Update some en api docs (#20496)

* Fix api docs. test=document-fix

* Fix en docs. test=develop

* Fix the doc of dynamic_gru. test=document_fix

* Update API.spec. test=document_fix

* Fix codestyle test=develop, test=document_fix

paddle/fluid/API.spec

@@ -127,15 +127,15 @@ paddle.fluid.layers.center_loss (ArgSpec(args=['input', 'label', 'num_classes',
 paddle.fluid.layers.embedding (ArgSpec(args=['input', 'size', 'is_sparse', 'is_distributed', 'padding_idx', 'param_attr', 'dtype'], varargs=None, keywords=None, defaults=(False, False, None, None, 'float32')), ('document', 'c51fcac7a4f5786ca41f27fa60bd22c5'))
 paddle.fluid.layers.dynamic_lstm (ArgSpec(args=['input', 'size', 'h_0', 'c_0', 'param_attr', 'bias_attr', 'use_peepholes', 'is_reverse', 'gate_activation', 'cell_activation', 'candidate_activation', 'dtype', 'name'], varargs=None, keywords=None, defaults=(None, None, None, None, True, False, 'sigmoid', 'tanh', 'tanh', 'float32', None)), ('document', 'd4a82e2f5feb20c4a23ced8054e047ed'))
 paddle.fluid.layers.dynamic_lstmp (ArgSpec(args=['input', 'size', 'proj_size', 'param_attr', 'bias_attr', 'use_peepholes', 'is_reverse', 'gate_activation', 'cell_activation', 'candidate_activation', 'proj_activation', 'dtype', 'name', 'h_0', 'c_0', 'cell_clip', 'proj_clip'], varargs=None, keywords=None, defaults=(None, None, True, False, 'sigmoid', 'tanh', 'tanh', 'tanh', 'float32', None, None, None, None, None)), ('document', 'b35fe3e0c2ecca15a8be658277e064ec'))
-paddle.fluid.layers.dynamic_gru (ArgSpec(args=['input', 'size', 'param_attr', 'bias_attr', 'is_reverse', 'gate_activation', 'candidate_activation', 'h_0', 'origin_mode'], varargs=None, keywords=None, defaults=(None, None, False, 'sigmoid', 'tanh', None, False)), ('document', '83617c165827e030636c80486d5de6f3'))
-paddle.fluid.layers.gru_unit (ArgSpec(args=['input', 'hidden', 'size', 'param_attr', 'bias_attr', 'activation', 'gate_activation', 'origin_mode'], varargs=None, keywords=None, defaults=(None, None, 'tanh', 'sigmoid', False)), ('document', '33974b9bfa69f2f1eb85e6f956dff04e'))
+paddle.fluid.layers.dynamic_gru (ArgSpec(args=['input', 'size', 'param_attr', 'bias_attr', 'is_reverse', 'gate_activation', 'candidate_activation', 'h_0', 'origin_mode'], varargs=None, keywords=None, defaults=(None, None, False, 'sigmoid', 'tanh', None, False)), ('document', 'a3364b36fb3190b9bd75e419aa75573b'))
+paddle.fluid.layers.gru_unit (ArgSpec(args=['input', 'hidden', 'size', 'param_attr', 'bias_attr', 'activation', 'gate_activation', 'origin_mode'], varargs=None, keywords=None, defaults=(None, None, 'tanh', 'sigmoid', False)), ('document', '0b10a755b469d0b85b3a5cac38b4cf01'))
 paddle.fluid.layers.linear_chain_crf (ArgSpec(args=['input', 'label', 'param_attr', 'length'], varargs=None, keywords=None, defaults=(None, None)), ('document', 'b28bdb43160e9667be2a3457d19d9f5b'))
 paddle.fluid.layers.crf_decoding (ArgSpec(args=['input', 'param_attr', 'label', 'length'], varargs=None, keywords=None, defaults=(None, None)), ('document', '708ce0348b74d3e0c7885c2c524b7fa7'))
 paddle.fluid.layers.cos_sim (ArgSpec(args=['X', 'Y'], varargs=None, keywords=None, defaults=None), ('document', '48ec1ba2d75c4e2faf8d9a47350462ae'))
 paddle.fluid.layers.cross_entropy (ArgSpec(args=['input', 'label', 'soft_label', 'ignore_index'], varargs=None, keywords=None, defaults=(False, -100)), ('document', 'd1985a930a59c3bd41a7c1d72594f5b9'))
 paddle.fluid.layers.bpr_loss (ArgSpec(args=['input', 'label', 'name'], varargs=None, keywords=None, defaults=(None,)), ('document', 'ae57e6e5136dade436f0df1f11770afa'))
 paddle.fluid.layers.square_error_cost (ArgSpec(args=['input', 'label'], varargs=None, keywords=None, defaults=None), ('document', '4ed09e115b50ec7393674c4c09d223a2'))
