This class holds two mutually inverse functions for transforming
data, i.e., allows us to transform data forward and backward. It should hold
b@backward(b@forward(x))==x
for a Transformation b
and values
x
in the domain of the Transformation. At the same time,
b@forward(b@backward(y))==y
should hold for all y
in the image
of the Transformation.
A transformation is furthermore accompanied by a positive complexity
.
Only Transformation.identity
has complexity 0L
. All other
transformations should have a larger complexity. If we simply log-scale some
data (e.g., via Transformation.log
) by just applying the
log
function, this could have complexity 1L
. If we have a
transformation involving n
variables whose values we decide upon,
then we should pick complexity n+1L
: If we first move the data by
3 units and then divide it by 2, i.e., apply something like (x+3)/2
,
this transformation should have a complexity of 3
- we chose two
values and applied them in a function.
forward
the foward transformation function
backward
the inverse of the transformation function, i.e., the backwards transformation
complexity
a measure of the transformation complexity, e.g., one plus the number of constants involved in the transformation - only the identity transformation has complexity 0
1 2 3 4 5 6 7 8 9 10 |
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.