[MRG] Domain adaptation and unbalanced solvers with backend support (#343)

* First draft

* Add matrix inverse and square root to backend

* Eigen decomposition for older versions of pytorch (1.8.1 and older)

* Corrected eigen decomposition for pytorch 1.8.1 and older

* Spectral theorem is a thing

* Optimization

* small optimization

* More functions converted

* pep8

* remove a warning and prepare torch meshgrid for future torch release (which will change default indexing)

* dots and pep8

* Meshgrid corrected for older version and prepared for future versions changes

* New backend functions

* Base transport

* LinearTransport

* All transport classes + pep8

* PR added to release file

* Jcpot barycenter test

* unbalanced with backend

* pep8

* bug solve

* test of domain adaptation with backends

* solve bug for tic toc & macos

* solving scipy deprecation warning

* solving scipy deprecation warning attempt2

* solving scipy deprecation warning attempt3

* A warning is triggered when a float->int conversion is detected

* bug solve

* docs

* release file updated

* Better handling of float->int conversion in EMD

* Corrected test for is_floating_point

* docs

* release file updated

* cupy does not allow implicit cast

* fromnumpy

* added test

* test da tf jax

* test unbalanced with no provided histogram

* using type_as argument in unif function correctly

* pep8

* transport plan cast in emd changed behaviour, now trying to cast as histogram's dtype, defaulting to cost matrix

Co-authored-by: Rémi Flamary <remi.flamary@gmail.com>

7 files changed, 744 insertions, 381 deletions

diff --git a/ot/backend.py b/ot/backend.py
index 6e0bc3d..361ffba 100644
--- a/ot/backend.py
+++ b/ot/backend.py
@@ -87,7 +87,9 @@ Performance
 # License: MIT License
 
 import numpy as np
-import scipy.special as scipy
+import scipy
+import scipy.linalg
+import scipy.special as special
 from scipy.sparse import issparse, coo_matrix, csr_matrix
 import warnings
 import time
@@ -102,7 +104,7 @@ except ImportError:
 try:
     import jax
     import jax.numpy as jnp
-    import jax.scipy.special as jscipy
+    import jax.scipy.special as jspecial
     from jax.lib import xla_bridge
     jax_type = jax.numpy.ndarray
 except ImportError:
@@ -202,13 +204,29 @@ class Backend():
     def __str__(self):
         return self.__name__
 
-    # convert to numpy
-    def to_numpy(self, a):
+    # convert batch of tensors to numpy
+    def to_numpy(self, *arrays):
+        """Returns the numpy version of tensors"""
+        if len(arrays) == 1:
+            return self._to_numpy(arrays[0])
+        else:
+            return [self._to_numpy(array) for array in arrays]
+
+    # convert a tensor to numpy
+    def _to_numpy(self, a):
         """Returns the numpy version of a tensor"""
         raise NotImplementedError()
 
-    # convert from numpy
-    def from_numpy(self, a, type_as=None):
+    # convert batch of arrays from numpy
+    def from_numpy(self, *arrays, type_as=None):
+        """Creates tensors cloning a numpy array, with the given precision (defaulting to input's precision) and the given device (in case of GPUs)"""
+        if len(arrays) == 1:
+            return self._from_numpy(arrays[0], type_as=type_as)
+        else:
+            return [self._from_numpy(array, type_as=type_as) for array in arrays]
+
+    # convert an array from numpy
+    def _from_numpy(self, a, type_as=None):
         """Creates a tensor cloning a numpy array, with the given precision (defaulting to input's precision) and the given device (in case of GPUs)"""
         raise NotImplementedError()
 
@@ -536,6 +554,16 @@ class Backend():
         """
         raise NotImplementedError()
 
+    def argmin(self, a, axis=None):
+        r"""
+        Returns the indices of the minimum values of a tensor along given dimensions.
+
+        This function follows the api from :any:`numpy.argmin`
+
+        See: https://numpy.org/doc/stable/reference/generated/numpy.argmin.html
+        """
+        raise NotImplementedError()
+
     def mean(self, a, axis=None):
         r"""
         Computes the arithmetic mean of a tensor along given dimensions.
@@ -786,6 +814,72 @@ class Backend():
         """
         raise NotImplementedError()
 
+    def solve(self, a, b):
+        r"""
+        Solves a linear matrix equation, or system of linear scalar equations.
+
+        This function follows the api from :any:`numpy.linalg.solve`.
+
+        See: https://numpy.org/doc/stable/reference/generated/numpy.linalg.solve.html
+        """
+        raise NotImplementedError()
+
+    def trace(self, a):
+        r"""
+        Returns the sum along diagonals of the array.
+
+        This function follows the api from :any:`numpy.trace`.
+
+        See: https://numpy.org/doc/stable/reference/generated/numpy.trace.html
+        """
+        raise NotImplementedError()
+
+    def inv(self, a):
+        r"""
+        Computes the inverse of a matrix.
+
+        This function follows the api from :any:`scipy.linalg.inv`.
+
+        See: https://docs.scipy.org/doc/scipy/reference/generated/scipy.linalg.inv.html
+        """
+        raise NotImplementedError()
+
+    def sqrtm(self, a):
+        r"""
+        Computes the matrix square root. Requires input to be definite positive.
+
+        This function follows the api from :any:`scipy.linalg.sqrtm`.
+
+        See: https://docs.scipy.org/doc/scipy/reference/generated/scipy.linalg.sqrtm.html
+        """
+        raise NotImplementedError()
+
+    def isfinite(self, a):
+        r"""
+        Tests element-wise for finiteness (not infinity and not Not a Number).
+
+        This function follows the api from :any:`numpy.isfinite`.
+
+        See: https://numpy.org/doc/stable/reference/generated/numpy.isfinite.html
+        """
+        raise NotImplementedError()
+
+    def array_equal(self, a, b):
+        r"""
+        True if two arrays have the same shape and elements, False otherwise.
+
+        This function follows the api from :any:`numpy.array_equal`.
+
+        See: https://numpy.org/doc/stable/reference/generated/numpy.array_equal.html
+        """
+        raise NotImplementedError()
+
+    def is_floating_point(self, a):
+        r"""
+        Returns whether or not the input consists of floats
+        """
+        raise NotImplementedError()
+
 
 class NumpyBackend(Backend):
     """
@@ -802,10 +896,10 @@ class NumpyBackend(Backend):
 
     rng_ = np.random.RandomState()
 
-    def to_numpy(self, a):
+    def _to_numpy(self, a):
         return a
 
-    def from_numpy(self, a, type_as=None):
+    def _from_numpy(self, a, type_as=None):
         if type_as is None:
             return a
         elif isinstance(a, float):
@@ -936,6 +1030,9 @@ class NumpyBackend(Backend):
     def argmax(self, a, axis=None):
         return np.argmax(a, axis=axis)
 
+    def argmin(self, a, axis=None):
+        return np.argmin(a, axis=axis)
+
     def mean(self, a, axis=None):
         return np.mean(a, axis=axis)
 
@@ -955,7 +1052,7 @@ class NumpyBackend(Backend):
         return np.unique(a)
 
     def logsumexp(self, a, axis=None):
-        return scipy.logsumexp(a, axis=axis)
+        return special.logsumexp(a, axis=axis)
 
     def stack(self, arrays, axis=0):
         return np.stack(arrays, axis)
@@ -1004,8 +1101,11 @@ class NumpyBackend(Backend):
         else:
             return a
 
-    def where(self, condition, x, y):
-        return np.where(condition, x, y)
+    def where(self, condition, x=None, y=None):
+        if x is None and y is None:
+            return np.where(condition)
+        else:
+            return np.where(condition, x, y)
 
     def copy(self, a):
         return a.copy()
@@ -1046,6 +1146,27 @@ class NumpyBackend(Backend):
             results[key] = (t1 - t0) / n_runs
         return results
 
+    def solve(self, a, b):
+        return np.linalg.solve(a, b)
+
+    def trace(self, a):
+        return np.trace(a)
+
+    def inv(self, a):
+        return scipy.linalg.inv(a)
+
+    def sqrtm(self, a):
+        return scipy.linalg.sqrtm(a)
+
+    def isfinite(self, a):
+        return np.isfinite(a)
+
+    def array_equal(self, a, b):
+        return np.array_equal(a, b)
+
+    def is_floating_point(self, a):
+        return a.dtype.kind == "f"
+
 
 class JaxBackend(Backend):
     """
@@ -1075,13 +1196,15 @@ class JaxBackend(Backend):
                 jax.device_put(jnp.array(1, dtype=jnp.float64), d)
             ]
 
-    def to_numpy(self, a):
+    def _to_numpy(self, a):
         return np.array(a)
 
     def _change_device(self, a, type_as):
         return jax.device_put(a, type_as.device_buffer.device())
 
-    def from_numpy(self, a, type_as=None):
+    def _from_numpy(self, a, type_as=None):
+        if isinstance(a, float):
+            a = np.array(a)
         if type_as is None:
             return jnp.array(a)
         else:
@@ -1216,6 +1339,9 @@ class JaxBackend(Backend):
     def argmax(self, a, axis=None):
         return jnp.argmax(a, axis=axis)
 
+    def argmin(self, a, axis=None):
+        return jnp.argmin(a, axis=axis)
+
     def mean(self, a, axis=None):
         return jnp.mean(a, axis=axis)
 
@@ -1235,7 +1361,7 @@ class JaxBackend(Backend):
         return jnp.unique(a)
 
     def logsumexp(self, a, axis=None):
-        return jscipy.logsumexp(a, axis=axis)
+        return jspecial.logsumexp(a, axis=axis)
 
     def stack(self, arrays, axis=0):
         return jnp.stack(arrays, axis)
@@ -1293,8 +1419,11 @@ class JaxBackend(Backend):
         # Currently, JAX does not support sparse matrices
         return a
 
-    def where(self, condition, x, y):
-        return jnp.where(condition, x, y)
+    def where(self, condition, x=None, y=None):
+        if x is None and y is None:
+            return jnp.where(condition)
+        else:
+            return jnp.where(condition, x, y)
 
     def copy(self, a):
         # No need to copy, JAX arrays are immutable
@@ -1339,6 +1468,28 @@ class JaxBackend(Backend):
             results[key] = (t1 - t0) / n_runs
         return results
 
+    def solve(self, a, b):
+        return jnp.linalg.solve(a, b)
+
+    def trace(self, a):
+        return jnp.trace(a)
+
+    def inv(self, a):
+        return jnp.linalg.inv(a)
+
+    def sqrtm(self, a):
+        L, V = jnp.linalg.eigh(a)
+        return (V * jnp.sqrt(L)[None, :]) @ V.T
+
+    def isfinite(self, a):
+        return jnp.isfinite(a)
+
+    def array_equal(self, a, b):
+        return jnp.array_equal(a, b)
+
+    def is_floating_point(self, a):
+        return a.dtype.kind == "f"
+
 
 class TorchBackend(Backend):
     """
@@ -1384,10 +1535,10 @@ class TorchBackend(Backend):
 
         self.ValFunction = ValFunction
 
-    def to_numpy(self, a):
+    def _to_numpy(self, a):
         return a.cpu().detach().numpy()
 
-    def from_numpy(self, a, type_as=None):
+    def _from_numpy(self, a, type_as=None):
         if isinstance(a, float):
             a = np.array(a)
         if type_as is None:
@@ -1564,6 +1715,9 @@ class TorchBackend(Backend):
     def argmax(self, a, axis=None):
         return torch.argmax(a, dim=axis)
 
+    def argmin(self, a, axis=None):
+        return torch.argmin(a, dim=axis)
+
     def mean(self, a, axis=None):
         if axis is not None:
             return torch.mean(a, dim=axis)
@@ -1580,8 +1734,11 @@ class TorchBackend(Backend):
         return torch.linspace(start, stop, num, dtype=torch.float64)
 
     def meshgrid(self, a, b):
-        X, Y = torch.meshgrid(a, b)
-        return X.T, Y.T
+        try:
+            return torch.meshgrid(a, b, indexing="xy")
+        except TypeError:
+            X, Y = torch.meshgrid(a, b)
+            return X.T, Y.T
 
     def diag(self, a, k=0):
         return torch.diag(a, diagonal=k)
@@ -1659,8 +1816,11 @@ class TorchBackend(Backend):
         else:
             return a
 
-    def where(self, condition, x, y):
-        return torch.where(condition, x, y)
+    def where(self, condition, x=None, y=None):
+        if x is None and y is None:
+            return torch.where(condition)
+        else:
+            return torch.where(condition, x, y)
 
     def copy(self, a):
         return torch.clone(a)
@@ -1718,6 +1878,28 @@ class TorchBackend(Backend):
             torch.cuda.empty_cache()
         return results
 
