[MRG] Backend for gromov (#294)

* bregman: small correction

* gromov backend first draft

* Removing decorators

* Reworked casting method

* Bug solve

* Removing casting

* Bug solve

* toarray renamed todense ; expand_dims removed

* Warning (jax not supporting sparse matrix) moved

* Mistake corrected

* test backend

* Sparsity test for older versions of pytorch

* Trying pytorch/1.10

* Attempt to correct torch sparse bug

* Backend version of gromov tests

* Random state introduced for remaining gromov functions

* review changes

* code coverage

* Docs (first draft, to be continued)

* Gromov docs

* Prettified docs

* mistake corrected in the docs

* little change

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

Author: ncassereau

ot/backend.py

@@ -26,6 +26,7 @@
 
 import numpy as np
 import scipy.special as scipy
+from scipy.sparse import issparse, coo_matrix, csr_matrix
 
 try:
     import torch
@@ -539,6 +540,86 @@ def reshape(self, a, shape):
         """
         raise NotImplementedError()
 
+    def coo_matrix(self, data, rows, cols, shape=None, type_as=None):
+        r"""
+        Creates a sparse tensor in COOrdinate format.
+
+        This function follows the api from :any:`scipy.sparse.coo_matrix`
+
+        See: https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.coo_matrix.html
+        """
+        raise NotImplementedError()
+
+    def issparse(self, a):
+        r"""
+        Checks whether or not the input tensor is a sparse tensor.
+
+        This function follows the api from :any:`scipy.sparse.issparse`
+
+        See: https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.issparse.html
+        """
+        raise NotImplementedError()
+
+    def tocsr(self, a):
+        r"""
+        Converts this matrix to Compressed Sparse Row format.
+
+        This function follows the api from :any:`scipy.sparse.coo_matrix.tocsr`
+
+        See: https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.coo_matrix.tocsr.html
+        """
+        raise NotImplementedError()
+
+    def eliminate_zeros(self, a, threshold=0.):
+        r"""
+        Removes entries smaller than the given threshold from the sparse tensor.
+
+        This function follows the api from :any:`scipy.sparse.csr_matrix.eliminate_zeros`
+
+        See: https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.sparse.csr_matrix.eliminate_zeros.html
+        """
+        raise NotImplementedError()
+
+    def todense(self, a):
+        r"""
+        Converts a sparse tensor to a dense tensor.
+
+        This function follows the api from :any:`scipy.sparse.csr_matrix.toarray`
+
+        See: https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.csr_matrix.toarray.html
+        """
+        raise NotImplementedError()
+
+    def where(self, condition, x, y):
+        r"""
+        Returns elements chosen from x or y depending on condition.
+
+        This function follows the api from :any:`numpy.where`
+
+        See: https://numpy.org/doc/stable/reference/generated/numpy.where.html
+        """
+        raise NotImplementedError()
+
+    def copy(self, a):
+        r"""
+        Returns a copy of the given tensor.
+
+        This function follows the api from :any:`numpy.copy`
+
+        See: https://numpy.org/doc/stable/reference/generated/numpy.copy.html
+        """
+        raise NotImplementedError()
+
+    def allclose(self, a, b, rtol=1e-05, atol=1e-08, equal_nan=False):
+        r"""
+        Returns True if two arrays are element-wise equal within a tolerance.
+
+        This function follows the api from :any:`numpy.allclose`
+
+        See: https://numpy.org/doc/stable/reference/generated/numpy.allclose.html
+        """
+        raise NotImplementedError()
+
 
 class NumpyBackend(Backend):
     """
@@ -712,6 +793,46 @@ def stack(self, arrays, axis=0):
     def reshape(self, a, shape):
         return np.reshape(a, shape)
 
+    def coo_matrix(self, data, rows, cols, shape=None, type_as=None):
+        if type_as is None:
+            return coo_matrix((data, (rows, cols)), shape=shape)
+        else:
+            return coo_matrix((data, (rows, cols)), shape=shape, dtype=type_as.dtype)
+
+    def issparse(self, a):
+        return issparse(a)
+
+    def tocsr(self, a):
+        if self.issparse(a):
+            return a.tocsr()
+        else:
+            return csr_matrix(a)
+
+    def eliminate_zeros(self, a, threshold=0.):
+        if threshold > 0:
+            if self.issparse(a):
+                a.data[self.abs(a.data) <= threshold] = 0
+            else:
+                a[self.abs(a) <= threshold] = 0
+        if self.issparse(a):
+            a.eliminate_zeros()
+        return a
+
+    def todense(self, a):
+        if self.issparse(a):
+            return a.toarray()
+        else:
+            return a
+
+    def where(self, condition, x, y):
+        return np.where(condition, x, y)
+
+    def copy(self, a):
+        return a.copy()
+
+    def allclose(self, a, b, rtol=1e-05, atol=1e-08, equal_nan=False):
+        return np.allclose(a, b, rtol=rtol, atol=atol, equal_nan=equal_nan)
+
 
 class JaxBackend(Backend):
     """
@@ -889,6 +1010,48 @@ def stack(self, arrays, axis=0):
     def reshape(self, a, shape):
         return jnp.reshape(a, shape)
 
