matplotlib-users Mailing List for matplotlib

Hi everyone,
I use matplotlib to render a figure in a tkinter (the Tix library more precisely) canvas.
It works very well but I can't turn off the autoscale (and I would like to), even by setting
ax.set_autoscale_on(False). When I test with ax.get_autoscale_on(), the result is False, but the
axes continues to autoscale.
I didn't had this problem in the past with ubuntu 8.04. I have it since I made the update to the
8.10 distribution so I guess that it's because the version of matplotlib I use have changed also
(but I don't remember the number of this previous version). Now I use python 2.5.2, Tix 8.4.0, mpl
0.98.3, numpy 1.2.1 ppa release, scipy 0.7.0 ppa release.
Here is the graphic part of my app :
class GraphFrame(Tix.Frame):
 def __init__(self,master):
 Tix.Frame.__init__(self,master,bd=10)
 self.gen = Tix.Frame(self)
 self.fps = Figure(figsize=(5,4),dpi=100,facecolor='w')
 self.tlps = 'Phase Space'
 self.xlps = {'xlabel' : r'$x$','fontsize' : 16}
 self.ylps = {'ylabel' : r'$p$','rotation' : 'horizontal','fontsize' : 16}
 self.aps = self.fps.add_subplot(111)
 self.aps.set_title(self.tlps)
 self.aps.set_xlabel(**self.xlps)
 self.aps.set_ylabel(**self.ylps)
 self.canvasps = FigureCanvasTkAgg(self.fps,master=self.gen)
 self.canvasps.get_tk_widget().pack(side=Tix.TOP,fill=Tix.BOTH,expand=1)
 self.toolbar = NavigationToolbar2TkAgg(self.canvasps, self.gen)
 self.toolbar.update()
 self.canvasps._tkcanvas.pack(side=Tix.TOP, fill=Tix.BOTH, expand=1)
 self.gen.grid(row=0, columnspan=14, sticky='NWSE')
 self.aps.set_autoscale_on(False) #doesn't work !!!
# self.aps.autoscale_view(scalex=False,scaley=False)
 self.psLin = []
 self.cl = ('r','g','b','c','y','m','k')
 self.coch = self.canvasps.mpl_connect('button_press_event', self.onpsclick)
 self.crh = self.canvasps.mpl_connect('button_release_event', self.onpsrelease)
 self.cmh = self.canvasps.mpl_connect('motion_notify_event', self.onpsmotion)
 self.cFrame = None
 self.press = False
 def ocps_connect(self):
 self.coch = self.canvasps.mpl_connect('button_press_event', self.onpsclick)
 self.crh = self.canvasps.mpl_connect('button_release_event', self.onpsrelease)
 self.cmh = self.canvasps.mpl_connect('motion_notify_event', self.onpsmotion)
 def ocps_disconnect(self):
 self.canvasps.mpl_disconnect(self.coch)
 self.canvasps.mpl_disconnect(self.crh)
 self.canvasps.mpl_disconnect(self.cmh)
#some method I use to update the graph
 def psaddData_m(self,u,xmin,xmax,pmin,pmax,m=','):
 line = lines.Line2D(u[:,0],u[:,1],
 linestyle='None',
 marker=m,
 color=self.cl[np.mod(len(self.psLin)-1,6)])
 self.psLin.append(line)
 self.psDraw(xmin,xmax,pmin,pmax)
 def psaddData_l(self,u,xmin,xmax,pmin,pmax,l='-'):
 line = lines.Line2D(u[:,0],u[:,1],
 linestyle=l,
 color=self.cl[np.mod(len(self.psLin)-1,6)])
 self.psLin.append(line)
 self.psDraw(xmin,xmax,pmin,pmax)
 def psdelData(self,n):
 del self.psLin[n]
 self.aps.clear()
# self.aps.cla()
 for l in self.psLin:
 self.aps.add_line(l)
 self.aps.set_title(self.tlps)
 self.aps.set_xlabel(**self.xlps)
 self.aps.set_ylabel(**self.ylps)
 self.aps.redraw_in_frame()
 self.canvasps.blit()
 def psDraw(self,xmin,xmax,pmin,pmax):
# self.aps.clear()
 self.aps.cla()
 self.aps.set_xlim(xmin,xmax)
 self.aps.set_ylim(pmin,pmax)
 for l in self.psLin:
 self.aps.add_line(l)
 self.aps.set_title(self.tlps)
 self.aps.set_xlabel(**self.xlps)
 self.aps.set_ylabel(**self.ylps)
 self.aps.draw()
 self.canvasps.blit()
# self.aps.set_autoscale_on(False)
# self.aps.autoscale_view(scalex=False,scaley=False)
# a = self.aps.get_autoscale_on()
# print a
 def psifRedraw(self):
 self.aps.clear()
# self.aps.cla()
 for l in self.psLin:
 self.aps.add_line(l)
 self.aps.set_title(self.tlps)
 self.aps.set_xlabel(**self.xlps)
 self.aps.set_ylabel(**self.ylps)
 self.aps.redraw_in_frame()
 self.canvasps.blit()
 def psRedraw(self):
 self.aps.redraw_in_frame()
 self.canvasps.blit()
# click event handling
 def onpsclick(self,event):
 Bhv=self.cFrame.stDico['psMode'].get()
 if event.inaxes!=self.aps: return
 if Bhv == 'Nothing': return
 self.press = True
 if Bhv == 'Traj':
 niter=int(self.cFrame.stDico['n iter'].get())
 jb = self.cFrame.TrajJacob.get()
 if jb:
 lj = float(self.cFrame.TJDirlStr.get())
 hj = float(self.cFrame.TJDirhderStr.get())
 jnb = self.cFrame.nTrajJacob.get()
 if jnb:
 ljn = float(self.cFrame.nTJDirlStr.get())
 hjn = float(self.cFrame.nTJDirhderStr.get())
 v = np.array([event.xdata,event.ydata])
 s = [v]
 if jb: sj = [Jacob(v,hj,utils.dfridr)]
 if jnb: sjn = [Jacob(v,hjn,utils.dfridr)]
 for i in xrange(0,niter):
 u = pm.Map(v)
 s.append(u)
 v = u
 if jb: sj.append(Jacob(v,hj,utils.dfridr))
 if jnb: sjn.append(np.dot(sjn[-1],Jacob(v,hjn,utils.dfridr)))
 w = np.vstack(s)
 line = lines.Line2D(w[:,0],w[:,1],color='b')
 if jb:
 for i in xrange(len(sj)):
 J = sj[i]
 v = s[i]
 (lr,vr) = eig(J,right=True)
 if reduce(lambda x,y : (np.abs(x)-1.)*(np.abs(y)-1.),lr) >= 0:
 print 'Problem : The point '+str(i+1)+' is not hyperbolic'
 print 'J=',J
 print 'l=',lr
 else:
 if abs(lr[0]) < 1.:
 u1 = vr[:,0]
 u2 = vr[:,1]
 else:
 u1 = vr[:,1]
 u2 = vr[:,0]
 ul1 = np.vstack([v-lj*u1,v+lj*u1])
 ul2 = np.vstack([v-lj*u2,v+lj*u2])
 line1 = lines.Line2D(ul1[:,0],ul1[:,1],color='b')
 line2 = lines.Line2D(ul2[:,0],ul2[:,1],color='r')
 self.aps.add_line(line1)
 self.aps.add_line(line2)
 if jnb:
 for i in xrange(len(sjn)):
 J = sjn[i]
 v = s[i]
 (lr,vr) = eig(J,right=True)
 if reduce(lambda x,y : (np.abs(x)-1.)*(np.abs(y)-1.),lr) >= 0:
 print 'Problem : The traj '+str(i+1)+' is not hyperbolic'
 print 'J=',J
 print 'l=',lr
 else:
 if abs(lr[0]) < 1.:
 u1 = vr[:,0]
 u2 = vr[:,1]
 else:
 u1 = vr[:,1]
 u2 = vr[:,0]
 ul1 = np.vstack([v-ljn*u1,v+ljn*u1])
 ul2 = np.vstack([v-ljn*u2,v+ljn*u2])
 line1 = lines.Line2D(ul1[:,0],ul1[:,1],color='g')
 line2 = lines.Line2D(ul2[:,0],ul2[:,1],color='m')
 self.aps.add_line(line1)
 self.aps.add_line(line2)
 elif Bhv == '1it':
 v = np.array([event.xdata,event.ydata])
 u = pm.Map(v)
 w = np.vstack([v,u])
 line = lines.Line2D(w[:,0],w[:,1],
 linestyle='None',
 marker='+',
 markersize=10.,
 color='k')
 elif Bhv == 'Preim':
 xmin=float(self.cFrame.stDico['pixmin'].get())
 xmax=float(self.cFrame.stDico['pixmax'].get())
 pmin=float(self.cFrame.stDico['pipmin'].get())
 pmax=float(self.cFrame.stDico['pipmax'].get())
 nx=int(self.cFrame.stDico['pinx'].get())
 ny=int(self.cFrame.stDico['pinp'].get())
 tol=float(self.cFrame.stDico['pitol'].get())
 it=int(self.cFrame.stDico['piter'].get())
 al=float(self.cFrame.stDico['pialpha'].get())
 npim = self.cFrame.preimmVar.get()
 v = np.array([event.xdata,event.ydata])
 u = preMap(npim,v,xmin,xmax,pmin,pmax,nx,ny,tol,it,al)
 if u != None:
 w = np.vstack([v,u])
 else:
 w = v
 w.shape = 1,2
 line = lines.Line2D(w[:,0],w[:,1],
 linestyle='None',
 marker='+',
 markersize=10.,
 color='k')
 elif Bhv == 'Jacob':
 l = float(self.cFrame.DirlStr.get())
 h = float(self.cFrame.DirhderStr.get())
 v = np.array([event.xdata,event.ydata])
 J = Jacob(v,h,utils.dfridr)
 (lr,vr) = eig(J,right=True)
 if reduce(lambda x,y : (np.abs(x)-1.)*(np.abs(y)-1.),lr) >= 0:
 print 'Problem : The point is not hyperbolic'
 print 'J=',J
 print 'l=',lr
 return
 if abs(lr[0]) < 1.:
 u1 = vr[:,0]
 u2 = vr[:,1]
 else:
 u1 = vr[:,1]
 u2 = vr[:,0]
 ul1 = np.vstack([v-l*u1,v+l*u1])
 ul2 = np.vstack([v-l*u2,v+l*u2])
 line = lines.Line2D(ul1[:,0],ul1[:,1],color='b')
 line1 = lines.Line2D(ul2[:,0],ul2[:,1],color='r')
 self.aps.add_line(line1)
 self.aps.add_line(line)
# self.aps.set_title(self.tlps)
# self.aps.set_xlabel(**self.xlps)
# self.aps.set_ylabel(**self.ylps)
 self.aps.redraw_in_frame()
 self.canvasps.blit()
 def onpsmotion(self,event):
 Bhv=self.cFrame.stDico['psMode'].get()
 if event.inaxes!=self.aps: return
 if self.press == False: return
 if Bhv == 'Nothing': return
 self.aps.clear()
# self.aps.cla()
 for l in self.psLin:
 self.aps.add_line(l)
 self.aps.set_title(self.tlps)
 self.aps.set_xlabel(**self.xlps)
 self.aps.set_ylabel(**self.ylps)
 if Bhv == 'Traj':
 niter=int(self.cFrame.stDico['n iter'].get())
 jb = self.cFrame.TrajJacob.get()
 if jb:
 lj = float(self.cFrame.TJDirlStr.get())
 hj = float(self.cFrame.TJDirhderStr.get())
 jnb = self.cFrame.nTrajJacob.get()
 if jnb:
 ljn = float(self.cFrame.nTJDirlStr.get())
 hjn = float(self.cFrame.nTJDirhderStr.get())
 v = np.array([event.xdata,event.ydata])
 s = [v]
 if jb: sj = [Jacob(v,hj,utils.dfridr)]
 if jnb: sjn = [Jacob(v,hjn,utils.dfridr)]
 for i in xrange(0,niter):
 u = pm.Map(v)
 s.append(u)
 v = u
 if jb: sj.append(Jacob(v,hj,utils.dfridr))
 if jnb: sjn.append(np.dot(sjn[-1],Jacob(v,hjn,utils.dfridr)))
 w = np.vstack(s)
 line = lines.Line2D(w[:,0],w[:,1],color='b')
 if jb:
 for i in xrange(len(sj)):
 J = sj[i]
 v = s[i]
 (lr,vr) = eig(J,right=True)
 if reduce(lambda x,y : (np.abs(x)-1.)*(np.abs(y)-1.),lr) >= 0:
 print 'Problem : The point '+str(i+1)+' is not hyperbolic'
 print 'J=',J
 print 'l=',lr
 else:
 if abs(lr[0]) < 1.:
 u1 = vr[:,0]
 u2 = vr[:,1]
 else:
 u1 = vr[:,1]
 u2 = vr[:,0]
 ul1 = np.vstack([v-lj*u1,v+lj*u1])
 ul2 = np.vstack([v-lj*u2,v+lj*u2])
 line1 = lines.Line2D(ul1[:,0],ul1[:,1],color='b')
 line2 = lines.Line2D(ul2[:,0],ul2[:,1],color='r')
 self.aps.add_line(line1)
 self.aps.add_line(line2)
 if jnb:
 for i in xrange(len(sjn)):
 J = sjn[i]
 v = s[i]
 (lr,vr) = eig(J,right=True)
 if reduce(lambda x,y : (np.abs(x)-1.)*(np.abs(y)-1.),lr) >= 0:
 print 'Problem : The traj '+str(i+1)+' is not hyperbolic'
 print 'J=',J
 print 'l=',lr
 else:
 if abs(lr[0]) < 1.:
 u1 = vr[:,0]
 u2 = vr[:,1]
 else:
 u1 = vr[:,1]
 u2 = vr[:,0]
 ul1 = np.vstack([v-ljn*u1,v+ljn*u1])
 ul2 = np.vstack([v-ljn*u2,v+ljn*u2])
 line1 = lines.Line2D(ul1[:,0],ul1[:,1],color='g')
 line2 = lines.Line2D(ul2[:,0],ul2[:,1],color='m')
 self.aps.add_line(line1)
 self.aps.add_line(line2)
 elif Bhv == '1it':
 v = np.array([event.xdata,event.ydata])
 u = pm.Map(v)
 w = np.vstack([v,u])
 line = lines.Line2D(w[:,0],w[:,1],
 linestyle='None',
 marker='+',
 markersize=10.,
 color='k')
 elif Bhv == 'Preim':
 xmin=float(self.cFrame.stDico['pixmin'].get())
 xmax=float(self.cFrame.stDico['pixmax'].get())
 pmin=float(self.cFrame.stDico['pipmin'].get())
 pmax=float(self.cFrame.stDico['pipmax'].get())
 nx=int(self.cFrame.stDico['pinx'].get())
 ny=int(self.cFrame.stDico['pinp'].get())
 tol=float(self.cFrame.stDico['pitol'].get())
 it=int(self.cFrame.stDico['piter'].get())
 al=float(self.cFrame.stDico['pialpha'].get())
 npim = self.cFrame.preimmVar.get()
 v = np.array([event.xdata,event.ydata])
 u = preMap(npim,v,xmin,xmax,pmin,pmax,nx,ny,tol,it,al)
 if u != None:
 w = np.vstack([v,u])
 else:
 w = v
 w.shape = 1,2
 line = lines.Line2D(w[:,0],w[:,1],
 linestyle='None',
 marker='+',
 markersize=10.,
 color='k')
 elif Bhv == 'Jacob':
 l = float(self.cFrame.DirlStr.get())
 h = float(self.cFrame.DirhderStr.get())
 v = np.array([event.xdata,event.ydata])
 J = Jacob(v,h,utils.dfridr)
 (lr,vr) = eig(J,right=True)
 if reduce(lambda x,y : (np.abs(x)-1.)*(np.abs(y)-1.),lr) >= 0:
 print 'Problem : The point is not hyperbolic'
 print 'J=',J
 print 'l=',lr
 return
 if abs(lr[0]) < 1.:
 u1 = vr[:,0]
 u2 = vr[:,1]
 else:
 u1 = vr[:,1]
 u2 = vr[:,0]
 ul1 = np.vstack([v-l*u1,v+l*u1])
 ul2 = np.vstack([v-l*u2,v+l*u2])
 line = lines.Line2D(ul1[:,0],ul1[:,1],color='b')
 line1 = lines.Line2D(ul2[:,0],ul2[:,1],color='r')
 self.aps.add_line(line1)
 self.aps.add_line(line)
# self.aps.set_title(self.tlps)
# self.aps.set_xlabel(**self.xlps)
# self.aps.set_ylabel(**self.ylps)
 self.aps.redraw_in_frame()
 self.canvasps.blit()
 def onpsrelease(self,event):
 self.press = False
 self.aps.clear()
# self.aps.cla()
 for l in self.psLin:
 self.aps.add_line(l)
 self.aps.set_title(self.tlps)
 self.aps.set_xlabel(**self.xlps)
 self.aps.set_ylabel(**self.ylps)
 self.aps.redraw_in_frame()
 self.canvasps.blit()
# end
I don't know if it is a bug or something else but thank you in advance if you can help me.