+    def solve(self, a, b):
+        return torch.linalg.solve(a, b)
+
+    def trace(self, a):
+        return torch.trace(a)
+
+    def inv(self, a):
+        return torch.linalg.inv(a)
+
+    def sqrtm(self, a):
+        L, V = torch.linalg.eigh(a)
+        return (V * torch.sqrt(L)[None, :]) @ V.T
+
+    def isfinite(self, a):
+        return torch.isfinite(a)
+
+    def array_equal(self, a, b):
+        return torch.equal(a, b)
+
+    def is_floating_point(self, a):
+        return a.dtype.is_floating_point
+
 
 class CupyBackend(Backend):  # pragma: no cover
     """
@@ -1741,10 +1923,12 @@ class CupyBackend(Backend):  # pragma: no cover
             cp.array(1, dtype=cp.float64)
         ]
 
-    def to_numpy(self, a):
+    def _to_numpy(self, a):
         return cp.asnumpy(a)
 
-    def from_numpy(self, a, type_as=None):
+    def _from_numpy(self, a, type_as=None):
+        if isinstance(a, float):
+            a = np.array(a)
         if type_as is None:
             return cp.asarray(a)
         else:
@@ -1884,6 +2068,9 @@ class CupyBackend(Backend):  # pragma: no cover
     def argmax(self, a, axis=None):
         return cp.argmax(a, axis=axis)
 
+    def argmin(self, a, axis=None):
+        return cp.argmin(a, axis=axis)
+
     def mean(self, a, axis=None):
         return cp.mean(a, axis=axis)
 
@@ -1982,8 +2169,11 @@ class CupyBackend(Backend):  # pragma: no cover
         else:
             return a
 
-    def where(self, condition, x, y):
-        return cp.where(condition, x, y)
+    def where(self, condition, x=None, y=None):
+        if x is None and y is None:
+            return cp.where(condition)
+        else:
+            return cp.where(condition, x, y)
 
     def copy(self, a):
         return a.copy()
@@ -2035,6 +2225,28 @@ class CupyBackend(Backend):  # pragma: no cover
         pinned_mempool.free_all_blocks()
         return results
 
+    def solve(self, a, b):
+        return cp.linalg.solve(a, b)
+
+    def trace(self, a):
+        return cp.trace(a)
+
+    def inv(self, a):
+        return cp.linalg.inv(a)
+
+    def sqrtm(self, a):
+        L, V = cp.linalg.eigh(a)
+        return (V * self.sqrt(L)[None, :]) @ V.T
+
+    def isfinite(self, a):
+        return cp.isfinite(a)
+
+    def array_equal(self, a, b):
+        return cp.array_equal(a, b)
+
+    def is_floating_point(self, a):
+        return a.dtype.kind == "f"
+
 
 class TensorflowBackend(Backend):
 
@@ -2060,13 +2272,16 @@ class TensorflowBackend(Backend):
                 "To use TensorflowBackend, you need to activate the tensorflow "
                 "numpy API. You can activate it by running: \n"
                 "from tensorflow.python.ops.numpy_ops import np_config\n"
-                "np_config.enable_numpy_behavior()"
+                "np_config.enable_numpy_behavior()",
+                stacklevel=2
             )
 
-    def to_numpy(self, a):
+    def _to_numpy(self, a):
         return a.numpy()
 
-    def from_numpy(self, a, type_as=None):
+    def _from_numpy(self, a, type_as=None):
+        if isinstance(a, float):
+            a = np.array(a)
         if not isinstance(a, self.__type__):
             if type_as is None:
                 return tf.convert_to_tensor(a)
@@ -2208,6 +2423,9 @@ class TensorflowBackend(Backend):
     def argmax(self, a, axis=None):
         return tnp.argmax(a, axis=axis)
 
+    def argmin(self, a, axis=None):
+        return tnp.argmin(a, axis=axis)
+
     def mean(self, a, axis=None):
         return tnp.mean(a, axis=axis)
 
@@ -2309,8 +2527,11 @@ class TensorflowBackend(Backend):
         else:
             return a
 
-    def where(self, condition, x, y):
-        return tnp.where(condition, x, y)
+    def where(self, condition, x=None, y=None):
+        if x is None and y is None:
+            return tnp.where(condition)
+        else:
+            return tnp.where(condition, x, y)
 
     def copy(self, a):
         return tf.identity(a)
@@ -2364,3 +2585,24 @@ class TensorflowBackend(Backend):
                     results[key] = (t1 - t0) / n_runs
 
         return results
+
+    def solve(self, a, b):
+        return tf.linalg.solve(a, b)
+
+    def trace(self, a):
+        return tf.linalg.trace(a)
+
+    def inv(self, a):
+        return tf.linalg.inv(a)
+
+    def sqrtm(self, a):
+        return tf.linalg.sqrtm(a)
+
+    def isfinite(self, a):
+        return tnp.isfinite(a)
+
+    def array_equal(self, a, b):
+        return tnp.array_equal(a, b)
+
+    def is_floating_point(self, a):
+        return a.dtype.is_floating
diff --git a/ot/bregman.py b/ot/bregman.py
index fc20175..c06af2f 100644
--- a/ot/bregman.py
+++ b/ot/bregman.py
@@ -2525,8 +2525,7 @@ def unmix(a, D, M, M0, h0, reg, reg0, alpha, numItermax=1000,
         # geometric interpolation
         delta = nx.exp(alpha * nx.log(other) + (1 - alpha) * nx.log(inv_new))
         K = projR(K, delta)
-        K0 = nx.dot(nx.diag(nx.dot(D.T, delta / inv_new)), K0)
-
+        K0 = nx.dot(D.T, delta / inv_new)[:, None] * K0
         err = nx.norm(nx.sum(K0, axis=1) - old)
         old = new
         if log:
@@ -2656,16 +2655,16 @@ def jcpot_barycenter(Xs, Ys, Xt, reg, metric='sqeuclidean', numItermax=100,
             classes = nx.unique(Ys[d])
 
         # build the corresponding D_1 and D_2 matrices
-        Dtmp1 = nx.zeros((nbclasses, nsk), type_as=Xs[0])
-        Dtmp2 = nx.zeros((nbclasses, nsk), type_as=Xs[0])
+        Dtmp1 = np.zeros((nbclasses, nsk))
+        Dtmp2 = np.zeros((nbclasses, nsk))
 
         for c in classes:
-            nbelemperclass = nx.sum(Ys[d] == c)
+            nbelemperclass = float(nx.sum(Ys[d] == c))
             if nbelemperclass != 0:
-                Dtmp1[int(c), Ys[d] == c] = 1.
-                Dtmp2[int(c), Ys[d] == c] = 1. / (nbelemperclass)
-        D1.append(Dtmp1)
-        D2.append(Dtmp2)
+                Dtmp1[int(c), nx.to_numpy(Ys[d] == c)] = 1.
+                Dtmp2[int(c), nx.to_numpy(Ys[d] == c)] = 1. / (nbelemperclass)
+        D1.append(nx.from_numpy(Dtmp1, type_as=Xs[0]))
+        D2.append(nx.from_numpy(Dtmp2, type_as=Xs[0]))
 
         # build the cost matrix and the Gibbs kernel
         Mtmp = dist(Xs[d], Xt, metric=metric)
diff --git a/ot/da.py b/ot/da.py
index 841f31a..0b9737e 100644
--- a/ot/da.py
+++ b/ot/da.py
@@ -12,12 +12,12 @@ Domain adaptation with optimal transport
 # License: MIT License
 
 import numpy as np
-import scipy.linalg as linalg
 
+from .backend import get_backend
 from .bregman import sinkhorn, jcpot_barycenter
 from .lp import emd
 from .utils import unif, dist, kernel, cost_normalization, label_normalization, laplacian, dots
-from .utils import check_params, BaseEstimator
+from .utils import list_to_array, check_params, BaseEstimator
 from .unbalanced import sinkhorn_unbalanced
 from .optim import cg
 from .optim import gcg
@@ -60,13 +60,13 @@ def sinkhorn_lpl1_mm(a, labels_a, b, M, reg, eta=0.1, numItermax=10,
 
     Parameters
     ----------
-    a : np.ndarray (ns,)
+    a : array-like (ns,)
         samples weights in the source domain
-    labels_a : np.ndarray (ns,)
+    labels_a : array-like (ns,)
         labels of samples in the source domain
-    b : np.ndarray (nt,)
+    b : array-like (nt,)
         samples weights in the target domain
-    M : np.ndarray (ns,nt)
+    M : array-like (ns,nt)
         loss matrix
     reg : float
         Regularization term for entropic regularization >0
@@ -86,7 +86,7 @@ def sinkhorn_lpl1_mm(a, labels_a, b, M, reg, eta=0.1, numItermax=10,
 
     Returns
     -------
-    gamma : (ns, nt) ndarray
+    gamma : (ns, nt) array-like
         Optimal transportation matrix for the given parameters
     log : dict
         log dictionary return only if log==True in parameters
@@ -111,26 +111,28 @@ def sinkhorn_lpl1_mm(a, labels_a, b, M, reg, eta=0.1, numItermax=10,
     ot.optim.cg : General regularized OT
 
     """
+    a, labels_a, b, M = list_to_array(a, labels_a, b, M)
+    nx = get_backend(a, labels_a, b, M)
+
     p = 0.5
     epsilon = 1e-3
 
     indices_labels = []
-    classes = np.unique(labels_a)
+    classes = nx.unique(labels_a)
     for c in classes:
-        idxc, = np.where(labels_a == c)
+        idxc, = nx.where(labels_a == c)
         indices_labels.append(idxc)
 
-    W = np.zeros(M.shape)
-
+    W = nx.zeros(M.shape, type_as=M)
     for cpt in range(numItermax):
         Mreg = M + eta * W
         transp = sinkhorn(a, b, Mreg, reg, numItermax=numInnerItermax,
                           stopThr=stopInnerThr)
         # the transport has been computed. Check if classes are really
         # separated
-        W = np.ones(M.shape)
+        W = nx.ones(M.shape, type_as=M)
         for (i, c) in enumerate(classes):
-            majs = np.sum(transp[indices_labels[i]], axis=0)
+            majs = nx.sum(transp[indices_labels[i]], axis=0)
             majs = p * ((majs + epsilon) ** (p - 1))
             W[indices_labels[i]] = majs
 
@@ -174,13 +176,13 @@ def sinkhorn_l1l2_gl(a, labels_a, b, M, reg, eta=0.1, numItermax=10,
 
     Parameters
     ----------
-    a : np.ndarray (ns,)
+    a : array-like (ns,)
         samples weights in the source domain
-    labels_a : np.ndarray (ns,)
+    labels_a : array-like (ns,)
         labels of samples in the source domain
-    b : np.ndarray (nt,)
+    b : array-like (nt,)
         samples in the target domain
-    M : np.ndarray (ns,nt)
+    M : array-like (ns,nt)
         loss matrix
     reg : float
         Regularization term for entropic regularization >0
@@ -200,7 +202,7 @@ def sinkhorn_l1l2_gl(a, labels_a, b, M, reg, eta=0.1, numItermax=10,
 
     Returns
     -------
-    gamma : (ns, nt) ndarray
+    gamma : (ns, nt) array-like
         Optimal transportation matrix for the given parameters
     log : dict
         log dictionary return only if log==True in parameters
@@ -222,22 +224,25 @@ def sinkhorn_l1l2_gl(a, labels_a, b, M, reg, eta=0.1, numItermax=10,
     ot.optim.gcg : Generalized conditional gradient for OT problems
 
     """
-    lstlab = np.unique(labels_a)
+    a, labels_a, b, M = list_to_array(a, labels_a, b, M)
+    nx = get_backend(a, labels_a, b, M)
+
+    lstlab = nx.unique(labels_a)
 
     def f(G):
         res = 0
         for i in range(G.shape[1]):
             for lab in lstlab:
                 temp = G[labels_a == lab, i]
-                res += np.linalg.norm(temp)
+                res += nx.norm(temp)
         return res
 
     def df(G):
-        W = np.zeros(G.shape)
+        W = nx.zeros(G.shape, type_as=G)
         for i in range(G.shape[1]):
             for lab in lstlab:
                 temp = G[labels_a == lab, i]
-                n = np.linalg.norm(temp)
+                n = nx.norm(temp)
                 if n:
                     W[labels_a == lab, i] = temp / n
         return W
@@ -289,9 +294,9 @@ def joint_OT_mapping_linear(xs, xt, mu=1, eta=0.001, bias=False, verbose=False,
 
