In [1]:

    

import numpy as np


    

In [2]:

    

import matplotlib.pyplot as plt
%matplotlib inline


    

In [3]:

    

n_samples = 1000


    

In [4]:

    

x = np.zeros(n_samples)


    

In [5]:

    

x[1] = 1
c = np.cos(2*np.pi*0.005)


    

In [6]:

    

for i in range(2,n_samples):
    x[i]= 2*c*x[i-1] - x[i-2]


    

In [7]:

    

plt.plot(x)


    

    
Out[7]:





[<matplotlib.lines.Line2D at 0x7fd04e95af60>]






    

In [8]:

    

X = np.array([[x[i-1],x[i-2]] for i in range(2,1000)])
Y = np.array([x[i] for i in range(2,1000)])


    

In [9]:

    

coeffs_true = np.array([2*c, -1]).reshape(-1,1)


    

In [10]:

    

coeffs_true


    

    
Out[10]:





array([[ 1.99901312],
       [-1.        ]])

In [11]:

    

import tensorflow as tf


    

In [12]:

    

X_tf = tf.placeholder(dtype=tf.float32, shape=[None,2], name="X_tf")
Y_tf = tf.placeholder(dtype=tf.float32, shape=[None,1], name="Y_tf")


    

In [13]:

    

c_tf = tf.Variable(tf.random_normal([2,1], stddev=1.0, dtype=tf.float32))
# c_tf = tf.Variable(initial_value=coeffs_true)


    

In [14]:

    

loss = tf.reduce_sum(
    tf.square(
        tf.subtract(
            tf.matmul(X_tf,c_tf), Y_tf
        )
    )
)


    

In [15]:

    

train_op = tf.train.AdamOptimizer(learning_rate=0.01, epsilon=1E-12).minimize(loss)


    

In [18]:

    

sess = tf.InteractiveSession()
sess.run(tf.global_variables_initializer())


    

In [19]:

    

loss_list = []


    

In [20]:

    

sess.run(c_tf, feed_dict={X_tf:X, Y_tf:Y.reshape(-1,1)})


    

    
Out[20]:





array([[ 1.67598951],
       [-1.56020331]], dtype=float32)

In [21]:

    

for i in range(10000):
    sess.run(train_op, feed_dict={X_tf:X, Y_tf:Y.reshape(-1,1)})
    loss_val = sess.run(loss, feed_dict={X_tf:X, Y_tf:Y.reshape(-1,1)})
    loss_list.append(loss_val)


    

In [22]:

    

plt.plot(np.log10(loss_list))


    

    
Out[22]:





[<matplotlib.lines.Line2D at 0x7fd0400a1710>]






    

In [293]:

    

sess.run(c_tf, feed_dict={X_tf:X, Y_tf:Y.reshape(-1,1)})


    

    
Out[293]:





array([[ 1.99580693],
       [-0.99679369]], dtype=float32)

In [23]:

    

coeffs_true


    

    
Out[23]:





array([[ 1.99901312],
       [-1.        ]])

In [ ]: