TTCF rebinning

Add a rebinning utility to TTCF classes.

To do:

• Put in place the interface for MatrixEventCorrelator classes
• Implement binning in matrix_evtcorrelator.cl and in utils.cl
  • Check that results are the same for binning=1
  • Add unit test
• Implement binning in matrix_evtcorrelator_time.cl
  • Check that results are the same for binning=1
  • Add unit test

About

The (numerator) TTCF result for time pair (t_1, t_2) is \text{TTCF}(t_1, t_2) = \displaystyle\sum_p I(t_1, p) I(t_2, p).

The most intuitive way of storing the TTCF result is to use cartesian coordinates (t_1, t_2). Matrix (2D array) is the natural data structure mapping a pair of time indices (t_1, t_2) to the \text{TTCF}(t_1, t_2).

corr_matrix_num[t1, t2] = sum_p{I(t1, p) I(t2, p)}

It can easily be extended to three dimensions to account for the scattering vector index qbin (0, 1, 2, ...):

corr_matrix_num_3D[qbin, t1, t2] = sum_p{I(t1, p) I(t2, p)}`

Each correlation matrix has normally a shape (n_frames, n_frames). In the case of TTCF, the matrix is symmetric (as I(t_1) I(t_2) = I(t_2) I(t_1)). For large number of frames, it makes sense to use another data structure which avoids this redundancy.

In the correlator software, TTCF is by default stored in what is called a flattened matrix. This is a one-dimensional array, where

• The first n_frames items correspond to first line 0 of correlation matrix
• The next n_frames - 1 items correspond to the second line of correlation matrix
• and so on

Rebinning can be done with a coordinate change:

\text{TTCF}[\vec{\rho}(t_1, t_2)] = \ldots

\vec{\rho}(t_1, t_2) = (\frac{t_1}{b}, t_1, t_2) where b is the (integer) binning factor.