BIN
Syntax: BIN\WEIGHTS w x xbin xcount
BIN\WEIGHTS\AVERAGE w x xbin xcount
BIN\WEIGHTS\EMPTY w x xbin xcount
BIN\WEIGHTS\EDGES w x xbin xcount
BIN\WEIGHTS\EDGES\AVERAGE w x xbin xcount
BIN\WEIGHTS\EDGES\EMPTY w x xbin xcount
By default, the i_th event causes the bin count to be incremented by 1.
If a weight vector, w, is entered, you must indicate that it is there by
using the \WEIGHTS qualifier. The i_th event causes the bin count to be
incremented by w[i].
Syntax: BIN\NBINS x xbin xcount n { xmin xmax }
Defaults: xmin = min(x), xmax = max(x)
By default, the bins are defined by their centres, given in vector xbin,
which must be strictly monotonically increasing. If the \NBINS qualifier
is used, the number of bins, n, is expected. A new vector, xbin, will be
created which will contain n elements. If the numbers xmin and xmax are
not entered, they default to the minimum and maximum of vector x. The xbin
vector will be: xbin[i] = xmin+(i-0.5)*(xmax-xmin)/n for i=1,2,...,n
Syntax: BIN\LAGRANGE x xbin xcount
If the \LAGRANGE qualifier is used, \WEIGHTS, \EDGES, \AVERAGES, and
\EMPTY are not allowed. If n=len(xbin), define the bin ranges, r[i]
r[1] = xbin[1]-(xbin[2]-xbin[1])/2
r[i] = xbin[i]-(xbin[i]-xbin[i-1])/2 for i=2,3,...,n
r[n+1] = xbin[n]+(xbin[n]-xbin[n-1])/2
For each i=1,2,...,len(x) find j so that r[j] <= x[i] < r[j+1] for
some j=1,2,...,n. If j = n, then xcount[n] is incremented by 1,
otherwise, let w = (x[i]-xbin[j])/(r[j+1]+r[j])/2 then xcount[j] is
incremented by 1-w and xcount[j+1] is incremented by w.
Syntax: BIN\AVERAGE x xbin xcount
BIN\AVERAGE\EDGES x xbin xcount
The \AVERAGE qualifier means that the output xcount vector will contain
the average value for each bin. An internal counter is kept for each
bin, and the value for xcount[i] will be divided by the number of events
in bin i before it is output. Thus, BIN\EMPTY results in the same output
as BIN\AVERAGE. \AVERAGE can be used with \WEIGHT and \EDGES, but not
with \EMPTY.
Syntax: BIN\EMPTY x xbin xcount
BIN\EMPTY\EDGES x xbin xcount
The \EMPTY qualifier means that an event is counted in a bin only if
that bin is empty. So only the first event encountered for each bin
will be counted in that bin. \EMPTY can be used with \WEIGHT and \EDGES,
but not with \AVERAGE.
Syntax: BIN\EDGES x xbin xcount
By default, bins are defined by their centres. If the \EDGES qualifier
is used, bins are defined by their edges. The bin edges must be given
in vector xbin. The length of xcount will be one less than the length of
xbin. A weight vector, w, may be specified if you use the \WEIGHTS
qualifier. If xbin[j] <= x[i] < xbin[j+1] then xcount[j] is incremented
by 1, or by the weight, w[i].