# Disk Foward Modelling (DiskFM)

This tutorial presents how to use the forward modelling routines specific to disk modelling and disk parameter retrieval.

If you use this feature, please cite:

## Why DiskFM?

As noted in Pueyo (2016), “in practice Forward Modeling with disks is complicated by the fact that [it] cannot be simplified using a simple PSF as the astrophysical model: every hypothetical disk morphology must be explored”. Indeed, because of their complex geometries, the forward modelling have to be repeated a lot of time on disks with slightly different parameters. All these geometries are then compared to the klipped reduced image of the data, within an MCMC or a Chi-square wrapper.

However, once measured for a set of reduction parameters, the Karhunen-Loeve (KL) basis do not change. One can save the KL vectors in a file once so they do not have to be recomputed every time. For a new disk model, the forward modelling is therfore only a array reformating and a matrix multiplication, which can be optimized to be only a few seconds. These routines are implemented in PyKLIP and showed on this page. DiskFM currently only supports KLIP ADI, SDI ADI+SDI and RDI reductions (but currently not RDI+ADI/SDI or NMF).

## DiskFM Requirements

diskFM on a single model can be done on a personnal computer. However, the full parameter space exploration with the Chi-square or MCMC wrapper (out of the scope of this this tutorial) can be computationally very intensive, taking easily a few days, even parallized on a large server.

You also need the following pieces of data to forward model the data:

• A model of disk (this tutorial do not include disk modelling)

• The instrument PSF or a model of the PSF

• A set of to run PSF subtraction on

## Set up

First import an instrument data set and convolve your 2D disk model by the instrument PSF:

```import glob
import numpy as np
import pyklip.instruments.GPI as GPI
from astropy.convolution import convolve
from pyklip.fmlib.diskfm import DiskFM
import pyklip.fm as fm

# read in the data into a dataset
filelist = sorted(glob.glob("path/to/dataset/*.fits"))
dataset = GPI.GPIData(filelist)

# convolved the 2D disk model
disk_model_convolved = convolve(disk_model,instrument_psf, boundary = 'wrap')
```

## Simple disk Forward Modelling

This code then shows how to initialize the DiskFM object and to do a forward modelling:

```numbasis = [3, 10, 20] # different KL numbers we applied to the disk.
aligned_center=[140, 140] # indicate the position of the star

# initialize the DiskFM object
diskobj = DiskFM(dataset.input.shape, numbasis, dataset, disk_model_convolved,
aligned_center=aligned_center)
```

To run the forward modelling, just run:

```fm.klip_dataset(dataset, diskobj, outputdir="output_path/", fileprefix="my_favorite_disk",
numbasis=numbasis, maxnumbasis=100, aligned_center=aligned_center,
mode='ADI', annuli=1, subsections=1, movement=1)
```

the code will save two fits files in outputdir, containing the klipped data and the associated disk forward model.

Most of the parameters implemented for psf forward model KLIP correction with pyklip can be used (see Picking KLIP Parameters for Disks) with the following exceptions:

• spectrum specific keywords (spectrum, flux_overlap, calibrate_flux)

• specific correction modes filtering the data (corr_smooth, highpass)

• other specific correction parameters (N_pix_sector, padding, annuli_spacing)

Mode parameter can be set only to ‘ADI’, ‘SDI’ and ‘ADI+SDI’.`aligned_center` is the position were the klip reduction will center the reduced image. The code will raise an error if it is not set to the position to which you set the star in your model.

## DiskFM for MCMC or Chi-Square

For an MCMC or Chi-Square you can create the KL basis and then save them to forward model multiple models on a dataset without recomputing them every time. If you would like save the KL basis then you will need to signal it during the initialization of the DiskFM object, then apply fm.klip_dataset to measure and ave the forward model KL basis and parameters:

```diskobj = DiskFM(dataset.input.shape, numbasis, dataset,
disk_model_convolved, aligned_center=aligned_center,
basis_filename = 'path/to/dir/klip-basis.h5', save_basis = True)

fm.klip_dataset(dataset, diskobj, outputdir="output_path/", fileprefix="my_favorite_disk",
numbasis=numbasis, maxnumbasis=100, aligned_center=aligned_center,
mode='ADI', annuli=1, subsections=1, movement=1)
```

