def add_layer(inputs, in_size, out_size, activation_function=None):
  # add one more layer and return the output of this layer
  Weights = tf.Variable(tf.random_normal([in_size, out_size]))
  biases = tf.Variable(tf.zeros([1, out_size]) + 0.1)
  Wx_plus_b = tf.matmul(inputs, Weights) + biases
  if activation_function is None:
    outputs = Wx_plus_b
  else:
    outputs = activation_function(Wx_plus_b)
  return outputs

# Make up some real data
x_data = np.linspace(-1,1,300)[:, np.newaxis]
noise = np.random.normal(0, 0.05, x_data.shape)
y_data = np.square(x_data) - 0.5 + noise

numpy.linspace(start, stop, num=50, endpoint=True, retstep=False, dtype=None)[source] 
Return evenly spaced numbers over a specified interval. 
Returns num evenly spaced samples, calculated over the interval [start, stop]. 

# define placeholder for inputs to network
xs = tf.placeholder(tf.float32, [None, 1])
ys = tf.placeholder(tf.float32, [None, 1])

# add hidden layer
l1 = add_layer(xs, 1, 10, activation_function=tf.nn.relu)
# add output layer
prediction = add_layer(l1, 10, 1, activation_function=None)

# the error between prediciton and real data
loss = tf.reduce_mean(tf.reduce_sum(tf.square(ys - prediction),reduction_indices=[1]))
train_step = tf.train.GradientDescentOptimizer(0.1).minimize(loss)

from __future__ import print_function
import tensorflow as tf
import numpy as np
import matplotlib.pyplot as plt

def add_layer(inputs, in_size, out_size, activation_function=None):
  # add one more layer and return the output of this layer
  Weights = tf.Variable(tf.random_normal([in_size, out_size]))
  biases = tf.Variable(tf.zeros([1, out_size]) + 0.1)
  Wx_plus_b = tf.matmul(inputs, Weights) + biases
  if activation_function is None:
    outputs = Wx_plus_b
  else:
    outputs = activation_function(Wx_plus_b)
  return outputs

# Make up some real data
x_data = np.linspace(-1,1,300)[:, np.newaxis]
noise = np.random.normal(0, 0.05, x_data.shape)
y_data = np.square(x_data) - 0.5 + noise

# define placeholder for inputs to network
xs = tf.placeholder(tf.float32, [None, 1])
ys = tf.placeholder(tf.float32, [None, 1])
# add hidden layer
l1 = add_layer(xs, 1, 10, activation_function=tf.nn.relu)
# add output layer
prediction = add_layer(l1, 10, 1, activation_function=None)

# the error between prediciton and real data
loss = tf.reduce_mean(tf.reduce_sum(tf.square(ys - prediction),
           reduction_indices=[1]))
train_step = tf.train.GradientDescentOptimizer(0.1).minimize(loss)

# important step
init = tf.initialize_all_variables()
sess = tf.Session()
sess.run(init)

# plot the real data
fig = plt.figure()
ax = fig.add_subplot(1,1,1)
ax.scatter(x_data, y_data)
plt.ion()
plt.show()

for i in range(1000):
  # training
  sess.run(train_step, feed_dict={xs: x_data, ys: y_data})
  if i % 50 == 0:
    # to visualize the result and improvement
    try:
      ax.lines.remove(lines[0])
    except Exception:
      pass
    prediction_value = sess.run(prediction, feed_dict={xs: x_data})
    # plot the prediction
    lines = ax.plot(x_data, prediction_value, 'r-', lw=5)
    plt.pause(0.1)