     Parameters
     ----------
-    xs : np.ndarray (ns,d)
+    xs : array-like (ns,d)
         samples in the source domain
-    xt : np.ndarray (nt,d)
+    xt : array-like (nt,d)
         samples in the target domain
     mu : float,optional
         Weight for the linear OT loss (>0)
@@ -315,9 +320,9 @@ def joint_OT_mapping_linear(xs, xt, mu=1, eta=0.001, bias=False, verbose=False,
 
     Returns
     -------
-    gamma : (ns, nt) ndarray
+    gamma : (ns, nt) array-like
         Optimal transportation matrix for the given parameters
-    L : (d, d) ndarray
+    L : (d, d) array-like
         Linear mapping matrix ((:math:`d+1`, `d`) if bias)
     log : dict
         log dictionary return only if log==True in parameters
@@ -336,13 +341,15 @@ def joint_OT_mapping_linear(xs, xt, mu=1, eta=0.001, bias=False, verbose=False,
     ot.optim.cg : General regularized OT
 
     """
+    xs, xt = list_to_array(xs, xt)
+    nx = get_backend(xs, xt)
 
     ns, nt, d = xs.shape[0], xt.shape[0], xt.shape[1]
 
     if bias:
-        xs1 = np.hstack((xs, np.ones((ns, 1))))
-        xstxs = xs1.T.dot(xs1)
-        Id = np.eye(d + 1)
+        xs1 = nx.concatenate((xs, nx.ones((ns, 1), type_as=xs)), axis=1)
+        xstxs = nx.dot(xs1.T, xs1)
+        Id = nx.eye(d + 1, type_as=xs)
         Id[-1] = 0
         I0 = Id[:, :-1]
 
@@ -350,8 +357,8 @@ def joint_OT_mapping_linear(xs, xt, mu=1, eta=0.001, bias=False, verbose=False,
             return x[:-1, :]
     else:
         xs1 = xs
-        xstxs = xs1.T.dot(xs1)
-        Id = np.eye(d)
+        xstxs = nx.dot(xs1.T, xs1)
+        Id = nx.eye(d, type_as=xs)
         I0 = Id
 
         def sel(x):
@@ -360,7 +367,8 @@ def joint_OT_mapping_linear(xs, xt, mu=1, eta=0.001, bias=False, verbose=False,
     if log:
         log = {'err': []}
 
-    a, b = unif(ns), unif(nt)
+    a = unif(ns, type_as=xs)
+    b = unif(nt, type_as=xt)
     M = dist(xs, xt) * ns
     G = emd(a, b, M)
 
@@ -368,23 +376,26 @@ def joint_OT_mapping_linear(xs, xt, mu=1, eta=0.001, bias=False, verbose=False,
 
     def loss(L, G):
         """Compute full loss"""
-        return np.sum((xs1.dot(L) - ns * G.dot(xt)) ** 2) + mu * \
-            np.sum(G * M) + eta * np.sum(sel(L - I0) ** 2)
+        return (
+            nx.sum((nx.dot(xs1, L) - ns * nx.dot(G, xt)) ** 2)
+            + mu * nx.sum(G * M)
+            + eta * nx.sum(sel(L - I0) ** 2)
+        )
 
     def solve_L(G):
         """ solve L problem with fixed G (least square)"""
-        xst = ns * G.dot(xt)
-        return np.linalg.solve(xstxs + eta * Id, xs1.T.dot(xst) + eta * I0)
+        xst = ns * nx.dot(G, xt)
+        return nx.solve(xstxs + eta * Id, nx.dot(xs1.T, xst) + eta * I0)
 
     def solve_G(L, G0):
         """Update G with CG algorithm"""
-        xsi = xs1.dot(L)
+        xsi = nx.dot(xs1, L)
 
         def f(G):
-            return np.sum((xsi - ns * G.dot(xt)) ** 2)
+            return nx.sum((xsi - ns * nx.dot(G, xt)) ** 2)
 
         def df(G):
-            return -2 * ns * (xsi - ns * G.dot(xt)).dot(xt.T)
+            return -2 * ns * nx.dot(xsi - ns * nx.dot(G, xt), xt.T)
 
         G = cg(a, b, M, 1.0 / mu, f, df, G0=G0,
                numItermax=numInnerItermax, stopThr=stopInnerThr)
@@ -481,9 +492,9 @@ def joint_OT_mapping_kernel(xs, xt, mu=1, eta=0.001, kerneltype='gaussian',
 
     Parameters
     ----------
-    xs : np.ndarray (ns,d)
+    xs : array-like (ns,d)
         samples in the source domain
-    xt : np.ndarray (nt,d)
+    xt : array-like (nt,d)
         samples in the target domain
     mu : float,optional
         Weight for the linear OT loss (>0)
@@ -513,9 +524,9 @@ def joint_OT_mapping_kernel(xs, xt, mu=1, eta=0.001, kerneltype='gaussian',
 
     Returns
     -------
-    gamma : (ns, nt) ndarray
+    gamma : (ns, nt) array-like
         Optimal transportation matrix for the given parameters
-    L : (ns, d) ndarray
+    L : (ns, d) array-like
         Nonlinear mapping matrix ((:math:`n_s+1`, `d`) if bias)
     log : dict
         log dictionary return only if log==True in parameters
@@ -534,15 +545,17 @@ def joint_OT_mapping_kernel(xs, xt, mu=1, eta=0.001, kerneltype='gaussian',
     ot.optim.cg : General regularized OT
 
     """
+    xs, xt = list_to_array(xs, xt)
+    nx = get_backend(xs, xt)
 
     ns, nt = xs.shape[0], xt.shape[0]
 
     K = kernel(xs, xs, method=kerneltype, sigma=sigma)
     if bias:
-        K1 = np.hstack((K, np.ones((ns, 1))))
-        Id = np.eye(ns + 1)
+        K1 = nx.concatenate((K, nx.ones((ns, 1), type_as=xs)), axis=1)
+        Id = nx.eye(ns + 1, type_as=xs)
         Id[-1] = 0
-        Kp = np.eye(ns + 1)
+        Kp = nx.eye(ns + 1, type_as=xs)
         Kp[:ns, :ns] = K
 
         # ls regu
@@ -550,12 +563,12 @@ def joint_OT_mapping_kernel(xs, xt, mu=1, eta=0.001, kerneltype='gaussian',
         # Kreg=I
 
         # RKHS regul
-        K0 = K1.T.dot(K1) + eta * Kp
+        K0 = nx.dot(K1.T, K1) + eta * Kp
         Kreg = Kp
 
     else:
         K1 = K
-        Id = np.eye(ns)
+        Id = nx.eye(ns, type_as=xs)
 
         # ls regul
         # K0 = K1.T.dot(K1)+eta*I
@@ -568,7 +581,8 @@ def joint_OT_mapping_kernel(xs, xt, mu=1, eta=0.001, kerneltype='gaussian',
     if log:
         log = {'err': []}
 
-    a, b = unif(ns), unif(nt)
+    a = unif(ns, type_as=xs)
+    b = unif(nt, type_as=xt)
     M = dist(xs, xt) * ns
     G = emd(a, b, M)
 
@@ -576,28 +590,31 @@ def joint_OT_mapping_kernel(xs, xt, mu=1, eta=0.001, kerneltype='gaussian',
 
     def loss(L, G):
         """Compute full loss"""
-        return np.sum((K1.dot(L) - ns * G.dot(xt)) ** 2) + mu * \
-            np.sum(G * M) + eta * np.trace(L.T.dot(Kreg).dot(L))
+        return (
+            nx.sum((nx.dot(K1, L) - ns * nx.dot(G, xt)) ** 2)
+            + mu * nx.sum(G * M)
+            + eta * nx.trace(dots(L.T, Kreg, L))
+        )
 
     def solve_L_nobias(G):
         """ solve L problem with fixed G (least square)"""
-        xst = ns * G.dot(xt)
-        return np.linalg.solve(K0, xst)
+        xst = ns * nx.dot(G, xt)
+        return nx.solve(K0, xst)
 
     def solve_L_bias(G):
         """ solve L problem with fixed G (least square)"""
-        xst = ns * G.dot(xt)
-        return np.linalg.solve(K0, K1.T.dot(xst))
+        xst = ns * nx.dot(G, xt)
+        return nx.solve(K0, nx.dot(K1.T, xst))
 
     def solve_G(L, G0):
         """Update G with CG algorithm"""
-        xsi = K1.dot(L)
+        xsi = nx.dot(K1, L)
 
         def f(G):
-            return np.sum((xsi - ns * G.dot(xt)) ** 2)
+            return nx.sum((xsi - ns * nx.dot(G, xt)) ** 2)
 
         def df(G):
-            return -2 * ns * (xsi - ns * G.dot(xt)).dot(xt.T)
+            return -2 * ns * nx.dot(xsi - ns * nx.dot(G, xt), xt.T)
 
         G = cg(a, b, M, 1.0 / mu, f, df, G0=G0,
                numItermax=numInnerItermax, stopThr=stopInnerThr)
@@ -681,15 +698,15 @@ def OT_mapping_linear(xs, xt, reg=1e-6, ws=None,
 
     Parameters
     ----------
-    xs : np.ndarray (ns,d)
+    xs : array-like (ns,d)
         samples in the source domain
-    xt : np.ndarray (nt,d)
+    xt : array-like (nt,d)
         samples in the target domain
     reg : float,optional
         regularization added to the diagonals of covariances (>0)
-    ws : np.ndarray (ns,1), optional
+    ws : array-like (ns,1), optional
         weights for the source samples
-    wt : np.ndarray (ns,1), optional
+    wt : array-like (ns,1), optional
         weights for the target samples
     bias: boolean, optional
         estimate bias :math:`\mathbf{b}` else :math:`\mathbf{b} = 0` (default:True)
@@ -699,9 +716,9 @@ def OT_mapping_linear(xs, xt, reg=1e-6, ws=None,
 
     Returns
     -------
-    A : (d, d) ndarray
+    A : (d, d) array-like
         Linear operator
-    b : (1, d) ndarray
+    b : (1, d) array-like
         bias
     log : dict
         log dictionary return only if log==True in parameters
@@ -719,36 +736,38 @@ def OT_mapping_linear(xs, xt, reg=1e-6, ws=None,
 
 
     """
+    xs, xt = list_to_array(xs, xt)
+    nx = get_backend(xs, xt)
 
     d = xs.shape[1]
 
     if bias:
-        mxs = xs.mean(0, keepdims=True)
-        mxt = xt.mean(0, keepdims=True)
+        mxs = nx.mean(xs, axis=0)[None, :]
+        mxt = nx.mean(xt, axis=0)[None, :]
 
         xs = xs - mxs
         xt = xt - mxt
     else:
-        mxs = np.zeros((1, d))
-        mxt = np.zeros((1, d))
+        mxs = nx.zeros((1, d), type_as=xs)
+        mxt = nx.zeros((1, d), type_as=xs)
 
     if ws is None:
-        ws = np.ones((xs.shape[0], 1)) / xs.shape[0]
+        ws = nx.ones((xs.shape[0], 1), type_as=xs) / xs.shape[0]
 
     if wt is None:
-        wt = np.ones((xt.shape[0], 1)) / xt.shape[0]
+        wt = nx.ones((xt.shape[0], 1), type_as=xt) / xt.shape[0]
 
-    Cs = (xs * ws).T.dot(xs) / ws.sum() + reg * np.eye(d)
-    Ct = (xt * wt).T.dot(xt) / wt.sum() + reg * np.eye(d)
+    Cs = nx.dot((xs * ws).T, xs) / nx.sum(ws) + reg * nx.eye(d, type_as=xs)
+    Ct = nx.dot((xt * wt).T, xt) / nx.sum(wt) + reg * nx.eye(d, type_as=xt)
 
-    Cs12 = linalg.sqrtm(Cs)
-    Cs_12 = linalg.inv(Cs12)
+    Cs12 = nx.sqrtm(Cs)
+    Cs_12 = nx.inv(Cs12)
 
-    M0 = linalg.sqrtm(Cs12.dot(Ct.dot(Cs12)))
+    M0 = nx.sqrtm(dots(Cs12, Ct, Cs12))
 
-    A = Cs_12.dot(M0.dot(Cs_12))
+    A = dots(Cs_12, M0, Cs_12)
 
-    b = mxt - mxs.dot(A)
+    b = mxt - nx.dot(mxs, A)
 
     if log:
         log = {}
@@ -798,15 +817,15 @@ def emd_laplace(a, b, xs, xt, M, sim='knn', sim_param=None, reg='pos', eta=1, al
 
