pyBAST: Bayesian Astrometry in Python

Date:	May 22, 2012
Version:	0.3
Authors:	Berian James Joshua S. Bloom
Web site:	https://github.com/berianjames/pyBAST
Copyright:	This document has been placed in the public domain.
License:	This code is released under the MIT license.

pyBAST: Bayesian Astrometry

pyBAST is a Python implementation of the Bayesian Astrometry framework. It provides a module for handling probability distributions that represent astronomical objects and for analysing the changes to these distributions between images.

Typical interactive use might look like:

>>> import pyBA
>>> import numpy as np
>>> data = np.loadtxt('examples/astrom_match_stats')
>>> nties = len(data)

# Load array data into objects
>>> objectsA = np.array([pyBA.Bivarg(mu=data[i,0:2], sigma=data[i,2:5]) for i in range(nties)])
>>> objectsB = np.array([pyBA.Bivarg(mu=data[i,5:7], sigma=data[i,7:10]) for i in range(nties)])

# Select random subset of objects (speeds up testing)
>>> nsamp = 100
>>> ix = np.random.permutation(nties)[:nsamp]

# Compute background mapping
>>> from pyBA.background import distance
>>> S = pyBA.background.suggest_mapping(objectsA,objectsB)
>>> P = pyBA.background.MAP(objectsA[ix], objectsB[ix], mu0=S.mu, prior=pyBA.Bgmap(), norm_approx=True)

# Create astrometric mapping and condition the local distortions
>>> D = pyBA.Amap(P,objectsA[ix], objectsB[ix])
>>> D.condition()

# Plot regression onto regular grid
>>> nres = 30
>>> D.draw_realisation(res=nres)

This functionality is provided in an example script (pyBAST_example.py) and also, with detailed comments, in an iPython notebook (pyBAST_example.ipynb; also in pyBAST_example.pdf).

For non-interactive use, a command utility pyBAST is provided:

> ./pyBAST -h
usage: pyBAST [-h] {fit,summary,apply} ...

Perform probabilistic astrometry with pyBA.

positional arguments:
   {fit,summary,apply}  pyBA command option: should be 'fit', 'summary' or
                        'apply'
     fit                determine astrometric mapping solution
     summary            summarize astrometric mapping solution
     apply              apply astrometric mapping solution at new locations

optional arguments:
  -h, --help           show this help message and exit

This provides the functionality to fit an astrometric solution (which is written compactly to disk), summarize that solution and then apply it to arbitrary locations:

> ./pyBAST fit -h
usage: pyBAST fit [-h] [-s N] [-r n] file [output]

Determine astrometric mapping solution

positional arguments:
   file                 Path to input data file
   output               Optional[=file.pyBA] path to save output pyBA solution.

optional arguments:
 -h, --help           show this help message and exit
 -s N, --subsample N  Use only N random objects from data set
 -r n, --reject n     Excludes objects with > n sigma residuals

> ./pyBAST summary -h
usage: pyBAST summary [-h] [-p] file

Summarize astrometric mapping solution

positional arguments:
  file        Path to astrometric mapping file

optional arguments:
  -h, --help  show this help message and exit
  -p, --plot  Plot astrometric map on grid.

> ./pyBAST apply -h
usage: pyBAST apply [-h] [-xy x y] [-g res] file [batchfile]

positional arguments:
  file                Path to astrometric mapping file
  batchfile           Optional path to file with list of coordinates

optional arguments:
  -h, --help          show this help message and exit
  -xy x y             Map coordinate pair (x,y)
  -g res, --grid res  Map grid of coordinates with density res

What can Bayesian Astrometry in pyBAST do?

pyBAST provides:

• Classes for respresenting astronomical objects and astrometric mappings as probability distributions
• Maximum likelihood and multivariate normal likelihood approximation routines with these objects.
• A full non-parametric astrometic analysis of local distortions using gaussian processes
• MCMC likelihood computation (using emcee)
• A helpful set of examples

It aspires to (but does not yet) provide:

• An interface with wcslib and pyfits
• Handling of priors on object proper motions, parallax
• Robust support for parallel computation on cluster (though n.b. that native threading via BLAS will occur by default)

See the TODO and ROADMAP documents for short- and long-term targets, respectively.

The rest of this README provides a short overview of the package. Detailed instructions will be provided in the documentation (by version 0.4).

Representation of astronomical objects

Bayesian astrometry represents astronomical objects as bivariate gaussians. The bivarg module provides the routines for creating these objects. Upon initialisation, these objects are assigned the following properties:

1. Fundamental descriptors of the distribution:

• mu: A two-vector representing the central location of the objects
• sigma: A 2x2 covariance matrix representing the uncertainity in the location of the object.
• theta: A complementary representation of the covariance between the x- and y-coordinates.

2. Derived quantities used for manipulating objects

• E,*V*: The eigenvalues and eigenvectors of the covariance matrix, used for linear transformations of the distribution.
• det, chol, trace: The determinant, Cholesky root and the trace of the covariance matrix.

Manipulating bivarg objects

Computing 'distance' between objects

Astrometry between image frames

Validating astrometric solutions

Exporting astrometric solutions

Thanks

This work was funded by NSF grant #0941742. The following people contributed to the development of this package: Adam Miller, Henrik Brink, Joey Richards, Dan Starr.