Re: [Matplotlib-users] Polyfit help

[John H. <jdh...@ac...>]

>>>>> "Brian" == Brian B <b-m...@bb...> writes:

    Brian> Hello, I graph of weather data from a CGI script using the
    Brian> Agg backend only. The graph is a common time
    Brian> vs. temperature 2D line plot. Since the graph plots every n
    Brian> minutes, the lines on the graph tend to look pointed and
    Brian> not very aesthetically pleasing (as many people have
    Brian> informed me.)  I did some research and found I needed to do
    Brian> curve fitting.

    Brian> I'm trying to use 8th order polynomial fitting. I have
    Brian> found a sample on the Web that shows how to use matplotlib
    Brian> to do a best-fit line from polyfit, but I want a curve that
    Brian> follows the curve of weather temperature data.

    Brian> I plot the data using a list of X-coordinates and a list of
    Brian> Y-coordinates.  I assume I can call polyfit with (x,y,8)
    Brian> for 8th order polynomial fitting.  However, I am not sure
    Brian> what to do with the results. I have tried to translate the
    Brian> 1st order polyfit example for my needs but I don't think I
    Brian> am using the polyfit data correctly.

You would need to use polyval to get the results of polyfit (there is
an example in the matplotlib Users Guide in the Cookbook chapter for a
3rd order fit), but I don't think you want to use an 8-th order
polynomial for this -- as you indicate below, a spline or a filter is
a better choice.

    Brian> Also, it has been suggested that a spline or Butterworth
    Brian> filter on the data may yield more predictable results. I
    Brian> have found some of this functionality in SciPy and a nifty
    Brian> module in a language called Octave. Would matplotlib
    Brian> benefit from this?

Use spline if you want a curve that passes through all your data, use
butterworth or convolution if you want to smooth your data.

scipy is your best bet -- scipy spline and a butterworth filter
examples from my scipy examples directory are included.  In general,
we try to stay focused on plotting in matplotlib rather than
algorithms, and leave algorithms to the scipy folks.  They are working
hard on getting a modular package that is easy to install.  I think it
would be useful to provide some wrappers around scipy in the
matplotlib.mlab module that exposed a matlab interface to some of
their algorithms, with imports done in such a way that having the
additional scipy functionality would be optional

Here is a scipy spline example, plotted with mpl

    from scipy import arange, sin, pi, interpolate
    from pylab import plot, show
    # Cubic-spline
    t = arange(0, 2.0, 0.1)
    y = sin(2*pi*t)
    tck = interpolate.splrep(t, y, s=0)
    tnew = arange(0, 2.0, 0.01)
    ynew = interpolate.splev(tnew, tck, der=0)
    plot(t, y, 'o', tnew, ynew)
    show()


And here is a butterworth filter.  Note that filters can introduce
phase shifts in your data (illustrated in this example) so use with
caution!

    from __future__ import division
    from scipy import signal, arange, sin, pi, linspace, transpose
    from RandomArray import normal
    from pylab import plot, show, subplot
    from scipy.signal import buttord, butter, lfilter

    dt = 0.001
    t = arange(0.0, 10.0, dt)
    nse = normal(0.0, 0.1, t.shape)
    #s = 
    s = normal(0.0, 1.0, (len(t),22))
    for i in range(22):
    s[:,i] += sin(2*pi*t)

    lpcf = 3
    lpsf = 5
    Nyq = 1/(2*dt)
    Rp = 2
    Rs = 20
    Wp = lpcf/Nyq
    Ws = lpsf/Nyq
    [n,Wn] = buttord(Wp,Ws,Rp,Rs)
    [b,a] = butter(n,Wn)
    xlp = transpose(lfilter(b,a,transpose(s)))


    subplot(311)
    plot(t, s[:,0])
    subplot(312)
    plot(t, xlp[:,0])
    subplot(313)
    plot(t, xlp[:,1])

    show()


    Brian> Any assistance is much appreciated. I'm just starting out
    Brian> on this type of stuff but it is fascinating to work with!

Have fun!

JDH