# transforms - Transforming variables, scales and coordinates¶

"The Grammar of Graphics (2005)" by Wilkinson, Anand and Grossman describes three types of transformations.

• Variable transformations - Used to make statistical operations on variables appropriate and meaningful. They are also used to new variables.
• Scale transformations - Used to make statistical objects displayed on dimensions appropriate and meaningful.
• Coordinate transformations - Used to manipulate the geometry of graphics to help perceive relationships and find meaningful structures for representing variations.

Variable and scale transformations are similar in-that they lead to plotted objects that are indistinguishable. Typically, variable transformation is done outside the graphics system and so the system cannot provide transformation specific guides & decorations for the plot. The trans is aimed at being useful for scale and coordinate transformations.

class mizani.transforms.trans(**kwargs)[source]

Base class for all transforms

This class is used to transform data and also tell the x and y axes how to create and label the tick locations.

The key methods to override are trans.transform() and trans.inverse(). Alternately, you can quickly create a transform class using the trans_new() function.

Parameters: kwargs (dict) -- Attributes of the class to set/override

Examples

By default trans returns one minor break between every pair of major break

>>> major = [0, 1, 2]
>>> t = trans()
>>> t.minor_breaks(major)
array([0.5, 1.5])


Create a trans that returns 4 minor breaks

>>> t = trans(minor_breaks=minor_breaks(4))
>>> t.minor_breaks(major)
array([0.2, 0.4, 0.6, 0.8, 1.2, 1.4, 1.6, 1.8])

aesthetic = None

Aesthetic that the transform works on

dataspace_is_numerical = True

Whether the untransformed data is numerical

domain = (-inf, inf)

Limits of the transformed data

format = <mizani.formatters.mpl_format object>

Function to format breaks

breaks_ = None

Callable to calculate breaks

minor_breaks = None

Callable to calculate minor_breaks

static transform(x)[source]

Transform of x

static inverse(x)[source]

Inverse of x

breaks(limits)[source]

Calculate breaks in data space and return them in transformed space.

Expects limits to be in transform space, this is the same space as that where the domain is specified.

This method wraps around breaks_() to ensure that the calculated breaks are within the domain the transform. This is helpful in cases where an aesthetic requests breaks with limits expanded for some padding, yet the expansion goes beyond the domain of the transform. e.g for a probability transform the breaks will be in the domain [0, 1] despite any outward limits.

Parameters: limits (tuple) -- The scale limits. Size 2. out -- Major breaks array_like
mizani.transforms.trans_new(name, transform, inverse, breaks=None, minor_breaks=None, _format=None, domain=(-inf, inf), doc='', **kwargs)[source]

Create a transformation class object

Parameters: name (str) -- Name of the transformation transform (callable f(x)) -- A function (preferably a ufunc) that computes the transformation. inverse (callable f(x)) -- A function (preferably a ufunc) that computes the inverse of the transformation. breaks (callable f(limits)) -- Function to compute the breaks for this transform. If None, then a default good enough for a linear domain is used. minor_breaks (callable f(major, limits)) -- Function to compute the minor breaks for this transform. If None, then a default good enough for a linear domain is used. _format (callable f(breaks)) -- Function to format the generated breaks. domain (array_like) -- Domain over which the transformation is valid. It should be of length 2. doc (str) -- Docstring for the class. **kwargs (dict) -- Attributes of the transform, e.g if base is passed in kwargs, then t.base would be a valied attribute. out -- Transform class trans
mizani.transforms.log_trans(base=None, **kwargs)[source]

Create a log transform class for base

Parameters: base (float) -- Base for the logarithm. If None, then the natural log is used. kwargs (dict) -- Keyword arguments passed onto trans_new(). Should not include the transform or inverse. out -- Log transform class type
class mizani.transforms.log10_trans(**kwargs)

Log 10 Transformation

transform = <ufunc 'log10'>
class mizani.transforms.log2_trans(**kwargs)

Log 2 Transformation

transform = <ufunc 'log2'>
mizani.transforms.exp_trans(base=None, **kwargs)[source]

Create a exponential transform class for base

This is inverse of the log transform.

Parameters: base (float) -- Base of the logarithm kwargs (dict) -- Keyword arguments passed onto trans_new(). Should not include the transform or inverse. out -- Exponential transform class type
class mizani.transforms.log1p_trans(**kwargs)[source]

Log plus one Transformation

transform = <ufunc 'log1p'>
inverse = <ufunc 'expm1'>
class mizani.transforms.identity_trans(**kwargs)[source]

Identity Transformation

class mizani.transforms.reverse_trans(**kwargs)[source]

Reverse Transformation

transform = <ufunc 'negative'>
inverse = <ufunc 'negative'>
class mizani.transforms.sqrt_trans(**kwargs)[source]

Square-root Transformation

transform = <ufunc 'sqrt'>
inverse = <ufunc 'square'>
class mizani.transforms.asn_trans(**kwargs)[source]

Arc-sin square-root Transformation

static transform(x)[source]

Transform of x

static inverse(x)[source]

Inverse of x

class mizani.transforms.atanh_trans(**kwargs)[source]

Arc-tangent Transformation

transform = <ufunc 'arctanh'>
inverse = <ufunc 'tanh'>
mizani.transforms.boxcox_trans(p, **kwargs)[source]

Boxcox Transformation

Parameters: p (float) -- Power parameter, commonly denoted by lower-case lambda in formulae kwargs (dict) -- Keyword arguments passed onto trans_new(). Should not include the transform or inverse.
mizani.transforms.probability_trans(distribution, *args, **kwargs)[source]

Probability Transformation

Parameters: distribution (str) -- Name of the distribution. Valid distributions are listed at scipy.stats. Any of the continuous or discrete distributions. args (tuple) -- Arguments passed to the distribution functions. kwargs (dict) -- Keyword arguments passed to the distribution functions.

Notes

Make sure that the distribution is a good enough approximation for the data. When this is not the case, computations may run into errors. Absence of any errors does not imply that the distribution fits the data.

class mizani.transforms.logit_trans(**kwargs)

Logit Transformation

mizani.transforms.probit_trans

alias of mizani.transforms.norm_trans

class mizani.transforms.datetime_trans(**kwargs)[source]

Datetime Transformation

static transform(x)[source]

Transform from date to a numerical format

static inverse(x)[source]

Transform to date from numerical format

class mizani.transforms.timedelta_trans(**kwargs)[source]

Timedelta Transformation

static transform(x)[source]

Transform from Timeddelta to numerical format

static inverse(x)[source]

Transform to Timedelta from numerical format

class mizani.transforms.pd_timedelta_trans(**kwargs)[source]

Pandas timedelta Transformation

static transform(x)[source]

Transform from Timeddelta to numerical format

static inverse(x)[source]

Transform to Timedelta from numerical format

mizani.transforms.gettrans(t)[source]

Return a trans object

Parameters: t (str | callable | type | trans) -- name of transformation function out trans