Then, in any python session you can create a disk object and you can forward model disks with the loaded KL basis vectors without needing to measure this basis. The disk forward model will be output to fmout:

```diskobj = DiskFM(dataset.input.shape, numbasis, dataset,
disk_model_convolved, aligned_center=aligned_center,

# do the forward modelling on a new model
new_disk_model_convolved=convolve(new_disk_model,instrument_psf, boundary='wrap')
diskobj.update_disk(new_disk_model_convolved)
fmout=diskobj.fm_parallelized()

# do the forward modelling on a third model
third_disk_model_convolved=convolve(third_disk_model,instrument_psf, boundary='wrap')
diskobj.update_disk(third_disk_model_convolved)
fmout=diskobj.fm_parallelized()
```

These last 3 lines are specifically what should be repeated withinin the MCMC or Chi-Square wapper.

Note that even if you have already created a DiskFM object to save the FM (ie even if you have runned diskFM with save_basis = True) in this python session, you still need to re-create the DiskFM object and load it (ie, you still need diskFM with load_from_basis = True).

In previous version, the dataset itself (input images) were not saved in the .h5 files, only the KL coeficients. This caused problems because you could run the same KL coefficients with slightly different datasets (for example the order of the frames were not identical) the code would run but provide wrong forward models. This has now beed solved and all the information necessary is saved inside the .h5 file, including intial frames and reduction paramters.

## Speeding up DiskFM

The time is a key element here if you want to produce hundreds of thousands of forward modelling models. A smart choice of pyklip parameters can reduce the time for a single disk forward model:

• use OWA to limit only in the zone where the disk is.

• limit the number of sections (small annuli and subsections number).

• reduce the number of wavelengths. We recall this very usefull pyklip function to rebin quickly the number of wavelength, which should be applied immediatly after loading the dataset:

```dataset.spectral_collapse(collapse_channels=1, align_frames=True)
```
• determine the best KL number parameters in advance and use only one, e.g.:

```numbasis = [3]
```

Finally, due to the fact that numpy also parallelizes linear algebra routines across multiple cores, performance can actually sharply decrease when multiprocessing in a mcmc. Please read Note on parallelized performance on this subject.

## Multiwavelength DiskFM

If you put a multi-wavelenght dataset (e.g. IFS), the code will produce a multi-wavelenght forward model. In that case, you can use a simple 2D model for the disk and the code will duplicate this model and apply the forward modelling separately on each of those at every wavelengths. Or you can use a 3D model (n_wl, x, y) and the code will apply the forward modelling separately on each of those at every wavelengths.

Alhtough everything we said in the previous sections on saving and loading the KL basis still apply multiwavelength disk forward modelling is long (it can take up to a few minutes or hours for a single forward modelling depending on the number of wavelengths) and we do not recommand to use this in an MCMC wrapper.

## Full DiskFM tutorial

We recall all the steps in a single block

```import glob
import numpy as np
import pyklip.instruments.GPI as GPI
from astropy.convolution import convolve
from pyklip.fmlib.diskfm import DiskFM
import pyklip.fm as fm

# read in the data into a dataset
filelist = sorted(glob.glob("path/to/dataset/*.fits"))
dataset = GPI.GPIData(filelist)

# in case of multiWL data, you might want to stack them first to speed things up
dataset.spectral_collapse(collapse_channels=1, align_frames=True)

numbasis = [3] # different KL numbers we applied to the disk.
aligned_center=[140, 140] # indicate the position of the star

# convolved the disk model
disk_model_convolved = convolve(disk_model,instrument_psf, boundary = 'wrap')

# initialize the DiskFM class
diskobj = DiskFM(dataset.input.shape, numbasis, dataset,
disk_model_convolved, aligned_center=aligned_center,
basis_filename = 'path/to/dir/klip-basis.pkl', save_basis = True)

# run klip to find and save FM basis
fm.klip_dataset(dataset, diskobj, outputdir="path/", fileprefix="my_favorite_disk",
numbasis=numbasis, maxnumbasis=100, aligned_center=aligned_center,
mode='ADI', annuli=2, subsections=1, minrot=3)

# ----------------------------------------------------------------------------
# starting from here you can close the session and reopen later if you want
# ----------------------------------------------------------------------------

# load Klip parameters and FM basis
diskobj = DiskFM(dataset.input.shape, numbasis, dataset,
disk_model_convolved, aligned_center=aligned_center,