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<h4><a name="layer-quantile">8.3.16 <code>quantile</code></a></h4>
<p>Plots a line through a given quantile of the values
binned within each pixel column (or row) of a plot.
The line is optionally smoothed
using a configurable kernel and width,
to even out noise arising from the pixel binning.
Instead of a simple line through a given quantile,
it is also possible to fill the region between two quantiles.
</p>
<p>One way to use this is to draw a line estimating a function
<i>y=f(x)</i> (or <i>x=g(y)</i>) sampled by a noisy set
of data points in two dimensions.
</p>
<p>
<strong>Usage Overview:</strong>
<pre>
layerN=quantile colorN=<rrggbb>|red|blue|... transparencyN=0..1
quantilesN=<low-frac>[,<high-frac>] thickN=<pixels>
smoothN=+<width>|-<count>
kernelN=square|linear|epanechnikov|cos|cos2|gauss3|gauss6
horizontalN=true|false <pos-coord-paramsN> 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>
<dl>
<dt><strong>Positional Coordinate Parameters:</strong></dt>
<dd>The positional coordinates
<code><pos-coord-paramsN></code>
give a position for each row of the input table.
Their form depends on the plot geometry,
i.e. which plotting command is used.
For a plane plot (<a href="plot2plane.html"><code>plot2plane</code></a>)
the parameters would be
<code>xN</code> and <code>yN</code>.
The coordinate parameter values are in all cases strings
interpreted as numeric expressions based on column names.
These can be column names, fixed values or algebraic
expressions as described in <a href="jel.html">Section 10</a>.
</dd>
</dl>
</p>
<p>
<strong>Example:</strong>
</p>
<div align="center"><img src="plot2-layer-quantile.png" alt="" align="middle"></div>
<p><pre> stilts plot2plane <strong>in=tgas_source.fits</strong> <strong>x=phot_g_mean_mag</strong> <strong>y=phot_g_mean_flux_error</strong>
ylog=true xmax=15 ymin=10
layer.d=mark color.d=99ff99
<strong>layer.q4=quantile</strong> <strong>quantiles.q4=0.25,0.75</strong> <strong>color.q4=magenta</strong> <strong>transparency.q4=0.35</strong>
<strong>layer.q2=quantile</strong> <strong>quantiles.q2=0.5</strong> <strong>color.q2=SkyBlue</strong> <strong>thick.q2=4</strong>
<strong>smooth.q=0.05</strong>
leglabel.q4=Quartiles leglabel.q2=Median legseq=.q4,.q2 legpos=0.95,0.95</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>horizontalN = true|false</code> <em>(Boolean)</em></strong></dt>
<dd>Determines whether the trace bins are horizontal
or vertical.
If <code>true</code>, there is a <i>y</i> value calculated
for each pixel column, and
if <code>false</code>, there is an <i>x</i> value for each
pixel row.
<p>[Default: <code>true</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>quantilesN = <low-frac>[,<high-frac>]</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 the quantile or quantile range
of values that should be marked in each pixel column (or row).
The value may be a single number in the range 0..1
indicating the quantile which should be marked.
Alternatively, it may be a pair of numbers,
each in the range 0..1,
separated by commas (<code><lo>,<hi></code>)
indicating two quantile lines bounding an area to be filled.
A pair of equal values "<code>a,a</code>"
is equivalent to the single value "<code>a</code>".
The default is <code>0.5</code>,
which means to mark the median value in each column,
and could equivalently be specified <code>0.5,0.5</code>.
<p>[Default: <code>0.5</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.
This is the characteristic width of the kernel function
to be convolved with the density in one dimension
to smooth the quantile function.
<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>0</code>]
</p>
</dd>
<dt><strong><code>thickN = <pixels></code> <em>(Integer)</em></strong></dt>
<dd>Sets the minimum extent of the markers that are plotted
in each pixel column (or row) to indicate the designated
value range.
If the range is zero sized
(<code>quantiles</code>
specifies a single value rather than a pair)
this will give the actual thickness of the plotted line.
If the range is non-zero however, the line may be thicker
than this in places according to the quantile positions.
<p>[Default: <code>3</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>
</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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