深度学习的始祖框架，grandfather级别的框架 —— Theano —— 示例代码学习（5）

代码1：（求雅可比矩阵， jacobian矩阵求解）

import theano
from theano import tensor

# Creating a vector
x = tensor.dvector('x')

# Creating 'y' expression
y = (2 * x ** 3)

# Computing derivative
Output, updates = theano.scan(lambda i, y, x : tensor.grad(y[i], x),\
                               sequences=tensor.arange(y.shape[0]),\
                                  non_sequences=[y, x])

# Creating function
# fun = theano.function([x], Output, updates=updates)
fun = theano.function([x], Output)

# Calling function
print( fun([3,3]) )

运行结果：

代码2：（求黑森矩阵， Hession矩阵求解）

import theano
from theano import tensor

# Creating a vector
x = tensor.dvector('x')

# Creating 'y' expression
y = (2 * x ** 3)

# Calculating cost
cost = y.sum()

# Computing derivative
derivative = tensor.grad(cost, x)
output, updates = theano.scan(lambda i, derivative,x : \
                              tensor.grad(derivative[i], x),\
                               sequences=tensor.arange(derivative.shape[0]),\
                                 non_sequences=[derivative, x])

# Creating function
# fun = theano.function([x], output, updates=updates)
fun = theano.function([x], output)

# Calling function
print( fun([3,3]) )

运行结果：

代码3：（theano自定义列表List类型）

import theano.typed_list

# Creating typedlist
f1 = theano.typed_list.TypedListType(theano.tensor.fvector)()

# Creating a vector
f2 = theano.tensor.fvector()

# Appending 'f1' and 'f2'
f3 = theano.typed_list.append(f1, f2)

# Creating function which takes two vectors 'f1' and 'f2' as input and gives 'f3' as output
fun = theano.function([f1, f2], f3)

# Calling function
print( fun([[1,2]], [2]) )
print( type(fun([[1,2]], [2])) )

运行结果：

代码4：（theano的switch选择函数）

import theano
from theano import tensor

# Creating two scalars
x, y = tensor.scalars('x', 'y')
xx, yy = tensor.vectors('xx', 'yy')

# switch expression
switch_expression = tensor.switch(tensor.gt(x, y), x, y)
switch_expression2 = tensor.switch(tensor.gt(xx, yy), xx, yy)

# Creating function
fun = theano.function([x, y], switch_expression, mode=theano.compile.mode.Mode(linker='vm'))
fun2 = theano.function([xx, yy], switch_expression2, mode=theano.compile.mode.Mode(linker='vm'))

# Calling function fun(12,11)
print( fun(12,11) )

print( fun2([2, 2, 2], [1, 1, 1]) )

print( fun2([2, 0, 2], [1, 3, 1]) )

运行结果：

代码5：

import theano

# Creating a theano variable 'x' with value 10
x = theano.shared(10, 'xxx')

#This will just print the variable x
print(x)

# Eval function
print(x.eval()) #This will print its actual value

运行结果：

代码6：（和概率推断框架pymc3联合使用）（PyMC3框架联合使用）

import theano
from theano import tensor
import pymc3 as pm

# Creating pymc3 model
model = pm.Model()

# Creating tensor variable
mu = tensor.scalar('mu')

# Log-normal distribution
distribution = pm.Normal.dist(0, 1).logp(mu)

# Creating function
fun = theano.function([mu], distribution)

# Calling function
print( fun(4) )

运行结果：

代码7：

import theano
from theano import tensor
from theano.ifelse import ifelse

# Creating variables
# Input neuron
x = tensor.vector('x')
# Weight
w = tensor.vector('w')
# Bias
b = tensor.scalar('b')

# Creating expression:
z = tensor.dot(x,w)+b

# Output neuron
o = ifelse(tensor.lt(z,0),0,1)
fun_neural_network = theano.function([x,w,b],o)

# Defining Inputs, Weights and bias
inputs = [ [0, 0], [0, 1], [1, 0], [1, 1] ]
weights = [ 1, 1]
bias = 0

# Iterate through all inputs and find outputs:
for ip in range(len(inputs)):
    m = inputs[ip]
    out = fun_neural_network(m,weights,bias)
    print('The output for x1 = {} & x2 = {} is {}'.format(m[0],m[1],out))

运行结果：

代码8：

import theano
from theano import tensor
from theano.ifelse import ifelse

import numpy as np
from random import random

# Creating variables:
x = tensor.matrix('x') #Input neurons

w1 = theano.shared(np.array([random(),random()])) #Random generation of weights
w2 = theano.shared(np.array([random(),random()]))
w3 = theano.shared(np.array([random(),random()]))
b1 = theano.shared(1.) #Bias
b2 = theano.shared(1.)

rate_of_learning = 0.01 # Learning rate
y1 = 1/(1+tensor.exp(-tensor.dot(x,w1)-b1))
y2 = 1/(1+tensor.exp(-tensor.dot(x,w2)-b1))
x2 = tensor.stack([y1,y2],axis=1)
y3 = 1/(1+tensor.exp(-tensor.dot(x2,w3)-b2))
actual = tensor.vector('actual') #Actual output
cost = -(actual*tensor.log(y3) + (1-actual)*tensor.log(1-y3)).sum()
dervw1,dervw2,dervw3,dervb1,dervb2 = tensor.grad(cost,[w1,w2,w3,b1,b2])

# Model training
model_train = theano.function( inputs = [x, actual],\
                               outputs = [y3, cost],\
                               updates = [ [w1, w1-rate_of_learning*dervw1],\
                                           [w2, w2-rate_of_learning*dervw2],\
                                           [w3, w3-rate_of_learning*dervw3],\
                                           [b1, b1-rate_of_learning*dervb1],\
                                           [b2, b2-rate_of_learning*dervb2] ] )

inputs = [ [0, 0], [0, 1], [1, 0], [1, 1] ]
outputs = [0,1,0,1]

# Iterate through all inputs and find outputs:
cost = []
for i in range(100000):
    pred, cost_iteration = model_train(inputs, outputs)
    cost.append(cost_iteration)

# Output
print('The outputs of the Neural network are => ')

for i in range(len(inputs)):
    print('The output for x1 = {} | x2 = {} => {}'.format(inputs[i][0],inputs[i][1],pred[i]))

运行结果：

代码9：（矩阵拼接）

import theano
from theano import tensor

# Creating two matrices
a, b = tensor.matrices('a', 'b')

# Using concatenate function
merge_c = tensor.concatenate([a, b])

# Creating function
cancat_function = theano.function([a, b], merge_c)

# Calling function
print( cancat_function([[1,2]], [[1,2], [3,4]]) )

运行结果：