-paddle.fluid.layers.chunk_eval (ArgSpec(args=['input', 'label', 'chunk_scheme', 'num_chunk_types', 'excluded_chunk_types', 'seq_length'], varargs=None, keywords=None, defaults=(None, None)), ('document', 'b02844e0ad4bd713c5fe6802aa13219c'))
+paddle.fluid.layers.chunk_eval (ArgSpec(args=['input', 'label', 'chunk_scheme', 'num_chunk_types', 'excluded_chunk_types', 'seq_length'], varargs=None, keywords=None, defaults=(None, None)), ('document', 'a8aa2071cae18df1e8dde9183d64bfb1'))
 paddle.fluid.layers.sequence_conv (ArgSpec(args=['input', 'num_filters', 'filter_size', 'filter_stride', 'padding', 'padding_start', 'bias_attr', 'param_attr', 'act', 'name'], varargs=None, keywords=None, defaults=(3, 1, True, None, None, None, None, None)), ('document', 'ebddcc5a1073ef065d22b4673e36b1d2'))
 paddle.fluid.layers.conv2d (ArgSpec(args=['input', 'num_filters', 'filter_size', 'stride', 'padding', 'dilation', 'groups', 'param_attr', 'bias_attr', 'use_cudnn', 'act', 'name', 'data_format'], varargs=None, keywords=None, defaults=(1, 0, 1, None, None, None, True, None, None, 'NCHW')), ('document', 'e91c63b8ac8c35982c0ac518537e44bf'))
 paddle.fluid.layers.conv3d (ArgSpec(args=['input', 'num_filters', 'filter_size', 'stride', 'padding', 'dilation', 'groups', 'param_attr', 'bias_attr', 'use_cudnn', 'act', 'name', 'data_format'], varargs=None, keywords=None, defaults=(1, 0, 1, None, None, None, True, None, None, 'NCDHW')), ('document', 'feff9c8ebb4d4d0be5345f9042f57c8e'))
@@ -149,14 +149,14 @@ paddle.fluid.layers.adaptive_pool3d (ArgSpec(args=['input', 'pool_size', 'pool_t
 paddle.fluid.layers.batch_norm (ArgSpec(args=['input', 'act', 'is_test', 'momentum', 'epsilon', 'param_attr', 'bias_attr', 'data_layout', 'in_place', 'name', 'moving_mean_name', 'moving_variance_name', 'do_model_average_for_mean_and_var', 'fuse_with_relu', 'use_global_stats'], varargs=None, keywords=None, defaults=(None, False, 0.9, 1e-05, None, None, 'NCHW', False, None, None, None, False, False, False)), ('document', '1400433bae7876d0407ae205be39b7a1'))
 paddle.fluid.layers.instance_norm (ArgSpec(args=['input', 'epsilon', 'param_attr', 'bias_attr', 'name'], varargs=None, keywords=None, defaults=(1e-05, None, None, None)), ('document', '23d6fba8ad8495f67a66d8878be5b0be'))
 paddle.fluid.layers.data_norm (ArgSpec(args=['input', 'act', 'epsilon', 'param_attr', 'data_layout', 'in_place', 'name', 'moving_mean_name', 'moving_variance_name', 'do_model_average_for_mean_and_var'], varargs=None, keywords=None, defaults=(None, 1e-05, None, 'NCHW', False, None, None, None, False)), ('document', '5ba4cdb4ea5c03382da545335ffc05b7'))
-paddle.fluid.layers.beam_search_decode (ArgSpec(args=['ids', 'scores', 'beam_size', 'end_id', 'name'], varargs=None, keywords=None, defaults=(None,)), ('document', '83e08f21af41ac8bac37aeab1f86fdd0'))
+paddle.fluid.layers.beam_search_decode (ArgSpec(args=['ids', 'scores', 'beam_size', 'end_id', 'name'], varargs=None, keywords=None, defaults=(None,)), ('document', 'eafa177a7fed6178a51c1affa7f46a40'))
 paddle.fluid.layers.conv2d_transpose (ArgSpec(args=['input', 'num_filters', 'output_size', 'filter_size', 'padding', 'stride', 'dilation', 'groups', 'param_attr', 'bias_attr', 'use_cudnn', 'act', 'name', 'data_format'], varargs=None, keywords=None, defaults=(None, None, 0, 1, 1, None, None, None, True, None, None, 'NCHW')), ('document', 'ed24c2d0f82cd9a3b40488157285a584'))
 paddle.fluid.layers.conv3d_transpose (ArgSpec(args=['input', 'num_filters', 'output_size', 'filter_size', 'padding', 'stride', 'dilation', 'groups', 'param_attr', 'bias_attr', 'use_cudnn', 'act', 'name', 'data_format'], varargs=None, keywords=None, defaults=(None, None, 0, 1, 1, None, None, None, True, None, None, 'NCDHW')), ('document', 'efb1e3bc87339cb26faa2edae210e8b0'))
 paddle.fluid.layers.sequence_expand (ArgSpec(args=['x', 'y', 'ref_level', 'name'], varargs=None, keywords=None, defaults=(-1, None)), ('document', '10e122eb755c2bd1f78ef2332b28f1a0'))