Jonathan

Hi all,
I am trying to produce a weighted histogram.
The help text for "hist" here:
http://matplotlib.sourceforge.net/api/pyplot_api.html#matplotlib.pyplot.hist
has a mention of adding weights, but it is not noted in the command line 
section where this should appear.
Calling:
hist(data,20,data_weights)
gives the error:
 File 
"/usr/local/python-2.5.2/lib/python2.5/site-packages/matplotlib/pyplot.py", 
line 1868, in hist
 ret = gca().hist(*args, **kwargs)
 File 
"/usr/local/python-2.5.2/lib/python2.5/site-packages/matplotlib/axes.py", 
line 6236, in hist
 normed=bool(normed), new=True)
 File 
"/usr/local/python-2.5.2/lib/python2.5/site-packages/numpy/lib/function_base.py", 
line 353, in histogram
 mn, mx = range
ValueError: too many values to unpack
Calling:
hist(data,20,weights=data_weights)
gives the error:
 File 
"/usr/local/python-2.5.2/lib/python2.5/site-packages/matplotlib/pyplot.py", 
line 1868, in hist
 ret = gca().hist(*args, **kwargs)
 File 
"/usr/local/python-2.5.2/lib/python2.5/site-packages/matplotlib/axes.py", 
line 6371, in hist
 p.update(kwargs)
 File 
"/usr/local/python-2.5.2/lib/python2.5/site-packages/matplotlib/artist.py", 
line 453, in update
 raise AttributeError('Unknown property %s'%k)
AttributeError: Unknown property weights
There's no indication in the help text of where or how to insert the 
weights array.
Thanks in advance,
Michael

Perhaps this is a new feature since you sent this request, but I just came
across 
pylab.suptitle('my super title')
Seems to work fairly well, but the font sizes don't appear to behave as well
as I'd like.
Tommy Grav wrote:
> 
> I have a plot that is divided into four subplots.
> 
> pylab.figure()
> pylab.subplot(221)
> pylab.plot(a,b,"k-")
> pylab.subplot(222)
> pylab.plot(a,b,"k-")
> pylab.subplot(223)
> pylab.plot(a,b,"k-")
> pylab.subplot(224)
> pylab.plot(a,b,"k-")
> 
> I would like to add a title to the entire plot, but pylab.title() only
> applies to the most recent subplot. I have tried
> 
> pylab.figure()
> pylab.subplot(111)
> pylab.title("Title Here")
> pylab.subplot(221)
> pylab.plot(a,b,"k-")
> pylab.subplot(222)
> pylab.plot(a,b,"k-")
> pylab.subplot(223)
> pylab.plot(a,b,"k-")
> pylab.subplot(224)
> pylab.plot(a,b,"k-")
> 
> but this does not work as I do not create a plot for
> the subplot(111) instance. Is there some way of getting
> the type of title I want easily?
> 
> Cheers
> Tommy
> 
> -------------------------------------------------------------------------
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> 
-- 
View this message in context: http://www.nabble.com/title-when-using-subplot-tp15066004p24357703.html
Sent from the matplotlib - users mailing list archive at Nabble.com.

Hi,
Windows XP
Python 2.5.2
matplotlib 0.98.5.2
I try to use numpoints for a legend my plot, but without luck. I always 
end up having three points in the legend despite setting numpoints=1 (see 
below towards the end of the code).
Things work nicely though in a much simpler script.
Help is greatly appreciated. 