     Parameters
     ----------
-    a : np.ndarray (ns,)
+    a : array-like (ns,)
         samples weights in the source domain
-    b : np.ndarray (nt,)
+    b : array-like (nt,)
         samples weights in the target domain
-    xs : np.ndarray (ns,d)
+    xs : array-like (ns,d)
         samples in the source domain
-    xt : np.ndarray (nt,d)
+    xt : array-like (nt,d)
         samples in the target domain
-    M : np.ndarray (ns,nt)
+    M : array-like (ns,nt)
         loss matrix
     sim : string, optional
         Type of similarity ('knn' or 'gauss') used to construct the Laplacian.
@@ -834,7 +853,7 @@ def emd_laplace(a, b, xs, xt, M, sim='knn', sim_param=None, reg='pos', eta=1, al
 
     Returns
     -------
-    gamma : (ns, nt) ndarray
+    gamma : (ns, nt) array-like
         Optimal transportation matrix for the given parameters
     log : dict
         log dictionary return only if log==True in parameters
@@ -862,9 +881,12 @@ def emd_laplace(a, b, xs, xt, M, sim='knn', sim_param=None, reg='pos', eta=1, al
         raise ValueError(
             'Similarity parameter should be an int or a float. Got {type} instead.'.format(type=type(sim_param).__name__))
 
+    a, b, xs, xt, M = list_to_array(a, b, xs, xt, M)
+    nx = get_backend(a, b, xs, xt, M)
+
     if sim == 'gauss':
         if sim_param is None:
-            sim_param = 1 / (2 * (np.mean(dist(xs, xs, 'sqeuclidean')) ** 2))
+            sim_param = 1 / (2 * (nx.mean(dist(xs, xs, 'sqeuclidean')) ** 2))
         sS = kernel(xs, xs, method=sim, sigma=sim_param)
         sT = kernel(xt, xt, method=sim, sigma=sim_param)
 
@@ -874,9 +896,13 @@ def emd_laplace(a, b, xs, xt, M, sim='knn', sim_param=None, reg='pos', eta=1, al
 
         from sklearn.neighbors import kneighbors_graph
 
-        sS = kneighbors_graph(X=xs, n_neighbors=int(sim_param)).toarray()
+        sS = nx.from_numpy(kneighbors_graph(
+            X=nx.to_numpy(xs), n_neighbors=int(sim_param)
+        ).toarray(), type_as=xs)
         sS = (sS + sS.T) / 2
-        sT = kneighbors_graph(xt, n_neighbors=int(sim_param)).toarray()
+        sT = nx.from_numpy(kneighbors_graph(
+            X=nx.to_numpy(xt), n_neighbors=int(sim_param)
+        ).toarray(), type_as=xt)
         sT = (sT + sT.T) / 2
     else:
         raise ValueError('Unknown similarity type {sim}. Currently supported similarity types are "knn" and "gauss".'.format(sim=sim))
@@ -885,12 +911,14 @@ def emd_laplace(a, b, xs, xt, M, sim='knn', sim_param=None, reg='pos', eta=1, al
     lT = laplacian(sT)
 
     def f(G):
-        return alpha * np.trace(np.dot(xt.T, np.dot(G.T, np.dot(lS, np.dot(G, xt))))) \
-            + (1 - alpha) * np.trace(np.dot(xs.T, np.dot(G, np.dot(lT, np.dot(G.T, xs)))))
+        return (
+            alpha * nx.trace(dots(xt.T, G.T, lS, G, xt))
+            + (1 - alpha) * nx.trace(dots(xs.T, G, lT, G.T, xs))
+        )
 
     ls2 = lS + lS.T
     lt2 = lT + lT.T
-    xt2 = np.dot(xt, xt.T)
+    xt2 = nx.dot(xt, xt.T)
 
     if reg == 'disp':
         Cs = -eta * alpha / xs.shape[0] * dots(ls2, xs, xt.T)
@@ -898,8 +926,10 @@ def emd_laplace(a, b, xs, xt, M, sim='knn', sim_param=None, reg='pos', eta=1, al
         M = M + Cs + Ct
 
     def df(G):
-        return alpha * np.dot(ls2, np.dot(G, xt2))\
-            + (1 - alpha) * np.dot(xs, np.dot(xs.T, np.dot(G, lt2)))
+        return (
+            alpha * dots(ls2, G, xt2)
+            + (1 - alpha) * dots(xs, xs.T, G, lt2)
+        )
 
     return cg(a, b, M, reg=eta, f=f, df=df, G0=None, numItermax=numItermax, numItermaxEmd=numInnerItermax,
               stopThr=stopThr, stopThr2=stopInnerThr, verbose=verbose, log=log)
@@ -919,7 +949,7 @@ def distribution_estimation_uniform(X):
         The uniform distribution estimated from :math:`\mathbf{X}`
     """
 
-    return unif(X.shape[0])
+    return unif(X.shape[0], type_as=X)
 
 
 class BaseTransport(BaseEstimator):
@@ -973,6 +1003,7 @@ class BaseTransport(BaseEstimator):
         self : object
             Returns self.
         """
+        nx = self._get_backend(Xs, ys, Xt, yt)
 
         # check the necessary inputs parameters are here
         if check_params(Xs=Xs, Xt=Xt):
@@ -984,14 +1015,14 @@ class BaseTransport(BaseEstimator):
             if (ys is not None) and (yt is not None):
 
                 if self.limit_max != np.infty:
-                    self.limit_max = self.limit_max * np.max(self.cost_)
+                    self.limit_max = self.limit_max * nx.max(self.cost_)
 
                 # assumes labeled source samples occupy the first rows
                 # and labeled target samples occupy the first columns
-                classes = [c for c in np.unique(ys) if c != -1]
+                classes = [c for c in nx.unique(ys) if c != -1]
                 for c in classes:
-                    idx_s = np.where((ys != c) & (ys != -1))
-                    idx_t = np.where(yt == c)
+                    idx_s = nx.where((ys != c) & (ys != -1))
+                    idx_t = nx.where(yt == c)
 
                     # all the coefficients corresponding to a source sample
                     # and a target sample :
@@ -1062,23 +1093,24 @@ class BaseTransport(BaseEstimator):
         transp_Xs : array-like, shape (n_source_samples, n_features)
             The transport source samples.
         """
+        nx = self.nx
 
         # check the necessary inputs parameters are here
         if check_params(Xs=Xs):
 
-            if np.array_equal(self.xs_, Xs):
+            if nx.array_equal(self.xs_, Xs):
 
                 # perform standard barycentric mapping
-                transp = self.coupling_ / np.sum(self.coupling_, 1)[:, None]
+                transp = self.coupling_ / nx.sum(self.coupling_, axis=1)[:, None]
 
                 # set nans to 0
-                transp[~ np.isfinite(transp)] = 0
+                transp[~ nx.isfinite(transp)] = 0
 
                 # compute transported samples
-                transp_Xs = np.dot(transp, self.xt_)
+                transp_Xs = nx.dot(transp, self.xt_)
             else:
                 # perform out of sample mapping
-                indices = np.arange(Xs.shape[0])
+                indices = nx.arange(Xs.shape[0])
                 batch_ind = [
                     indices[i:i + batch_size]
                     for i in range(0, len(indices), batch_size)]
@@ -1087,20 +1119,20 @@ class BaseTransport(BaseEstimator):
                 for bi in batch_ind:
                     # get the nearest neighbor in the source domain
                     D0 = dist(Xs[bi], self.xs_)
-                    idx = np.argmin(D0, axis=1)
+                    idx = nx.argmin(D0, axis=1)
 
                     # transport the source samples
-                    transp = self.coupling_ / np.sum(
-                        self.coupling_, 1)[:, None]
-                    transp[~ np.isfinite(transp)] = 0
-                    transp_Xs_ = np.dot(transp, self.xt_)
+                    transp = self.coupling_ / nx.sum(
+                        self.coupling_, axis=1)[:, None]
+                    transp[~ nx.isfinite(transp)] = 0
+                    transp_Xs_ = nx.dot(transp, self.xt_)
 
                     # define the transported points
                     transp_Xs_ = transp_Xs_[idx, :] + Xs[bi] - self.xs_[idx, :]
 
                     transp_Xs.append(transp_Xs_)
 
-                transp_Xs = np.concatenate(transp_Xs, axis=0)
+                transp_Xs = nx.concatenate(transp_Xs, axis=0)
 
             return transp_Xs
 
@@ -1127,26 +1159,27 @@ class BaseTransport(BaseEstimator):
            International Conference on Artificial Intelligence and Statistics (AISTATS), 2019.
 
         """
+        nx = self.nx
 
         # check the necessary inputs parameters are here
         if check_params(ys=ys):
 
-            ysTemp = label_normalization(np.copy(ys))
-            classes = np.unique(ysTemp)
+            ysTemp = label_normalization(nx.copy(ys))
+            classes = nx.unique(ysTemp)
             n = len(classes)
-            D1 = np.zeros((n, len(ysTemp)))
+            D1 = nx.zeros((n, len(ysTemp)), type_as=self.coupling_)
 
             # perform label propagation
-            transp = self.coupling_ / np.sum(self.coupling_, 0, keepdims=True)
+            transp = self.coupling_ / nx.sum(self.coupling_, axis=0)[None, :]
 
             # set nans to 0
-            transp[~ np.isfinite(transp)] = 0
+            transp[~ nx.isfinite(transp)] = 0
 
             for c in classes:
                 D1[int(c), ysTemp == c] = 1
 
             # compute propagated labels
-            transp_ys = np.dot(D1, transp)
+            transp_ys = nx.dot(D1, transp)
 
             return transp_ys.T
 
@@ -1176,23 +1209,24 @@ class BaseTransport(BaseEstimator):
         transp_Xt : array-like, shape (n_source_samples, n_features)
             The transported target samples.
         """
+        nx = self.nx
 
         # check the necessary inputs parameters are here
         if check_params(Xt=Xt):
 
-            if np.array_equal(self.xt_, Xt):
+            if nx.array_equal(self.xt_, Xt):
 
                 # perform standard barycentric mapping
-                transp_ = self.coupling_.T / np.sum(self.coupling_, 0)[:, None]
+                transp_ = self.coupling_.T / nx.sum(self.coupling_, 0)[:, None]
 
                 # set nans to 0
-                transp_[~ np.isfinite(transp_)] = 0
+                transp_[~ nx.isfinite(transp_)] = 0
 
                 # compute transported samples
-                transp_Xt = np.dot(transp_, self.xs_)
+                transp_Xt = nx.dot(transp_, self.xs_)
             else:
                 # perform out of sample mapping
-                indices = np.arange(Xt.shape[0])
+                indices = nx.arange(Xt.shape[0])
                 batch_ind = [
                     indices[i:i + batch_size]
                     for i in range(0, len(indices), batch_size)]
@@ -1200,20 +1234,20 @@ class BaseTransport(BaseEstimator):
                 transp_Xt = []
                 for bi in batch_ind:
                     D0 = dist(Xt[bi], self.xt_)
-                    idx = np.argmin(D0, axis=1)
+                    idx = nx.argmin(D0, axis=1)
 
                     # transport the target samples
-                    transp_ = self.coupling_.T / np.sum(
+                    transp_ = self.coupling_.T / nx.sum(
                         self.coupling_, 0)[:, None]
-                    transp_[~ np.isfinite(transp_)] = 0
-                    transp_Xt_ = np.dot(transp_, self.xs_)
+                    transp_[~ nx.isfinite(transp_)] = 0
+                    transp_Xt_ = nx.dot(transp_, self.xs_)
 
                     # define the transported points
                     transp_Xt_ = transp_Xt_[idx, :] + Xt[bi] - self.xt_[idx, :]
 
                     transp_Xt.append(transp_Xt_)
 
-                transp_Xt = np.concatenate(transp_Xt, axis=0)
+                transp_Xt = nx.concatenate(transp_Xt, axis=0)
 
             return transp_Xt
 
@@ -1230,26 +1264,27 @@ class BaseTransport(BaseEstimator):
         transp_ys : array-like, shape (n_source_samples, nb_classes)
             Estimated soft source labels.
         """
+        nx = self.nx
 
         # check the necessary inputs parameters are here
         if check_params(yt=yt):
 
-            ytTemp = label_normalization(np.copy(yt))
-            classes = np.unique(ytTemp)
+            ytTemp = label_normalization(nx.copy(yt))
+            classes = nx.unique(ytTemp)
             n = len(classes)
-            D1 = np.zeros((n, len(ytTemp)))
+            D1 = nx.zeros((n, len(ytTemp)), type_as=self.coupling_)
 
