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<h4><a name="layer-densogram">8.3.20 <code>densogram</code></a></h4>
<p>Represents smoothed density of data values
along the horizontal axis using a colourmap.
This is like a
<a href="layer-kde.html">Kernel Density Estimate</a>
(smoothed histogram with bins 1 pixel wide),
but instead of representing the data extent vertically
as bars or a line,
values are represented by a fixed-size pixel-width column
of a colour from a colour map.
A smoothing kernel, whose width and shape may be varied,
is applied to each data point.
</p>
<p>This is a rather unconventional way to represent density data,
and this plotting mode is probably not very useful.
But hey, nobody's forcing you to use it.
</p>
<p>
<strong>Usage Overview:</strong>
<pre>
layerN=densogram colorN=<rrggbb>|red|blue|... smoothN=+<width>|-<count>
kernelN=square|linear|epanechnikov|cos|cos2|gauss3|gauss6
densemapN=<map-name>|<color>-<color>[-<color>...]
denseclipN=<lo>,<hi> denseflipN=true|false
densequantN=<number> densefuncN=log|linear|sqrt|square
densesubN=<lo>,<hi> cumulativeN=true|false sizeN=<pixels>
posN=<fraction> 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-densogram.png" alt="" align="middle"></div>
<p><pre> stilts plot2plane <strong>in=tgas_source.fits</strong> <strong>x=hypot(pmra_error,pmdec_error)</strong>
xlog=true <strong>normalise=maximum</strong>
color=grey layer1=histogram layer2=kde
<strong>layer3=densogram</strong> <strong>densemap3=skyblue-yellow-hotpink</strong> <strong>densefunc3=log</strong>
<strong>size3=50</strong> <strong>pos3=0.5</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>denseclipN = <lo>,<hi></code> <em>(<a href="http://andromeda.star.bris.ac.uk/starjavadocs/uk/ac/starlink/ttools/plot2/Subrange.html">Subrange</a>)</em></strong></dt>
<dd>Defines a subrange of the colour ramp to be used for
Density shading.
The value is specified as a (low,high) comma-separated pair
of two numbers between 0 and 1.
<p>If the full range <code>0,1</code> is used,
the whole range of colours specified by the selected
shader will be used.
But if for instance a value of <code>0,0.5</code> is given,
only those colours at the left hand end of the ramp
will be seen.
</p>
<p>If the null (default) value is chosen,
a default clip will be used.
This generally covers most or all of the range 0-1
but for colour maps which fade to white,
a small proportion of the lower end may be excluded,
to ensure that all the colours are visually distinguishable
from a white background.
This default is usually a good idea if the colour map
is being used with something like a scatter plot,
where markers are plotted against a white background.
However, for something like a density map when the whole
plotting area is tiled with colours from the map,
it may be better to supply the whole range
<code>0,1</code> explicitly.
</p>
</dd>
<dt><strong><code>denseflipN = true|false</code> <em>(Boolean)</em></strong></dt>
<dd>If true, the colour map on the
Density
axis will be reversed.
<p>[Default: <code>false</code>]
</p>
</dd>
<dt><strong><code>densefuncN = log|linear|sqrt|square</code> <em>(<a href="http://andromeda.star.bris.ac.uk/starjavadocs/uk/ac/starlink/ttools/plot2/Scaling.html">Scaling</a>)</em></strong></dt>
<dd>Defines the way that values in the
Density
range are mapped to the selected colour ramp.
<p>The available options are:
<ul>
<li><code>log</code>: Logarithmic scaling
</li>
<li><code>linear</code>: Linear scaling
</li>
<li><code>sqrt</code>: Square root scaling
</li>
<li><code>square</code>: Square scaling
</li>
</ul>
</p>
<p>[Default: <code>linear</code>]
</p>
</dd>
<dt><strong><code>densemapN = <map-name>|<color>-<color>[-<color>...]</code> <em>(<a href="http://andromeda.star.bris.ac.uk/starjavadocs/uk/ac/starlink/ttools/plot/Shader.html">Shader</a>)</em></strong></dt>
<dd>Color map used for
Density
axis shading.
