mxnet symbol類定義：https://github.com/apache/incubator-mxnet/blob/master/python/mxnet/symbol/symbol.py
對於一個symbol，可分爲non-grouped和grouped。且symbol具有輸出，和輸出屬性。比如，對於Variable而言，其輸入和輸出就是它自己。對於c = a+b，c的內部有個_plus0 symbol，對於_plus0這個symbol，它的輸入是a，b，輸出是_plus0_output。
class Symbol(SymbolBase):
"""Symbol is symbolic graph of the mxnet."""
# disable dictionary storage, also do not have parent type.
# pylint: disable=no-member
其中，Symbol還不是最基礎的類，Symbol類繼承了SymbolBase這個類。
而SymbolBase這個類實際是在
https://github.com/apache/incubator-mxnet/blob/master/python/mxnet/symbol/_internal.py
中引用的，通過以下方式引用：
from .._ctypes.symbol import SymbolBase, _set_symbol_class, _set_np_symbol_class
而SymbolBase的定義是在：https://github.com/apache/incubator-mxnet/blob/master/python/mxnet/_ctypes/symbol.py
這裏暫時先不管SymbolBase，這應該是是python調用c++接口創建的一個類。
回到Symbol中來，對於mxnet符號式編程而言，定義的任何網絡，或者變量，都是symbol類型，所以，瞭解這個類就顯得很重要。
Symbol類中有幾類函數：
1、普通函數
2、__xx__ 函數
3、@property 修飾的函數
4、函數名爲xx，實際調用op.xx的函數
1、普通函數
attr
根據key返回symbol對應的屬性字符串，只對non-grouped symbols起作用。
def attr(self, key):
"""Returns the attribute string for corresponding input key from the symbol.
list_attr
得到symbol的所有屬性
def list_attr(self, recursive=False):
"""Gets all attributes from the symbol.
attr_dict
遞歸的得到symbol和孩子的屬性
def attr_dict(self):
"""Recursively gets all attributes from the symbol and its children.
Example
-------
>>> a = mx.sym.Variable('a', attr={'a1':'a2'})
>>> b = mx.sym.Variable('b', attr={'b1':'b2'})
>>> c = a+b
>>> c.attr_dict()
{'a': {'a1': 'a2'}, 'b': {'b1': 'b2'}}
_set_attr
通過key-value方式，對attr進行設置
def _set_attr(self, **kwargs):
"""Sets an attribute of the symbol.
For example. A._set_attr(foo="bar") adds the mapping ``"{foo: bar}"``
to the symbol's attribute dictionary.
get_internals
獲取symbol的所有內部節點symbol，是一個group類型（包括輸入，輸出節點symbol）。如果我們想階段一個network，應該獲取它某內部節點的輸出，這樣才能作爲新增加的symbol的輸入。
def get_internals(self):
"""Gets a new grouped symbol `sgroup`. The output of `sgroup` is a list of
outputs of all of the internal nodes.
get_children
獲取當前symbol輸出節點的inputs
def get_children(self):
"""Gets a new grouped symbol whose output contains
inputs to output nodes of the original symbol.
list_arguments
列出當前symbol的所有參數（可以配合call對symbol進行改造）
def list_arguments(self):
"""Lists all the arguments in the symbol.
list_outputs
列出當前smybol的所有輸出，如果當前symbol是grouped類型，回遍歷輸出每一個symbol的輸出
def list_outputs(self):
"""Lists all the outputs in the symbol.
list_auxiliary_states
列出symbol中的輔助狀態參數，比如BN
def list_auxiliary_states(self):
"""Lists all the auxiliary states in the symbol.
Example
-------
>>> a = mx.sym.var('a')
>>> b = mx.sym.var('b')
>>> c = a + b
>>> c.list_auxiliary_states()
[]
Example of auxiliary states in `BatchNorm`.
list_inputs
列出當前symbol的所有輸入參數，和輔助狀態，等價於 list_arguments和 list_auxiliary_states
def list_inputs(self):
"""Lists all arguments and auxiliary states of this Symbol.
2、__xx__函數
__repr__
對於gruop symbol，它是沒有name屬性的，print或者回車，結果就是其內部symbol節點的name
__iter__(self):
普通的symbol長度都只有1，只有Grouped 的symbol，長度才大於1：return (self[i] for i in range(len(self)))
算數及邏輯運算：
+，-，*, /,%,abs,**, 取負(-x)，==，!=，>，>=，<，<=， # 使用時，要注意Broadcasting 是否支持
def __abs__(self):
"""x.__abs__() <=> abs(x) <=> x.abs() <=> mx.symbol.abs(x, y)"""
return self.abs()
def __add__(self, other):
"""x.__add__(y) <=> x+y
其他
__copy__和__deep_copy__
通過deep_copy，創建一個深拷貝，返回輸入對象的一個拷貝，包括它當前所有參數的當前狀態，比如weight，bias等
__call__
表示symbol的實例是一個可調用對象。可以返回一個新的symbol，這個symbol繼承了之前symbol的權重啥的，但是和之前的symbol是不同的對象，可以輸入參數對symbol進行組合。
def __call__(self, *args, **kwargs):
"""Composes symbol using inputs.