             # perform label propagation
-            transp = self.coupling_ / np.sum(self.coupling_, 1)[:, None]
+            transp = self.coupling_ / nx.sum(self.coupling_, 1)[:, None]
 
             # set nans to 0
-            transp[~ np.isfinite(transp)] = 0
+            transp[~ nx.isfinite(transp)] = 0
 
             for c in classes:
                 D1[int(c), ytTemp == c] = 1
 
             # compute propagated samples
-            transp_ys = np.dot(D1, transp.T)
+            transp_ys = nx.dot(D1, transp.T)
 
             return transp_ys.T
 
@@ -1330,14 +1365,15 @@ class LinearTransport(BaseTransport):
         self : object
             Returns self.
         """
+        nx = self._get_backend(Xs, ys, Xt, yt)
 
         self.mu_s = self.distribution_estimation(Xs)
         self.mu_t = self.distribution_estimation(Xt)
 
         # coupling estimation
         returned_ = OT_mapping_linear(Xs, Xt, reg=self.reg,
-                                      ws=self.mu_s.reshape((-1, 1)),
-                                      wt=self.mu_t.reshape((-1, 1)),
+                                      ws=nx.reshape(self.mu_s, (-1, 1)),
+                                      wt=nx.reshape(self.mu_t, (-1, 1)),
                                       bias=self.bias, log=self.log)
 
         # deal with the value of log
@@ -1348,8 +1384,8 @@ class LinearTransport(BaseTransport):
             self.log_ = dict()
 
         # re compute inverse mapping
-        self.A1_ = linalg.inv(self.A_)
-        self.B1_ = -self.B_.dot(self.A1_)
+        self.A1_ = nx.inv(self.A_)
+        self.B1_ = -nx.dot(self.B_, self.A1_)
 
         return self
 
@@ -1378,10 +1414,11 @@ class LinearTransport(BaseTransport):
         transp_Xs : array-like, shape (n_source_samples, n_features)
             The transport source samples.
         """
+        nx = self.nx
 
         # check the necessary inputs parameters are here
         if check_params(Xs=Xs):
-            transp_Xs = Xs.dot(self.A_) + self.B_
+            transp_Xs = nx.dot(Xs, self.A_) + self.B_
 
             return transp_Xs
 
@@ -1411,10 +1448,11 @@ class LinearTransport(BaseTransport):
         transp_Xt : array-like, shape (n_source_samples, n_features)
             The transported target samples.
         """
+        nx = self.nx
 
         # check the necessary inputs parameters are here
         if check_params(Xt=Xt):
-            transp_Xt = Xt.dot(self.A1_) + self.B1_
+            transp_Xt = nx.dot(Xt, self.A1_) + self.B1_
 
             return transp_Xt
 
@@ -2112,6 +2150,7 @@ class MappingTransport(BaseEstimator):
         self : object
             Returns self
         """
+        self._get_backend(Xs, ys, Xt, yt)
 
         # check the necessary inputs parameters are here
         if check_params(Xs=Xs, Xt=Xt):
@@ -2158,19 +2197,20 @@ class MappingTransport(BaseEstimator):
         transp_Xs : array-like, shape (n_source_samples, n_features)
             The transport source samples.
         """
+        nx = self.nx
 
         # check the necessary inputs parameters are here
         if check_params(Xs=Xs):
 
-            if np.array_equal(self.xs_, Xs):
+            if nx.array_equal(self.xs_, Xs):
                 # perform standard barycentric mapping
-                transp = self.coupling_ / np.sum(self.coupling_, 1)[:, None]
+                transp = self.coupling_ / nx.sum(self.coupling_, 1)[:, None]
 
                 # set nans to 0
-                transp[~ np.isfinite(transp)] = 0
+                transp[~ nx.isfinite(transp)] = 0
 
                 # compute transported samples
-                transp_Xs = np.dot(transp, self.xt_)
+                transp_Xs = nx.dot(transp, self.xt_)
             else:
                 if self.kernel == "gaussian":
                     K = kernel(Xs, self.xs_, method=self.kernel,
@@ -2178,8 +2218,10 @@ class MappingTransport(BaseEstimator):
                 elif self.kernel == "linear":
                     K = Xs
                 if self.bias:
-                    K = np.hstack((K, np.ones((Xs.shape[0], 1))))
-                transp_Xs = K.dot(self.mapping_)
+                    K = nx.concatenate(
+                        [K, nx.ones((Xs.shape[0], 1), type_as=K)], axis=1
+                    )
+                transp_Xs = nx.dot(K, self.mapping_)
 
             return transp_Xs
 
@@ -2396,6 +2438,7 @@ class JCPOTTransport(BaseTransport):
         self : object
             Returns self.
         """
+        self._get_backend(*Xs, *ys, Xt, yt)
 
         # check the necessary inputs parameters are here
         if check_params(Xs=Xs, Xt=Xt, ys=ys):
@@ -2438,28 +2481,29 @@ class JCPOTTransport(BaseTransport):
         batch_size : int, optional (default=128)
             The batch size for out of sample inverse transform
         """
+        nx = self.nx
 
         transp_Xs = []
 
         # check the necessary inputs parameters are here
         if check_params(Xs=Xs):
 
-            if all([np.allclose(x, y) for x, y in zip(self.xs_, Xs)]):
+            if all([nx.allclose(x, y) for x, y in zip(self.xs_, Xs)]):
 
                 # perform standard barycentric mapping for each source domain
 
                 for coupling in self.coupling_:
-                    transp = coupling / np.sum(coupling, 1)[:, None]
+                    transp = coupling / nx.sum(coupling, 1)[:, None]
 
                     # set nans to 0
-                    transp[~ np.isfinite(transp)] = 0
+                    transp[~ nx.isfinite(transp)] = 0
 
                     # compute transported samples
-                    transp_Xs.append(np.dot(transp, self.xt_))
+                    transp_Xs.append(nx.dot(transp, self.xt_))
             else:
 
                 # perform out of sample mapping
-                indices = np.arange(Xs.shape[0])
+                indices = nx.arange(Xs.shape[0])
                 batch_ind = [
                     indices[i:i + batch_size]
                     for i in range(0, len(indices), batch_size)]
@@ -2470,23 +2514,22 @@ class JCPOTTransport(BaseTransport):
                     transp_Xs_ = []
 
                     # get the nearest neighbor in the sources domains
-                    xs = np.concatenate(self.xs_, axis=0)
-                    idx = np.argmin(dist(Xs[bi], xs), axis=1)
+                    xs = nx.concatenate(self.xs_, axis=0)
+                    idx = nx.argmin(dist(Xs[bi], xs), axis=1)
 
                     # transport the source samples
                     for coupling in self.coupling_:
-                        transp = coupling / np.sum(
-                            coupling, 1)[:, None]
-                        transp[~ np.isfinite(transp)] = 0
-                        transp_Xs_.append(np.dot(transp, self.xt_))
+                        transp = coupling / nx.sum(coupling, 1)[:, None]
+                        transp[~ nx.isfinite(transp)] = 0
+                        transp_Xs_.append(nx.dot(transp, self.xt_))
 
-                    transp_Xs_ = np.concatenate(transp_Xs_, axis=0)
+                    transp_Xs_ = nx.concatenate(transp_Xs_, axis=0)
 
                     # define the transported points
                     transp_Xs_ = transp_Xs_[idx, :] + Xs[bi] - xs[idx, :]
                     transp_Xs.append(transp_Xs_)
 
-                transp_Xs = np.concatenate(transp_Xs, axis=0)
+                transp_Xs = nx.concatenate(transp_Xs, axis=0)
 
             return transp_Xs
 
@@ -2512,32 +2555,36 @@ class JCPOTTransport(BaseTransport):
            "Optimal transport for multi-source domain adaptation under target shift",
            International Conference on Artificial Intelligence and Statistics (AISTATS), 2019.
         """
+        nx = self.nx
 
         # check the necessary inputs parameters are here
         if check_params(ys=ys):
-            yt = np.zeros((len(np.unique(np.concatenate(ys))), self.xt_.shape[0]))
+            yt = nx.zeros(
+                (len(nx.unique(nx.concatenate(ys))), self.xt_.shape[0]),
+                type_as=ys[0]
+            )
             for i in range(len(ys)):
-                ysTemp = label_normalization(np.copy(ys[i]))
-                classes = np.unique(ysTemp)
+                ysTemp = label_normalization(nx.copy(ys[i]))
+                classes = nx.unique(ysTemp)
                 n = len(classes)
                 ns = len(ysTemp)
 
                 # perform label propagation
-                transp = self.coupling_[i] / np.sum(self.coupling_[i], 1)[:, None]
+                transp = self.coupling_[i] / nx.sum(self.coupling_[i], 1)[:, None]
 
                 # set nans to 0
-                transp[~ np.isfinite(transp)] = 0
+                transp[~ nx.isfinite(transp)] = 0
 
                 if self.log:
                     D1 = self.log_['D1'][i]
                 else:
-                    D1 = np.zeros((n, ns))
+                    D1 = nx.zeros((n, ns), type_as=transp)
 
                     for c in classes:
                         D1[int(c), ysTemp == c] = 1
 
                 # compute propagated labels
-                yt = yt + np.dot(D1, transp) / len(ys)
+                yt = yt + nx.dot(D1, transp) / len(ys)
 
             return yt.T
 
@@ -2555,14 +2602,15 @@ class JCPOTTransport(BaseTransport):
         transp_ys : list of K array-like objects, shape K x (nk_source_samples, nb_classes)
             A list of estimated soft source labels
         """
+        nx = self.nx
 
         # check the necessary inputs parameters are here
         if check_params(yt=yt):
             transp_ys = []
-            ytTemp = label_normalization(np.copy(yt))
-            classes = np.unique(ytTemp)
+            ytTemp = label_normalization(nx.copy(yt))
+            classes = nx.unique(ytTemp)
             n = len(classes)
-            D1 = np.zeros((n, len(ytTemp)))
+            D1 = nx.zeros((n, len(ytTemp)), type_as=self.coupling_[0])
 
             for c in classes:
                 D1[int(c), ytTemp == c] = 1
@@ -2570,12 +2618,12 @@ class JCPOTTransport(BaseTransport):
             for i in range(len(self.xs_)):
 
                 # perform label propagation
-                transp = self.coupling_[i] / np.sum(self.coupling_[i], 1)[:, None]
+                transp = self.coupling_[i] / nx.sum(self.coupling_[i], 1)[:, None]
 
                 # set nans to 0
-                transp[~ np.isfinite(transp)] = 0
+                transp[~ nx.isfinite(transp)] = 0
 
                 # compute propagated labels
-                transp_ys.append(np.dot(D1, transp.T).T)
+                transp_ys.append(nx.dot(D1, transp.T).T)
 
             return transp_ys
diff --git a/ot/lp/__init__.py b/ot/lp/__init__.py
index d9b6fa9..abf7fe0 100644
--- a/ot/lp/__init__.py
+++ b/ot/lp/__init__.py
@@ -225,6 +225,13 @@ def emd(a, b, M, numItermax=100000, log=False, center_dual=True, numThreads=1):
         from all compatible backends. But the algorithm uses the C++ CPU backend
         which can lead to copy overhead on GPU arrays.
 
+    .. note:: This function will cast the computed transport plan to the data type
+        of the provided input with the following priority: :math:`\mathbf{a}`,
+        then :math:`\mathbf{b}`, then :math:`\mathbf{M}` if marginals are not provided.
+        Casting to an integer tensor might result in a loss of precision.
+        If this behaviour is unwanted, please make sure to provide a
+        floating point input.
+
     Uses the algorithm proposed in :ref:`[1] <references-emd>`.
 