 paddle.fluid.layers.sequence_expand_as (ArgSpec(args=['x', 'y', 'name'], varargs=None, keywords=None, defaults=(None,)), ('document', '858c432e7cbd8bb952cc2eb555457d50'))
 paddle.fluid.layers.sequence_pad (ArgSpec(args=['x', 'pad_value', 'maxlen', 'name'], varargs=None, keywords=None, defaults=(None, None)), ('document', 'df08b9c499ab3a90f95d08ab5b6c6c62'))
 paddle.fluid.layers.sequence_unpad (ArgSpec(args=['x', 'length', 'name'], varargs=None, keywords=None, defaults=(None,)), ('document', 'e478180d5bc010a84f35af958cafa62c'))
-paddle.fluid.layers.lstm_unit (ArgSpec(args=['x_t', 'hidden_t_prev', 'cell_t_prev', 'forget_bias', 'param_attr', 'bias_attr', 'name'], varargs=None, keywords=None, defaults=(0.0, None, None, None)), ('document', 'fe126c58e4339410e875ab1eba246d21'))
+paddle.fluid.layers.lstm_unit (ArgSpec(args=['x_t', 'hidden_t_prev', 'cell_t_prev', 'forget_bias', 'param_attr', 'bias_attr', 'name'], varargs=None, keywords=None, defaults=(0.0, None, None, None)), ('document', 'f5a878b6166f34878376a58d7e6fa95c'))
 paddle.fluid.layers.reduce_sum (ArgSpec(args=['input', 'dim', 'keep_dim', 'name'], varargs=None, keywords=None, defaults=(None, False, None)), ('document', 'ecb55075fdf89a866bcede85e60aebad'))
 paddle.fluid.layers.reduce_mean (ArgSpec(args=['input', 'dim', 'keep_dim', 'name'], varargs=None, keywords=None, defaults=(None, False, None)), ('document', '968c9b17affaf714e5021c3dc8d68c73'))
 paddle.fluid.layers.reduce_max (ArgSpec(args=['input', 'dim', 'keep_dim', 'name'], varargs=None, keywords=None, defaults=(None, False, None)), ('document', 'd37e3a9a05c00e032d4b7876c4f6b414'))
@@ -181,7 +181,7 @@ paddle.fluid.layers.im2sequence (ArgSpec(args=['input', 'filter_size', 'stride',
 paddle.fluid.layers.nce (ArgSpec(args=['input', 'label', 'num_total_classes', 'sample_weight', 'param_attr', 'bias_attr', 'num_neg_samples', 'name', 'sampler', 'custom_dist', 'seed', 'is_sparse'], varargs=None, keywords=None, defaults=(None, None, None, None, None, 'uniform', None, 0, False)), ('document', '38297567127888e01542857839058d52'))
 paddle.fluid.layers.sampled_softmax_with_cross_entropy (ArgSpec(args=['logits', 'label', 'num_samples', 'num_true', 'remove_accidental_hits', 'use_customized_samples', 'customized_samples', 'customized_probabilities', 'seed'], varargs=None, keywords=None, defaults=(1, True, False, None, None, 0)), ('document', 'd4435a63d34203339831ee6a86ef9242'))
 paddle.fluid.layers.hsigmoid (ArgSpec(args=['input', 'label', 'num_classes', 'param_attr', 'bias_attr', 'name', 'path_table', 'path_code', 'is_custom', 'is_sparse'], varargs=None, keywords=None, defaults=(None, None, None, None, None, False, False)), ('document', 'b83e7dfa81059b39bb137922dc914f50'))
-paddle.fluid.layers.beam_search (ArgSpec(args=['pre_ids', 'pre_scores', 'ids', 'scores', 'beam_size', 'end_id', 'level', 'is_accumulated', 'name', 'return_parent_idx'], varargs=None, keywords=None, defaults=(0, True, None, False)), ('document', '1270395ce97a4e1b556104abbb14f096'))
+paddle.fluid.layers.beam_search (ArgSpec(args=['pre_ids', 'pre_scores', 'ids', 'scores', 'beam_size', 'end_id', 'level', 'is_accumulated', 'name', 'return_parent_idx'], varargs=None, keywords=None, defaults=(0, True, None, False)), ('document', '2b505ddaa309fd7b9be5445e41ca76d5'))
 paddle.fluid.layers.row_conv (ArgSpec(args=['input', 'future_context_size', 'param_attr', 'act'], varargs=None, keywords=None, defaults=(None, None)), ('document', 'a6477957b44907787b3c74157400b80c'))
 paddle.fluid.layers.multiplex (ArgSpec(args=['inputs', 'index'], varargs=None, keywords=None, defaults=None), ('document', '2c4d1ae83da6ed35e3b36ba1b3b51d23'))
 paddle.fluid.layers.layer_norm (ArgSpec(args=['input', 'scale', 'shift', 'begin_norm_axis', 'epsilon', 'param_attr', 'bias_attr', 'act', 'name'], varargs=None, keywords=None, defaults=(True, True, 1, 1e-05, None, None, None, None)), ('document', '678de6d6d0c93da74189990b039daae8'))
