hankel-transform

This program computes the numerical Fourier transform of a spherically symetric function in 3-dimensions, often called the Hankel transform.

This program computes the direct and inverse discrete hankel transform, F, of a 3 dimensional sphericaly symetric function f
for general informations on Hankel transforms, see http://en.wikipedia.org/wiki/Hankel_transform

In a nutshell, the hankel transform is the Fourier transform of a spherically symmetric (i.e., radial) function. The Hankel transform of the function f(r) is noted F(k) in what follows:

F(k) = 4 pi int _0 ^\infty  f(r) sin(kr)/(kr) r^2 dr         (1)

f(r) = 1/(2 pi^2) int _0 ^\infty F(k) sin(kr)/(kr) k^2 dk    (2)

More details on how to get, compile and use the code are given below, but in a nutshell, it:

• asks the user if he wants forward or inverse (backward) transform, i.e. to apply equation (1) or (2) above.
• do the forward or backward transform
• prints the resulting transformed function to transformed.out.

It uses the rude trapezoidal method for the integration. That's barely legal :)
see http://en.wikipedia.org/wiki/Trapezoidal_rule

How to get the latest version of hankel-transform?

In your terminal:

git clone https://github.com/maxlevesque/hankel-transform
cd hankel-transform

How to compile hankel-transform?

gfortran src/main.f90 -o hankel-transform

What is expected as input?

An example input file is given as example-input__dat.in.

Input file should be named "dat.in", and should contain data in format x1 y1 x2 y2 ... xn yn

Then, answer the questions.

How to use hankel-transform

./hankel-transform

The output file

The output file is named transformed.out.

Notes & Todo

dat.in must not have emply lines, even at the end of the file.
One should write a parser for the input file.

Revisions

19/07/2011 02/11/2011

Author

Written by Maximilien Levesque, researcher at Ecole Normale Supérieure, Paris. I wrote this program to compute the Hankel transform of radial potentials like the Lennard-Jones interaction potential.

This was done when I was in postdoc at Ecole Normale Superieure, in Paris, in the theoretical chemistry group of Daniel Borgis (@dborgis).

I would be pleased to receive feedback, bug-reports, etc.

Credits

Many thanks to Julien Beutier. He kept track of this program I had lost!