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<HTML>
<HEAD>
<TITLE>BIN command</TITLE>
</HEAD>
<BODY BGCOLOR="#FFFFFF" TEXT="#000000">
<P><font size="+3" color="green"><B>BIN command</B></font></P>
<TABLE border="1" cols="2" frame="box" rules="all" width="572">
<TR>
<TD width="15%" valign="top"><B>Syntax</B>:</TD>
<TD width="85%" valign="top"><CODE>
BIN x xbin xcount<br />
BIN\NBINS x xbin xcount n { xmin xmax }</CODE>
</TD></TR>
<TR>
<TD width="15%" valign="top"><B>Qualifiers</B>:</TD>
<TD width="85%" valign="top"><CODE>
\WEIGHTS, \EDGES, \NBINS, \DISCARD, \EMPTY, \AVERAGE, \LAGRANGE</CODE>
</TD></TR>
<TR>
<TD width="15%" valign="top"><B>Defaults</B>:</TD>
<TD width="85%" valign="top"><CODE>
\-WEIGHTS, \-EDGES, \-NBINS, \-DISCARD, \-EMPTY, \-AVERAGE, \LAGRANGE, xmin = min(x), xmax = max(x)</CODE>
</TD></TR>
</TABLE>
<P>
The <CODE>BIN</CODE> command sorts an input vector,
<CODE>x</CODE>, into a grid of bins and accumulates
the counts per bin into an output vector,
<CODE>xcount</CODE>. Each element of <CODE>x</CODE> is considered only once, so elements
are never counted as being in more than one bin. By default, the bins are
defined by their centers, given in vector <CODE>xbin</CODE>, which must be strictly
monotonically increasing. If <CODE><i>n</i> =
<a href="../Functions/VariableCharacteristics/len.htm">LEN</a>(xbin)</CODE>,
define the bin ranges, <CODE><i>r<sub>i</sub></i></CODE></P>
<P>
<CODE><i>r</i><sub>1</sub> = xbin[1] - (xbin[2] - xbin[1])/2</CODE></P>
<P>
<CODE><i>r<sub>i</sub></i> = xbin[<i>i</i>] - (xbin[<i>i</i>] - xbin[<i>i</i>-1])/2</CODE> for
<CODE><i>i</i> = 2, 3, ..., <i>n</i></CODE></P>
<P>
<CODE><i>r</i><sub><i>n</i>+1</sub> = xbin[<i>n</i>] + (xbin[<i>n</i>] - xbin[<i>n</i>-1])/2</CODE></P>
<P>
For each
<CODE><i>i</i> = 1, 2, ..., LEN(x)</CODE>, if <CODE><i>r<sub>j</sub></i> ≤ x[<i>i</i>]
< <i>r<sub>j+1</sub></i></CODE> for some
<CODE><i>j</i> = 1, 2, ..., <i>n</i></CODE> then
<CODE>xcount[<i>j</i>]</CODE> is
incremented by <CODE>1</CODE>, or by the weight,
<CODE>w[<i>i</i>]</CODE>. By default, events below <CODE><i>r</i><sub>1</sub></CODE> will be placed in
the first bin, and events above <CODE><i>r</i><sub><i>n</i>+1</sub></CODE> will be placed in
the last bin. If the <CODE>\DISCARD</CODE> qualifier is used, events outside this
range will be discarded.</P>
<P>
<a href="weights.htm"><font size="+1" color="olive">Weights</font></a><br />
<a href="nbins.htm"><font size="+1" color="olive">Number of bins</font></a><br />
<a href="lagrange.htm"><font size="+1" color="olive">Lagrange</font></a><br />
<a href="average.htm"><font size="+1" color="olive">Average</font></a><br />
<a href="empty.htm"><font size="+1" color="olive">Count only if empty</font></a><br />
<a href="edges.htm"><font size="+1" color="olive">Edge defined bins</font></a>
</P>
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</HTML>
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