CODEWITHSUNDEEP
pythonnumpymatplotlibscipyspline
gc5
gc5

Reputation: 9868

How to plot line (polygonal chain) with numpy/scipy/matplotlib with minimal smoothing

I am trying to plot a line in matplotlib.. I am searching for the right type of interpolation.. I want something like this

taken from canvasxpress.org/line.html

where every line is smoothed. I tried several combination of scipy and matplotlib, such as

x_new = np.arange(x, x_length, 1)
tck = interpolate.splrep(x, y, s=3)
y_new = interpolate.splev(x_new, tck, der=0)
ax.plot(x_new, y_new, color+lstyle)

but the best result I get is

my result

The line represents an increasing variable.. so it is a wrong representation. What can I search for?

Thanks

Edit: I am thinking about implementing a method from myself, but I don't know if it has been already done.. pseudo code is the following

take x and y
calculate spline for each three points 
x[0], x[1], x[2] ... x[1], x[2], x[3] ... and so on
for each y[n] sums every computation done for it and divide by number of 
computations (i.e. y[1] is computed for triplette x[0..2] and x[1..3] so the 
sum is divided by two (average for each point is taken as its value)

Upvotes: 10

Views: 6155

Answers (5)

Warren Weckesser
Warren Weckesser

Reputation: 114811

For that type of graph, you want monotonic interpolation. The PchipInterpolator class (which you can refer to by its shorter alias pchip) in scipy.interpolate can be used:

import numpy as np
from scipy.interpolate import pchip
import matplotlib.pyplot as plt


# Data to be interpolated.
x = np.arange(10.0)
y = np.array([5.0, 10.0, 20.0, 15.0, 13.0, 22.0, 20.0, 15.0, 12.0, 16.0])

# Create the interpolator.
interp = pchip(x, y)

# Dense x for the smooth curve.
xx = np.linspace(0, 9.0, 101)

# Plot it all.
plt.plot(xx, interp(xx))
plt.plot(x, y, 'bo')
plt.ylim(0, 25)
plt.grid(True)
plt.show()

Result:

enter image description here

Upvotes: 12

gg349
gg349

Reputation: 22681

I have looked around a bit. What you want is called

Monotone cubic interpolation,

see wikipedia here. You have a discussion on mathexchange about it here and I have found an implementation in python here. Let me know if this works!

Upvotes: 1

Bitwise
Bitwise

Reputation: 7805

It is important to understand that the interpolation is not just a line for visualization. It is a mathematical model representing how you think the system behaves (the system which generates the data that you measured). Different types of interpolations represent different assumptions about the system.

So, if you know that your system is such that a variable can only increase, you should fit an appropriate model (i.e. use the appropriate interpolation). Looking at your data, it looks like a 2nd degree polynomial or an exponential function might fit well. A Loess (local regression) fit will also work. You can use either tailored functions like numpy.polyfit(), or generic curve fitting with scipy.optimize.curve_fit(). If you have further knowledge about the system, you should use it to select which model to fit.

Upvotes: 1

sega_sai
sega_sai

Reputation: 8538

You should either look at

scipy.interpolate.LSQUnivariateSpline and play with k parameter (degree of the spline)

or scipy.interpolate.UnivariateSpline and play with k and s parameter.

Upvotes: 1

Nicolas Barbey
Nicolas Barbey

Reputation: 6797

The problem is not a display problem. It is an interpolation problem. You are interpolating using spline functions. Picking the right interpolation method is very much depending on the kind of data you have. You cannont expect to have an interpolation function which will behave right in every circumstances (the interpolation have no way to know that your function is increasing).

Upvotes: 1

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