@@ -281,7 +281,7 @@ paddle.fluid.layers.similarity_focus (ArgSpec(args=['input', 'axis', 'indexes',
 paddle.fluid.layers.hash (ArgSpec(args=['input', 'hash_size', 'num_hash', 'name'], varargs=None, keywords=None, defaults=(1, None)), ('document', 'a0b73c21be618cec0281e7903039e5e3'))
 paddle.fluid.layers.grid_sampler (ArgSpec(args=['x', 'grid', 'name'], varargs=None, keywords=None, defaults=(None,)), ('document', '90c74742f48c70b103f1fbb9eb129066'))
 paddle.fluid.layers.log_loss (ArgSpec(args=['input', 'label', 'epsilon', 'name'], varargs=None, keywords=None, defaults=(0.0001, None)), ('document', 'ef1701e11d60508fe8f02dd2a8c60bdf'))
-paddle.fluid.layers.add_position_encoding (ArgSpec(args=['input', 'alpha', 'beta', 'name'], varargs=None, keywords=None, defaults=(None,)), ('document', 'e399f9436fed5f7ff480d8532e42c937'))
+paddle.fluid.layers.add_position_encoding (ArgSpec(args=['input', 'alpha', 'beta', 'name'], varargs=None, keywords=None, defaults=(None,)), ('document', 'bd8b28e6c1640b13a42b0524f86f7800'))
 paddle.fluid.layers.bilinear_tensor_product (ArgSpec(args=['x', 'y', 'size', 'act', 'name', 'param_attr', 'bias_attr'], varargs=None, keywords=None, defaults=(None, None, None, None)), ('document', '6755168c4b2308e1e4f54cb56fa7dcb2'))
 paddle.fluid.layers.merge_selected_rows (ArgSpec(args=['x', 'name'], varargs=None, keywords=None, defaults=(None,)), ('document', 'b2b0e5d5c155ce24bafc38b78cd0b164'))
 paddle.fluid.layers.get_tensor_from_selected_rows (ArgSpec(args=['x', 'name'], varargs=None, keywords=None, defaults=(None,)), ('document', '2c568321feb4d16c41a83df43f95089d'))
@@ -922,7 +922,7 @@ paddle.fluid.transpiler.DistributeTranspilerConfig.__init__ (ArgSpec(args=['self
 paddle.fluid.nets.simple_img_conv_pool (ArgSpec(args=['input', 'num_filters', 'filter_size', 'pool_size', 'pool_stride', 'pool_padding', 'pool_type', 'global_pooling', 'conv_stride', 'conv_padding', 'conv_dilation', 'conv_groups', 'param_attr', 'bias_attr', 'act', 'use_cudnn'], varargs=None, keywords=None, defaults=(0, 'max', False, 1, 0, 1, 1, None, None, None, True)), ('document', '5e89c978199c4ecce2b26d5fed1ec52b'))
 paddle.fluid.nets.sequence_conv_pool (ArgSpec(args=['input', 'num_filters', 'filter_size', 'param_attr', 'act', 'pool_type', 'bias_attr'], varargs=None, keywords=None, defaults=(None, 'sigmoid', 'max', None)), ('document', 'b2d435f782ac8ea3ca480b8d24e7f5b4'))
 paddle.fluid.nets.glu (ArgSpec(args=['input', 'dim'], varargs=None, keywords=None, defaults=(-1,)), ('document', '3efe197c8e3e75f84a4c464d8b74e943'))
-paddle.fluid.nets.scaled_dot_product_attention (ArgSpec(args=['queries', 'keys', 'values', 'num_heads', 'dropout_rate'], varargs=None, keywords=None, defaults=(1, 0.0)), ('document', 'b1a07a0000eb9103e3a143ca8c13de5b'))
+paddle.fluid.nets.scaled_dot_product_attention (ArgSpec(args=['queries', 'keys', 'values', 'num_heads', 'dropout_rate'], varargs=None, keywords=None, defaults=(1, 0.0)), ('document', '375898e47266633635f4c2096e1ac296'))
 paddle.fluid.nets.img_conv_group (ArgSpec(args=['input', 'conv_num_filter', 'pool_size', 'conv_padding', 'conv_filter_size', 'conv_act', 'param_attr', 'conv_with_batchnorm', 'conv_batchnorm_drop_rate', 'pool_stride', 'pool_type', 'use_cudnn'], varargs=None, keywords=None, defaults=(1, 3, None, None, False, 0.0, 1, 'max', True)), ('document', 'a59c581d5969266427e841abe69f694a'))
 paddle.fluid.optimizer.SGDOptimizer ('paddle.fluid.optimizer.SGDOptimizer', ('document', 'fc09d6e6c1083cec2dce51f6f9f4ecaf'))
 paddle.fluid.optimizer.SGDOptimizer.__init__ (ArgSpec(args=['self', 'learning_rate', 'regularization', 'name'], varargs=None, keywords=None, defaults=(None, None)), ('document', '6adf97f83acf6453d4a6a4b1070f3754'))

