BIN2D command

Syntax: BIN2D x y xbin ybin mcounts nx ny { xmin xmax ymin ymax }
BIN2D\MATRIX mdata mxin myin mout
Qualifiers: \WEIGHTS, \EMPTY, \MATRIX, \XDISCARD, \YDISCARD
Defaults: \-WEIGHTS, \-EMPTY, \-MATRIX, \-XDISCARD, \-YDISCARD, xmin = min(x), xmax = max(x) ymin = min(y), ymax = max(y)

The BIN2D command forms a matrix of bins of data by sorting the vectors x and y into grids of bins which are returned in vectors xbin and ybin. The accumulated matrix of total counts per bin is returned in matrix mcounts. If the numbers xmin and xmax are not entered, they default to the minimum and maximum of x. Similarly, if the numbers ymin and ymax are not entered, they default to the minimum and maximum of y.

xbini = xmin+(i-1/2)(xmax-xmin)/nx   for   i=1,2,...,nx

ybinj = ymin+(j-1/2)(ymax-ymin)/ny   for   j=1,2,...,ny

The point (xk,yk) will be accumulated in mcountsi,j, where

row: i = int((yk-ymin)/(ymax-ymin)*ny)+1
column: j = int((xk-xmin)/(xmax-xmin)*nx)+1

Dimensions

The lengths of x and y must be equal. If a weight vector, w, is supplied, it must also be the same length.

The vectors xbin and ybin and the matrix mcounts will be created. xbin will have nx elements, ybin will have ny elements, and matrix mcounts will have nx columns and ny rows.

Extremes

By default, events below xmin are placed in the first bin column, events above xmax are placed in the last bin column, events below ymin are placed in the first bin row, and events above ymax are placed in the last bin row. If the \XDISCARD qualifier is used, events below xmin are discarded, and events above xmax are discarded. If the \YDISCARD qualifier is used, events below ymin are discarded, and events above ymax are discarded.

Weights

Syntax: BIN2D\WEIGHTS w x y xbin ybin mcounts nx ny { xmin xmax ymin ymax }

If a vector of weights is entered, you must indicate that it is there by using the \WEIGHTS qualifier. The weight w must be a vector. The ith event causes the bin count to be incremented by wi.

Increment only if empty

Syntax: BIN2D\EMPTY w x y xbin ybin mcounts nx ny { xmin xmax ymin ymax }

If the \EMPTY qualifier is used, an event is counted in a bin only if that bin is empty. Only the first event encountered for each bin will be counted in that bin. \EMPTY cannot be used with \MATRIX.

Defined by box corners

Syntax: BIN2D\MATRIX mdata mx my mcounts

The BIN2D\MATRIX command calculates the sum of the data points given by matrix mdata within a set of boxes. The x-coordinates of the boxes are given in matrix mx, the y-coordinates are given in matrix my. Matrices mx and my must be the same size. A data point is taken to be inside a box if it is interior or on an edge. Each data point is considered only once, so a data point is never taken to be in more than one of the boxes. The coordinates of the data points are the row and column indices, for example, mdata[3,4] is row 3 and column 4 so it is at (x,y) location (4,3). The x and y-coordinates in mx and my should be in this index space of coordinates. The qualifiers \EMPTY and \WEIGHTS cannot be used with \MATRIX.