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<h4><a name="layer-kde">8.3.18 <code>kde</code></a></h4>
<p>Plots a Discrete Kernel Density Estimate
giving a smoothed frequency of data values along the
horizontal axis, using a fixed-width smoothing kernel.
This is a generalisation of a histogram in which
the bins are always 1 pixel wide,
and a smoothing kernel is applied to each bin.
The width and shape of the kernel may be varied.
</p>
<p>This is suitable for cases where
the division into discrete bins
done by a normal histogram is unnecessary or troublesome.
</p>
<p>Note this is not a true Kernel Density Estimate,
since, for performance reasons,
the smoothing is applied to the (pixel-width) bins
rather than to each data sample.
The deviation from a true KDE caused by this quantisation
will be at the pixel level,
hence in most cases not visually apparent.
</p>
<p>
<strong>Usage Overview:</strong>
<pre>
layerN=kde colorN=<rrggbb>|red|blue|... transparencyN=0..1
smoothN=+<width>|-<count>
kernelN=square|linear|epanechnikov|cos|cos2|gauss3|gauss6
cumulativeN=true|false normaliseN=none|area|unit|maximum|height
fillN=solid|line|semi thickN=<pixels> xN=<num-expr>
weightN=<num-expr> inN=<table> ifmtN=<in-format>
istreamN=true|false icmdN=<cmds>
</pre>
</p>
<p>All the parameters listed here
affect only the relevant layer,
identified by the suffix
<code>N</code>.
</p>
<p>
<strong>Example:</strong>
</p>
<div align="center"><img src="plot2-layer-kde.png" alt="" align="middle"></div>
<p><pre> stilts plot2plane <strong>layer1=kde</strong> <strong>in1=rrlyrae.fits</strong> <strong>x1=p1</strong></pre></p>
<p>
<dl>
<dt><strong><code>colorN = <rrggbb>|red|blue|...</code> <em>(<a href="http://docs.oracle.com/javase/6/docs/api/java/awt/Color.html">Color</a>)</em></strong></dt>
<dd>The color of plotted data,
given by name or as a hexadecimal RGB value.
<p>The standard plotting colour names are
<code>red</code>, <code>blue</code>, <code>green</code>, <code>grey</code>, <code>magenta</code>, <code>cyan</code>, <code>orange</code>, <code>pink</code>, <code>yellow</code>, <code>black</code>, <code>light_grey</code>, <code>white</code>.
However, many other common colour names (too many to list here)
are also understood.
The list currently contains those colour names understood
by most web browsers,
from <code>AliceBlue</code> to <code>YellowGreen</code>,
listed e.g. in the
<em>Extended color keywords</em> section of
the <a href="http://www.w3c.org/TR/css3-color#svg-color">CSS3</a> standard.
</p>
<p>Alternatively, a six-digit hexadecimal number <em>RRGGBB</em>
may be supplied,
optionally prefixed by "<code>#</code>" or "<code>0x</code>",
giving red, green and blue intensities,
e.g. "<code>ff00ff</code>", "<code>#ff00ff</code>"
or "<code>0xff00ff</code>" for magenta.
</p>
<p>[Default: <code>red</code>]
</p>
</dd>
<dt><strong><code>cumulativeN = true|false</code> <em>(Boolean)</em></strong></dt>
<dd>If true, the histogram bars plotted are calculated
cumulatively;
each bin includes the counts from all previous bins.
<p>[Default: <code>false</code>]
</p>
</dd>
<dt><strong><code>fillN = solid|line|semi</code> <em>(<a href="http://andromeda.star.bris.ac.uk/starjavadocs/uk/ac/starlink/ttools/plot2/layer/FillMode.html">FillMode</a>)</em></strong></dt>
<dd>How the density function is represented.
<p>The available options are:
<ul>
<li><code>solid</code>: area between level and axis is filled with solid colour
</li>
<li><code>line</code>: level is marked by a wiggly line
</li>
<li><code>semi</code>: level is marked by a wiggly line, and area below it is filled with a transparent
colour
</li>
</ul>
</p>
<p>[Default: <code>semi</code>]
</p>
</dd>
<dt><strong><code>icmdN = <cmds></code> <em>(<a href="http://andromeda.star.bris.ac.uk/starjavadocs/uk/ac/starlink/ttools/filter/ProcessingStep.html">ProcessingStep[]</a>)</em></strong></dt>
<dd>Specifies processing to be performed on
the layer N input table as specified by parameter <code>inN</code>.
