https://github.com/jcgoran/fftlog-python
FFTlog in Python
https://github.com/jcgoran/fftlog-python
Last synced: 9 months ago
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FFTlog in Python
- Host: GitHub
- URL: https://github.com/jcgoran/fftlog-python
- Owner: JCGoran
- Created: 2021-02-10T12:28:10.000Z (almost 5 years ago)
- Default Branch: master
- Last Pushed: 2021-10-13T09:23:49.000Z (about 4 years ago)
- Last Synced: 2025-01-29T04:47:32.530Z (11 months ago)
- Language: Python
- Size: 1020 KB
- Stars: 0
- Watchers: 2
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
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README
# 1D FFTlog in Python
Stupid simple implementation of the FFTlog algorithm in Python, first described in [Hamilton, 2000][hamilton].
In essence, the code computes the following integral:
or, in Latex (in case the above doesn't display properly):
```plaintext
I_\ell^n(y)
=
\frac{1}{2 \pi^2}
\int_0^\infty
\text{d}x\,
x^2\,
\frac{j_\ell(x y)}{(x y)^n}\,
f(x)
```
where `j_\ell` are the spherical Bessel functions of degree `\ell`, and `f(x)` is the input function, usually taken to be the [matter power spectrum][power-spectrum].
Code is heavily based on [twoFAST.jl][twofast-repo], and has been verified with their implementation on the reference [power spectrum][twofast-data].
# Installation
Clone the repo:
```bash
git clone https://github.com/JCGoran/repo
```
You need the `numpy` and `scipy` packages for the FFTlog module to work.
You can install them using `pip` from the `requirements.txt` file:
```bash
pip3 install -r requirements.txt
```
You can add a `--user` flag to the above if you don't want to install those packages system-wide.
# Usage
See the provided `example.py` file; note that it needs the `matplotlib` package to perform the plotting.
An abridged version would be:
1. Import the module:
```python
import fftlog
```
2. Input: two arrays, `x`, and `f(x)`; `f(x)` must be sampled on a large enough range of `x`, otherwise spurious oscillations may appear in the output.
3. To create an FFTlog:
```python
# prepares the FFTlog with ell = 0, n = 0, with 2048 sampling points
result = fftlog.FFTlog(x, y, 0, 0, 2048)
# performs the transformation in place with min(y_output) = 1
result.transform(1)
# alternatively, you can instead directly assign the output with:
# x_transform, y_transform = result.transform(1)
```
# License
GPL 3.0
# TODO
Make PyPI package.
[hamilton]: https://arxiv.org/abs/astro-ph/9905191
[twofast-repo]: https://github.com/hsgg/twoFAST.jl
[power-spectrum]: https://en.wikipedia.org/wiki/Matter_power_spectrum
[twofast-data]: https://github.com/hsgg/TwoFAST.jl/blob/master/test/data/planck_base_plikHM_TTTEEE_lowTEB_lensing_post_BAO_H070p6_JLA_matterpower.dat