python/paddle/fluid/nets.py

@@ -363,67 +363,67 @@ def scaled_dot_product_attention(queries,
                                  num_heads=1,
                                  dropout_rate=0.):
     """
-    The dot-product attention.
-
+    This interface Multi-Head Attention using scaled dot product.
     Attention mechanism can be seen as mapping a query and a set of key-value
-    pairs to an output. The output is computed as a weighted sum of the values,
-    where the weight assigned to each value is computed by a compatibility
-    function (dot-product here) of the query with the corresponding key.
+    pairs to an output. Multi-Head Attention performs attention using multi-head
+    parallel, and the inputs of attention would be transformed by linear projection.
+    The formula is as follows:
 
-    The dot-product attention can be implemented through (batch) matrix
-    multipication as follows:
+    .. math::
 
-        .. math::
+        MultiHead(Q, K, V ) & = Concat(head_1, ..., head_h)
+
+        where \  head_i & = Attention(QW_i^Q , KW_i^K , VW_i^V )
 
-            Attention(Q, K, V)= softmax(QK^\mathrm{T})V
+        Attention(Q, K, V) & = softmax (\\frac{QK^\mathrm{T}}{\sqrt{d_k}}) V
 
-    Refer to `Attention Is All You Need
-    <https://arxiv.org/pdf/1706.03762.pdf>`_.
+    For more details, please refer to `Attention Is All You Need
+    <https://arxiv.org/pdf/1706.03762.pdf>`_ .
+
+    Note that the implementation is adapted to batch, and all matrix multiplication
+    in :math:`Attention(Q, K, V)` is batched matrix multiplication. Refer to
+    :ref:`api_fluid_layers_matmul` .
 
