bounds - Limiting data values for a palette

Continuous variables have values anywhere in the range minus infinite to plus infinite. However, when creating a visual representation of these values what usually matters is the relative difference between the values. This is where rescaling comes into play.

The values are mapped onto a range that a scale can deal with. For graphical representation that range tends to be \([0, 1]\) or \([0, n]\), where \(n\) is some number that makes the plotted object overflow the plotting area.

Although a scale may be able handle the \([0, n]\) range, it may be desirable to have a lower bound greater than zero. For example, if data values get mapped to zero on a scale whose graphical representation is the size/area/radius/length some data will be invisible. The solution is to restrict the lower bound e.g. \([0.1, 1]\). Similarly you can restrict the upper bound -- using these functions.

mizani.bounds.censor(x, range=(0, 1), only_finite=True)

Convert any values outside of range to a NULL type object.

Parameters:

xnumpy:array_like

Values to manipulate

rangepython:tuple

(min, max) giving desired output range

only_finitebool

If True (the default), will only modify finite values.

Returns:

xnumpy:array_like

Censored array

Notes

All values in x should be of the same type. only_finite parameter is not considered for Datetime and Timedelta types.

The NULL type object depends on the type of values in x.

• float - float('nan')

• int - float('nan')

• datetime.datetime : np.datetime64(NaT)

• datetime.timedelta : np.timedelta64(NaT)

Examples

>>> a = [1, 2, np.inf, 3, 4, -np.inf, 5]
>>> censor(a, (0, 10))
[1, 2, inf, 3, 4, -inf, 5]
>>> censor(a, (0, 10), False)
[1, 2, nan, 3, 4, nan, 5]
>>> censor(a, (2, 4))
[nan, 2, inf, 3, 4, -inf, nan]

mizani.bounds.expand_range(range, mul=0, add=0, zero_width=1)

Expand a range with a multiplicative or additive constant

Parameters:

rangepython:tuple

Range of data. Size 2.

mulpython:int | python:float

Multiplicative constant

addpython:int | python:float | timedelta

Additive constant

zero_widthpython:int | python:float | timedelta

Distance to use if range has zero width

Returns:

outpython:tuple

Expanded range

Notes

If expanding datetime or timedelta types, add and zero_width must be suitable timedeltas i.e. You should not mix types between Numpy, Pandas and the datetime module.

Examples

>>> expand_range((3, 8))
(3, 8)
>>> expand_range((0, 10), mul=0.1)
(-1.0, 11.0)
>>> expand_range((0, 10), add=2)
(-2, 12)
>>> expand_range((0, 10), mul=.1, add=2)
(-3.0, 13.0)
>>> expand_range((0, 1))
(0, 1)

When the range has zero width

>>> expand_range((5, 5))
(4.5, 5.5)

mizani.bounds.rescale(x, to=(0, 1), _from=None)

Rescale numeric vector to have specified minimum and maximum.

Parameters:

xnumpy:array_like | numeric

1D vector of values to manipulate.

topython:tuple

output range (numeric vector of length two)

_frompython:tuple

input range (numeric vector of length two). If not given, is calculated from the range of x

Returns:

outnumpy:array_like

Rescaled values

Examples

>>> x = [0, 2, 4, 6, 8, 10]
>>> rescale(x)
array([0. , 0.2, 0.4, 0.6, 0.8, 1. ])
>>> rescale(x, to=(0, 2))
array([0. , 0.4, 0.8, 1.2, 1.6, 2. ])
>>> rescale(x, to=(0, 2), _from=(0, 20))
array([0. , 0.2, 0.4, 0.6, 0.8, 1. ])

mizani.bounds.rescale_max(x, to=(0, 1), _from=None)

Rescale numeric vector to have specified maximum.

Parameters:

xnumpy:array_like | numeric

1D vector of values to manipulate.

topython:tuple

output range (numeric vector of length two)

_frompython:tuple

input range (numeric vector of length two). If not given, is calculated from the range of x. Only the 2nd (max) element is essential to the output.

Returns:

outnumpy:array_like

Rescaled values

Examples

>>> x = [0, 2, 4, 6, 8, 10]
>>> rescale_max(x, (0, 3))
array([0. , 0.6, 1.2, 1.8, 2.4, 3. ])

Only the 2nd (max) element of the parameters to and _from are essential to the output.

