wxpython + matplotlib: autoresizing a matplotlib figure

This python program plots a figure in a wxpython window.

How can I change the program so that:

• the figure resizes when I resize the window
• the main window cannot be resized smaller than a particular dimension? (say, half the default size of the window)

.

# adapted from:
# http://wiki.wxpython.org/Getting%20Started
# http://www.cs.colorado.edu/~kena/classes/5448/s11/presentations/pearse.pdf

import wx
import pylab as pl
import matplotlib
from matplotlib.backends.backend_wxagg import FigureCanvasWxAgg as FigureCanvas

class GUIPanel(wx.Panel):
    def __init__(self, parent):
        wx.Panel.__init__(self, parent)
        self.parent = parent

        # create some sizers
        sizer = wx.BoxSizer(wx.VERTICAL)

        # A button
        self.button =wx.Button(self, label="Tada!")
        self.Bind(wx.EVT_BUTTON, self.OnClick,self.button)

        # put up a figure
        self.figure = pl.figure()
        self.axes = self.drawplot(self.figure)
        self.canvas = FigureCanvas(self, -1, self.figure)

        sizer.Add(self.canvas, 0, wx.ALIGN_CENTER|wx.ALL)
        sizer.Add(self.button, 0, wx.ALIGN_CENTER|wx.ALL)

        self.SetSizerAndFit(sizer)  
    def log(self, fmt, *args):
        print (fmt % args)
    def OnClick(self,event):
        self.log("button clicked, id#%d\n", event.GetId())
    def drawplot(self, fig):
        ax = fig.add_subplot(1,1,1)
        t = pl.arange(0,1,0.001)
        ax.plot(t,t*t)
        ax.grid()
        return ax

app = wx.App(False)
frame = wx.Frame(None)
panel = GUIPanel(frame)
frame.Fit()
frame.Center()
frame.Show()
app.MainLoop()