The value of this parameter is one or more of the filter
commands described in <a href="filterSteps.html">Section 6.1</a>.
If more than one is given, they must be separated by
semicolon characters (";").
This parameter can be repeated multiple times on the same
command line to build up a list of processing steps.
The sequence of commands given in this way
defines the processing pipeline which is performed on the table.
<p>Commands may alteratively be supplied in an external file,
by using the indirection character '@'.
Thus a value of "<code>@filename</code>"
causes the file <code>filename</code> to be read for a list
of filter commands to execute. The commands in the file
may be separated by newline characters and/or semicolons.
</p>
</dd>
<dt><strong><code>ifmtN = <in-format></code> <em>(String)</em></strong></dt>
<dd>Specifies the format of the input table as specified by parameter <code>inN</code>.
The known formats are listed in <a href="inFormats.html">Section 5.2.1</a>.
This flag can be used if you know what format your
table is in.
If it has the special value
<code>(auto)</code> (the default),
then an attempt will be
made to detect the format of the table automatically.
This cannot always be done correctly however, in which case
the program will exit with an error explaining which
formats were attempted.
<p>[Default: <code>(auto)</code>]
</p>
</dd>
<dt><strong><code>inN = <table></code> <em>(<a href="http://www.starlink.ac.uk/stil/javadocs/uk/ac/starlink/table/StarTable.html">StarTable</a>)</em></strong></dt>
<dd>The location of the input table.
This may take one of the following forms:
<ul>
<li>A filename.</li>
<li>A URL.</li>
<li>The special value "<code>-</code>",
meaning standard input.
In this case the input format must be given explicitly
using the <code>ifmtN</code>
parameter.
Note that not all formats can be streamed in this way.
</li>
<li>A system command line with
either a "<code><</code>" character at the start,
or a "<code>|</code>" character at the end
("<code><syscmd</code>" or
"<code>syscmd|</code>").
This executes the given pipeline and reads from its
standard output.
This will probably only work on unix-like systems.
</li>
</ul>
In any case, compressed data in one of the supported compression
formats (gzip, Unix compress or bzip2) will be decompressed
transparently.
</dd>
<dt><strong><code>istreamN = true|false</code> <em>(Boolean)</em></strong></dt>
<dd>If set true, the input table
specified by the <code>inN</code> parameter
will be read as a stream.
It is necessary to give the
<code>ifmtN</code> parameter
in this case.
Depending on the required operations and processing mode,
this may cause the read to fail (sometimes it is necessary
to read the table more than once).
It is not normally necessary to set this flag;
in most cases the data will be streamed automatically
if that is the best thing to do.
However it can sometimes result in less resource usage when
processing large files in certain formats (such as VOTable).
<p>[Default: <code>false</code>]
</p>
</dd>
<dt><strong><code>kernelN = square|linear|epanechnikov|cos|cos2|gauss3|gauss6</code> <em>(<a href="http://andromeda.star.bris.ac.uk/starjavadocs/uk/ac/starlink/ttools/plot2/layer/Kernel1dShape.html">Kernel1dShape</a>)</em></strong></dt>
<dd>The functional form of the smoothing kernel.
The functions listed refer to the unscaled shape;
all kernels are normalised to give a total area of unity.
