kde
Plots a Discrete Kernel Density Estimate giving a smoothed frequency of data values along the horizontal axis, using a fixedwidth 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.
This is suitable for cases where the division into discrete bins done by a normal histogram is unnecessary or troublesome.
Note this is not a true Kernel Density Estimate, since, for performance reasons, the smoothing is applied to the (pixelwidth) 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.
A weighting may be applied to the calculated levels
by supplying the
weight
coordinate.
In this case you can choose how these weights are aggregated
in each pixel bin using the
combine
parameter.
The result is something like a smoothed version of the
corresponding weighted histogram.
Note that some combinations of the available parameters
(e.g. a normalised cumulative medianaggregated KDE)
may not make much visual sense.
Usage Overview:
layerN=kde colorN=<rrggbb>redblue... transparencyN=0..1 smoothN=+<width><count> combineN=sumsumperunitcount... kernelN=squarelinearepanechnikovcoscos2gauss3gauss6 cumulativeN=noneforwardreverse normaliseN=noneareaunitmaximumheight fillN=solidlinesemi thickN=<pixels> xN=<numexpr> weightN=<numexpr> inN=<table> ifmtN=<informat> istreamN=truefalse icmdN=<cmds>
All the parameters listed here
affect only the relevant layer,
identified by the suffix
N
.
Example:
stilts plot2plane ymin=0 layer1=kde in1=rrlyrae.fits x1=p1
colorN = <rrggbb>redblue...
(Color)
The standard plotting colour names are
red
, blue
, green
, grey
, magenta
, cyan
, orange
, pink
, yellow
, black
, light_grey
, white
.
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 AliceBlue
to YellowGreen
,
listed e.g. in the
Extended color keywords section of
the CSS3 standard.
Alternatively, a sixdigit hexadecimal number RRGGBB
may be supplied,
optionally prefixed by "#
" or "0x
",
giving red, green and blue intensities,
e.g. "ff00ff
", "#ff00ff
"
or "0xff00ff
" for magenta.
[Default: red
]
combineN = sumsumperunitcount...
(Combiner)
sumperunit
and
mean
make sense,
others such as
sum
do not.
The combined values are those given by the
weight
coordinate,
but if no weight is supplied,
a weighting of unity is assumed.
The available options are:
sum
: the sum of all the combined values per binsumperunit
: the sum of all the combined values per unit of bin sizecount
: the number of nonblank values per bin (weight is ignored)countperunit
: the number of nonblank values per unit of bin size (weight is ignored)mean
: the mean of the combined valuesmedian
: the median of the combined values (may be slow)min
: the minimum of all the combined valuesmax
: the maximum of all the combined valuesstdev
: the sample standard deviation of the combined valueshit
: 1 if any values present, NaN otherwise (weight is ignored)[Default: sumperunit
]
cumulativeN = noneforwardreverse
(Cumulation)
forward
/reverse
the histogram bars plotted are calculated
cumulatively;
each bin includes the counts from all previous bins
working up/down the independent axis.
Note that setting cumulative plotting may not make much sense with some other parameter values, for instance averaging aggregation modes.
For reasons of backward compatibility,
the values true
and false
may be used as aliases for
forward
and none
.
The available options are:
none
: The value plotted for each bin uses the samples accumulated in that bin.forward
: The value plotted for each bin uses the samples accumulated all the way from negative infinity to that bin.reverse
: The value plotted for each bin uses the samples accumulated all the way from positive infinity to that bin.[Default: none
]
fillN = solidlinesemi
(FillMode)
The available options are:
solid
: area between level and axis is filled with solid colourline
: level is marked by a wiggly linesemi
: level is marked by a wiggly line, and area below it is filled with a transparent colour[Default: semi
]
icmdN = <cmds>
(ProcessingStep[])
inN
.
The value of this parameter is one or more of the filter
commands described in Section 6.1.
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.
Commands may alteratively be supplied in an external file,
by using the indirection character '@'.
Thus a value of "@filename
"
causes the file filename
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,
and lines which are blank or which start with a
'#
' character are ignored.
ifmtN = <informat>
(String)
inN
.
The known formats are listed in Section 5.1.1.
This flag can be used if you know what format your
table is in.
If it has the special value
(auto)
(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.
This parameter is ignored for schemespecified tables.
[Default: (auto)
]
inN = <table>
(StarTable)

",
meaning standard input.
In this case the input format must be given explicitly
using the ifmtN
parameter.
Note that not all formats can be streamed in this way.:<schemename>:<schemeargs>
.<
" character at the start,
or a "
" character at the end
("<syscmd
" or
"syscmd
").
This executes the given pipeline and reads from its
standard output.
This will probably only work on unixlike systems.istreamN = truefalse
(Boolean)
inN
parameter
will be read as a stream.
It is necessary to give the
ifmtN
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).
This parameter is ignored for schemespecified tables.
[Default: false
]
kernelN = squarelinearepanechnikovcoscos2gauss3gauss6
(Kernel1dShape)
The available options are:
square
: Uniform value: f(x)=1, x=0..1linear
: Triangle: f(x)=1x, x=0..1epanechnikov
: Parabola: f(x)=1x*x, x=0..1cos
: Cosine: f(x)=cos(x*pi/2), x=0..1cos2
: Cosine squared: f(x)=cos^2(x*pi/2), x=0..1gauss3
: Gaussian truncated at 3.0 sigma: f(x)=exp(x*x/2), x=0..3gauss6
: Gaussian truncated at 6.0 sigma: f(x)=exp(x*x/2), x=0..6[Default: epanechnikov
]
normaliseN = noneareaunitmaximumheight
(Normalisation)
Note that some of the normalisation options may not make much sense with some other parameter values, for instance averaging aggregation modes.
The available options are:
none
: No normalisation is performed.area
: The total area of histogram bars is normalised to unity. For cumulative plots, this behaves like height
.unit
: Histogram bars are scaled by the inverse of the bin width in data units. For cumulative plots, this behaves like none
.maximum
: The height of the tallest histogram bar is normalised to unity. For cumulative plots, this behaves like height
.height
: The total height of histogram bars is normalised to unity.[Default: none
]
smoothN = +<width><count>
(BinSizer)
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.
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.
[Default: 100
]
thickN = <pixels>
(Integer)
[Default: 2
]
transparencyN = 0..1
(Double)
[Default: 0
]
weightN = <numexpr>
(String)
The value is a numeric algebraic expression based on column names as described in Section 10.
xN = <numexpr>
(String)
The value is a numeric algebraic expression based on column names as described in Section 10.