diff --git a/t3f/__init__.py b/t3f/__init__.py
index a71ba25a..bda67e89 100644
--- a/t3f/__init__.py
+++ b/t3f/__init__.py
@@ -8,4 +8,4 @@
 from t3f.regularizers import *
 from t3f.riemannian import *
 from t3f.shapes import *
-from t3f.decompositions import *
\ No newline at end of file
+from t3f.decompositions import *
diff --git a/t3f/batch_ops_test.py b/t3f/batch_ops_test.py
index f365d79c..7d7514db 100644
--- a/t3f/batch_ops_test.py
+++ b/t3f/batch_ops_test.py
@@ -13,7 +13,7 @@ def testConcatMatrix(self):
     first = initializers.random_matrix_batch(((2, 3), (3, 3)), batch_size=1)
     second = initializers.random_matrix_batch(((2, 3), (3, 3)), batch_size=4)
     third = initializers.random_matrix_batch(((2, 3), (3, 3)), batch_size=3)
-    first_res = batch_ops.concat_along_batch_dim((first))
+    first_res = batch_ops.concat_along_batch_dim(first)
     first_res = ops.full(first_res)
     first_second_res = batch_ops.concat_along_batch_dim((first, second))
     first_second_res = ops.full(first_second_res)
@@ -40,7 +40,8 @@ def testConcatMatrix(self):
       first_second_third_desired_val = res[5]
       self.assertAllClose(first_res_val, first_desired_val)
       self.assertAllClose(first_second_res_val, first_second_desired_val)
-      self.assertAllClose(first_second_third_res_val, first_second_third_desired_val)
+      self.assertAllClose(first_second_third_res_val,
+                          first_second_third_desired_val)
 
   def testBatchMultiply(self):
     # Test multiplying batch of TTMatrices by individual numbers.
diff --git a/t3f/decompositions.py b/t3f/decompositions.py
index 1aab56a3..3e0aa336 100644
--- a/t3f/decompositions.py
+++ b/t3f/decompositions.py
@@ -379,7 +379,8 @@ def _round_batch_tt(tt, max_tt_rank, epsilon):
   tt_cores[0] = tf.reshape(tt_cores[0], core_shape)
   if not are_tt_ranks_defined:
     ranks = None
-  return TensorTrainBatch(tt_cores, tt.get_raw_shape(), ranks, batch_size=tt.batch_size)
+  return TensorTrainBatch(tt_cores, tt.get_raw_shape(), ranks,
+                          batch_size=tt.batch_size)
 
 
 def orthogonalize_tt_cores(tt, left_to_right=True):
@@ -513,7 +514,8 @@ def _orthogonalize_batch_tt_cores_left_to_right(tt):
 
     tt_cores[core_idx] = tf.reshape(curr_core, new_core_shape)
 
-    next_core = tf.reshape(tt_cores[core_idx + 1], (batch_size, triang_shape[2], -1))
+    next_core_shape = (batch_size, triang_shape[2], -1)
+    next_core = tf.reshape(tt_cores[core_idx + 1], next_core_shape)
     tt_cores[core_idx + 1] = tf.matmul(triang, next_core)
 
   if tt.is_tt_matrix():
diff --git a/t3f/kronecker.py b/t3f/kronecker.py
index 9508c6be..315ccbed 100644
--- a/t3f/kronecker.py
+++ b/t3f/kronecker.py
@@ -4,6 +4,7 @@
 from t3f.tensor_train import TensorTrain
 from t3f import ops
 
+
 def determinant(kron_a):
   """Computes the determinant of a given Kronecker-factorized matrix. 
 
@@ -95,10 +96,10 @@ def slog_determinant(kron_a):
     core_pow = pows / i_shapes[core_idx].value
     logdet += tf.log(core_abs_det) * core_pow
     det_sign *= core_det_sign**(core_pow)
-  
-  
+
   return det_sign, logdet
 
+
 def inv(kron_a):
   """Computes the inverse of a given Kronecker-factorized matrix.
 