<p>A mixed bag of colour ramps are available:
<code>inferno</code>,
<code>magma</code>,
<code>plasma</code>,
<code>viridis</code>,
<code>cubehelix</code>,
<code>sron</code>,
<code>rainbow</code>,
<code>rainbow2</code>,
<code>rainbow3</code>,
<code>pastel</code>,
<code>accent</code>,
<code>gnuplot</code>,
<code>gnuplot2</code>,
<code>specxby</code>,
<code>set1</code>,
<code>paired</code>,
<code>hotcold</code>,
<code>rdbu</code>,
<code>piyg</code>,
<code>brbg</code>,
<code>cyan-magenta</code>,
<code>red-blue</code>,
<code>brg</code>,
<code>heat</code>,
<code>cold</code>,
<code>light</code>,
<code>greyscale</code>,
<code>colour</code>,
<code>standard</code>,
<code>bugn</code>,
<code>bupu</code>,
<code>orrd</code>,
<code>pubu</code>,
<code>purd</code>,
<code>huecl</code>,
<code>hue</code>,
<code>intensity</code>,
<code>rgb_red</code>,
<code>rgb_green</code>,
<code>rgb_blue</code>,
<code>hsv_h</code>,
<code>hsv_s</code>,
<code>hsv_v</code>,
<code>yuv_y</code>,
<code>yuv_u</code>,
<code>yuv_v</code>,
<code>scale_hsv_s</code>,
<code>scale_hsv_v</code>,
<code>scale_yuv_y</code>,
<code>mask</code>,
<code>blacker</code>,
<code>whiter</code>,
<code>transparency</code>.
<em>Note:</em>
many of these, including rainbow-like ones,
are frowned upon by the visualisation community.
</p>
<p>You can also construct your own custom colour map
by giving a sequence of colour names separated by
minus sign ("<code>-</code>") characters.
In this case the ramp is a linear interpolation
between each pair of colours named,
using the same syntax as when specifying
a colour value.
So for instance
"<code>yellow-hotpink-#0000ff</code>"
would shade from yellow via hot pink to blue.
</p>
<p>[Default: <code>inferno</code>]
</p>
</dd>
<dt><strong><code>densequantN = <number></code> <em>(Double)</em></strong></dt>
<dd>Allows the colour map used for the
Density
axis to be quantised.
If an integer value N is chosen
then the colour map will be viewed as N discrete evenly-spaced
levels,
so that only N different colours will appear in the plot.
This can be used to generate a contour-like effect,
and may make it easier to trace the boundaries of
regions of interest by eye.
<p>If left blank, the colour map is
nominally continuous (though in practice it may be quantised
to a medium-sized number like 256).
</p>
</dd>
<dt><strong><code>densesubN = <lo>,<hi></code> <em>(<a href="http://andromeda.star.bris.ac.uk/starjavadocs/uk/ac/starlink/ttools/plot2/Subrange.html">Subrange</a>)</em></strong></dt>
<dd>Defines a normalised adjustment to the data range of the
Density axis.
The value may be specified as a comma-separated pair
of two numbers,
giving the lower and upper bounds of the range of
of interest respectively.
This sub-range is applied to the data range that would
otherwise be used, either automatically calculated
or explicitly supplied;
zero corresponds to the lower bound and one to the upper.
<p>The default value "<code>0,1</code>" therefore has
no effect.
The range could be restricted to its lower half
with the value <code>0,0.5</code>.
</p>
<p>[Default: <code>0,1</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>posN = <fraction></code> <em>(Double)</em></strong></dt>
<dd>Determines where on the plot region the density bar
appears.
The value should be in the range 0..1;
zero corresponds to the bottom of the plot
and one to the top.
<p>[Default: <code>0.05</code>]
</p>
</dd>
<dt><strong><code>sizeN = <pixels></code> <em>(Integer)</em></strong></dt>
<dd>Height of the density bar in pixels.
<p>[Default: <code>12</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>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:
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