Returns
-------
The resulting symbol.
"""
s = self.__copy__() # 這裏對symbol實例做了一次深拷貝，返回的新的symbol
s._compose(*args, **kwargs) # 實際調用的_compose函數
return s
# 對當前的symbol進行編譯，返回一個新的symbol，可以指定新symbol的name，其他輸入參數必須是symbol類型
# 當前symbol的輸入參數，可以通過 .list_arguments()獲取
def _compose(self, *args, **kwargs):
"""Composes symbol using inputs.
x._compose(y, z) <=> x(y,z)
This function mutates the current symbol.
Example
-------
Returns
-------
The resulting symbol.
"""
name = kwargs.pop('name', None)
if name:
name = c_str(name)
if len(args) != 0 and len(kwargs) != 0:
raise TypeError('compose only accept input Symbols \
either as positional or keyword arguments, not both')
這裏，我改變了b，將其輸入參數的x的值變爲了tt。
__getitem__
如果symbol的長度只有1，那麼返回的就是它的輸出symbol，如果symbol長度>1，可以通過切片訪問其輸出symbol，返回的也是一個Group symbol。symbol可以分爲non-grouped和grouped。
獲取內部節點symbol還可以輸入str，但輸入的str必須屬於list_outputs()，
def __getitem__(self, index):
"""x.__getitem__(i) <=> x[i]
Returns a sliced view of the input symbol.
Parameters
----------
index : int or str
Indexing key
"""
output_count = len(self)
if isinstance(index, py_slice):
# 輸入切片
if isinstance(index, string_types):
# 輸入字符串
# Returning this list of names is expensive. Some symbols may have hundreds of outputs
output_names = self.list_outputs()
idx = None
for i, name in enumerate(output_names):
if name == index:
if idx is not None:
raise ValueError('There are multiple outputs with name \"%s\"' % index)
idx = i
if idx is None:
raise ValueError('Cannot find output that matches name \"%s\"' % index)
index = idx
symbol.py 除了Symbol這個類之外，還有遊離在外的函數：
1、
def var(name, attr=None, shape=None, lr_mult=None, wd_mult=None, dtype=None,
init=None, stype=None, **kwargs):
"""Creates a symbolic variable with specified name.
# for back compatibility
Variable = var # 調用 mx.sym.var和mx.sym.Variable 等價
2、
def Group(symbols, create_fn=Symbol):
"""Creates a symbol that contains a collection of other symbols, grouped together.
A classic symbol (`mx.sym.Symbol`) will be returned if all the symbols in the list
are of that type; a numpy symbol (`mx.sym.np._Symbol`) will be returned if all the
symbols in the list are of that type. A type error will be raised if a list of mixed
classic and numpy symbols are provided.
Example
-------
>>> a = mx.sym.Variable('a')
>>> b = mx.sym.Variable('b')
>>> mx.sym.Group([a,b])
<Symbol Grouped>
Parameters
----------
symbols : list
List of symbols to be grouped.
3、
def load(fname):
"""Loads symbol from a JSON file.
You also get the benefit being able to directly load/save from cloud storage(S3, HDFS).
Returns
-------
sym : Symbol
The loaded symbol.
See Also
--------
Symbol.save : Used to save symbol into file.
# 輸入文件可以是hdfs文件
4、
數學相關函數，輸入可爲scalar或者是symbol
def pow(base, exp):
"""Returns element-wise result of base element raised to powers from exp element.
base 和 exp可以是數字或者symbol
# def power(base, exp): # 實際調用pow
def maximum(left, right):
def minimum(left, right):
def hypot(left, right): # 返回直角三角形的斜邊
def eye(N, M=0, k=0, dtype=None, **kwargs):
"""Returns a new symbol of 2-D shpae, filled with ones on the diagonal and zeros elsewhere. # 返回2D shape的symbol，對角線爲1，其餘位置爲0
def zeros(shape, dtype=None, **kwargs):
"""Returns a new symbol of given shape and type, filled with zeros. # 返回一個shape的全0 symbol
def ones(shape, dtype=None, **kwargs):
"""Returns a new symbol of given shape and type, filled with ones.
def full(shape, val, dtype=None, **kwargs):
"""Returns a new array of given shape and type, filled with the given value `val`.
def arange(start, stop=None, step=1.0, repeat=1, infer_range=False, name=None, dtype=None):
"""Returns evenly spaced values within a given interval.
def arange(start, stop=None, step=1.0, repeat=1, infer_range=False, name=None, dtype=None):
"""Returns evenly spaced values within a given interval.
def linspace(start, stop, num, endpoint=True, name=None, dtype=None):
"""Return evenly spaced numbers within a specified interval.
def histogram(a, bins=10, range=None, **kwargs):
"""Compute the histogram of the input data.
def split_v2(ary, indices_or_sections, axis=0, squeeze_axis=False):
"""Split an array into multiple sub-arrays.