In [513]:

    

import math
import random
import numpy as np
from matplotlib import mlab
from matplotlib import pylab as plt
%matplotlib inline


#Функции вычисления значения гауссиана и композиции гауссиана в наборе точек при заданных параметрах, возвращает Array из NumPy:
def gaussian(omg, prm):
    return (1/(prm[0]*math.sqrt(2*math.pi)))*np.exp(-(omg-prm[1])**2/(2*prm[0]**2))


def gaussComp(omg, prm):
    a = np.zeros(omg.size)
    for gauss in prm:
        a = a + gaussian(omg, gauss)
    return a

#Изначальные параметры:
omgMin = -10
omgMax = 40
paramsOriginal = [[1, 0], [1.5,20], [3, 10]]

#Строим эталонный набор данных:
omgOriginal = np.linspace(omgMin, omgMax, 100000, endpoint = False)
yOriginal = gaussComp(omgOriginal, paramsOriginal)

plt.plot (omgOriginal, yOriginal,'green')


    

    
Out[513]:





[<matplotlib.lines.Line2D at 0x21ef5990>]






    

In [514]:

    

#Строим тренировочный набор данных:
m = 150
omgTrain = np.linspace(omgMin, omgMax, m, endpoint = False)
yTrain = gaussComp(omgTrain, paramsOriginal)

plt.plot(omgTrain,yTrain, 'x')


    

    
Out[514]:





[<matplotlib.lines.Line2D at 0x224954b0>]






    

In [515]:

    

#Вычисление весовых функций и градиентов:
#Batch

def JB(omg, y, prm):
    Jv = (0.5/len(omg))*(gaussComp(omg, prm) - y)**2
    return np.sum(Jv)

def gradientB(omg, y, prm):
    prm = prm.tolist()
    grad = np.zeros((len(prm), 2))
    j = 0
    for gauss in prm:
        grad[j][0] = (1/m)*np.sum((gaussComp(omg, prm)-y)*((-1/gauss[0])*gaussian(omg, gauss) + gaussian(omg, gauss)*((omg-gauss[1])**2/gauss[0]**3)))
        grad[j][1] = (1/m)*np.sum((gaussComp(omg, prm)-y)*gaussian(omg, gauss)*(omg-gauss[1])*(1/(gauss[0]**2))) 
        j = j + 1
    return grad

#Stochastic
def JS(omg, y, prm):
    Jv = (1/2)*(gaussComp(omg, prm) - y)**2
    return np.sum(Jv)

def gradientS(omg, y, prm):
    grad = np.zeros((len(prm), 2))
    j = 0
    for gauss in prm:
        grad[j][0] = np.sum((gaussComp(omg, prm)-y)*((-1/gauss[0])*gaussian(omg, gauss) + gaussian(omg, gauss)*((omg-gauss[1])**2/gauss[0]**3)))
        grad[j][1] = np.sum((gaussComp(omg, prm)-y)*gaussian(omg, gauss)*(omg-gauss[1])*(1/(gauss[0]**2)))
        j = j + 1
    return grad


    

In [516]:

    

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 [517]:

    

N = 70000
alpha = 1
initialParams = [[2,-1], [1, 25], [5, 12]]


    

In [518]:

    

#Batch Gradient Descent
paramsB = np.array(initialParams)
Jb = []
I = []

for i in range(N):
    I.append(i)
    Jb.append(JB(omgTrain, yTrain, paramsB))
    paramsB = paramsB - alpha*gradientB(omgTrain, yTrain, paramsB)
    


print(paramsB)

#Построим графики:

yBatch = gaussComp(omgOriginal, paramsB.tolist())
errorB = yOriginal - yBatch
plotFour(omgOriginal, yOriginal, yBatch, I, Jb)


    

    




[[  1.00002927e+00   2.53141552e-05]
 [  1.49918458e+00   2.00014818e+01]
 [  3.01119459e+00   1.00310597e+01]]






    






<matplotlib.figure.Figure at 0x21e8a130>






    

In [519]:

    

#N = 25000
#alpha = 2
#initialParams = [[2,-1], [1, 25]]


    

In [520]:

    

#Stochastic Gradient Descent
paramsS = np.array(initialParams)
Js = []
Is = []

for i in range(N):
    K = random.randint(0, omgTrain.size - 1)
    omgK = np.array(omgTrain[K])
    yK = np.array(yTrain[K])
    Is.append(i)
    Js.append(JB(omgTrain, yTrain, paramsS))
    paramsS = paramsS - alpha*gradientS(omgK, yK, paramsS)
print(paramsS)

#Графики:
yStochastic = gaussComp(omgOriginal, paramsS.tolist())
plotFour(omgOriginal, yOriginal, yStochastic, Is, Js)


    

    




[[  1.00002200e+00  -1.25286161e-05]
 [  1.49897321e+00   2.00019976e+01]
 [  3.01811218e+00   1.00417443e+01]]






    






<matplotlib.figure.Figure at 0x15dfe2d0>






    

In [521]:

    

#Minibatch Gradient Descent


    

In [522]:

    

fig = plt.figure()
fig, ax1 = plt.subplots(1,1)

ax1 = plt.subplot(111)
ax1.set_title('All methods and original:')
ax1.plot(omgOriginal, yOriginal, 'b--', )
ax1.plot(omgOriginal, yBatch, 'g')
ax1.plot(omgOriginal, yStochastic, 'r')
fig.subplots_adjust(left = 0, bottom = 0, right = 2, top = 2, hspace = 0.2, wspace = 0.2)


    

    






<matplotlib.figure.Figure at 0x2245e5b0>