How can I get matplotlib to make a colorbar with a color centered on 0?

I'm plotting a Wigner distribution of some data, and at extreme parts of the distribution the value tends to be near 0. It also tends to oscillate a lot, making my test plot look like this:

The waves in the blue "sea" have an amplitude around 1E-18, but because they oscillate around 0 they cross a line in the colorbar.

How can I make a contourf() plot that has a color centered on zero instead of having zero as a boundary value?

I think you want something like this:

class set_cbar_zero(Normalize):
  """
  set_cbar_zero(midpoint = float)       default: midpoint = 0.

  Normalizes and sets the center of any colormap to the desired valua which 
  is set using midpoint. 
  """
  def __init__(self, vmin = None, vmax = None, midpoint = 0., clip = False):
    self.midpoint = midpoint
    Normalize.__init__(self, vmin, vmax, clip)

  def __call__(self, value, clip = None):
    x, y = [self.vmin, self.midpoint, self.vmax], [0, 0.5, 1]
    return numpy.ma.masked_array(numpy.interp(value, x, y))

You can then normalize the colorbar which should solve your problem, if I understood it correctly

import numpy 
import matplotlib.pylab as plt

data = numpy.random.random((30, 95))

plt.figure()
plt.imshow(data, cmap = "hot", norm = set_cbar_zero())
plt.show()