Epoch Folding

Gregory & Loredo Algorithm

1. sitar_glvary( t, [; tmin=#, tmax=#, mmax=#, thresh=#, nbins=#, texp=array, frac_exp=array]);
   Use the Gregory-Loredo algorithm to find the odds ratios that even divisions of a lightcurve are better descriptions of the data than a constant lightcurve. A 'best estimate' lightcurve can also be output for a lightcurve with nbins.
   Run as: isis> fold = sitar_glvary(t; tmin=#, tmax=#, mmax=#, thresh=#, nbins=#, texp=array, frac_exp=array);
   Variables in [] are optional qualifiers.
   Omitted qualifier variables take on default values.
   
   Inputs:
   • t : Array of event times
   Optional Qualifier Inputs:
   • tmin : The minimum time to consider (Default=min(t)-1)
   • tmax : The maximum time to consider (Default=max(t)+1)
   • mmax : Consider lightcurve divisions from 2 to mmax evenly spaced bins. (Default=300)
   • thresh : Truncate the maximum number of partitions considered by ignoring partitionings for which-- \sum_m(odds ratio) < max(\sum_n(odds ratio))/exp(thresh) , where n = 2 -> mmax. I.e., the more partitionings you have, the less significant the results tend to become. thresh sets a minimum probability: (1-p_min) ~ exp(thresh)*(1-p_peak). (Default=2.)
   • nbins : Create an output lightcurve with nbins. (Default=mmax)
   • texp, : A pair of arrays that give values for the fractional exposure frac_exp as a function of time. *** Only non-zero values of exposure will be retained ***, which will then be interpolated and used to correct the lightcurve rates. These arrays must have a minimum of five entries. (Default is for no correction.)
   Outputs:
   • gl.p : Total probability that some evenly partitioned lightcurve, with up to gl.mmax bins, is a better description than a constant lightcurve
   • gl.ppart : The probability for an individual evenly partitioned lightcurve that it is a better description than a constant lightcurve
   • gl.lodds_sum : The natural logarithm of the sum of the odds ratios comparing lightcurves with two or more partitions to a constant lightcurve. gl.p == exp(gl.lodds_sum)/[1+exp(gl.lodds_sum)]
   • gl.mpeak : The number of partitions for the evenly partitioned lightcurve with the maximum probability.
   • gl.mmax : The maximum number of partitions actually used (influenced by the setting of the thresh parameter)
   • gl.m : The number of partitions corresponding to each evenly partitioned lightcurve considered (=[2:mmax])
   • gl.pm : Total probability that some evenly partitioned lightcurve is a better description than a constant lightcurve for each maximum number of partitions considered ([2:mmax])
   • gl.nj : The counts histogram corresponding to each partitioning above
   • gl.aj : The integrated fractional exposure for each partitioning above
   • gl.a_avg : The averaged fractional exposure.
   • gl.tmin : The value of tmin actually used (maximum of [tmin,min(texp)]);
   • gl.tmax : The value of tmax actually used (minimum of [tmax,max(texp)]);
   • gl.tlc : The output lightcurve times (an array with input nbins bins)
   • gl.rate : Best estimate of the lightcuve rates at the above times
   • gl.erate : Best estimate of the lightcuve rate errors at the above times