plot

[NB: Documentation is out of sync with development]

Summary

XSLT functions for SVG plotting

Functions for computing new points

• Linear smoothing
• [In progress] Weighted smoothing
• [In progress] LOWESS smoothing

Functions for drawing SVG

• Linear regression lines
• [In progress] Linear regression parabolas
• Bézier splines

Metadata

Author: David J. Birnbaum
Email: djbpitt@gmail.com
URL: http://www.obdurodon.org
Repo: https://github.com/djbpitt/plot

To use

1. Clone the repo.
2. Edit ee_config.xml or he_config.xml to adapt for your filesystem locations.
3. The regression, lowess, smoothing. and spline packages can be incorporating into your code with <xsl:use-package>. The lib package is used by the others, and does not have to be imported directly.

Notes

1. All point data is assumed to be in SVG coordinates, that is, with negative Y pointing up and positive Y pointing down. Input data in regular Cartesian coordinates must be preprocessed accordingly.
2. Debug versions of the functions are intended to be run on their own. The subdirectories include driver XSLT stylesheets that generate sample output. Run with saxon -config:path_to_config -it -xsl:driver_filename.xsl.

Regression line functions

Synopsis

The regression_line() functions draw a regression line. Support for drawing a parabola is under development.

Functions

djb:regression_line($points as xs:string+, $debug as xs:boolean) as (element(svg:g), map(*))

Argument	Type	Default	Meaning
$points	xs:string+	(required)	A sequence of at least three strings, representing points in SVG coordinate space, each of which has the form X,Y, so that the X and Y values are separated by a comma without intervening whitespace. For example, the input "50,182", "100,166", "150,87", "200,191", "250,106" describes five points. Each X and Y value may include a decimal point and may be preceded by + or -.
$debug	xs:boolean	False	If set to True, the function returns debugging information, in the form of a map, along with the primary SVG <g> result.
Result	element(svg:g)	(none)	If $debug is False, an SVG <g> element that contains just an SVG <line> element representing a regression line through the data points. The <line> element has on @x1, @y1, x2, and @y2 attributes, plus a @class attribute with the value "regression", which can be used by the classing program to control the rendering (specifying values for @stroke, stroke-width, etc.). If $debug is True, the <g> also plots the original points and a connecting SVG <polyline>, includes a background SVG <rect>, and specifies CSS for @stroke and @stroke-width.
Result	map(*)	(none)	If $debug is True, in addition to the SVG <g> element, a map(*) with xs:double values for "m" (slope) and "b" (intercept) is returned. If $debug is False, this map is not returned.

Note

The function raises a fatal error if:

1. $points contains fewer than three strings, each representing a point, or
2. any point does not match the pattern X,Y, with no whitespace and where X and Y are doubles with optional leading + or - signs, or
3. X is not ordered monotonically (consecutive equal values are allowed).

---

djb:regression_line($points as xs:string+) as element(svg:g)

Argument	Type	Default	Meaning
$points	xs:string+	(required)	A sequence of at least three strings, representing points in SVG coordinate space, each of which has the form X,Y, so that the X and Y values are separated by a comma without intervening whitespace. For example, the input "50,182", "100,166", "150,87", "200,191", "250,106" describes five points. Each X and Y value may include a decimal point and may be preceded by + or -.
Result	element(svg:g)	(none)	An SVG <g> element that contains just an SVG <line> element representing a regression line through the data points. The <line> element has on @x1, @y1, x2, and @y2 attributes, plus a @class attribute with the value "regression", which can be used by the classing program to control the rendering (specifying values for @stroke, stroke-width, etc.).

Notes

1. The function raises a fatal error if:
   1. $points contains fewer than three strings, each representing a point, or
   2. any point does not match the pattern X,Y, with no whitespace and where X and Y are doubles with optional leading + or - signs, or
   3. X is not ordered monotonically (consecutive equal values are allowed).
2. The arity-1 version of djb:regression_line() is equivalent to calling the arity-2 version and specifying False as the value of the $debug argument.

Smoothing functions

Synopsis

The smoothing package implements a simple moving average by returning each input point with the X value unchanged, while the Y value is replaced by the average of the points within a window of size $window (default value is 3) centered on the point at X. The windows is always the same size; if there are not enough points (toward the beginning and end of the sequence of points) to center the current point, missing points are made up on the other side. For example, with a window size of 3, both the first and second points return the average of the first three points, and the fourth returns the average of the second, third, and fourth.

Smoothing reduces the extent of the impact of outliers, making it easier to see a trend. But because the neighboring points carry as much weight as the central one, a local peak or trough does not mean the correspnding original data point is necessarily higher (resp. lower) than its immediate neighors.

Functions

djb:smoothing($points as xs:string+, $window as xs:integer) as xs:string+

Argument	Type	Default	Meaning
$points	xs:string	(required)	A sequence of at least three strings, representing points in SVG coordinate space, each of which has the form X,Y, so that the X and Y values are separated by a comma without intervening whitespace. For example, the input "50,182", "100,166", "150,87", "200,191", "250,106" describes five points. Each X and Y value may include a decimal point and may be preceded by + or -.
$window	xs:integer	3	The number of points whose Y value is incorporated into the simple moving average returned for each input point. $window must be a positive odd number.
Result	xs:string+	(none)	A sequence of strings in the same format as $points, but with the Y values modified by smoothing.

Notes

The function raises a fatal error if:

1. $points contains fewer than three strings, each representing a point, or
2. any point does not match the pattern X,Y, with no whitespace and where X and Y are doubles with optional leading + or - signs, or
3. X is not ordered monotonically (consecutive equal values are allowed), or
4. $window is not an odd positive integer.

djb:smoothing($points as xs:string+) as xs:string+

Argument	Type	Default	Meaning
$points	xs:string	(required)	A sequence of at least three strings, representing points in SVG coordinate space, each of which has the form X,Y, so that the X and Y values are separated by a comma without intervening whitespace. For example, the input "50,182", "100,166", "150,87", "200,191", "250,106" describes five points. Each X and Y value may include a decimal point and may be preceded by + or -.
Result	xs:string+	(none)	A sequence of strings in the same format as $points, but with the Y values modified by smoothing.

Notes

1. The function raises a fatal error if:
   1. $points contains fewer than three strings, each representing a point, or
   2. any point does not match the pattern X,Y, with no whitespace and where X and Y are doubles with optional leading + or - signs, or
   3. X is not ordered monotonically (consecutive equal values are allowed).
2. The arity-1 version of djb:smoothing() is equivalent to calling the arity-2 version and specifying 3 as the value of the $window argument.