Cheers 
Oliver
[CODE START]
# Import necessary modules
import numpy as np
import matplotlib.pyplot as plt
# Import data for correlation plot
assC = np.loadtxt('Apples_flowerFlavour_assC_corrPlot.txt')
all = np.loadtxt('Apples_flowerFlavour_allAssessors_corrPlot.txt')
x_assC = assC[:,1].copy()
y_assC = assC[:,0].copy()
x_all = all[:,1].copy()
y_all = all[:,0].copy()
# Plot values 
fig = plt.figure()
ax = fig.add_subplot(111)
ax.scatter(x_all, y_all, s=10, c='w', marker='o', edgecolor='grey', 
label='_')
# NOTE: label='_' excludes the lable from legend
ax.scatter([x_assC[0]], [y_assC[0]], s=50, c='r', marker='s', label='Apple 
Golden')
ax.scatter([x_assC[1]], [y_assC[1]], s=50, c='r', marker='v', 
label='Granny Smith')
ax.scatter([x_assC[2]], [y_assC[2]], s=50, c='r', marker='d', label='Green 
Star')
ax.scatter([x_assC[3]], [y_assC[3]], s=50, c='r', marker='^', 
label='Kanzi')
ax.scatter([x_assC[4]], [y_assC[4]], s=50, c='r', marker='>', label='Pink 
Lady')
ax.scatter([x_assC[5]], [y_assC[5]], s=50, c='r', marker='<', label='Royal 
Gala')
ax.scatter([x_assC[6]], [y_assC[6]], s=35, c='r', marker='o', 
label='Ecological')
ax.plot([0,10], [0,10], 'b--')
ax.set_xlim(0,10)
ax.set_ylim(0,10)
# Fix legend settings
plt.legend(loc='lower right', shadow=True, numpoints=1)
ltext = plt.gca().get_legend().get_texts()
plt.setp(ltext[0], fontsize = 10, color = 'k')
ax.set_xlabel('panel average')
ax.set_ylabel('assessor C')
plt.show()
[CODE END]
 

Jae-Joon Lee wrote:
> Well, if you think something is wrong, I guess you may have chosen a
> wrong tool.
> MPL is mainly for 2d plotting, and not very strong for animation
> although it supports some.
I just think that I have a nice hammer, a nice nail ... and not a clue
on how to use a hammer (I'm a python noob, and high level language noob
in general, the highest level language I used before starting python was
C ... for embedded devices)
I just though that I was thinking in the wrong way.
> One possible option in your case is to save your plot as an image in
> each round. And at the next round, you plot the newly available data
> upon the shifted image.
> 
> http://matplotlib.sourceforge.net/examples/animation/animation_blit_gtk2.html
thanks, this looks great :)
----
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----

On Tue, Jun 30, 2009 at 12:09 PM, Ondrej Certik<on...@ce...> wrote:
> Hi,
>
> this must have been answered many times already, but I searched the
> archives, online docs, but couldn't find anything.
>
> If I do:
>
> $ python
> Python 2.6.2 (release26-maint, Apr 19 2009, 01:58:18)
> [GCC 4.3.3] on linux2
> Type "help", "copyright", "credits" or "license" for more information.
>>>> import pylab
>>>> pylab.plot([1, 3, 3])
> [<matplotlib.lines.Line2D object at 0x2154350>]
>>>> pylab.show()
>>>> pylab.show()
>>>>
>
> the first pylab.show() shows the plot and stays hanging (this is ok)
> and then if I close it, to get back to the shell, the second call to
> show() does nothing.
>
> One fix is to use:
>
> ipython --pylab
>
> but if I just want to call regular python, or from my own script ---
> how do I plot for the second time?
I still haven't figured out how to fix it, so any feedback would be appreciated.
Thanks,
Ondrej

Meant to copy this to the list as well for completeness.
---------- Forwarded message ----------
From: Rick Muller <rpm...@gm...>
Date: Sun, Jul 5, 2009 at 2:03 PM
Subject: Re: [Matplotlib-users] Empty squares at end of data after
interpolation with griddata?
To: Jeff Whitaker <js...@fa...>
The link should work now. What you say about extrapolation makes perfect
sense. I wonder why those points aren't being computed. In any case, thanks
for the help!
Rick
On Sun, Jul 5, 2009 at 7:27 AM, Jeff Whitaker <js...@fa...> wrote:
>
> http://files.getdropbox.com/u/533499/griddata-example-text.png
>>
>
>
> Rick: That URL doesn't work.
>
> griddata won't do extrapolation, that is it won't interpolate outside the
> convex hull of the data. That's probably why you see those empty squares at
> the edges.
>
> --
Rick Muller
rpm...@gm...
-- 
Rick Muller
rpm...@gm...