<p>The available options are:
<ul>
<li><code>square</code>: Uniform value: f(x)=1, |x|=0..1
</li>
<li><code>linear</code>: Triangle: f(x)=1-|x|, |x|=0..1
</li>
<li><code>epanechnikov</code>: Parabola: f(x)=1-x*x, |x|=0..1
</li>
<li><code>cos</code>: Cosine: f(x)=cos(x*pi/2), |x|=0..1
</li>
<li><code>cos2</code>: Cosine squared: f(x)=cos^2(x*pi/2), |x|=0..1
</li>
<li><code>gauss3</code>: Gaussian truncated at 3.0 sigma: f(x)=exp(-x*x/2), |x|=0..3
</li>
<li><code>gauss6</code>: Gaussian truncated at 6.0 sigma: f(x)=exp(-x*x/2), |x|=0..6
</li>
</ul>
</p>
<p>[Default: <code>epanechnikov</code>]
</p>
</dd>
<dt><strong><code>normaliseN = none|area|unit|maximum|height</code> <em>(<a href="http://andromeda.star.bris.ac.uk/starjavadocs/uk/ac/starlink/ttools/plot2/layer/Normalisation.html">Normalisation</a>)</em></strong></dt>
<dd>Defines how, if at all, the bars of histogram-like plots
are normalised or otherwise scaled vertically.
<p>When used in the time plot only, time-specific options
like <code>per_second</code>
and <code>per_day</code>
are available.
</p>
<p>The available options are:
<ul>
<li><code>none</code>: No normalisation is performed.
</li>
<li><code>area</code>: The total area of histogram bars is normalised to unity. For cumulative plots, this
behaves like <code>height</code>.
</li>
<li><code>unit</code>: Histogram bars are scaled by the inverse of the bin width in data units. For cumulative
plots, this behaves like <code>none</code>.
</li>
<li><code>maximum</code>: The height of the tallest histogram bar is normalised to unity. For cumulative plots,
this behaves like <code>height</code>.
</li>
<li><code>height</code>: The total height of histogram bars is normalised to unity.
</li>
</ul>
</p>
<p>[Default: <code>none</code>]
</p>
</dd>
<dt><strong><code>smoothN = +<width>|-<count></code> <em>(<a href="http://andromeda.star.bris.ac.uk/starjavadocs/uk/ac/starlink/ttools/plot2/layer/BinSizer.html">BinSizer</a>)</em></strong></dt>
<dd>Configures the smoothing width for kernel density
estimation.
This is the characteristic width of the kernel function
to be convolved with the density to produce the visible plot.
<p>If the supplied value is a positive number
it is interpreted as a fixed width in the data coordinates
of the X axis
(if the X axis is logarithmic, the value is a fixed factor).
If it is a negative number, then it will be interpreted
as the approximate number of smooothing widths that fit
in the width of the visible plot
(i.e. plot width / smoothing width).
If the value is zero, no smoothing is applied.
</p>
<p>When setting this value graphically,
you can use either the slider to adjust the bin count
or the numeric entry field to fix the bin width.
</p>
<p>[Default: <code>-100</code>]
</p>
</dd>
<dt><strong><code>thickN = <pixels></code> <em>(Integer)</em></strong></dt>
<dd>Thickness of plotted line in pixels.
<p>[Default: <code>2</code>]
</p>
</dd>
<dt><strong><code>transparencyN = 0..1</code> <em>(Double)</em></strong></dt>
<dd>Transparency with which components are plotted,
in the range 0 (opaque) to 1 (invisible).
The value is 1-alpha.
<p>[Default: <code>0</code>]
</p>
</dd>
<dt><strong><code>weightN = <num-expr></code> <em>(String)</em></strong></dt>
<dd>Weighting of data points.
If supplied, each point contributes a value
to the histogram equal to the data value
multiplied by this coordinate.
If not supplied, the effect is the same as
supplying a fixed value of one.
<p>The value is a numeric algebraic expression based on column names
as described in <a href="jel.html">Section 10</a>.
</p>
</dd>
<dt><strong><code>xN = <num-expr></code> <em>(String)</em></strong></dt>
<dd>Horizontal coordinate.
<p>The value is a numeric algebraic expression based on column names
as described in <a href="jel.html">Section 10</a>.
</p>
</dd>
</dl>
</p>
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<hr><i>STILTS - Starlink Tables Infrastructure Library Tool Set<br>Starlink User Note256<br>STILTS web page:
<a href="http://www.starlink.ac.uk/stilts/">http://www.starlink.ac.uk/stilts/</a><br>Author email:
<a href="mailto:m.b.taylor@bristol.ac.uk">m.b.taylor@bristol.ac.uk</a><br>Mailing list:
<a href="mailto:topcat-user@jiscmail.ac.uk">topcat-user@jiscmail.ac.uk</a><br></i></body>
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