     Parameters
@@ -290,12 +297,16 @@ def emd(a, b, M, numItermax=100000, log=False, center_dual=True, numThreads=1):
     a, b, M = list_to_array(a, b, M)
 
     a0, b0, M0 = a, b, M
+    if len(a0) != 0:
+        type_as = a0
+    elif len(b0) != 0:
+        type_as = b0
+    else:
+        type_as = M0
     nx = get_backend(M0, a0, b0)
 
     # convert to numpy
-    M = nx.to_numpy(M)
-    a = nx.to_numpy(a)
-    b = nx.to_numpy(b)
+    M, a, b = nx.to_numpy(M, a, b)
 
     # ensure float64
     a = np.asarray(a, dtype=np.float64)
@@ -330,15 +341,23 @@ def emd(a, b, M, numItermax=100000, log=False, center_dual=True, numThreads=1):
         u, v = estimate_dual_null_weights(u, v, a, b, M)
 
     result_code_string = check_result(result_code)
+    if not nx.is_floating_point(type_as):
+        warnings.warn(
+            "Input histogram consists of integer. The transport plan will be "
+            "casted accordingly, possibly resulting in a loss of precision. "
+            "If this behaviour is unwanted, please make sure your input "
+            "histogram consists of floating point elements.",
+            stacklevel=2
+        )
     if log:
         log = {}
         log['cost'] = cost
-        log['u'] = nx.from_numpy(u, type_as=a0)
-        log['v'] = nx.from_numpy(v, type_as=b0)
+        log['u'] = nx.from_numpy(u, type_as=type_as)
+        log['v'] = nx.from_numpy(v, type_as=type_as)
         log['warning'] = result_code_string
         log['result_code'] = result_code
-        return nx.from_numpy(G, type_as=M0), log
-    return nx.from_numpy(G, type_as=M0)
+        return nx.from_numpy(G, type_as=type_as), log
+    return nx.from_numpy(G, type_as=type_as)
 
 
 def emd2(a, b, M, processes=1,
@@ -364,6 +383,14 @@ def emd2(a, b, M, processes=1,
         from all compatible backends. But the algorithm uses the C++ CPU backend
         which can lead to copy overhead on GPU arrays.
 
+    .. note:: This function will cast the computed transport plan and
+        transportation loss to the data type of the provided input with the
+        following priority: :math:`\mathbf{a}`, then :math:`\mathbf{b}`,
+        then :math:`\mathbf{M}` if marginals are not provided.
+        Casting to an integer tensor might result in a loss of precision.
+        If this behaviour is unwanted, please make sure to provide a
+        floating point input.
+
     Uses the algorithm proposed in :ref:`[1] <references-emd2>`.
 
     Parameters
@@ -432,12 +459,16 @@ def emd2(a, b, M, processes=1,
     a, b, M = list_to_array(a, b, M)
 
     a0, b0, M0 = a, b, M
+    if len(a0) != 0:
+        type_as = a0
+    elif len(b0) != 0:
+        type_as = b0
+    else:
+        type_as = M0
     nx = get_backend(M0, a0, b0)
 
     # convert to numpy
-    M = nx.to_numpy(M)
-    a = nx.to_numpy(a)
-    b = nx.to_numpy(b)
+    M, a, b = nx.to_numpy(M, a, b)
 
     a = np.asarray(a, dtype=np.float64)
     b = np.asarray(b, dtype=np.float64)
@@ -470,14 +501,22 @@ def emd2(a, b, M, processes=1,
 
             result_code_string = check_result(result_code)
             log = {}
-            G = nx.from_numpy(G, type_as=M0)
+            if not nx.is_floating_point(type_as):
+                warnings.warn(
+                    "Input histogram consists of integer. The transport plan will be "
+                    "casted accordingly, possibly resulting in a loss of precision. "
+                    "If this behaviour is unwanted, please make sure your input "
+                    "histogram consists of floating point elements.",
+                    stacklevel=2
+                )
+            G = nx.from_numpy(G, type_as=type_as)
             if return_matrix:
                 log['G'] = G
-            log['u'] = nx.from_numpy(u, type_as=a0)
-            log['v'] = nx.from_numpy(v, type_as=b0)
+            log['u'] = nx.from_numpy(u, type_as=type_as)
+            log['v'] = nx.from_numpy(v, type_as=type_as)
             log['warning'] = result_code_string
             log['result_code'] = result_code
-            cost = nx.set_gradients(nx.from_numpy(cost, type_as=M0),
+            cost = nx.set_gradients(nx.from_numpy(cost, type_as=type_as),
                                     (a0, b0, M0), (log['u'], log['v'], G))
             return [cost, log]
     else:
@@ -491,10 +530,18 @@ def emd2(a, b, M, processes=1,
             if np.any(~asel) or np.any(~bsel):
                 u, v = estimate_dual_null_weights(u, v, a, b, M)
 
-            G = nx.from_numpy(G, type_as=M0)
-            cost = nx.set_gradients(nx.from_numpy(cost, type_as=M0),
-                                    (a0, b0, M0), (nx.from_numpy(u, type_as=a0),
-                                                   nx.from_numpy(v, type_as=b0), G))
+            if not nx.is_floating_point(type_as):
+                warnings.warn(
+                    "Input histogram consists of integer. The transport plan will be "
+                    "casted accordingly, possibly resulting in a loss of precision. "
+                    "If this behaviour is unwanted, please make sure your input "
+                    "histogram consists of floating point elements.",
+                    stacklevel=2
+                )
+            G = nx.from_numpy(G, type_as=type_as)
+            cost = nx.set_gradients(nx.from_numpy(cost, type_as=type_as),
+                                    (a0, b0, M0), (nx.from_numpy(u, type_as=type_as),
+                                                   nx.from_numpy(v, type_as=type_as), G))
 
             check_result(result_code)
             return cost
diff --git a/ot/optim.py b/ot/optim.py
index f25e2c9..5a1d605 100644
--- a/ot/optim.py
+++ b/ot/optim.py
@@ -9,12 +9,19 @@ Generic solvers for regularized OT
 # License: MIT License
 
 import numpy as np
-from scipy.optimize.linesearch import scalar_search_armijo
+import warnings
 from .lp import emd
 from .bregman import sinkhorn
-from ot.utils import list_to_array
+from .utils import list_to_array
 from .backend import get_backend
 
+with warnings.catch_warnings():
+    warnings.simplefilter("ignore")
+    try:
+        from scipy.optimize import scalar_search_armijo
+    except ImportError:
+        from scipy.optimize.linesearch import scalar_search_armijo
+
 # The corresponding scipy function does not work for matrices
 
 
diff --git a/ot/unbalanced.py b/ot/unbalanced.py
index 15e180b..503cc1e 100644
--- a/ot/unbalanced.py
+++ b/ot/unbalanced.py
@@ -8,9 +8,9 @@ Regularized Unbalanced OT solvers
 
 from __future__ import division
 import warnings
-import numpy as np
-from scipy.special import logsumexp
 
+from .backend import get_backend
+from .utils import list_to_array
 # from .utils import unif, dist
 
 
@@ -43,12 +43,12 @@ def sinkhorn_unbalanced(a, b, M, reg, reg_m, method='sinkhorn', numItermax=1000,
 
     Parameters
     ----------
-    a : np.ndarray (dim_a,)
+    a : array-like (dim_a,)
         Unnormalized histogram of dimension `dim_a`
-    b : np.ndarray (dim_b,) or np.ndarray (dim_b, n_hists)
+    b : array-like (dim_b,) or array-like (dim_b, n_hists)
         One or multiple unnormalized histograms of dimension `dim_b`.
         If many, compute all the OT distances :math:`(\mathbf{a}, \mathbf{b}_i)_i`
-    M : np.ndarray (dim_a, dim_b)
+    M : array-like (dim_a, dim_b)
         loss matrix
     reg : float
         Entropy regularization term > 0
@@ -70,12 +70,12 @@ def sinkhorn_unbalanced(a, b, M, reg, reg_m, method='sinkhorn', numItermax=1000,
     Returns
     -------
     if n_hists == 1:
-        - gamma : (dim_a, dim_b) ndarray
+        - gamma : (dim_a, dim_b) array-like
             Optimal transportation matrix for the given parameters
         - log : dict
             log dictionary returned only if `log` is `True`
     else:
-        - ot_distance : (n_hists,) ndarray
+        - ot_distance : (n_hists,) array-like
             the OT distance between :math:`\mathbf{a}` and each of the histograms :math:`\mathbf{b}_i`
         - log : dict
             log dictionary returned only if `log` is `True`
@@ -172,12 +172,12 @@ def sinkhorn_unbalanced2(a, b, M, reg, reg_m, method='sinkhorn',
 
     Parameters
     ----------
-    a : np.ndarray (dim_a,)
+    a : array-like (dim_a,)
         Unnormalized histogram of dimension `dim_a`
-    b : np.ndarray (dim_b,) or np.ndarray (dim_b, n_hists)
+    b : array-like (dim_b,) or array-like (dim_b, n_hists)
         One or multiple unnormalized histograms of dimension `dim_b`.
         If many, compute all the OT distances :math:`(\mathbf{a}, \mathbf{b}_i)_i`
-    M : np.ndarray (dim_a, dim_b)
+    M : array-like (dim_a, dim_b)
         loss matrix
     reg : float
         Entropy regularization term > 0
@@ -198,7 +198,7 @@ def sinkhorn_unbalanced2(a, b, M, reg, reg_m, method='sinkhorn',
 
     Returns
     -------
-    ot_distance : (n_hists,) ndarray
+    ot_distance : (n_hists,) array-like
         the OT distance between :math:`\mathbf{a}` and each of the histograms :math:`\mathbf{b}_i`
     log : dict
         log dictionary returned only if `log` is `True`
@@ -239,9 +239,10 @@ def sinkhorn_unbalanced2(a, b, M, reg, reg_m, method='sinkhorn',
     ot.unbalanced.sinkhorn_reg_scaling: Unbalanced Sinkhorn with epslilon scaling :ref:`[9, 10] <references-sinkhorn-unbalanced2>`
 
     """
-    b = np.asarray(b, dtype=np.float64)
+    b = list_to_array(b)
     if len(b.shape) < 2:
         b = b[:, None]
+
     if method.lower() == 'sinkhorn':
         return sinkhorn_knopp_unbalanced(a, b, M, reg, reg_m,
                                          numItermax=numItermax,
@@ -291,12 +292,12 @@ def sinkhorn_knopp_unbalanced(a, b, M, reg, reg_m, numItermax=1000,
 
     Parameters
     ----------
-    a : np.ndarray (dim_a,)
+    a : array-like (dim_a,)
         Unnormalized histogram of dimension `dim_a`
-    b : np.ndarray (dim_b,) or np.ndarray (dim_b, n_hists)
+    b : array-like (dim_b,) or array-like (dim_b, n_hists)
         One or multiple unnormalized histograms of dimension `dim_b`
         If many, compute all the OT distances (a, b_i)
-    M : np.ndarray (dim_a, dim_b)
+    M : array-like (dim_a, dim_b)
         loss matrix
     reg : float
         Entropy regularization term > 0
@@ -315,12 +316,12 @@ def sinkhorn_knopp_unbalanced(a, b, M, reg, reg_m, numItermax=1000,
     Returns
     -------
     if n_hists == 1:
-        - gamma : (dim_a, dim_b) ndarray
+        - gamma : (dim_a, dim_b) array-like
             Optimal transportation matrix for the given parameters
         - log : dict
             log dictionary returned only if `log` is `True`
     else:
-        - ot_distance : (n_hists,) ndarray
+        - ot_distance : (n_hists,) array-like
             the OT distance between :math:`\mathbf{a}` and each of the histograms :math:`\mathbf{b}_i`
         - log : dict
             log dictionary returned only if `log` is `True`
@@ -354,17 +355,15 @@ def sinkhorn_knopp_unbalanced(a, b, M, reg, reg_m, numItermax=1000,
     ot.optim.cg : General regularized OT
 
     """
-
-    a = np.asarray(a, dtype=np.float64)
-    b = np.asarray(b, dtype=np.float64)
-    M = np.asarray(M, dtype=np.float64)
+    M, a, b = list_to_array(M, a, b)
+    nx = get_backend(M, a, b)
 
     dim_a, dim_b = M.shape
 
     if len(a) == 0:
-        a = np.ones(dim_a, dtype=np.float64) / dim_a
+        a = nx.ones(dim_a, type_as=M) / dim_a
     if len(b) == 0:
-        b = np.ones(dim_b, dtype=np.float64) / dim_b
+        b = nx.ones(dim_b, type_as=M) / dim_b
 
     if len(b.shape) > 1:
         n_hists = b.shape[1]
@@ -377,17 +376,14 @@ def sinkhorn_knopp_unbalanced(a, b, M, reg, reg_m, numItermax=1000,
     # we assume that no distances are null except those of the diagonal of
     # distances
     if n_hists:
-        u = np.ones((dim_a, 1)) / dim_a
-        v = np.ones((dim_b, n_hists)) / dim_b
+        u = nx.ones((dim_a, 1), type_as=M) / dim_a
+        v = nx.ones((dim_b, n_hists), type_as=M) / dim_b
         a = a.reshape(dim_a, 1)
     else:
-        u = np.ones(dim_a) / dim_a
-        v = np.ones(dim_b) / dim_b
+        u = nx.ones(dim_a, type_as=M) / dim_a
+        v = nx.ones(dim_b, type_as=M) / dim_b
 
