theano基礎學習筆記1

1.定義變量

theano中的變量類型有字節、整數、浮點數、複數等多種形式，
byte: bscalar, bvector, bmatrix, brow, bcol, btensor3, btensor4
16-bit integers: wscalar, wvector, wmatrix, wrow, wcol, wtensor3, wtensor4
32-bit integers: iscalar, ivector, imatrix, irow, icol, itensor3, itensor4
64-bit integers: lscalar, lvector, lmatrix, lrow, lcol, ltensor3, ltensor4
float: fscalar, fvector, fmatrix, frow, fcol, ftensor3, ftensor4
double: dscalar, dvector, dmatrix, drow, dcol, dtensor3, dtensor4
complex: cscalar, cvector, cmatrix, crow, ccol, ctensor3, ctensor4
以常用到的dscalar爲例，定義浮點數使用dscalar 它表示的是有64位浮點數的標量

import theano
import theano.tensor as T 
x = T.dscalar('x')
x.type
T.dscalar

輸出都爲TensorType(float64, scalar)
下面爲簡單的例子

from __future__ import print_function
import theano
from theano import pp
a = theano.tensor.vector()  # declare variable
b = theano.tensor.vector()  # declare variable
out = a ** 2 + b ** 2 + 2 * a * b  # build symbolic expression
f = theano.function([a, b], out)   # compile function
print(f([1, 2], [4, 5]))  # prints [ 25.  49.]
print(pp(out))  #a**2+b**2+2*a*b

上面的例子中定義了兩個矢量a和b,進行的運算是a2+b2+2ab ,在theano中需要通過function函數來定義,function函數中一個輸入一個輸出矢量對應位置相加平方也就是(1+4)2=25 和(2+5)2=49

import theano
import numpy
from theano import pp
a = theano.tensor.vector()  # declare variable
b = theano.tensor.vector()  # declare variable
c = a ** 2 + b ** 2 + 2 * a * b  # build symbolic expression
numpy.allclose(c.eval({a : [1,2], b : [4,5]}), [25,49]) #True

2.計算梯度

T.grad=∂y∂x ,下面的程序比較簡單就不做說明。

import numpy
import theano
import theano.tensor as T
from theano import pp
x = T.dscalar('x')
y = x ** 2
gy = T.grad(y, x)
pp(gy)  # print out the gradient prior to optimization
'((fill((x ** TensorConstant{2}), TensorConstant{1.0}) * TensorConstant{2}) * (x ** (TensorConstant{2} - TensorConstant{1})))'
f = theano.function([x], gy)
f(4)  #array(8.0)
numpy.allclose(f(94.2), 188.4)  #True

3. In設置缺省值

from theano import In
from theano import function
x, y = T.dscalars('x', 'y')
z = x + y
f = function([x, In(y, value=1)], z)
f(2)  #array(3.0)

4. shared共享變量

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

5.創建隨機數

from theano.tensor.shared_randomstreams import RandomStreams
from theano import function
srng = RandomStreams(seed=234)
rv_u = srng.uniform((2,2))
rv_n = srng.normal((2,2))
f = function([], rv_u)
g = function([], rv_n, no_default_updates=True)    #Not updating rv_n.rng
nearly_zeros = function([], rv_u + rv_u - 2 * rv_u)

6.logistic regression

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]))