[SciPy-User] integrals and quad

Oleksandr Huziy guziy.sasha@gmail....
Wed Aug 15 15:36:47 CDT 2012


Hi,

I am not sure if it falls under the elegant, but what if you take the
integrals for parts and then apply cumsum:
>>> import numpy as np
>>> t1 = np.linspace(0,3,50)
>>> t2 = t1[1:]
>>> t1 = t1[:-1]
>>> parts = map(lambda x1,x2: quad(f,x1,x2)[0], t1,t2)
>>> F = np.cumsum(parts)

Probably you'd want to add 0 at the start of the result...

Cheers
--
Oleksandr (Sasha) Huziy

2012/8/15 <josef.pktd@gmail.com>

> On Wed, Aug 15, 2012 at 4:15 PM, nicky van foreest <vanforeest@gmail.com>
> wrote:
> > Hi,
> >
> > Given some function f it is easy with scipy.integrate.quad to compute
> > the integral of f for some given endpoint. However, I need the
> > integral at many endpoints, that is, I want to plot \int_0^t f(x) dx.
> > How can this be done in an efficient and elegant way?
> >
> > To illustrate I used the following code.
> >
> > from numpy import cumsum, linspace, vectorize
> > from scipy.integrate import quad
> > from  pylab import plot, show
> >
> > def f(x):
> >     return x
> >
> > F = vectorize(lambda t: quad(f, 0, t)[0]) # must be wasteful
> >
> >
> > t = linspace(0,3, 50)
> >
> > FF = cumsum(f(t))*(t[1]-t[0])  # simple, but inaccurate, note that
> > t[1]-t[0] is the grid size, a bit like dx in the integral
> >
> > plot(t,f(t))
> > plot(t, F(t))
> > plot(t, F)
> > show()
> >
> > I suspect that calling F at many values is wasteful, since the
> > integral is evaluated at the same points many times. The trick with
> > using cumsum must save some work (an O(n) algo), but is less accurate
> > as is shown by the graphs. So, I don't like to use cumsum, and I also
> > don't like to use a vectorized quad. Is there something better?
>
> cumtrapz is the only one that works (when I looked at this)
> I also tried odeint for this once before, but didn't really use it.
>
> Josef
>
> >
> > thanks
> >
> > Nicky
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