## Basic Use

Nexus Pipeline for analyzing the effects of baryonic matter on cosmological
structures in IllustrisTNG simulations

The `PyCosmoMMF` package contains the algorithms necessary for a Multiscale
Morphological Analysis (MMF) of cosmological simulations. The purpose of this
package is to streamline our modified version of the NEXUS+ algorithm. We used
the `julia` version of this package in our work
([Sunseri et al. 2022](https://ui.adsabs.harvard.edu/abs/2023PhRvD.107b3514S/abstract))
to analyze the effects of baryonic matter on the Cosmic Web.

The NEXUS+ algorithm contains several steps as described in our paper
([Sunseri et al. 2022](https://ui.adsabs.harvard.edu/abs/2023PhRvD.107b3514S/abstract)).
In general, we start with a density field (note: we more specifically mean a 1 +
δ field), smooth it with a logarithmic Gaussian smoothing filter, then compute
the hessian of the smoothed density field, use the eigenvalues of the hessian
matrix to calculate the structure type signatures, find the maximum signatures
over a range of smoothing scales, and apply physically based threshold criterion
to categorize structures within the Cosmic Web. The entire package is
implemented in `python` and all of these steps are summarized inside of two
functions. The first function `maximum_signature()` does the first several steps
of the NEXUS+ algorithm to compute the maximum structure signatures, the second
function is `calc_structure_bools()` which uses physical criteria to tag
structures into 4 categories: clusters, filaments, walls, and voids.

We also make the data products from our paper
([Sunseri et al. 2022](https://ui.adsabs.harvard.edu/abs/2023PhRvD.107b3514S/abstract))
available for download at
[This Link](http://idark.ipmu.jp/~jia.liu/data/Baryon_Analysis_Data/)

### General Code Usage

The general usage of the package would look like:

#### Step I

We first calculate the maximum structure signatures across multiple smoothing
scales with the NEXUS+/NEXUS algorithm

```python
import PyCosmoMMF

density_field = np.load("path/to/density_field.npy")

Rs = [sqrt(2) ** n for n in range(10)]  # smoothing scales

max_signatures = PyCosmoMMF.maximum_signature(
    Rs, density_field, algorithm="NEXUSPLUS"
)  # compute maximum signatures
```

The output of `maximum_signature()` is a 4D Float Array where the 4th index
denotes the signature type: 0 = clusters, 1 = filaments, 2 = walls. An example
output of this can be seen below

```{image} images/final_NEXUSPLUS_Signatures_hydro.png
:class: only-light
```

```{image} images/final_NEXUSPLUS_Signatures_hydro_dark.png
:align: center
:class: only-dark
```

#### Step II

We then have the option of running the tagging scheme a few different ways. The
first important argument in `calc_structure_bools()` besides the `density_field`
and the `max_signatures` arrays is the `verbose_flag`. When set to `True` the
code gives a lot more information and provides a few plots. This is best turned
on when debugging the code. When `verbose_flag` is turned on there is an
additional output to the `calc_structure_bools()` function: `summary_data` which
is a dictionary containing all the relevant extra information one might need. It
can be used to make the mass change curves for filaments and walls. Consult the
API Docs tab for a detailed summary of what is inside `summary_data`.

**_Verbose Flag On:_**

```python
verbose_flag = True  # or False


clusbool, filbool, wallbool, voidbool, summary_data = PyCosmoMMF.calc_structure_bools(
    density_field, max_signatures, verbose_flag
)  # tag structures
```

**_Verbose Flag Off:_**

```python
verbose_flag = False


clusbool, filbool, wallbool, voidbool = PyCosmoMMF.calc_structure_bools(
    density_field, max_signatures, verbose_flag
)  # tag structures
```

We also note in the `calc_structure_bools()` function, one can use their own
cluster boolean filter instead of the one generated by the NEXUS+ formalism
(using virialization of clusters as a tool for determining spurious detections).
This is helpful if you want to use a more trusted cluster/halo finder algorithm
(FoF, Rockstar, etc...). For more information on the NEXUS+ method, see
[Cautun et al. 2013](https://academic.oup.com/mnras/article/429/2/1286/1038906).

**_External Cluster Boolean Filter:_**

```python
clusbool_ext = np.load(
    "path/to/cluster_boolean_filter.npy"
)  # load in externally computed boolean filter for clusters

verbose_flag = False


clusbool, filbool, wallbool, voidbool = PyCosmoMMF.calc_structure_bools(
    density_field, max_signatures, verbose_flag, clusbool_ext
)  # tag structures
```

Another important optional argument in the `calc_structure_bools()` function is
`overdensity_threshold`. The default value is `overdensity_threshold = 370` as
used in
[Cautun et al. 2013](https://academic.oup.com/mnras/article/429/2/1286/1038906)
but other values can be 200 or 500 corresponding to `R_200` or `R_500`.
`overdensity_threshold` is the overdensity parameter Δ, when clusters achieve an
average overdensity greater than this value, they are thought to be
virialized/collapsed.

The boolean filters for each structure type produced by `calc_structure_bools()`
can be used to tag structures within a density field, the results of this can be
seen below

```{image} images/final_tagging_figure.png
:class: only-light
```

```{image} images/final_tagging_figure_dark.png
:align: center
:class: only-dark
```

#### Additional Code Information

- Note: The NEXUS+ implementation of tagging clusters is highly dependent on the
  the grid resolution being used. The cluster boolean filter will only be
  physically motivated if the resolution of each voxel is roughly < 1 Mpc/h so
  clusters can be resolved.