     Args:
-        queries (Variable): The input variable which should be a 3-D Tensor.
-        keys (Variable): The input variable which should be a 3-D Tensor.
-        values (Variable): The input variable which should be a 3-D Tensor.
-        num_heads (int): Head number to compute the scaled dot product
-            attention. Default: 1.
-        dropout_rate (float): The dropout rate to drop the attention weight.
-            Default: 0.0.
+        queries (Variable): A 3-D Tensor with shape :math:`[N, L_q, d_k \\times h]` ,
+            where :math:`N` stands for batch size, :math:`L_q` for the sequence length
+            of query, :math:`d_k \\times h` for the feature size of query, :math:`h` for
+            head number. The data type should be float32 or float64.
+        keys (Variable): A 3-D Tensor with shape :math:`[N, L_k, d_k \\times h]` ,
+            where :math:`N` stands for batch size, :math:`L_k` for the sequence length
+            of key, :math:`d_k \\times h` for the feature size of key, :math:`h` for head
+            number. The data type should be the same as ``queries`` .
+        values (Variable): A 3-D Tensor with shape :math:`[N, L_k, d_v \\times h]` ,
+            where :math:`N` stands for batch size, :math:`L_k` for the sequence length
+            of key, :math:`d_v \\times h` for the feature size of value, :math:`h` for head
+            number. The data type should be the same as ``queries`` .
+        num_heads (int, optional): Indicate the number of head. If the numher
+            is 1, linear projection would not be performed on inputs. Default: 1.
+        dropout_rate (float, optional): The rate to drop the attention weight.
+            Default: 0.0, which means no dropout.
 
     Returns:
-        Variable: A 3-D Tensor computed by multi-head scaled dot product\
-            attention.
+        Variable: A 3-D Tensor with shape :math:`[N, L_q, d_v \\times h]` , \
+            where :math:`N` stands for batch size, :math:`L_q` for the sequence \
+            length of query, :math:`d_v \\times h` for the feature size of value. \
+            It has the same data type with inputs, representing the output of \
+            Multi-Head Attention.
 
     Raises:
-        ValueError: If input queries, keys, values are not 3-D Tensors.
-
-    NOTES:
-        1. When num_heads > 1, three linear projections are learned respectively
-           to map input queries, keys and values into queries', keys' and values'.
-           queries', keys' and values' have the same shapes with queries, keys
-           and values.
-        2. When num_heads == 1, scaled_dot_product_attention has no learnable
-           parameters.
+        ValueError: Inputs quries, keys and values should all be 3-D tensors.
+        ValueError: The hidden size of queries and keys should be the same.
+        ValueError: The max sequence length in query batch and in key batch should be the same.
+        ValueError: he hidden size of keys must be divisible by the number of attention heads.
+        ValueError: he hidden size of values must be divisible by the number of attention heads.
 
     Examples:
         .. code-block:: python
 
             import paddle.fluid as fluid
 
-            queries = fluid.layers.data(name="queries",
-                                        shape=[3, 5, 9],
-                                        dtype="float32",
-                                        append_batch_size=False)
-            queries.stop_gradient = False
-            keys = fluid.layers.data(name="keys",
-                                     shape=[3, 6, 9],
-                                     dtype="float32",
-                                     append_batch_size=False)
-            keys.stop_gradient = False
-            values = fluid.layers.data(name="values",
-                                       shape=[3, 6, 10],
-                                       dtype="float32",
-                                       append_batch_size=False)
-            values.stop_gradient = False
+            queries = fluid.data(name="queries", shape=[3, 5, 9], dtype="float32")
+            keys = fluid.data(name="keys", shape=[3, 6, 9], dtype="float32")
+            values = fluid.data(name="values", shape=[3, 6, 10], dtype="float32")
             contexts = fluid.nets.scaled_dot_product_attention(queries, keys, values)
             contexts.shape  # [3, 5, 10]
     """