## Astrophysics background

It is very common in Astrophysics to work with sky pixels. The sky is tassellated in patches with specific properties and a sky map is then a collection of intensity values for each pixel. The most common pixelization used in Cosmology is HEALPix.

Measurements from telescopes are then represented as an array of pixels that encode the pointing of the instrument at each timestamp and the measurement output.

## Sample timeline

import pandas as pd
import numba
import numpy as np


For simplicity let’s assume we have a sky with 50K pixels:

NPIX = 50000


And we have 50 million measurement from our instrument:

NTIME = int(50 * 1e6)


The pointing of our instrument is an array of pixels, random in our sample case:

pixels = np.random.randint(0, NPIX-1, NTIME)


Our data are also random:

timeline = np.random.randn(NTIME)


## Create a map of the sky with pandas

One of the most common operations is to sum all of our measurements in a sky map, so the value of each pixel in our sky map will be the sum of each individual measurement. The easiest way is to use the groupby operation in pandas:

timeline_pandas = pd.Series(timeline, index=pixels)

46889    0.407097
3638     1.300001
6345     0.174931
15742   -0.255958
34308    1.147338
dtype: float64

%time m = timeline_pandas.groupby(level=0).sum()

CPU times: user 4.09 s, sys: 471 ms, total: 4.56 s
Wall time: 4.55 s


## Create a map of the sky with numba

We would like to improve the performance of this operation using numba, which allows to produce automatically C-speed compiled code from pure python functions.

First we need to develop a pure python version of the code, test it, and then have numba optimize it:

def groupby_python(index, value, output):
for i in range(index.shape):
output[index[i]] += value[i]

m_python = np.zeros_like(m)

%time groupby_python(pixels, timeline, m_python)

CPU times: user 37.5 s, sys: 0 ns, total: 37.5 s
Wall time: 37.6 s

np.testing.assert_allclose(m_python, m)


Pure Python is slower than the pandas version implemented in cython.

### Optimize the function with numba.jit

numba.jit gets an input function and creates an compiled version with does not depend on slow Python calls, this is enforced by nopython=True, numba would throw an error if it would not be possible to run in nopython mode.

groupby_numba = numba.jit(groupby_python, nopython=True)

m_numba = np.zeros_like(m)

%time groupby_numba(pixels, timeline, m_numba)
CPU times: user 274 ms, sys: 5 ms, total: 279 ms
Wall time: 278 ms

np.testing.assert_allclose(m_numba, m)


Performance improvement is about 100x compared to Python and 20x compared to Pandas, pretty good!

## Use numba.jit as a decorator

The exact same result is obtained if we use numba.jit as a decorator:

@numba.jit(nopython=True)
def groupby_numba(index, value, output):
for i in range(index.shape):
output[index[i]] += value[i]