Databases
StackOverflow2013
Postsdbo
POpython: integrating a piecewise function
 

Note that there are some explanatory texts on larger screens.

plurals
  1. POpython: integrating a piecewise function
    primarykey
    data
    text
    <p>I want to integrate a piecewise a defined function that is multiplied by the Legendre polynomials. Unfortunately, I can't find how to use the nth Legendre polynomial of x in the <a href="http://docs.scipy.org/doc/numpy/reference/routines.polynomials.legendre.html" rel="nofollow">documentation</a>. I want to integrate each Legendre polynomial of x when <code>n = 1,..., 50</code> so I have set <code>n = np.arange(1, 51, 1)</code>.</p> <pre><code>import numpy as np import pylab from scipy import integrate n = np.arange(1, 51, 1) def f(x): if 0 &lt;= x &lt;= 1: return 1 if -1 &lt;= x &lt;= 0: return -1 </code></pre> <p>I suppose I need to define another function let's say <code>u(x)</code>.</p> <pre><code>c = [] def u(x): c.append((2. * n + 1) / 2. * integrate.quad(f(x) * insert Legendre polynomials here, -1., 1.)) return sum(c * Legendre poly, for nn in range(1, 51)) </code></pre> <p>So I would then return some <code>u(x)</code> with the first 50 terms expanding my piecewise function by Legendre polynomials.</p> <p><strong>Edit 1:</strong></p> <p>If this can't be done, I could use Rodrigues's Formula to compute the nth Legendre polynomial. However, I couldn't find anything useful when I was looking for computing nth derivatives in Python.</p> <pre><code>P_n(x) = \frac{1}{2^n n!}\frac{d^n}{dx^n}(x^2 - 1)^n </code></pre> <p>So this is an option if someone knows how to implement such a scheme in Python.</p> <p><strong>Edit 2:</strong></p> <p>Using Saullo Castro's answer, I have:</p> <pre><code>import numpy as np from scipy.integrate import quad def f(x, coef): global p p = np.polynomial.legendre.Legendre(coef=coef) if 0 &lt;= x &lt;= 1: return 1*p(x) if -1 &lt;= x &lt;= 0: return -1*p(x) c = [] for n in range(1, 51): c.append((2. * n + 1.) / 2. * quad(f, -1, 1, args=range(1,n+1))[0]) def g(x) return sum(c * p(x) for n in range(1, 51)) </code></pre> <p>However, if I print <code>c</code>, the values are wrong. The values should be <code>1.5, 0, -7/8, 0, ...</code></p> <p>Also, when I plot <code>g</code>, I would like to do <code>x = np.linspace(-1, 1, 500000)</code> so the plot is detailed but <code>c</code> is only 50. How can this be achieved?</p>
    singulars
    1. PO
      singulars
      1. PTAnswer
    1. This table or related slice is empty.
    1. PTQuestion
    1. USdustin
    1. USdustin
    plurals
    1. This table or related slice is empty.
    1. 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. POpython: integrating a piecewise function
      1. This table or related slice is empty.
      1. VTUpMod
    2. VO
      singulars
      1. POpython: integrating a piecewise function
      1. This table or related slice is empty.
      1. VTUpMod
    1. This table or related slice is empty.
 

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