Databases
StackOverflow2013
Postsdbo
POSpline representation with scipy.interpolate: Poor interpolation for low-amplitude, rapidly oscillating functions
 

Note that there are some explanatory texts on larger screens.

plurals
  1. POSpline representation with scipy.interpolate: Poor interpolation for low-amplitude, rapidly oscillating functions
    primarykey
    data
    text
    <p>I need to (numerically) calculate the first and second derivative of a function for which I've attempted to use both <code>splrep</code> and <code>UnivariateSpline</code> to create splines for the purpose of interpolation the function to take the derivatives.</p> <p>However, it seems that there's an inherent problem in the spline representation itself for functions who's magnitude is order 10^-1 or lower <em>and</em> are (rapidly) oscillating.</p> <p>As an example, consider the following code to create a spline representation of the sine function over the interval (0,6*pi) (so the function oscillates three times only):</p> <pre><code>import scipy from scipy import interpolate import numpy from numpy import linspace import math from math import sin k = linspace(0, 6.*pi, num=10000) #interval (0,6*pi) in 10'000 steps y=[] A = 1.e0 # Amplitude of sine function for i in range(len(k)): y.append(A*sin(k[i])) tck =interpolate.UnivariateSpline(x, y, w=None, bbox=[None, None], k=5, s=2) M=tck(k) </code></pre> <p>Below are the results for M for A = 1.e0 and A = 1.e-2</p> <p><a href="http://i.imgur.com/uEIxq.png" rel="nofollow">http://i.imgur.com/uEIxq.png</a> Amplitude = 1</p> <p><a href="http://i.imgur.com/zFfK0.png" rel="nofollow">http://i.imgur.com/zFfK0.png</a> Amplitude = 1/100</p> <p>Clearly the interpolated function created by the splines is totally incorrect! The 2nd graph does not even oscillate the correct frequency.</p> <p>Does anyone have any insight into this problem? Or know of another way to create splines within numpy/scipy? </p> <p>Cheers, Rory</p>
    singulars
    1. PO
      singulars
      1. PTAnswer
    1. This table or related slice is empty.
    1. PTQuestion
    1. USWill Vousden
    1. USRory Smith
    plurals
    1. This table or related slice is empty.
    1. PL
      singulars
      1. LTLinked
    2. PL
      singulars
      1. LTLinked
    1. This table or related slice is empty.
    1. PO
      singulars
      1. PTAnswer
    2. PO
      singulars
      1. PTAnswer
    1. VO
      singulars
      1. POSpline representation with scipy.interpolate: Poor interpolation for low-amplitude, rapidly oscillating functions
      1. This table or related slice is empty.
      1. VTUpMod
    2. VO
      singulars
      1. POSpline representation with scipy.interpolate: Poor interpolation for low-amplitude, rapidly oscillating functions
      1. This table or related slice is empty.
      1. VTUpMod
    3. VO
      singulars
      1. POSpline representation with scipy.interpolate: Poor interpolation for low-amplitude, rapidly oscillating functions
      1. This table or related slice is empty.
      1. VTUpMod
    1. COFYI: Don't do things like the for loop you have above. `y = A * numpy.sin(k)` does the same thing much, much faster.
      singulars
      1. POSpline representation with scipy.interpolate: Poor interpolation for low-amplitude, rapidly oscillating functions
      1. USJoe Kington
 

Querying!

 
Guidance
A row detail

Detail views are divided into sections. All the information in the data section comes from columns in the selected row. The other sections display data from other, related rows.

Related data can be related in a to-one or a to-many fashion. Captions of data related in a to-many fashion link to a list view showing a filtered view of the table.

Try moving around until you find a non-empty to-many entry and click on the label to get to one. You can move back to the root by clicking on the database name in the header.

SQuiL has stopped working due to an internal error.

If you are curious you may find further information in the browser console, which is accessible through the devtools (F12).

Reload