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<HTML>
<HEAD>
<TITLE>BIN2D command</TITLE>
</HEAD>
<BODY BGCOLOR="#FFFFFF" TEXT="#000000">
<P><font size="+3" color="green"><B>BIN2D command</B></font></P>
<TABLE border="1" cols="2" frame="box" rules="all" width="650">
<TR>
<TD width="15%" valign="top"><B>Syntax</B>:</TD>
<TD width="85%" valign="top"><CODE>
BIN2D x y xbin ybin mcounts nx ny { xmin xmax ymin ymax }<br />
BIN2D\MATRIX mdata mxin myin mout</CODE>
</TD></TR>
<TR>
<TD width="15%" valign="top"><B>Qualifiers</B>:</TD>
<TD width="85%" valign="top"><CODE>
\WEIGHTS, \EMPTY, \MATRIX, \XDISCARD, \YDISCARD</CODE>
</TD></TR>
<TR>
<TD width="15%" valign="top"><B>Defaults</B>:</TD>
<TD width="85%" valign="top"><CODE>
\-WEIGHTS, \-EMPTY, \-MATRIX, \-XDISCARD, \-YDISCARD, xmin = min(x), xmax = max(x) ymin = min(y),
ymax = max(y)</CODE>
</TD></TR>
</TABLE>
<P>
The <CODE>BIN2D</CODE> command forms a matrix of bins of data by sorting the
vectors <CODE>x</CODE> and <CODE>y</CODE> into
grids of bins which are returned in vectors <CODE>xbin</CODE> and
<CODE>ybin</CODE>. The accumulated matrix of total counts
per bin is returned in matrix <CODE>mcounts</CODE>. If the numbers
<CODE>xmin</CODE> and <CODE>xmax</CODE> are not
entered, they default to the minimum and maximum of <CODE>x</CODE>.
Similarly, if the numbers <CODE>ymin</CODE> and
<CODE>ymax</CODE> are not entered, they default to the minimum and maximum
of <CODE>y</CODE>.</p>
<p>
<center><CODE>xbin<sub>i</sub> =
xmin+(i-1/2)(xmax-xmin)/nx</CODE> for <code>i=1,2,...,nx</code></center></p>
<p>
<center><CODE>ybin<sub>j</sub> =
ymin+(j-1/2)(ymax-ymin)/ny</CODE> for <code>j=1,2,...,ny</code></center></p>
<p>
The point <code>(x<sub>k</sub>,y<sub>k</sub>)</code> will be accumulated in
<code>mcounts<sub>i,j</sub></code>,
where</p>
<p>
<table>
<tr><td align="right">row:</td>
<td><code>i = int((y<sub>k</sub>-ymin)/(ymax-ymin)*ny)+1</code></td></tr>
<tr><td align="right">column:</td>
<td><code>j = int((x<sub>k</sub>-xmin)/(xmax-xmin)*nx)+1</code></td></tr></table></p>
<p><font size="+1" color="green"><B>Dimensions</B></font></P>
<p>
The lengths of <CODE>x</CODE> and <CODE>y</CODE>
must be equal. If a weight vector, <CODE>w</CODE>, is supplied, it must also
be the same length.</p>
<p>
The vectors <CODE>xbin</CODE> and <CODE>ybin</CODE> and the matrix <CODE>mcounts</CODE> will be
created. <CODE>xbin</CODE> will have <code>nx</CODE> elements, <CODE>ybin</CODE> will have
<CODE>ny</CODE> elements, and matrix <CODE>mcounts</CODE> will have <CODE>nx</CODE> columns and
<CODE>ny</CODE> rows.</p>
<p><font size="+1" color="green"><B>Extremes</B></font></P>
<p>
By default, events below <CODE>xmin</CODE> are placed in the first bin
column, events above <CODE>xmax</CODE> are placed in the last bin column,
events below <CODE>ymin</CODE> are placed in the first bin row, and events
above <CODE>ymax</CODE> are placed in the last bin row. If the
<CODE>\XDISCARD</CODE> qualifier is used, events below <CODE>xmin</CODE> are discarded, and events above
<CODE>xmax</CODE> are discarded. If the <CODE>\YDISCARD</CODE> qualifier is used, events below
<CODE>ymin</CODE> are discarded, and events above <CODE>ymax</CODE> are discarded.</p>
<p><font size="+1" color="green"><B>Weights</B></font></P>
<TABLE border="1" cols="2" frame="box" rules="all" width="650">
<TR>
<TD width="15%" valign="top"><B>Syntax</B>:</TD>
<TD width="85%" valign="top"><CODE>
BIN2D\WEIGHTS w x y xbin ybin mcounts nx ny { xmin xmax ymin ymax }</CODE>
</TD></TR>
</TABLE>
<p>
If a vector of weights is entered, you must indicate that it is there by using the
<CODE>\WEIGHTS</CODE> qualifier. The weight <CODE>w</CODE> must be a vector. The
<code>i</code><sup>th</sup> event causes the bin count to be incremented by <CODE>w<sub>i</sub></CODE>.</p>
<p><font size=+1 color="green"><B>Increment only if empty</B></font></P>
<TABLE border="1" cols="2" frame="box" rules="all" width="650">
<TR>
<TD width="15%" valign="top"><B>Syntax</B>:</TD>
<TD width="85%" valign="top"><CODE>
BIN2D\EMPTY w x y xbin ybin mcounts nx ny { xmin xmax ymin ymax }</CODE>
</TD></TR>
</TABLE>
<p>
If the <CODE>\EMPTY</CODE> 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. <CODE>\EMPTY</CODE> cannot be used with <CODE>\MATRIX</CODE>.</p>
<p><font size="+1" color="green"><B>Defined by box corners</B></font></P>
<TABLE border="1" cols="2" frame="box" rules="all" width="650">
<TR>
<TD width="15%" valign="top"><B>Syntax</B>:</TD>
<TD width="85%" valign="top"><CODE>
BIN2D\MATRIX mdata mx my mcounts</CODE>
</TD></TR>
</TABLE>
<p>
The <CODE>BIN2D\MATRIX</CODE> command calculates the sum of the data
points given by matrix <CODE>mdata</CODE> within a set of boxes. The
<i>x</i>-coordinates of the boxes are given in matrix <CODE>mx</CODE>,
the <i>y</i>-coordinates are given in matrix <CODE>my</CODE>. Matrices
<CODE>mx</CODE> and <CODE>my</CODE> 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,
<CODE>mdata[3,4]</CODE> is row 3 and column 4 so it is at
<code>(<i>x</i>,<i>y</i>)</code> location <code>(4,3)</code>. The <i>x</i> and <i>y</i>-coordinates in
<CODE>mx</CODE> and <CODE>my</CODE> should be in
this index space of coordinates. The qualifiers <CODE>\EMPTY</CODE> and
<CODE>\WEIGHTS</CODE> cannot be used with <CODE>\MATRIX</CODE>.</p>
</BODY>
</HTML>
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