In [60]:

    

import torch as T
import math
import numpy as np
from matplotlib import mlab
from matplotlib import pylab as plt
from torch.autograd import Variable, grad
from tqdm import tqdm_notebook
from IPython.display import clear_output
%matplotlib inline

#equation: eq == x''(t) + omega^2*x(t)=0
#x(0)=0==x0, x'(0)=1==v0
#j = (eq(t))^2 + (H(t) - E)^2 + (x(0))^2 + (x'(0)-1)^2
#basis: sigmoid(Vi*t + Bi)

#Размер базиса и прочие параметры:
ammount = 1
m = 100

#Начальные условия и параметры системы:
x0 = 0.0
v0 = 1.0
M = 1.0
k = 1.0
omega2 = k/M
E = 0.5*(M*v0**2+k*x0**2)

#Область построения:

timeCont = T.linspace(0, 2*math.pi, 150)
timeTrain = T.linspace(0, 2*math.pi, m)

f1 = (T.sin(timeCont*math.sqrt(omega2))*math.sqrt(omega2)).numpy()
f2 = (T.sin(timeTrain*math.sqrt(omega2))*math.sqrt(omega2)).numpy()

plt.plot(timeCont.numpy(), f1, 'green')
plt.plot(timeTrain.numpy(), f2, 'x')


    

    
Out[60]:





[<matplotlib.lines.Line2D at 0x7f01dfeca208>]






    

In [61]:

    

W = Variable(T.Tensor([1]), requires_grad=True)
V = Variable(T.Tensor([1]), requires_grad=True)
B = Variable(T.Tensor([0]), requires_grad=True)
#W = Variable(T.Tensor(ammount).uniform_(-1, 1), requires_grad=True)
#V = Variable(T.Tensor(ammount).uniform_(-1, 1), requires_grad=True)
#B = Variable(T.Tensor(ammount).uniform_(-3,1), requires_grad=True)
#.random_(0,3)-1


    

In [62]:

    

'''
t = Variable(T.linspace(-15, 8*math.pi, 250))
I = Variable(T.Tensor(t.size()).fill_(1))
z = T.ger(V, t) + T.ger(B, I)
sigmoids = T.mul(T.sigmoid(z), T.ger(W,I))  
s=sigmoids.data
for i in range(ammount):
    plt.plot(t.data.numpy(), s[i].numpy()) 

'''
print(1)


    

    




1

In [63]:

    

#фактически x(t), прямой проход инс
def forward1(t):
    I = Variable(T.Tensor(t.size()).fill_(1))
    z = T.ger(V, t) + T.ger(B, I)
    return T.sum(T.mul(T.sigmoid(z), T.ger(W,I)) , 0)

def forward3(t):
    return W*T.sin(V*t + B)

def forward2(t):
    I = Variable(T.Tensor(t.size()).fill_(1))
    z = T.ger(V, t) + T.ger(B, I)
    return T.sum(T.mul(T.sin(z), T.ger(W,I)) , 0)

def J():
    tTr = Variable(timeTrain, requires_grad = True)
    X = forward3(tTr)
    X.backward(Variable(T.Tensor(m).fill_(1)), retain_graph = True, create_graph = True)
    v = tTr.grad.clone()
    tTr.grad.data.zero_()
    v.backward(Variable(T.Tensor(m).fill_(1)))
    a = tTr.grad.clone()
    e = a + X#*omega2
    #print(x.data[0])
    #print(v.data[0])
    #print(e)
    #H = 0.5*M*v*v+k*x*x*0.5
    return (T.sum((e)**2)) + (X.data[0])**2 + (v.data[0]-1)**2 #+ 20*(T.sum((H-E)**2))/m

    #T.autograd.backward(v, grad_variables  = tTr)
    #T.autograd.backward(x, grad_variables  = tTr, retain_graph = True, create_graph = True)


    

In [64]:

    

