## [Matplotlib-users] Re: Can matplotlib draw normal curves

 [Matplotlib-users] Re: Can matplotlib draw normal curves From: John Hunter - 2005-07-28 14:45:34 >>>>> "Rich" == Rich Shepard writes: Hi Rich, I'm CC-ing my reply to the matplotlib-users list, so other people can contribute to and benefit from the discussion. Rich> John, Last evening I read through the user guide and Rich> tutorial for matplotlib. Although I've done my scientific Rich> plotting using Gri (a better gnuplot) for years, and more Rich> recently with PSTricks, the philosophy and syntax of Rich> matplotlib is quite easy to grasp. Congratulations on a Rich> masterful job! Thanks! Rich> Despite my careful reading, I saw nothing about creating Rich> the types of curves I need to plot. A sample is attached. I Rich> need to be able to draw overlapping normal curves and S- and Rich> Z-curves at the ends of the range of x values. Can I do this Rich> with matplotlib, particularly by specifying end points, the Rich> x value where y=1.0, and the y value of the point of Rich> inflection? Rich> Plotting triangular and trapezoidal versions are easy as Rich> the connecting lines are straight. Doing the normal curves Rich> (complete and either half) is a challenge. matplotlib's general approach is that you compute the x and y vertices of the curves you want to plot and then pass it off to plot. So you could write a helper function to generate these points given your parameters of interest and then plot them. Eg for a normal pdf, matplotlib.mlab provides such a function from matplotlib.mlab import normpdf import matplotlib.numerix as nx import pylab as p x = nx.arange(-4, 4, 0.01) y = normpdf(x, 0, 1) # unit normal p.plot(x,y, color='red', lw=2) p.show() Of course, some curves do not have closed form expressions and are not amenable for such treatment. Some of the matplotlib backends have the capability to draw arbitrary paths with splines (cubic and quartic) but this functionality hasn't been exposed to the user yet. If you need this, let me know and I can provide an interface in an upcoming release. I had not heard of "S curves" and "Z curves", but a little bit of googling [1,2] suggests that the S curve is a sigmoid and the Z curve is simply 1-sigmoid. If this is what you are looking for, there are many simple forms for sigmoids: eg, the hill, boltzman, and arc tangent functions. Here is an example of the boltzman function import matplotlib.numerix as nx import pylab as p def boltzman(x, xmid, tau): """ evaluate the boltzman function with midpoint xmin and time constant tau over x """ return 1. / (1. + nx.exp(-x-xmid)/tau) x = nx.arange(-6, 6, .01) S = boltzman(x, 0, 1) Z = 1-boltzman(x, 0.5, 1) p.plot(x, S, x, Z, color='red', lw=2) p.show() See also http://mathworld.wolfram.com/SigmoidFunction.html. With a little arithmetic you can write a helper function that takes the midpoint and saturation point as arguments and computes the relevant parameters and points. From the book jacket on your home page [3], I'll anticipate your next question that you may want to fill the area below the intersection of the S and Z curves, which you can do with the magic of numerix and the fill function import matplotlib.numerix as nx import pylab as p def boltzman(x, xmid, tau): """ evaluate the boltzman function with midpoint xmin and time constant tau over x """ return 1. / (1. + nx.exp(-x-xmid)/tau) def fill_below_intersection(x, S, Z): """ fill the region below the intersection of S and Z """ #find the intersection point ind = nx.nonzero( nx.absolute(S-Z)==min(nx.absolute(S-Z)))[0] # compute a new curve which we will fill below Y = nx.zeros(S.shape, typecode=nx.Float) Y[:ind] = S[:ind] # Y is S up to the intersection Y[ind:] = Z[ind:] # and Z beyond it p.fill(x, Y, facecolor='blue', alpha=0.5) x = nx.arange(-6, 6, .01) S = boltzman(x, 0, 1) Z = 1-boltzman(x, 0.5, 1) p.plot(x, S, x, Z, color='red', lw=2) fill_below_intersection(x, S, Z) p.show() As these examples illustrate, matplotlib doesn't come with helper functions for all the kinds of curves people want to plot, but along with numerix and python, provides the basic tools to enable you to build them yourself. Hope this helps! JDH [1] http://www.nicholasgcarr.com/digital_renderings/archives/the_z_curve_and_it.shtml [2] http://bdn.borland.com/article/0,1410,32411,00.html [3] http://www.appl-ecosys.com/newstuff.html