In [123]:

    

import numpy as np
import math
from matplotlib import mlab
from matplotlib import pylab as plt
from theano import *
import theano.tensor as T
%matplotlib inline


    

In [124]:

    

#Определение Theano-символических объектов:
x = T.fvector('x')
x0 = T.fvector('x0')
s = T.fvector('s')
y = T.fvector('y')
alpha = T.lscalar('alpha')

#Создание Theano-функции определяющей сумму гауссианов:
gaussList, updates = scan(
        fn = lambda s, x0, prior_result, x: prior_result + (1/s)*T.exp(-(0.5*s**(-2))*(x - x0)**2),
        outputs_info = T.zeros_like(x),
        non_sequences = x,
        sequences = [s, x0]
)
gaussSummExp = gaussList[-1]

gaussSumm = theano.function(
    inputs = [x, s, x0],
    outputs = gaussSummExp,
    allow_input_downcast = True
)

#Изначальные параметры:
x_Min = -15
x_Max = 15
s_Original = np.array([1, 0.5, 1])
x0_Original = np.array([-5, 0, 5])

#Оригинальные данные:
x_Original = np.linspace(x_Min, x_Max, 10000, endpoint = False)
y_Original = gaussSumm(x_Original, s_Original, x0_Original)
plt.plot (x_Original, y_Original,'green')


    

    
Out[124]:





[<matplotlib.lines.Line2D at 0x1242aaf7e48>]






    

In [125]:

    

# Training set:
m_Train = 200
m = T.lscalar('m')
x_Train = np.linspace(x_Min, x_Max, m_Train, endpoint = False)
y_Train = gaussSumm(x_Train, s_Original, x0_Original)
plt.plot(x_Train, y_Train, 'x')


    

    
Out[125]:





[<matplotlib.lines.Line2D at 0x1242a390d68>]






    

In [126]:

    

def plotFour(omg, yOrig, yPred, I, J):
    error = abs(yOrig - yPred)
    fig = plt.figure()
    fig, ((ax1, ax2), (ax3, ax4)) = plt.subplots(2, 2)

    ax1 = plt.subplot(221)
    ax1.set_title('Original Function:')
    ax1.plot(omg, yOrig, 'blue')

    ax2 = plt.subplot(222)
    ax2.set_title('Fitted gaussComp() Function:')
    ax2.plot(omg, yPred,'red') 

    ax3 = plt.subplot(223)
    ax3.set_title('Cost Function:')
    ax3.plot(I, J)

    ax4 = plt.subplot(224)
    ax4.set_title('Error:')
    ax4.plot(omg, error)


    fig.subplots_adjust(left = 0, bottom = 0, right = 2, top = 2, hspace = 0.2, wspace = 0.2)


    

In [127]:

    

#Формирование выражения для ценовой функции:
jExprs = T.sum((gaussSummExp-y)**2)/(2*m)
J = theano.function(
    inputs = [x, y, m, s, x0],
    outputs = jExprs,
    allow_input_downcast = True
)

#Построение градиента ценовой цункции:
g_s = T.grad(jExprs, s)
g_x0 = T.grad(jExprs, x0)

initial_s = np.array([0.1, 2., 0.7]) 
initial_x0 = np.array([-6., 1., 6.]) 
#Определим оптимизируемые shared-параметры суммы гауссианов:
#nG = theano.shared(len(s_Original))
s_t = theano.shared(initial_s)
x0_t = theano.shared(initial_x0)
updates = [(s_t, s_t - alpha * g_s),
           (x0_t, x0_t - alpha * g_x0)]


    

In [128]:

    

x_T = np.linspace(x_Min, x_Max, 100000, endpoint = False)
y_T = gaussSumm(x_T, s_t.get_value(), x0_t.get_value())
plt.plot(x_T, y_T,)


    

    
Out[128]:





[<matplotlib.lines.Line2D at 0x1242df77208>]






    

In [129]:

    

#Theano-функция, обновляющая параметры  модели.
trainBatch = theano.function(
    inputs = [x, y, m, alpha, s, x0],
    outputs = jExprs,
    updates = updates,
    allow_input_downcast = True
)


    

In [130]:

    

def batch_Descent(x_Train, y_Train, N, alpha_batch, initial_s, initial_x0):
    s_t.set_value(initial_s)
    x0_t.set_value(initial_x0)
    J_l = []
    I = np.linspace(0, N-1, N)
    for i in range(N):
        J_l.append(trainBatch(x_Train, y_Train, len(x_Train), alpha_batch, s_t.get_value(), x0_t.get_value()))
    y_Pred = gaussSumm(x_Original, s_t.get_value(), x0_t.get_value())
    plotFour(x_Original, y_Original, y_Pred, I, J_l)
    return [s_t.get_value(), x0_t.get_value()]


    

In [131]:

    

initial_s = np.array([0.1, 2., 0.7]) 
initial_x0 = np.array([-6., 1., 6.]) 

N_B = 1000
alpha_batch = 1
prmB = batch_Descent(x_Train, y_Train, N_B, alpha_batch, initial_s, initial_x0)
print(prmB)


    

    




[array([ 1.00000006,  0.50000002,  1.        ]), array([ -5.00000023e+00,  -1.32545614e-08,   5.00000023e+00])]






    






<matplotlib.figure.Figure at 0x1242b819908>






    

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