BIN2D command
| Syntax: |
BIN2D x y xbin ybin mcounts nx ny { xmin xmax ymin ymax }
|
| 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.