-    # Next 3 lines equivalent to K= np.exp(-M/reg), but faster to compute
-    K = np.empty(M.shape, dtype=M.dtype)
-    np.divide(M, -reg, out=K)
-    np.exp(K, out=K)
+    K = nx.exp(M / (-reg))
 
     fi = reg_m / (reg_m + reg)
 
@@ -397,14 +393,14 @@ def sinkhorn_knopp_unbalanced(a, b, M, reg, reg_m, numItermax=1000,
         uprev = u
         vprev = v
 
-        Kv = K.dot(v)
+        Kv = nx.dot(K, v)
         u = (a / Kv) ** fi
-        Ktu = K.T.dot(u)
+        Ktu = nx.dot(K.T, u)
         v = (b / Ktu) ** fi
 
-        if (np.any(Ktu == 0.)
-                or np.any(np.isnan(u)) or np.any(np.isnan(v))
-                or np.any(np.isinf(u)) or np.any(np.isinf(v))):
+        if (nx.any(Ktu == 0.)
+                or nx.any(nx.isnan(u)) or nx.any(nx.isnan(v))
+                or nx.any(nx.isinf(u)) or nx.any(nx.isinf(v))):
             # we have reached the machine precision
             # come back to previous solution and quit loop
             warnings.warn('Numerical errors at iteration %s' % i)
@@ -412,8 +408,12 @@ def sinkhorn_knopp_unbalanced(a, b, M, reg, reg_m, numItermax=1000,
             v = vprev
             break
 
-        err_u = abs(u - uprev).max() / max(abs(u).max(), abs(uprev).max(), 1.)
-        err_v = abs(v - vprev).max() / max(abs(v).max(), abs(vprev).max(), 1.)
+        err_u = nx.max(nx.abs(u - uprev)) / max(
+            nx.max(nx.abs(u)), nx.max(nx.abs(uprev)), 1.
+        )
+        err_v = nx.max(nx.abs(v - vprev)) / max(
+            nx.max(nx.abs(v)), nx.max(nx.abs(vprev)), 1.
+        )
         err = 0.5 * (err_u + err_v)
         if log:
             log['err'].append(err)
@@ -426,11 +426,11 @@ def sinkhorn_knopp_unbalanced(a, b, M, reg, reg_m, numItermax=1000,
             break
 
     if log:
-        log['logu'] = np.log(u + 1e-300)
-        log['logv'] = np.log(v + 1e-300)
+        log['logu'] = nx.log(u + 1e-300)
+        log['logv'] = nx.log(v + 1e-300)
 
     if n_hists:  # return only loss
-        res = np.einsum('ik,ij,jk,ij->k', u, K, v, M)
+        res = nx.einsum('ik,ij,jk,ij->k', u, K, v, M)
         if log:
             return res, log
         else:
@@ -475,12 +475,12 @@ def sinkhorn_stabilized_unbalanced(a, b, M, reg, reg_m, tau=1e5, numItermax=1000
 
     Parameters
     ----------
-    a : np.ndarray (dim_a,)
+    a : array-like (dim_a,)
         Unnormalized histogram of dimension `dim_a`
-    b : np.ndarray (dim_b,) or np.ndarray (dim_b, n_hists)
+    b : array-like (dim_b,) or array-like (dim_b, n_hists)
         One or multiple unnormalized histograms of dimension `dim_b`.
         If many, compute all the OT distances :math:`(\mathbf{a}, \mathbf{b}_i)_i`
-    M : np.ndarray (dim_a, dim_b)
+    M : array-like (dim_a, dim_b)
         loss matrix
     reg : float
         Entropy regularization term > 0
@@ -501,12 +501,12 @@ def sinkhorn_stabilized_unbalanced(a, b, M, reg, reg_m, tau=1e5, numItermax=1000
     Returns
     -------
     if n_hists == 1:
-        - gamma : (dim_a, dim_b) ndarray
+        - gamma : (dim_a, dim_b) array-like
             Optimal transportation matrix for the given parameters
         - log : dict
             log dictionary returned only if `log` is `True`
     else:
-        - ot_distance : (n_hists,) ndarray
+        - ot_distance : (n_hists,) array-like
             the OT distance between :math:`\mathbf{a}` and each of the histograms :math:`\mathbf{b}_i`
         - log : dict
             log dictionary returned only if `log` is `True`
@@ -538,17 +538,15 @@ def sinkhorn_stabilized_unbalanced(a, b, M, reg, reg_m, tau=1e5, numItermax=1000
     ot.optim.cg : General regularized OT
 
     """
-
-    a = np.asarray(a, dtype=np.float64)
-    b = np.asarray(b, dtype=np.float64)
-    M = np.asarray(M, dtype=np.float64)
+    a, b, M = list_to_array(a, b, M)
+    nx = get_backend(M, a, b)
 
     dim_a, dim_b = M.shape
 
     if len(a) == 0:
-        a = np.ones(dim_a, dtype=np.float64) / dim_a
+        a = nx.ones(dim_a, type_as=M) / dim_a
     if len(b) == 0:
-        b = np.ones(dim_b, dtype=np.float64) / dim_b
+        b = nx.ones(dim_b, type_as=M) / dim_b
 
     if len(b.shape) > 1:
         n_hists = b.shape[1]
@@ -561,56 +559,52 @@ def sinkhorn_stabilized_unbalanced(a, b, M, reg, reg_m, tau=1e5, numItermax=1000
     # we assume that no distances are null except those of the diagonal of
     # distances
     if n_hists:
-        u = np.ones((dim_a, n_hists)) / dim_a
-        v = np.ones((dim_b, n_hists)) / dim_b
+        u = nx.ones((dim_a, n_hists), type_as=M) / dim_a
+        v = nx.ones((dim_b, n_hists), type_as=M) / dim_b
         a = a.reshape(dim_a, 1)
     else:
-        u = np.ones(dim_a) / dim_a
-        v = np.ones(dim_b) / dim_b
+        u = nx.ones(dim_a, type_as=M) / dim_a
+        v = nx.ones(dim_b, type_as=M) / dim_b
 
     # print(reg)
-    # Next 3 lines equivalent to K= np.exp(-M/reg), but faster to compute
-    K = np.empty(M.shape, dtype=M.dtype)
-    np.divide(M, -reg, out=K)
-    np.exp(K, out=K)
+    K = nx.exp(-M / reg)
 
     fi = reg_m / (reg_m + reg)
 
     cpt = 0
     err = 1.
-    alpha = np.zeros(dim_a)
-    beta = np.zeros(dim_b)
+    alpha = nx.zeros(dim_a, type_as=M)
+    beta = nx.zeros(dim_b, type_as=M)
     while (err > stopThr and cpt < numItermax):
         uprev = u
         vprev = v
 
-        Kv = K.dot(v)
-        f_alpha = np.exp(- alpha / (reg + reg_m))
-        f_beta = np.exp(- beta / (reg + reg_m))
+        Kv = nx.dot(K, v)
+        f_alpha = nx.exp(- alpha / (reg + reg_m))
+        f_beta = nx.exp(- beta / (reg + reg_m))
 
         if n_hists:
             f_alpha = f_alpha[:, None]
             f_beta = f_beta[:, None]
         u = ((a / (Kv + 1e-16)) ** fi) * f_alpha
-        Ktu = K.T.dot(u)
+        Ktu = nx.dot(K.T, u)
         v = ((b / (Ktu + 1e-16)) ** fi) * f_beta
         absorbing = False
-        if (u > tau).any() or (v > tau).any():
+        if nx.any(u > tau) or nx.any(v > tau):
             absorbing = True
             if n_hists:
-                alpha = alpha + reg * np.log(np.max(u, 1))
-                beta = beta + reg * np.log(np.max(v, 1))
+                alpha = alpha + reg * nx.log(nx.max(u, 1))
+                beta = beta + reg * nx.log(nx.max(v, 1))
             else:
-                alpha = alpha + reg * np.log(np.max(u))
-                beta = beta + reg * np.log(np.max(v))
-            K = np.exp((alpha[:, None] + beta[None, :] -
-                        M) / reg)
-            v = np.ones_like(v)
-        Kv = K.dot(v)
-
-        if (np.any(Ktu == 0.)
-                or np.any(np.isnan(u)) or np.any(np.isnan(v))
-                or np.any(np.isinf(u)) or np.any(np.isinf(v))):
+                alpha = alpha + reg * nx.log(nx.max(u))
+                beta = beta + reg * nx.log(nx.max(v))
+            K = nx.exp((alpha[:, None] + beta[None, :] - M) / reg)
+            v = nx.ones(v.shape, type_as=v)
+        Kv = nx.dot(K, v)
+
+        if (nx.any(Ktu == 0.)
+                or nx.any(nx.isnan(u)) or nx.any(nx.isnan(v))
+                or nx.any(nx.isinf(u)) or nx.any(nx.isinf(v))):
             # we have reached the machine precision
             # come back to previous solution and quit loop
             warnings.warn('Numerical errors at iteration %s' % cpt)
@@ -620,8 +614,9 @@ def sinkhorn_stabilized_unbalanced(a, b, M, reg, reg_m, tau=1e5, numItermax=1000
         if (cpt % 10 == 0 and not absorbing) or cpt == 0:
             # we can speed up the process by checking for the error only all
             # the 10th iterations
-            err = abs(u - uprev).max() / max(abs(u).max(), abs(uprev).max(),
-                                             1.)
+            err = nx.max(nx.abs(u - uprev)) / max(
+                nx.max(nx.abs(u)), nx.max(nx.abs(uprev)), 1.
+            )
             if log:
                 log['err'].append(err)
             if verbose:
@@ -636,25 +631,30 @@ def sinkhorn_stabilized_unbalanced(a, b, M, reg, reg_m, tau=1e5, numItermax=1000
                       "Try a larger entropy `reg` or a lower mass `reg_m`." +
                       "Or a larger absorption threshold `tau`.")
     if n_hists:
-        logu = alpha[:, None] / reg + np.log(u)
-        logv = beta[:, None] / reg + np.log(v)
+        logu = alpha[:, None] / reg + nx.log(u)
+        logv = beta[:, None] / reg + nx.log(v)
     else:
-        logu = alpha / reg + np.log(u)
-        logv = beta / reg + np.log(v)
+        logu = alpha / reg + nx.log(u)
+        logv = beta / reg + nx.log(v)
     if log:
         log['logu'] = logu
         log['logv'] = logv
     if n_hists:  # return only loss
-        res = logsumexp(np.log(M + 1e-100)[:, :, None] + logu[:, None, :] +
-                        logv[None, :, :] - M[:, :, None] / reg, axis=(0, 1))
-        res = np.exp(res)
+        res = nx.logsumexp(
+            nx.log(M + 1e-100)[:, :, None]
+            + logu[:, None, :]
+            + logv[None, :, :]
+            - M[:, :, None] / reg,
+            axis=(0, 1)
+        )
+        res = nx.exp(res)
         if log:
             return res, log
         else:
             return res
 
     else:  # return OT matrix
-        ot_matrix = np.exp(logu[:, None] + logv[None, :] - M / reg)
+        ot_matrix = nx.exp(logu[:, None] + logv[None, :] - M / reg)
         if log:
             return ot_matrix, log
         else:
@@ -683,9 +683,9 @@ def barycenter_unbalanced_stabilized(A, M, reg, reg_m, weights=None, tau=1e3,
 
     Parameters
     ----------
-    A : np.ndarray (dim, n_hists)
+    A : array-like (dim, n_hists)
         `n_hists` training distributions :math:`\mathbf{a}_i` of dimension `dim`
-    M : np.ndarray (dim, dim)
+    M : array-like (dim, dim)
         ground metric matrix for OT.
     reg : float
         Entropy regularization term > 0
@@ -693,7 +693,7 @@ def barycenter_unbalanced_stabilized(A, M, reg, reg_m, weights=None, tau=1e3,
         Marginal relaxation term > 0
     tau : float
         Stabilization threshold for log domain absorption.
-    weights : np.ndarray (n_hists,) optional
+    weights : array-like (n_hists,) optional
         Weight of each distribution (barycentric coodinates)
         If None, uniform weights are used.
     numItermax : int, optional
@@ -708,7 +708,7 @@ def barycenter_unbalanced_stabilized(A, M, reg, reg_m, weights=None, tau=1e3,
 
     Returns
     -------
-    a : (dim,) ndarray
+    a : (dim,) array-like
         Unbalanced Wasserstein barycenter
     log : dict
         log dictionary return only if log==True in parameters
@@ -726,9 +726,12 @@ def barycenter_unbalanced_stabilized(A, M, reg, reg_m, weights=None, tau=1e3,
 
