content: """
  ==========================
  SGD: convex loss functions
  ==========================
  
  A plot that compares the various convex loss functions supported by
  :class:`sklearn.linear_model.SGDClassifier` .
  """
  print(__doc__)
  
  import numpy as np
  import matplotlib.pyplot as plt
  
  
  def modified_huber_loss(y_true, y_pred):
      z = y_pred * y_true
      loss = -4 * z
      loss[z >= -1] = (1 - z[z >= -1]) ** 2
      loss[z >= 1.] = 0
      return loss
  
  
  xmin, xmax = -4, 4
  xx = np.linspace(xmin, xmax, 100)
  lw = 2
  plt.plot([xmin, 0, 0, xmax], [1, 1, 0, 0], color='gold', lw=lw,
           label="Zero-one loss")
  plt.plot(xx, np.where(xx < 1, 1 - xx, 0), color='teal', lw=lw,
           label="Hinge loss")
  plt.plot(xx, -np.minimum(xx, 0), color='yellowgreen', lw=lw,
           label="Perceptron loss")
  plt.plot(xx, np.log2(1 + np.exp(-xx)), color='cornflowerblue', lw=lw,
           label="Log loss")
  plt.plot(xx, np.where(xx < 1, 1 - xx, 0) ** 2, color='orange', lw=lw,
           label="Squared hinge loss")
  plt.plot(xx, modified_huber_loss(xx, 1), color='darkorchid', lw=lw,
           linestyle='--', label="Modified Huber loss")
  plt.ylim((0, 8))
  plt.legend(loc="upper right")
  plt.xlabel(r"Decision function $f(x)$")
  plt.ylabel("$L(y, f(x))$")
  plt.show()
  