@@ -142,6 +143,7 @@ def inv(kron_a):
   res_shape = kron_a.get_raw_shape()
   return TensorTrain(inv_cores, res_shape, res_ranks) 
 
+
 def cholesky(kron_a):
   """Computes the Cholesky decomposition of a given Kronecker-factorized matrix.
 
diff --git a/t3f/kronecker_test.py b/t3f/kronecker_test.py
index 0c69aa03..667ee70d 100644
--- a/t3f/kronecker_test.py
+++ b/t3f/kronecker_test.py
@@ -7,6 +7,7 @@
 from t3f import initializers
 from t3f import variables
 
+
 class KroneckerTest(tf.test.TestCase):
 
   def testIsKronNonKron(self):
@@ -38,11 +39,11 @@ def testSlogDet(self):
     # TODO: use kron and -1 * kron matrices, when mul is implemented 
     # the current version is platform-dependent
     
-    tf.set_random_seed(5) # negative derminant
+    tf.set_random_seed(5)  # negative derminant
     initializer = initializers.random_matrix(((2, 3), (2, 3)), tt_rank=1)
     kron_neg = variables.get_variable('kron_neg', initializer=initializer)
   
-    tf.set_random_seed(1) # positive determinant
+    tf.set_random_seed(1)  # positive determinant
     initializer = initializers.random_matrix(((2, 3), (2, 3)), tt_rank=1)
     kron_pos = variables.get_variable('kron_pos', initializer=initializer)
 
@@ -83,8 +84,8 @@ def testCholesky(self):
     K_2 = L_2.dot(L_2.T)
     K = np.kron(K_1, K_2)
     initializer = tensor_train.TensorTrain([K_1[None, :, :, None], 
-                                            K_2[None, :, :, None]], 
-                                            tt_ranks=7*[1])
+                                            K_2[None, :, :, None]],
+                                           tt_ranks=7*[1])
     kron_mat = variables.get_variable('kron_mat', initializer=initializer)
     init_op = tf.global_variables_initializer()
     with self.test_session() as sess:
diff --git a/t3f/ops.py b/t3f/ops.py
index 3bb140b6..6701eb29 100644
--- a/t3f/ops.py
+++ b/t3f/ops.py
@@ -52,12 +52,12 @@ def _full_tt(tt):
       intermediate_shape.append(raw_shape[0][i])
       intermediate_shape.append(raw_shape[1][i])
     res = tf.reshape(res, intermediate_shape)
-    transpose = []
+    transpose_params = []
     for i in range(0, 2 * num_dims, 2):
-      transpose.append(i)
+      transpose_params.append(i)
     for i in range(1, 2 * num_dims, 2):
-      transpose.append(i)
-    res = tf.transpose(res, transpose)
+      transpose_params.append(i)
+    res = tf.transpose(res, transpose_params)
     return tf.reshape(res, shape)
   else:
     return tf.reshape(res, shape)
@@ -166,7 +166,8 @@ def tt_tt_matmul(tt_matrix_a, tt_matrix_b):
     left_mode = a_shape[0][core_idx]
     right_mode = b_shape[1][core_idx]
     if is_res_batch:
-      core_shape = (batch_size, res_left_rank, left_mode, right_mode, res_right_rank)
+      core_shape = (batch_size, res_left_rank, left_mode, right_mode,
+                    res_right_rank)
     else:
       core_shape = (res_left_rank, left_mode, right_mode,
                     res_right_rank)
@@ -702,7 +703,8 @@ def add(tt_a, tt_b):
     raise ValueError('The batch sizes are different and not 1, broadcasting is '
                      'not available.')
 
