theano基础学习笔记1

1.定义变量

theano中的变量类型有字节、整数、浮点数、复数等多种形式， 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为例，定义浮点数使用dscalar 它表示的是有64位浮点数的标量

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

输出都为TensorType(float64, scalar) 下面为简单的例子

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

上面的例子中定义了两个矢量a和b,进行的运算是 a2+b2+2ab ,在theano中需要通过function函数来定义,function函数中一个输入一个输出矢量对应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.计算梯度

T.grad=∂y∂x ,下面的程序比较简单就不做说明。

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设置缺省值

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共享变量

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.创建随机数

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]))