def prod(x, axis=None, keepdims=False):
  if isinstance(axis, list):
    axis = tuple(axis)
  return np.prod(x, axis=axis, keepdims=keepdims)

import numpy as np
x=np.array([[2,4,6],[2,4,6]])
 
scaling = np.prod(x, axis=1, keepdims=False)
print(x)
print(scaling)

> from keras import backend as K
> input = K.placeholder((2, 3), dtype='float32')
> input
<tf.Tensor 'Placeholder_2:0' shape=(2, 3) dtype=float32>
# It doesn't work in-place as below.
> K.cast(input, dtype='float16')
<tf.Tensor 'Cast_1:0' shape=(2, 3) dtype=float16>
> input
<tf.Tensor 'Placeholder_2:0' shape=(2, 3) dtype=float32>
# you need to assign it.
> input = K.cast(input, dtype='float16')
> input
<tf.Tensor 'Cast_2:0' shape=(2, 3) dtype=float16>

# the type of float to use throughout the session. 整个模块都是用浮点型数据
_FLOATX = 'float32' # 数据类型为32位浮点型
_EPSILON = 1e-7 # 很小的常数
_IMAGE_DATA_FORMAT = 'channels_last' # 图像数据格式 最后显示通道，tensorflow格式

def epsilon():
  """Returns the value of the fuzz factor used in numeric expressions. 
    返回数值表达式中使用的模糊因子的值
    
  # Returns
    A float.
  # Example
  ```python
    > keras.backend.epsilon()
    1e-07
  ```
  """
  return _EPSILON

def set_epsilon(e):
  """Sets the value of the fuzz factor used in numeric expressions.
  # Arguments
    e: float. New value of epsilon.
  # Example
  ```python
    > from keras import backend as K
    > K.epsilon()
    1e-07
    > K.set_epsilon(1e-05)
    > K.epsilon()
    1e-05
  ```
  """
  global _EPSILON
  _EPSILON = e

def floatx():
  """Returns the default float type, as a string.
  (e.g. 'float16', 'float32', 'float64').
  # Returns
    String, the current default float type.
  # Example
  ```python
    > keras.backend.floatx()
    'float32'
  ```
  """
  return _FLOATX

def cast_to_floatx(x):
  """Cast a Numpy array to the default Keras float type.把numpy数组投影到默认的浮点类型
  # Arguments
    x: Numpy array.
  # Returns
    The same Numpy array, cast to its new type.
  # Example
  ```python
    > from keras import backend as K
    > K.floatx()
    'float32'
    > arr = numpy.array([1.0, 2.0], dtype='float64')
    > arr.dtype
    dtype('float64')
    > new_arr = K.cast_to_floatx(arr)
    > new_arr
    array([ 1., 2.], dtype=float32)
    > new_arr.dtype
    dtype('float32')
  ```
  """
  return np.asarray(x, dtype=_FLOATX)

 def image_data_format():
  """Returns the default image data format convention ('channels_first' or 'channels_last').
  # Returns
    A string, either `'channels_first'` or `'channels_last'`
  # Example
  ```python
    > keras.backend.image_data_format()
    'channels_first'
  ```
  """
  return _IMAGE_DATA_FORMAT
 
 
def set_image_data_format(data_format):
  """Sets the value of the data format convention.
  # Arguments
    data_format: string. `'channels_first'` or `'channels_last'`.
  # Example
  ```python
    > from keras import backend as K
    > K.image_data_format()
    'channels_first'
    > K.set_image_data_format('channels_last')
    > K.image_data_format()
    'channels_last'
  ```
  """
  global _IMAGE_DATA_FORMAT
  if data_format not in {'channels_last', 'channels_first'}:
    raise ValueError('Unknown data_format:', data_format)
  _IMAGE_DATA_FORMAT = str(data_format)
 
def normalize_data_format(value):
  """Checks that the value correspond to a valid data format.
  # Arguments
    value: String or None. `'channels_first'` or `'channels_last'`.
  # Returns
    A string, either `'channels_first'` or `'channels_last'`
  # Example
  ```python
    > from keras import backend as K
    > K.normalize_data_format(None)
    'channels_first'
    > K.normalize_data_format('channels_last')
    'channels_last'
  ```
  # Raises
    ValueError: if `value` or the global `data_format` invalid.
  """
  if value is None:
    value = image_data_format()
  data_format = value.lower()
  if data_format not in {'channels_first', 'channels_last'}:
    raise ValueError('The `data_format` argument must be one of '
             '"channels_first", "channels_last". Received: ' +
             str(value))
  return data_format

def set_image_dim_ordering(dim_ordering):
  """Legacy setter for `image_data_format`.
  # Arguments
    dim_ordering: string. `tf` or `th`.
  # Example
  ```python
    > from keras import backend as K
    > K.image_data_format()
    'channels_first'
    > K.set_image_data_format('channels_last')
    > K.image_data_format()
    'channels_last'
  ```
  # Raises
    ValueError: if `dim_ordering` is invalid.
  """
  global _IMAGE_DATA_FORMAT
  if dim_ordering not in {'tf', 'th'}:
    raise ValueError('Unknown dim_ordering:', dim_ordering)
  if dim_ordering == 'th':
    data_format = 'channels_first'
  else:
    data_format = 'channels_last'
  _IMAGE_DATA_FORMAT = data_format
 
 
def image_dim_ordering():
  """Legacy getter for `image_data_format`.
  # Returns
    string, one of `'th'`, `'tf'`
  """
  if _IMAGE_DATA_FORMAT == 'channels_first':
    return 'th'
  else:
    return 'tf'

from .common import epsilon
from .common import floatx
from .common import set_epsilon
from .common import set_floatx
from .common import cast_to_floatx
from .common import image_data_format
from .common import set_image_data_format
from .common import normalize_data_format

# Set Keras base dir path given KERAS_HOME env variable, if applicable.
# Otherwise either ~/.keras or /tmp.
if 'KERAS_HOME' in os.environ: # 环境变量
  _keras_dir = os.environ.get('KERAS_HOME')
else:
  _keras_base_dir = os.path.expanduser('~')
  if not os.access(_keras_base_dir, os.W_OK):
    _keras_base_dir = '/tmp'
  _keras_dir = os.path.join(_keras_base_dir, '.keras')
 
# Default backend: TensorFlow. 默认后台是TensorFlow
_BACKEND = 'tensorflow'
 
# Attempt to read Keras config file.读取keras配置文件
_config_path = os.path.expanduser(os.path.join(_keras_dir, 'keras.json'))
if os.path.exists(_config_path):
  try:
    with open(_config_path) as f:
      _config = json.load(f)
  except ValueError:
    _config = {}
  _floatx = _config.get('floatx', floatx())
  assert _floatx in {'float16', 'float32', 'float64'}
  _epsilon = _config.get('epsilon', epsilon())
  assert isinstance(_epsilon, float)
  _backend = _config.get('backend', _BACKEND)
  _image_data_format = _config.get('image_data_format',
                   image_data_format())
  assert _image_data_format in {'channels_last', 'channels_first'}
 
  set_floatx(_floatx)
  set_epsilon(_epsilon)
  set_image_data_format(_image_data_format)
  _BACKEND = _backend