#   ОТЛАДОЧНЫЙ КОД
#
'''
    
    if j.data[0] > jLast[0]:
        alpha = alpha*0.9
        W.data = wt
        V.data = vt
        B.data = bt
    wt = W.data
    vt = V.data
    bt = B.data
    
    
        if i==6000:
        alpha = 10**-7
    
    if i==14000:
        alpha = 10**-8
'''
#


#Y = forward2(Variable(timeCont))
#plt.plot(timeCont.numpy(), Y.data.numpy(),'red')


    

    
Out[64]:





'\n    \n    if j.data[0] > jLast[0]:\n        alpha = alpha*0.9\n        W.data = wt\n        V.data = vt\n        B.data = bt\n    wt = W.data\n    vt = V.data\n    bt = B.data\n    \n    \n        if i==6000:\n        alpha = 10**-7\n    \n    if i==14000:\n        alpha = 10**-8\n'

In [65]:

    

'''
N = 0
alpha = 10**-8
I = []
Er = []
Wgrad = []
#jLast = T.Tensor([10**5])

for i in tqdm_notebook(range(N)):
    I.append(i)
    j = J()
    j.backward()
    Er.append(j.data[0])
    Wgrad.append(W.grad.data)
    bg = B.grad.data
    vg = V.grad.data
    wg = W.grad.data
    B = Variable(B.data - alpha*wg, requires_grad=True)
    V = Variable(V.data - alpha*vg, requires_grad=True)
    W = Variable(W.data - alpha*wg, requires_grad=True)
    if i%400==0:
        clear_output()
        print(j.data)
    #jLast[0] = j.data[0]
    
    
    
    
print(alpha)
'''
print(1)


    

    




1

In [66]:

    

'''
Y = forward2(Variable(timeCont))
plt.plot(timeCont.numpy(), (Y-T.sin(Variable(timeCont))).data.numpy(),'red') 
'''
print(1)


    

    




1

In [67]:

    

#plt.plot(I, Er, 'red')


    

In [68]:

    

'''
t = Variable(T.linspace(-15, 8*math.pi, 250))
I = Variable(T.Tensor(t.size()).fill_(1))
z = T.ger(V, t) + T.ger(B, I)
sigmoids = T.mul(T.sigmoid(z), T.ger(W,I)) 
s=sigmoids.data
for i in range(ammount):
    plt.plot(t.data.numpy(), s[i].numpy()) 
    
'''
x = forward3(tTr)
x.grad_fn


    

    
Out[68]:





<torch.autograd.function.MulBackward at 0x7f0228f0c5e8>

In [73]:

    

W = Variable(T.Tensor([1]), requires_grad=True)
V = Variable(T.Tensor([1]), requires_grad=True)
B = Variable(T.Tensor([0]), requires_grad=True)
tTr = Variable(timeTrain, requires_grad = True)

'''
x.backward(Variable(T.Tensor(m).fill_(1)), retain_graph = True, create_graph = True)
v = tTr.grad.clone()
tTr.grad.data.zero_()
v.backward(Variable(T.Tensor(m).fill_(1)))
a = tTr.grad.clone()

#j0=J()
#j0.backward()
'''
j=J()
print(j)
j.backward()
print(V.grad)


    

    




Variable containing:
 0
[torch.FloatTensor of size 1]

Variable containing:
 103.1084
[torch.FloatTensor of size 1]

In [70]:

    

time=tTr
x = forward3(tTr)
plt.plot(time.data.numpy(), x.data.numpy(),'red')


    

    
Out[70]:





[<matplotlib.lines.Line2D at 0x7f01dfbcb320>]






    

In [71]:

    

plt.plot(time.data.numpy(), v.data.numpy(),'red')


    

    




---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
<ipython-input-71-f814a26da8a5> in <module>()
----> 1 plt.plot(time.data.numpy(), v.data.numpy(),'red')

NameError: name 'v' is not defined

In [ ]:

    

plt.plot(time.data.numpy(), a.data.numpy(),'red')


    

In [ ]: