Having Trouble Plotting the Cosmic Shear Power Spectrum Kernel?

[sunrah]

I'm having difficulty plotting the kernel $I(k_{1},k)$ of the cosmic shear power spectrum which is defined as
$I(k_{1},k) = k_{1}\int^{\infty}_{0}r j_{l}(k_{1}r)dr \int^{r}_{0}\frac{r-r'}{r'}j_{l}(kr')\sqrt{P^{\Phi\Phi}(k)}dr'$

where the j_l are spherical bessel functions.
I'v tried plotting I vs. k₁ using python's sympy and scipy, but with no luck. My laptop is incredibly slow and I'm not thrilled by the results. It doesn't help that I can't see what this curve should look like. All assistance appreciated. If you know any helpful resources that would also be great.

 

[fizzy]

OP, how do you hope to plot a double integral without solving it ? Maybe you are assuming we all know what you are doing.

gnuplot is quite flexible and powerful plotting tool but it needs a fn to plot it cannot plot an integral.

 

[sunrah]

OP, how do you hope to plot a double integral without solving it ? Maybe you are assuming we all know what you are doing.

gnuplot is quite flexible and powerful plotting tool but it needs a fn to plot it cannot plot an integral.

I'v now plotted it numerically but it takes such a long time on my laptop and I still need to increase the number of data points. Are there any techniques to speed up this kind of numerical integration task?

 

[fizzy]

OK , so what you have is a problem with numerical integration , not a plotting problem. That makes more sense.

If you rely on libraries ( I assume it's scipy providing the generic integration method ) you have to take what you get or dig the doc for information about options.

If you need something more specific, I suspect you are going to have to do some work. Sorry.

 

[fizzy]

I should also point out the python is an interpreted language and is probably not the best solution for doing this kind of intensive calculation. You could look for a C or Fortran library or other compiled language which would certainly reduce run times considerably.

Numerical integration is a standard problem. I'm sure many solutions are available now you realize that it is not a plotting problem.

Good luck.