newpythonuser - 1 year ago 133

Python Question

I'm trying to use Gaussian quadrature to approximate the integral of a function. (More info here: http://austingwalters.com/gaussian-quadrature/). The first function is on the interval [-1,1]. The second function is generalized to [a,b] by change of variable. The problem is that I keep getting the error "'numpy.ndarray' object is not callable". I assume (please correct me if I'm wrong) this means I've tried to call the arrays w and x as functions, but I'm not sure how to fix this.

This is the code

`from __future__ import division`

from pylab import *

from scipy.special.orthogonal import p_roots

def gauss1(f,n):

[x,w] = p_roots(n+1)

f = (1-x**2)**0.5

for i in range(n+1):

G = sum(w[i]*f(x[i]))

return G

def gauss(f,a,b,n):

[x,w] = p_roots(n+1)

f = (1-x**2)**0.5

for i in range(n+1):

G = 0.5*(b-a)*sum(w[i]*f(0.5*(b-a)*x[i]+ 0.5*(b+a)))

return G

These are the respective error messages

`gauss1(f,4)`

Traceback (most recent call last):

File "<ipython-input-82-43c8ecf7334a>", line 1, in <module>

gauss1(f,4)

File "C:/Users/Me/Desktop/hw8.py", line 16, in gauss1

G = sum(w[i]*f(x[i]))

TypeError: 'numpy.ndarray' object is not callable

gauss(f,0,1,4)

Traceback (most recent call last):

File "<ipython-input-83-5603d51e9206>", line 1, in <module>

gauss(f,0,1,4)

File "C:/Users/Me/Desktop/hw8.py", line 23, in gauss

G = 0.5*(b-a)*sum(w[i]*f(0.5*(b-a)*x[i]+ 0.5*(b+a)))

TypeError: 'numpy.ndarray' object is not callable

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Answer Source

As Will says you're getting confused between arrays and functions.

You need to define the function you want to integrate separately and pass it into gauss.

E.g.

```
def my_f(x):
return 2*x**2 - 3*x +15
gauss(m_f,2,1,-1)
```

You also don't need to loop as numpy arrays are vectorized objects.

```
def gauss1(f,n):
[x,w] = p_roots(n+1)
G=sum(w*f(x))
return G
def gauss(f,n,a,b):
[x,w] = p_roots(n+1)
G=0.5*(b-a)*sum(w*f(0.5*(b-a)*x+0.5*(b+a)))
return G
```

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