text: # Linear Regression: Inverse Matrix Method
  #----------------------------------
  #
  # This function shows how to use Tensorflow to
  # solve linear regression via the matrix inverse.
  #
  # Given Ax=b, solving for x:
  #  x = (t(A) * A)^(-1) * t(A) * b
  #  where t(A) is the transpose of A
  
  import matplotlib.pyplot as plt
  import numpy as np
  import tensorflow as tf
  from tensorflow.python.framework import ops
  ops.reset_default_graph()
  
  # Create graph
  sess = tf.Session()
  
  # Create the data
  x_vals = np.linspace(0, 10, 100)
  y_vals = x_vals + np.random.normal(0, 1, 100)
  
  # Create design matrix
  x_vals_column = np.transpose(np.matrix(x_vals))
  ones_column = np.transpose(np.matrix(np.repeat(1, 100)))
  A = np.column_stack((x_vals_column, ones_column))
  
  # Create b matrix
  b = np.transpose(np.matrix(y_vals))
  
  # Create tensors
  A_tensor = tf.constant(A)
  b_tensor = tf.constant(b)
  
  # Matrix inverse solution
  tA_A = tf.matmul(tf.transpose(A_tensor), A_tensor)
  tA_A_inv = tf.matrix_inverse(tA_A)
  product = tf.matmul(tA_A_inv, tf.transpose(A_tensor))
  solution = tf.matmul(product, b_tensor)
  
  solution_eval = sess.run(solution)
  
  # Extract coefficients
  slope = solution_eval[0][0]
  y_intercept = solution_eval[1][0]
  
  print('slope: ' + str(slope))
  print('y_intercept: ' + str(y_intercept))
  
  # Get best fit line
  best_fit = []
  for i in x_vals:
    best_fit.append(slope*i+y_intercept)
  
  # Plot the results
  plt.plot(x_vals, y_vals, 'o', label='Data')
  plt.plot(x_vals, best_fit, 'r-', label='Best fit line', linewidth=3)
  plt.legend(loc='upper left')
  plt.show()