 
     """
+    A, M = list_to_array(A, M)
+    nx = get_backend(A, M)
+
     dim, n_hists = A.shape
     if weights is None:
-        weights = np.ones(n_hists) / n_hists
+        weights = nx.ones(n_hists, type_as=A) / n_hists
     else:
         assert(len(weights) == A.shape[1])
 
@@ -737,47 +740,43 @@ def barycenter_unbalanced_stabilized(A, M, reg, reg_m, weights=None, tau=1e3,
 
     fi = reg_m / (reg_m + reg)
 
-    u = np.ones((dim, n_hists)) / dim
-    v = np.ones((dim, n_hists)) / dim
+    u = nx.ones((dim, n_hists), type_as=A) / dim
+    v = nx.ones((dim, n_hists), type_as=A) / dim
 
     # print(reg)
-    # Next 3 lines equivalent to K= np.exp(-M/reg), but faster to compute
-    K = np.empty(M.shape, dtype=M.dtype)
-    np.divide(M, -reg, out=K)
-    np.exp(K, out=K)
+    K = nx.exp(-M / reg)
 
     fi = reg_m / (reg_m + reg)
 
     cpt = 0
     err = 1.
-    alpha = np.zeros(dim)
-    beta = np.zeros(dim)
-    q = np.ones(dim) / dim
+    alpha = nx.zeros(dim, type_as=A)
+    beta = nx.zeros(dim, type_as=A)
+    q = nx.ones(dim, type_as=A) / dim
     for i in range(numItermax):
-        qprev = q.copy()
-        Kv = K.dot(v)
-        f_alpha = np.exp(- alpha / (reg + reg_m))
-        f_beta = np.exp(- beta / (reg + reg_m))
+        qprev = nx.copy(q)
+        Kv = nx.dot(K, v)
+        f_alpha = nx.exp(- alpha / (reg + reg_m))
+        f_beta = nx.exp(- beta / (reg + reg_m))
         f_alpha = f_alpha[:, None]
         f_beta = f_beta[:, None]
         u = ((A / (Kv + 1e-16)) ** fi) * f_alpha
-        Ktu = K.T.dot(u)
+        Ktu = nx.dot(K.T, u)
         q = (Ktu ** (1 - fi)) * f_beta
-        q = q.dot(weights) ** (1 / (1 - fi))
+        q = nx.dot(q, weights) ** (1 / (1 - fi))
         Q = q[:, None]
         v = ((Q / (Ktu + 1e-16)) ** fi) * f_beta
         absorbing = False
-        if (u > tau).any() or (v > tau).any():
+        if nx.any(u > tau) or nx.any(v > tau):
             absorbing = True
-            alpha = alpha + reg * np.log(np.max(u, 1))
-            beta = beta + reg * np.log(np.max(v, 1))
-            K = np.exp((alpha[:, None] + beta[None, :] -
-                        M) / reg)
-            v = np.ones_like(v)
-        Kv = K.dot(v)
-        if (np.any(Ktu == 0.)
-                or np.any(np.isnan(u)) or np.any(np.isnan(v))
-                or np.any(np.isinf(u)) or np.any(np.isinf(v))):
+            alpha = alpha + reg * nx.log(nx.max(u, 1))
+            beta = beta + reg * nx.log(nx.max(v, 1))
+            K = nx.exp((alpha[:, None] + beta[None, :] - M) / reg)
+            v = nx.ones(v.shape, type_as=v)
+        Kv = nx.dot(K, v)
+        if (nx.any(Ktu == 0.)
+                or nx.any(nx.isnan(u)) or nx.any(nx.isnan(v))
+                or nx.any(nx.isinf(u)) or nx.any(nx.isinf(v))):
             # we have reached the machine precision
             # come back to previous solution and quit loop
             warnings.warn('Numerical errors at iteration %s' % cpt)
@@ -786,8 +785,9 @@ def barycenter_unbalanced_stabilized(A, M, reg, reg_m, weights=None, tau=1e3,
         if (i % 10 == 0 and not absorbing) or i == 0:
             # we can speed up the process by checking for the error only all
             # the 10th iterations
-            err = abs(q - qprev).max() / max(abs(q).max(),
-                                             abs(qprev).max(), 1.)
+            err = nx.max(nx.abs(q - qprev)) / max(
+                nx.max(nx.abs(q)), nx.max(nx.abs(qprev)), 1.
+            )
             if log:
                 log['err'].append(err)
             if verbose:
@@ -804,8 +804,8 @@ def barycenter_unbalanced_stabilized(A, M, reg, reg_m, weights=None, tau=1e3,
                       "Or a larger absorption threshold `tau`.")
     if log:
         log['niter'] = i
-        log['logu'] = np.log(u + 1e-300)
-        log['logv'] = np.log(v + 1e-300)
+        log['logu'] = nx.log(u + 1e-300)
+        log['logv'] = nx.log(v + 1e-300)
         return q, log
     else:
         return q
@@ -833,15 +833,15 @@ def barycenter_unbalanced_sinkhorn(A, M, reg, reg_m, weights=None,
 
     Parameters
     ----------
-    A : np.ndarray (dim, n_hists)
+    A : array-like (dim, n_hists)
         `n_hists` training distributions :math:`\mathbf{a}_i` of dimension `dim`
-    M : np.ndarray (dim, dim)
+    M : array-like (dim, dim)
         ground metric matrix for OT.
     reg : float
         Entropy regularization term > 0
     reg_m: float
         Marginal relaxation term > 0
-    weights : np.ndarray (n_hists,) optional
+    weights : array-like (n_hists,) optional
         Weight of each distribution (barycentric coodinates)
         If None, uniform weights are used.
     numItermax : int, optional
@@ -856,7 +856,7 @@ def barycenter_unbalanced_sinkhorn(A, M, reg, reg_m, weights=None,
 
     Returns
     -------
-    a : (dim,) ndarray
+    a : (dim,) array-like
         Unbalanced Wasserstein barycenter
     log : dict
         log dictionary return only if log==True in parameters
@@ -874,40 +874,43 @@ def barycenter_unbalanced_sinkhorn(A, M, reg, reg_m, weights=None,
 
 
     """
+    A, M = list_to_array(A, M)
+    nx = get_backend(A, M)
+
     dim, n_hists = A.shape
     if weights is None:
-        weights = np.ones(n_hists) / n_hists
+        weights = nx.ones(n_hists, type_as=A) / n_hists
     else:
         assert(len(weights) == A.shape[1])
 
     if log:
         log = {'err': []}
 
-    K = np.exp(- M / reg)
+    K = nx.exp(-M / reg)
 
     fi = reg_m / (reg_m + reg)
 
-    v = np.ones((dim, n_hists))
-    u = np.ones((dim, 1))
-    q = np.ones(dim)
+    v = nx.ones((dim, n_hists), type_as=A)
+    u = nx.ones((dim, 1), type_as=A)
+    q = nx.ones(dim, type_as=A)
     err = 1.
 
     for i in range(numItermax):
-        uprev = u.copy()
-        vprev = v.copy()
-        qprev = q.copy()
+        uprev = nx.copy(u)
+        vprev = nx.copy(v)
+        qprev = nx.copy(q)
 
-        Kv = K.dot(v)
+        Kv = nx.dot(K, v)
         u = (A / Kv) ** fi
-        Ktu = K.T.dot(u)
-        q = ((Ktu ** (1 - fi)).dot(weights))
+        Ktu = nx.dot(K.T, u)
+        q = nx.dot(Ktu ** (1 - fi), weights)
         q = q ** (1 / (1 - fi))
         Q = q[:, None]
         v = (Q / Ktu) ** fi
 
-        if (np.any(Ktu == 0.)
-                or np.any(np.isnan(u)) or np.any(np.isnan(v))
-                or np.any(np.isinf(u)) or np.any(np.isinf(v))):
+        if (nx.any(Ktu == 0.)
+                or nx.any(nx.isnan(u)) or nx.any(nx.isnan(v))
+                or nx.any(nx.isinf(u)) or nx.any(nx.isinf(v))):
             # we have reached the machine precision
             # come back to previous solution and quit loop
             warnings.warn('Numerical errors at iteration %s' % i)
@@ -916,8 +919,9 @@ def barycenter_unbalanced_sinkhorn(A, M, reg, reg_m, weights=None,
             q = qprev
             break
             # compute change in barycenter
-        err = abs(q - qprev).max()
-        err /= max(abs(q).max(), abs(qprev).max(), 1.)
+        err = nx.max(nx.abs(q - qprev)) / max(
+            nx.max(nx.abs(q)), nx.max(nx.abs(qprev)), 1.0
+        )
         if log:
             log['err'].append(err)
         # if barycenter did not change + at least 10 iterations - stop
@@ -932,8 +936,8 @@ def barycenter_unbalanced_sinkhorn(A, M, reg, reg_m, weights=None,
 
     if log:
         log['niter'] = i
-        log['logu'] = np.log(u + 1e-300)
-        log['logv'] = np.log(v + 1e-300)
+        log['logu'] = nx.log(u + 1e-300)
+        log['logv'] = nx.log(v + 1e-300)
         return q, log
     else:
         return q
@@ -961,15 +965,15 @@ def barycenter_unbalanced(A, M, reg, reg_m, method="sinkhorn", weights=None,
 
     Parameters
     ----------
-    A : np.ndarray (dim, n_hists)
+    A : array-like (dim, n_hists)
         `n_hists` training distributions :math:`\mathbf{a}_i` of dimension `dim`
-    M : np.ndarray (dim, dim)
+    M : array-like (dim, dim)
         ground metric matrix for OT.
     reg : float
         Entropy regularization term > 0
     reg_m: float
         Marginal relaxation term > 0
-    weights : np.ndarray (n_hists,) optional
+    weights : array-like (n_hists,) optional
         Weight of each distribution (barycentric coodinates)
         If None, uniform weights are used.
     numItermax : int, optional
@@ -984,7 +988,7 @@ def barycenter_unbalanced(A, M, reg, reg_m, method="sinkhorn", weights=None,
 
     Returns
     -------
-    a : (dim,) ndarray
+    a : (dim,) array-like
         Unbalanced Wasserstein barycenter
     log : dict
         log dictionary return only if log==True in parameters
diff --git a/ot/utils.py b/ot/utils.py
index 725ca00..a23ce7e 100644
--- a/ot/utils.py
+++ b/ot/utils.py
@@ -15,7 +15,7 @@ from scipy.spatial.distance import cdist
 import sys
 import warnings
 from inspect import signature
-from .backend import get_backend
+from .backend import get_backend, Backend
 
 __time_tic_toc = time.time()
 
@@ -51,7 +51,8 @@ def kernel(x1, x2, method='gaussian', sigma=1, **kwargs):
 
 def laplacian(x):
     r"""Compute Laplacian matrix"""
-    L = np.diag(np.sum(x, axis=0)) - x
+    nx = get_backend(x)
+    L = nx.diag(nx.sum(x, axis=0)) - x
     return L
 
 
@@ -136,7 +137,7 @@ def unif(n, type_as=None):
         return np.ones((n,)) / n
     else:
         nx = get_backend(type_as)
-        return nx.ones((n,)) / n
+        return nx.ones((n,), type_as=type_as) / n
 
 
 def clean_zeros(a, b, M):
@@ -296,7 +297,8 @@ def cost_normalization(C, norm=None):
 
 def dots(*args):
     r""" dots function for multiple matrix multiply """
-    return reduce(np.dot, args)
+    nx = get_backend(*args)
+    return reduce(nx.dot, args)
 
 
 def label_normalization(y, start=0):
@@ -314,8 +316,9 @@ def label_normalization(y, start=0):
     y : array-like, shape (`n1`, )
         The input vector of labels normalized according to given start value.
     """
+    nx = get_backend(y)
 
-    diff = np.min(np.unique(y)) - start
+    diff = nx.min(nx.unique(y)) - start
     if diff != 0:
         y -= diff
     return y
@@ -482,6 +485,19 @@ class BaseEstimator(object):
     arguments (no ``*args`` or ``**kwargs``).
     """
 
+    nx: Backend = None
+
+    def _get_backend(self, *arrays):
+        nx = get_backend(
+            *[input_ for input_ in arrays if input_ is not None]
+        )
+        if nx.__name__ in ("jax", "tf"):
+            raise TypeError(
+                """JAX or TF arrays have been received but domain
+                adaptation does not support those backend.""")
+        self.nx = nx
+        return nx
+
     @classmethod
     def _get_param_names(cls):
         r"""Get parameter names for the estimator"""