-  is_batch_case = isinstance(tt_a, TensorTrainBatch) or isinstance(tt_b, TensorTrainBatch)
+  is_batch_case = isinstance(tt_a, TensorTrainBatch) or \
+                  isinstance(tt_b, TensorTrainBatch)
   batch_size = None
   if is_batch_case:
     if tt_a.is_tt_matrix():
diff --git a/t3f/ops_test.py b/t3f/ops_test.py
index 51206ba8..415537ca 100644
--- a/t3f/ops_test.py
+++ b/t3f/ops_test.py
@@ -69,7 +69,8 @@ def testFlatInnerTTTensbySparseTens(self):
         for rank in rank_list:
           for num_elements in [1, 10]:
             tt_1 = initializers.random_tensor(shape, tt_rank=rank)
-            sparse_flat_indices = np.random.choice(np.prod(shape), num_elements).astype(int)
+            sparse_flat_indices = np.random.choice(np.prod(shape), num_elements)
+            sparse_flat_indices = sparse_flat_indices.astype(int)
             sparse_indices = np.unravel_index(sparse_flat_indices, shape)
             sparse_indices = np.vstack(sparse_indices).transpose()
             values = np.random.randn(num_elements).astype(np.float32)
@@ -385,7 +386,6 @@ def testUnknownRanksTTMatmul(self):
       res_desired_val = sess.run(res_desired, {K_1: K_1_val, K_2: K_2_val})
       self.assertAllClose(res_desired_val, res_actual_val)
 
-
   def testHalfKnownRanksTTMatmul(self):
     # Tests tt_tt_matmul for the case  when one matrice has known ranks 
     # and the other one doesn't    
@@ -677,7 +677,7 @@ def _random_sparse(shape, non_zeros):
   sparse_indices = np.vstack(sparse_indices).transpose()
   values = np.random.randn(non_zeros).astype(np.float32)
   sparse = tf.SparseTensor(indices=sparse_indices, values=values,
-                             dense_shape=shape)
+                           dense_shape=shape)
   return sparse
 
 if __name__ == "__main__":
diff --git a/t3f/regularizers.py b/t3f/regularizers.py
index 6928e329..4c9e8650 100644
--- a/t3f/regularizers.py
+++ b/t3f/regularizers.py
@@ -31,9 +31,8 @@ def l2_regularizer(scale, scope=None):
   def l2(tt):
     """Applies l2 regularization to TensorTrain object."""
     with tf.name_scope(scope, 'l2_regularizer', [tt]) as name:
-      my_scale = tf.convert_to_tensor(scale,
-                                       dtype=tt.dtype.base_dtype,
-                                       name='scale')
+      my_scale = tf.convert_to_tensor(scale, dtype=tt.dtype.base_dtype,
+                                      name='scale')
       return tf.mul(my_scale, ops.frobenius_norm_squared(tt), name=name)
 
   return l2
@@ -68,9 +67,8 @@ def cores_regularizer(core_regularizer, scale, scope=None):
   def regularizer(tt):
     """Applies the regularization to TensorTrain object."""
     with tf.name_scope(scope, 'l2_regularizer', [tt]) as name:
-      my_scale = tf.convert_to_tensor(scale,
-                                       dtype=tt.dtype.base_dtype,
-                                       name='scale')
+      my_scale = tf.convert_to_tensor(scale, dtype=tt.dtype.base_dtype,
+                                      name='scale')
       penalty = 0.0
       for i in range(tt.ndims()):
         penalty += core_regularizer(tt.tt_cores[i])
diff --git a/t3f/riemannian_test.py b/t3f/riemannian_test.py
index b4030c4e..5bc42fd9 100644
--- a/t3f/riemannian_test.py
+++ b/t3f/riemannian_test.py
@@ -22,18 +22,20 @@ def testProjectOnItself(self):
   def testProject(self):
     # Compare our projection with the results obtained (and precomputed) from
     # tt.riemannian.project which is well tested.
-    tangent_tens_cores = ([[[-0.42095269,  0.02130842],
-         [-0.4181081 ,  0.42945687],
+    tangent_tens_cores = \
+      ([[[-0.42095269,  0.02130842],
+         [-0.4181081,  0.42945687],
          [ 0.45972439, -0.4525616 ],
          [-0.17159869, -0.14505528]]], [[[ 0.23344421],
          [ 0.81480049],
          [-0.92385135]],
 
