import theano
a = theano.tensor.vector()   # 引入tensor中的vector型
out = a + a**10
f = theano.function([a], out)
print(f([0,1,2]))            # 输出[0.   2. 1026.]

import theano
import theano.tensor as T
x = T.dmatrix('x')
s = 1/(1 + T.exp(-x))
logistic = theano.function([x], s)
logistic([[0, 1],[-1, -2]])       # 输出array([[0.5         ,0.73105858],
                                               [0.26894142 , 0.11920292]])

>>> a, b = T.dmatrices('a', 'b')             # dmatrices 提供多个输出，这是声明多变量的一个捷径
>>> diff = a - b
>>> abs_diff = abs(diff)
>>> diff_squared = diff**2
>>> f = theano.function([a, b], [diff, abs_diff, diff_squared])
  >>> f([[1, 1], [1, 1]], [[0, 1], [2, 3]])
     [array([[ 1., 0.],
            [-1., -2.]]), array([[ 1., 0.],
            [ 1., 2.]]), array([[ 1., 0.],
            [ 1., 4.]])]

>>> from theano import shared
>>> state = shared(0)
>>> inc = T.iscalar('inc')
>>> accumulator = function([inc], state, updates=[(state, state+inc)])

>>> print(state.get_value())
0
>>> accumulator(1)
array(0)
>>> print(state.get_value())
1
>>> accumulator(300)
array(1)
>>> print(state.get_value())
301

>>> state.set_value(-1)
>>> accumulator(3)
array(-1)
>>> print(state.get_value())
2                                            # 此时共享变量值为2，注意下文

  >>> decrementor = function([inc], state, updates=[(state, state-inc)])          # 定义另一个函数来共享shared variable
  >>> decrementor(2)                                                              # 给inc赋值为2
  array(2)                                                                        # 此时输出共享变量值还为2，注意上文
  >>> print(state.get_value())                                                    # update 将state更新为0
  0

>>> fn_of_state = state * 2 + inc
>>> # The type of foo must match the shared variable we are replacing
>>> # with the ``givens``
>>> foo = T.scalar(dtype=state.dtype)                                                 # 因为下文要用foo代替state，所以要获得相同类型
>>> skip_shared = function([inc, foo], fn_of_state, givens=[(state, foo)])            # 这里用foo代替state！
>>> skip_shared(1, 3) # we're using 3 for the state, not state.value                  # 这里的1 赋值给了inc， 3赋值给了foo， 在计算中，用foo代替了state 
array(7)                                                                              # state *2+inc变为 foo *2+inc ，所以为7
>>> print(state.get_value()) # old state still there, but we didn't use it            # state 值没变，所以仍然为0
0

> import theano
>>> import theano.tensor as T
>>> state = theano.shared(0)
>>> inc = T.iscalar('inc')
>>> accumulator = theano.function([inc], state, updates=[(state, state+inc)],on_unused_input='ignore')
>>> accumulator(10)
array(0)
>>> print(state.get_value())
10


>>> new_state = theano.shared(0)
>>> new_accumulator = accumulator.copy(swap={state:new_state})               # 利用swap参数将new_state替代原accumulate中的state
>>> new_accumulator(100)
[array(0)]
>>> print(new_state.get_value())
100


>>> print(state.get_value())                                                 # 原函数中的state值未变
10


>>> null_accumulator = accumulator.copy(delete_updates=True)                 # 再定义一个新的accumulator函数，新函数移除掉了update
  >>> null_accumulator(9000)                                      
  [array(10)]
  >>> print(state.get_value())                                                 # 这个新函数没有了uodates功能，同时也不再使用参数 inc
  10                                                                           # 如果没有移除updates，则值应该为9010。移除后，只剩state的值

>>> arr = np.arange(10)
>>> np.random.shuffle(arr)
>>> arr
[1 7 5 2 9 4 3 6 0 8]

>>> arr = np.arange(9).reshape((3, 3))
>>> np.random.shuffle(arr)
>>> arr
array([[3, 4, 5],
       [6, 7, 8],
       [0, 1, 2]])

>>> np.random.permutation(10)
array([1, 7, 4, 3, 0, 9, 2, 5, 8, 6])
>>> np.random.permutation([1, 4, 9, 12, 15])
array([15,  1,  9,  4, 12])
>>> arr = np.arange(9).reshape((3, 3))
>>> np.random.permutation(arr)
array([[6, 7, 8],
       [0, 1, 2],
       [3, 4, 5]])

import numpy
import theano
import theano.tensor as T
rng = numpy.random
N = 400     # training sample size
feats = 784 # number of input variables
# generate a dataset: D = (input_values, target_class)
D = (rng.randn(N, feats), rng.randint(size=N, low=0, high=2))
training_steps = 10000
# Declare Theano symbolic variables
x = T.dmatrix("x")
y = T.dvector("y")
# initialize the weight vector w randomly
# this and the following bias variable b
# are shared so they keep their values
# between training iterations (updates)
w = theano.shared(rng.randn(feats), name="w")
# initialize the bias term
b = theano.shared(0., name="b")
print("Initial model:")
print(w.get_value())
print(b.get_value())
# Construct Theano expression graph
p_1 = 1 / (1 + T.exp(-T.dot(x, w) - b)) # Probability that target = 1
prediction = p_1 > 0.5 # The prediction thresholded
xent = -y * T.log(p_1) - (1-y) * T.log(1-p_1) # Cross-entropy loss function
cost = xent.mean() + 0.01 * (w ** 2).sum()# The cost to minimize
gw, gb = T.grad(cost, [w, b]) # Compute the gradient of the cost
# w.r.t weight vector w and bias term b (we shall return to this in a following section of this tutorial)

# Compile
train = theano.function( inputs=[x,y], outputs=[prediction, xent], updates=((w, w - 0.1 * gw), (b, b - 0.1 * gb)))
predict = theano.function(inputs=[x], outputs=prediction)

# Train
for i in range(training_steps):
pred, err = train(D[0], D[1])
print("Final model:")
print(w.get_value())
print(b.get_value())
print("target values for D:")
print(D[1])
print("prediction on D:")
print(predict(D[0]))

>>> import theano
>>> import theano.tensor as T
>>> x = T.dvector('x')
>>> y = x ** 2
>>> J, updates = theano.scan(lambda i, y,x : T.grad(y[i], x), sequences=T.arange(y.shape[0]), non_sequences=[y,x])
>>> f = theano.function([x], J, updates=updates)
>>> f([4, 4])
array([[ 8., 0.],
[ 0., 8.]])