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Re: Confused by Integration
From: |
CdeMills |
Subject: |
Re: Confused by Integration |
Date: |
Tue, 16 Aug 2011 00:42:05 -0700 (PDT) |
Jason C. Wells wrote:
>
> I am confused by integration. I see that the various quad function take
> different types (scalar, vector) and give different outputs. I've been
> trying them out and watching how the quadrature behaves for each of
> them. E.g:
>
> function retval = integrand (x)
> x
> retval = x .^ 2
> endfunction
>
> # integral = quadv ("integrand", -Inf, Inf)
>
> a = -10: 1: 10;
> integral = quadgk ("integrand", a(1), a(end))
>
> Quadgk seems close to what I want, but the variable of integration
> "bounces around" which makes plotting impossible.
>
> x=
> -9.999989
> -9.435377
> -7.911791
> -5.669229
> -2.947694
> 0.012817
> 2.972302
> 5.690762
> 7.928196
>
> Ultimately I'd like to make a plot of the integral. It seems that all
> of the quadrature functions do not pay attention to the the range i've
> given. The functions do their own thing within the limits of integration.
>
> Does a person need to run the integration, then re-sort and
> re-interpolate in order to produce outputs at evenly spaced inputs?
>
> How do I integrate such that each output value corresponds with an input
> value taken from a range of from a linspace vector?
>
>
For the first point: contribution are done by volunteers. They have time to
code. Having a nice and unified interface to a lot of functions requires a
lot of work.
Second point: I suppose they're some kind of refinment algorithm, this
explains the bouncing back behaviour. If it's a problem, either try to
decompose it into ordered sequences, either sort them.
For the last point, I don't understand the issue. Either you're interested
into the integral, which is a scalar result, either you've a function
defined by a differential relationship. In the latter case, what you should
use is a function like lsode or similar. It will compute the integral over
segments defined by the user, so you have control over the points spacing.
Regards
Pascal
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