         [[-0.19279465],
-         [ 0.524976  ],
+         [ 0.524976],
          [-0.40149197]]])
     tangent_tens = TensorTrain(tangent_tens_cores, (4, 3), (1, 2, 1))
-    tens_cores = ([[[-1.01761142,  0.36075896, -0.2493624 ],
+    tens_cores = \
+      ([[[-1.01761142,  0.36075896, -0.2493624 ],
          [-0.99896565, -1.12685474,  1.02832458],
          [ 1.08739724, -0.6537435 ,  1.99975537],
          [ 0.35128005,  0.40395104, -0.16790072]]], [[[ 0.34105142],
@@ -53,7 +55,7 @@ def testProject(self):
        [-0.04847773, -0.72908174,  0.20142675],
        [ 0.34431125, -0.20935516, -1.15864246]]
     proj = riemannian.project_sum(tens, tangent_tens)
-    with self.test_session() as sess:
+    with self.test_session():
       self.assertAllClose(desired_projection, ops.full(proj).eval())
 
   def testProjectSum(self):
diff --git a/t3f/shapes.py b/t3f/shapes.py
index fb8ddef5..6b582f46 100644
--- a/t3f/shapes.py
+++ b/t3f/shapes.py
@@ -278,4 +278,4 @@ def expand_batch_dim(tt):
     for core_idx in range(tt.ndims()):
       tt_cores.append(tf.expand_dims(tt.tt_cores[core_idx], 0))
     return TensorTrainBatch(tt_cores, tt.get_raw_shape(), tt.get_tt_ranks(),
-                            batch_size=1)
\ No newline at end of file
+                            batch_size=1)
diff --git a/t3f/tensor_train.py b/t3f/tensor_train.py
index a647f41f..2bd53fb7 100644
--- a/t3f/tensor_train.py
+++ b/t3f/tensor_train.py
@@ -92,7 +92,7 @@ def __str__(self):
                                                tt_ranks)
     else:
       return "A Tensor Train%s of shape %s, TT-ranks: %s" % (variable_str,
-                                                              shape, tt_ranks)
+                                                             shape, tt_ranks)
 
   def __getitem__(self, slice_spec):
     """Basic indexing, returns a `TensorTrain` containing the specified region.
diff --git a/t3f/tensor_train_base.py b/t3f/tensor_train_base.py
index 31716723..4c00fb00 100644
--- a/t3f/tensor_train_base.py
+++ b/t3f/tensor_train_base.py
@@ -130,10 +130,9 @@ def eval(self, feed_dict=None, session=None):
       session: (Optional.) The `Session` to be used to evaluate this sparse
         tensor. If none, the default session will be used.
     """
-    # TODO: implement feed_dict
     if session is None:
       session = tf.get_default_session()
-    session.run(self.tt_cores)
+    session.run(self.tt_cores, feed_dict=feed_dict)
 
   # TODO: do we need this?
   # @staticmethod
diff --git a/t3f/variables.py b/t3f/variables.py
index e391ad67..2bfad59d 100644
--- a/t3f/variables.py
+++ b/t3f/variables.py
@@ -124,6 +124,5 @@ def assign(ref, value, validate_shape=None, use_locking=None, name=None):
                             value.get_tt_ranks(), value.batch_size,
                             convert_to_tensors=False)
   else:
-    return TensorTrain(new_cores, value.get_raw_shape(),
-                                  value.get_tt_ranks(),
-                                  convert_to_tensors=False)
+    return TensorTrain(new_cores, value.get_raw_shape(), value.get_tt_ranks(),
+                       convert_to_tensors=False)
diff --git a/t3f/variables_test.py b/t3f/variables_test.py
index de96a22d..da21cc45 100644
--- a/t3f/variables_test.py
+++ b/t3f/variables_test.py
@@ -5,6 +5,7 @@
 from t3f import ops
 from t3f import initializers
 
+
 class VariablesTest(tf.test.TestCase):
 
   def testGetExistingVariable(self):
@@ -74,7 +75,7 @@ def testAssign(self):
       self.assertAllClose(assigner_value, after_value)
       # Assert that the value actually changed:
       abs_diff = np.linalg.norm((init_value - after_value).flatten())
-      rel_diff = abs_diff / np.linalg.norm((init_value).flatten())
+      rel_diff = abs_diff / np.linalg.norm(init_value.flatten())
       self.assertGreater(rel_diff, 0.2)