+    def coo_matrix(self, data, rows, cols, shape=None, type_as=None):
+        # Currently, JAX does not support sparse matrices
+        data = self.to_numpy(data)
+        rows = self.to_numpy(rows)
+        cols = self.to_numpy(cols)
+        nx = NumpyBackend()
+        coo_matrix = nx.coo_matrix(data, rows, cols, shape=shape, type_as=type_as)
+        matrix = nx.todense(coo_matrix)
+        return self.from_numpy(matrix)
+
+    def issparse(self, a):
+        # Currently, JAX does not support sparse matrices
+        return False
+
+    def tocsr(self, a):
+        # Currently, JAX does not support sparse matrices
+        return a
+
+    def eliminate_zeros(self, a, threshold=0.):
+        # Currently, JAX does not support sparse matrices
+        if threshold > 0:
+            return self.where(
+                self.abs(a) <= threshold,
+                self.zeros((1,), type_as=a),
+                a
+            )
+        return a
+
+    def todense(self, a):
+        # Currently, JAX does not support sparse matrices
+        return a
+
+    def where(self, condition, x, y):
+        return jnp.where(condition, x, y)
+
+    def copy(self, a):
+        # No need to copy, JAX arrays are immutable
+        return a
+
+    def allclose(self, a, b, rtol=1e-05, atol=1e-08, equal_nan=False):
+        return jnp.allclose(a, b, rtol=rtol, atol=atol, equal_nan=equal_nan)
+
 
 class TorchBackend(Backend):
     """
@@ -999,7 +1162,7 @@ def maximum(self, a, b):
             a = torch.tensor([float(a)], dtype=b.dtype, device=b.device)
         if isinstance(b, int) or isinstance(b, float):
             b = torch.tensor([float(b)], dtype=a.dtype, device=a.device)
-        if torch.__version__ >= '1.7.0':
+        if hasattr(torch, "maximum"):
             return torch.maximum(a, b)
         else:
             return torch.max(torch.stack(torch.broadcast_tensors(a, b)), axis=0)[0]
@@ -1009,7 +1172,7 @@ def minimum(self, a, b):
             a = torch.tensor([float(a)], dtype=b.dtype, device=b.device)
         if isinstance(b, int) or isinstance(b, float):
             b = torch.tensor([float(b)], dtype=a.dtype, device=a.device)
-        if torch.__version__ >= '1.7.0':
+        if hasattr(torch, "minimum"):
             return torch.minimum(a, b)
         else:
             return torch.min(torch.stack(torch.broadcast_tensors(a, b)), axis=0)[0]
@@ -1129,3 +1292,50 @@ def stack(self, arrays, axis=0):
 
     def reshape(self, a, shape):
         return torch.reshape(a, shape)
+
+    def coo_matrix(self, data, rows, cols, shape=None, type_as=None):
+        if type_as is None:
+            return torch.sparse_coo_tensor(torch.stack([rows, cols]), data, size=shape)
+        else:
+            return torch.sparse_coo_tensor(
+                torch.stack([rows, cols]), data, size=shape,
+                dtype=type_as.dtype, device=type_as.device
+            )
+
+    def issparse(self, a):
+        return getattr(a, "is_sparse", False) or getattr(a, "is_sparse_csr", False)
+
+    def tocsr(self, a):
+        # Versions older than 1.9 do not support CSR tensors. PyTorch 1.9 and 1.10 offer a very limited support
+        return self.todense(a)
+
+    def eliminate_zeros(self, a, threshold=0.):
+        if self.issparse(a):
+            if threshold > 0:
+                mask = self.abs(a) <= threshold
+                mask = ~mask
+                mask = mask.nonzero()
+            else:
+                mask = a._values().nonzero()
+            nv = a._values().index_select(0, mask.view(-1))
+            ni = a._indices().index_select(1, mask.view(-1))
+            return self.coo_matrix(nv, ni[0], ni[1], shape=a.shape, type_as=a)
+        else:
+            if threshold > 0:
+                a[self.abs(a) <= threshold] = 0
+            return a
+
+    def todense(self, a):
+        if self.issparse(a):
+            return a.to_dense()
+        else:
+            return a
+
+    def where(self, condition, x, y):
+        return torch.where(condition, x, y)
+
+    def copy(self, a):
+        return torch.clone(a)
+
+    def allclose(self, a, b, rtol=1e-05, atol=1e-08, equal_nan=False):
+        return torch.allclose(a, b, rtol=rtol, atol=atol, equal_nan=equal_nan)