Background

Given a gravitational-wave HEALPix probability sky map, this Python package finds an optimal sequence of Dorado observations to maximize the probability of observing the (unknown) location of the gravitational-wave event, within one orbit.

The problem is formulated as a mixed integer programming problem with the following arrays of binary decision variables:

• schedule (npix × nrolls × ntimes - ntimes_per_exposure + 1): 1 if an observation of the field that is centered on the given HEALPix pixel, at a given roll angle, is begun on a given time step; or 0 otherwise

• pix (npix): 1 if the given HEALPix pixel is observed, or 0 otherwise

The problem has the following parameters:

• nexp (scalar, integer): the maximum number of exposures

• prob (npix, float): the probability sky map

• regard (npix × ntimes, binary): 1 if the field centered on the given HEALPix pixel is within the field of regard at the given time, 0 otherwise

The objective function is the sum over all of the pixels in the probability sky map for which the corresponding entry in pix is 1.

The constraints are:

• At most one observation is allowed at a time.

• At most nexp observations are allowed in total.

• A given pixel is observed if any field that contains it within its footprint is observed.

• A field may be observed only if it is within the field of regard.