In [1]:

    

# Import here
%matplotlib inline
import matplotlib.pylab as pylab
import matplotlib.pyplot as plt
import numpy as np
import theano
import theano.tensor as T

pylab.rcParams['figure.figsize'] = (9.0, 6.0)


    

In [2]:

    

def fourier_coeffs(x, n_max=8):
    n = np.arange(n_max).reshape((n_max, 1)) + 1.
    phase = 2. * np.pi * n * x
    c_sin = np.sin(phase)
    c_cos = np.cos(phase)
    return np.concatenate((c_sin, c_cos), axis=0)


    

In [3]:

    

t_x, t_y, t_nu = T.fmatrices('x', 'y', 'nu')
t_A = T.fmatrix(name='A')
t_a = T.fscalar(name='a')
t_xhat = T.dot(t_A, t_y + t_nu) + t_a
cost = T.mean((t_xhat - t_x) ** 2)
t_dA = T.grad(cost, t_A)
t_da = T.grad(cost, t_a)
f = theano.function(inputs=[t_x, t_y, t_nu, t_A, t_a],
                    outputs=[cost, t_xhat, t_dA, t_da])


    

In [32]:

    

n_max = 64
dim_fourier = 2 * n_max
A = np.ones((1, dim_fourier), dtype=np.float32) / dim_fourier
a = np.float32(0.)


    

In [33]:

    

sigma = 0.0
dim_batch = 1024
eta = np.float32(0.01)
for t in range(1000):
    x = 1.0 * np.random.uniform(size=(1, dim_batch)).astype(np.float32)
    y = fourier_coeffs(x, n_max=n_max).astype(np.float32)
    nu = sigma * np.random.randn(dim_fourier, dim_batch).astype(np.float32)
    cost, xhat, dA, da = f(x, y, nu, A, a)
    if (t + 1) % 100 == 0:
        print (t + 1), ':', cost
    A -= eta * dA
    a -= eta * da


    

    




100 : 0.0185615569353
200 : 0.00232937792316
300 : 0.00123705680016
400 : 0.00062116998015
500 : 0.000513570499606
600 : 0.000686192302965
700 : 0.000486438802909
800 : 0.00128111231606
900 : 0.000822594796773
1000 : 0.000632619252428

In [34]:

    

plt.plot(A.reshape(dim_fourier))


    

    
Out[34]:





[<matplotlib.lines.Line2D at 0x111fb2510>]






    

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