Array PDFs

To create binned PDFs, ntuples must be supplied for each distribution. The number of distributions to fit for from binned PDFs is set in the MXFP titles bank or through the command line prompt:

$signal_number  3  ! 3 distributions to be fitted for from binned PDFs

As the statistics required can be large, more than one ntuple can be read in for each distribution.

$ntuples_one   3    ! 3 ntuples for first distribution
$ntuples_two   3    ! 3 ntuples for second distribution
$ntuples_three   3  ! 3 ntuples for third distribution

For an unconstrained fit of spectrum, a PDF is made for each energy bin, and the amplitude of each bin is allowed to vary. The number of spectral bins and bin sizes are declared in the MXFP bank, along with the parameter used to determine the spectral bins (neutrino energy, event RSP energy, Nhits etc.) and which distribution(s) to bin spectrally. The default set in

mxf_array_pdfs.dat

is for only the CC spectrum to be fit for, with the ES distribution constrained. To over-ride this and constrain the CC shape, a pair of switches is required in the command file:

$constrain_one
$constrain_one_bins

As for the data, it is necessary to define the number of the ntuple containing the Monte Carlo data. It is assumed that the ntuple number and structure is the same for all the input ntuples, but it is allowed to differ from the data ntuple. The code also requires information on the size of this ntuple, and the positions of the required fitting parameters within it (these parameters are the same as for the data obviously!)

$use_ntuple  310   ! Use ntuple number 310 to make PDFs
$ntp_size    79    ! There are 79 parameters in this ntuple
$spec_param  48    ! Position of spectral binning parameter
$param_one  48     ! Position of first fitting parameter
$param_one  30     ! Position of second fitting parameter
$param_one  36     ! Position of third fitting parameter

Other information required from titles files is the number of bins and ranges for each fitting parameter. These can also be declared with the following symbolic commands:

* How many bins for each parameter?
$bins_one   40
$bins_two   30
$bins_three   30
* What is the minimum and maximum for the spectral binning parameter for an
* unconstrained fit?
$spec_min   5.511
$spec_max   20.011
* What is the minimum and maximum for each parameter we are fitting in?
$min_one    5.511
$max_one   20.011
$min_two    0.0
$max_two    0.7702546
$min_three -1.0
$max_three  1.0

The titles bank MXFP also contains information on the relative sizes of the bins for each parameter and also for spectral bins. This allows the use of uneven bin sizes for $cos(\theta_{sun})$ for example. Relative sizes are given in the titles file which are then converted into acutal bin sizes using information on the range of the parameter in the code. Defaults are set up in mxf_array_pdfs.dat which must be editted to change these.