Numerical integration Loop Python

Question

I would like to write a program that solves the definite integral below in a loop which considers a different value of the constant c per iteration.

I would then like each solution to the integral to be outputted into a new array.

How do I best write this program in python?

enter image description here

with limits between 0 and 1.

from scipy import integrate

integrate.quad

Is acceptable here. My major struggle is structuring the program.

Here is an old attempt (that failed)

# import c
fn = 'cooltemp.dat'
c = loadtxt(fn,unpack=True,usecols=[1])

I=[]
for n in range(len(c)):

    # equation
    eqn = 2*x*c[n]

    # integrate 
    result,error = integrate.quad(lambda x: eqn,0,1)

    I.append(result)

I = array(I)

Welcome to Stack Overflow! We encourage you to research your questions. If you've tried something already, please add it to the question - if not, research and attempt your question first, and then come back. — user647772
– user647772, Commented Aug 16, 2012 at 12:47
What method of numerical integration do you wish to use? Trapezoidal rule? Simpson's rule? Gaussian quadrature? Monte Carlo integration? Or do you just want the built-in scipy.integrate.quadrature function? Please specify some of these details and show your current progress and we will be happy to help. — ely
– ely, Commented Aug 16, 2012 at 12:49
integrate.quad is acceptable here. It's more structuring the program to iterate through the constants that I struggle with. — 8765674
– 8765674, Commented Aug 16, 2012 at 12:51
If c is a constant, why not use the standard solution c*x^2? — Roland Smith
– Roland Smith, Commented Aug 16, 2012 at 13:04

Nicolas Barbey · Accepted Answer · 2012-08-16 13:09:03Z

5

For instance to compute the given integral for c in [0, 9] :

[scipy.integrate.quadrature(lambda x: 2 * c * x, 0, 1)[0] for c in xrange(10)]

This is using list comprehension and lambda functions.

Alternatively, you could define the function which returns the integral from a given c as a ufunc (thanks to vectorize). This is perhaps more in the spirit of numpy.

>>> func = lambda c: scipy.integrate.quadrature(lambda x: 2 * c * x, 0, 1)[0]
>>> ndfunc = np.vectorize(func)
>>> ndfunc(np.arange(10))
array([ 0.,  1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9.])

edited Aug 16, 2012 at 13:09

answered Aug 16, 2012 at 12:59

Nicolas Barbey

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2 Comments

8765674 Over a year ago

This looks good. Rather than xrange(10) how do I get it to compute the integral for c equalling values from an array?

Nicolas Barbey Over a year ago

See alternative solution given above

mgilson · Accepted Answer · 2012-08-16 13:09:15Z

3

You're really close.

fn = 'cooltemp.dat'
c_values = loadtxt(fn,unpack=True,usecols=[1])

I=[]
for c in c_values: #can iterate over numpy arrays directly.  No need for `range(len(...))`

    # equation
    #eqn = 2*x*c[n] #This doesn't work, x not defined yet.

    # integrate 
    result,error = integrate.quad(lambda x: 2*c*x, 0, 1)

    I.append(result)

I = array(I)

I think you're a little confused about how lambda works.

my_func = lambda x: 2*x

is the same thing as:

def my_func(x):
    return 2*x

If you still don't like lambda, you can do this:

f(x,c):
   return 2*x*c

#...snip...
integral, error = integrate.quad(f, 0, 1, args=(c,) )

edited Aug 16, 2012 at 13:09

answered Aug 16, 2012 at 13:03

mgilson

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1 Comment

mgilson Over a year ago

@ElizabethPor -- I'm just glad to be helpful. Good luck with your integrations.

Andy Hayden · Accepted Answer · 2012-08-16 13:03:27Z

0

constants = [1,2,3]

integrals = []                                  #alternatively {}

from scipy import integrate

def f(x,c):
    2*x*c

for c in constants:
    integral, error = integrate.quad(lambda x: f(x,c),0.,1.)
    integrals.append(integral)                 #alternatively integrals[integral]

This will output a list of just like Nicolas answer, for whatever list of constants.

answered Aug 16, 2012 at 13:03

Andy Hayden

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