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Integral value

Posted on 2011-09-08
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Last Modified: 2012-05-12
Hi

I am using Python but I hope somebody in this area will be able to help me.

I have generated some x and y(x) results. These are stored in Python lists. I am able to plot this data using Matplotlib.

What I want to do now is to get the integral between x = a and x = b. I have looked at the simps method in the scipy module but that looks like it will only give the integral for the values I supply for x and y. This is not what I want. What I need is to supply the data points I know and then supply x = a and x = b (which in general won't be the extreme values I have supplied) and then calculate the integral.

For example, suppose I have supplied data x = 0, 1, 2, 3, 4 and 5, and I calculated the corresponding y(x) values. What I would like to do then is calculate the integral beween, for example, x = 1.5 and x = 2.7.

Can anybody help? There must be a way to do this in Python using one of the standard modules e.g. scipy?

Thanks in advance

Issac
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Question by:IssacJones
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by:TommySzalapski
ID: 36504666
Are you approximating this as a function or just the points? If just the points, then I take it you assume the graph has a straight line between points.

In that case y(2.7) = y(2)*.3 + y(3)*.7
y(1.5) = y(1)*.5 + y(2)*.5
And the integral between y(d) and y(e) is just (y(d) + y(e))*(e-d)/2
So you would just do that for each piece and sum them.
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by:TommySzalapski
ID: 36504687
So, in your example, get y(1.5) to y(2) and y(2) to y(2.7)
(y(1.5) + y(2))*.5/2 + (y(2) + y(2.7))*.7/2

Of course you would do this in some kind of a loop.
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by:IssacJones
ID: 36504835
Hi Tommy

Thanks for the suggestion but I would prefer to use an inbuilt Python module to do the work.

Issac
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TommySzalapski earned 250 total points
ID: 36505658
From section 6.2 here http://www.tau.ac.il/~kineret/amit/scipy_tutorial/
You can use interpolate.splrep to create a spline (set s=0 if you don't want it to smooth the curve)
Then you can use interpolate.splint to get the integral.
So it should look something like
splineCurve = interpolate.splrep(xvals,yvals,s=0)
integralValue = interpolate.splint(a, b, splineCurve)

I can't test it (don't have Python), but my knowledge of Math and C++ makes me think that will work quite nicely for you.
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Author Closing Comment

by:IssacJones
ID: 36506326
Thanks Tommy
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