=np.float64)

From c5b1c7cfa3bbf0bed056f2c7c6bedc0d0148a8ce Mon Sep 17 00:00:00 2001
From: "Mokhtar Z. Alaya" <mzalaya@sct-18-1bee-1581.univ-rouen.fr>
Date: Fri, 24 Jan 2020 09:23:02 +0100
Subject: [PATCH 37/39] modify pymanopt version in requirements

---
 requirements.txt | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/requirements.txt b/requirements.txt
index 5a3432b9f..d62190aef 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -4,6 +4,7 @@ cython
 matplotlib
 sphinx-gallery
 autograd
-pymanopt
+pymanopt== 0.2.4, python_version < '3'
+pymanopt, python_version >= '3'
 cvxopt
 pytest

From cae39790dd09a43decc56479d0704717db2ed729 Mon Sep 17 00:00:00 2001
From: "Mokhtar Z. Alaya" <mzalaya@sct-18-1bee-1581.univ-rouen.fr>
Date: Fri, 24 Jan 2020 09:32:47 +0100
Subject: [PATCH 38/39] modify pymanopt version in requirements

---
 requirements.txt | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/requirements.txt b/requirements.txt
index d62190aef..26053e862 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -4,7 +4,7 @@ cython
 matplotlib
 sphinx-gallery
 autograd
-pymanopt== 0.2.4, python_version < '3'
-pymanopt, python_version >= '3'
+pymanopt== 0.2.4, python_version < 3
+pymanopt, python_version >= 3
 cvxopt
 pytest

From 6d4ccaca7705646c9b46b1d01a001943b6c778a9 Mon Sep 17 00:00:00 2001
From: "Mokhtar Z. Alaya" <mzalaya@sct-18-1bee-1581.univ-rouen.fr>
Date: Fri, 24 Jan 2020 09:40:20 +0100
Subject: [PATCH 39/39] modify pymanopt version in requirements

---
 requirements.txt | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/requirements.txt b/requirements.txt
index 26053e862..c08822e45 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -4,7 +4,7 @@ cython
 matplotlib
 sphinx-gallery
 autograd
-pymanopt== 0.2.4, python_version < 3
-pymanopt, python_version >= 3
+pymanopt==0.2.4; python_version <'3'
+pymanopt; python_version >= '3'
 cvxopt
-pytest
+pytest
\ No newline at end of file