>>> rescale_max(x, (1, 3))
array([0. , 0.6, 1.2, 1.8, 2.4, 3. ])
>>> rescale_max(x, (0, 20))
array([ 0.,  4.,  8., 12., 16., 20.])

If max(x) < _from[1] then values will be scaled beyond the requested maximum (to[1]).

>>> rescale_max(x, to=(1, 3), _from=(-1, 6))
array([0., 1., 2., 3., 4., 5.])

If the values are the same, they taken on the requested maximum. This includes an array of all zeros.

>>> rescale_max([5, 5, 5])
array([1., 1., 1.])
>>> rescale_max([0, 0, 0])
array([1, 1, 1])

mizani.bounds.rescale_mid(x, to=(0, 1), _from=None, mid=0)

Rescale numeric vector to have specified minimum, midpoint, and maximum.

Parameters:

xnumpy:array_like | numeric

1D vector of values to manipulate.

topython:tuple

output range (numeric vector of length two)

_frompython:tuple

input range (numeric vector of length two). If not given, is calculated from the range of x

midnumeric

mid-point of input range

Returns:

outnumpy:array_like

Rescaled values

Examples

>>> rescale_mid([1, 2, 3], mid=1)
array([0.5 , 0.75, 1.  ])
>>> rescale_mid([1, 2, 3], mid=2)
array([0. , 0.5, 1. ])

mizani.bounds.squish_infinite(x, range=(0, 1))

Truncate infinite values to a range.

Parameters:

xnumpy:array_like

Values that should have infinities squished.

rangepython:tuple

The range onto which to squish the infinites. Must be of size 2.

Returns:

outnumpy:array_like

Values with infinites squished.

Examples

>>> squish_infinite([0, .5, .25, np.inf, .44])
[0.0, 0.5, 0.25, 1.0, 0.44]
>>> squish_infinite([0, -np.inf, .5, .25, np.inf], (-10, 9))
[0.0, -10.0, 0.5, 0.25, 9.0]

mizani.bounds.zero_range(x, tol=2.220446049250313e-14)

Determine if range of vector is close to zero.

Parameters:

xnumpy:array_like | numeric

Value(s) to check. If it is an array_like, it should be of length 2.

tolpython:float

Tolerance. Default tolerance is the machine epsilon times \(10^2\).

Returns:

outbool

Whether x has zero range.

Examples

>>> zero_range([1, 1])
True
>>> zero_range([1, 2])
False
>>> zero_range([1, 2], tol=2)
True

mizani.bounds.expand_range_distinct(range, expand=(0, 0, 0, 0), zero_width=1)

Expand a range with a multiplicative or additive constants

Similar to expand_range() but both sides of the range expanded using different constants

Parameters:

rangepython:tuple

Range of data. Size 2

expandpython:tuple

Length 2 or 4. If length is 2, then the same constants are used for both sides. If length is 4 then the first two are are the Multiplicative (mul) and Additive (add) constants for the lower limit, and the second two are the constants for the upper limit.

zero_widthpython:int | python:float | timedelta

Distance to use if range has zero width

Returns:

outpython:tuple

Expanded range

Examples

>>> expand_range_distinct((3, 8))
(3, 8)
>>> expand_range_distinct((0, 10), (0.1, 0))
(-1.0, 11.0)
>>> expand_range_distinct((0, 10), (0.1, 0, 0.1, 0))
(-1.0, 11.0)
>>> expand_range_distinct((0, 10), (0.1, 0, 0, 0))
(-1.0, 10)
>>> expand_range_distinct((0, 10), (0, 2))
(-2, 12)
>>> expand_range_distinct((0, 10), (0, 2, 0, 2))
(-2, 12)
>>> expand_range_distinct((0, 10), (0, 0, 0, 2))
(0, 12)
>>> expand_range_distinct((0, 10), (.1, 2))
(-3.0, 13.0)
>>> expand_range_distinct((0, 10), (.1, 2, .1, 2))
(-3.0, 13.0)
>>> expand_range_distinct((0, 10), (0, 0, .1, 2))
(0, 13.0)

mizani.bounds.squish(x, range=(0, 1), only_finite=True)

Squish values into range.

Parameters:

xnumpy:array_like

Values that should have out of range values squished.

rangepython:tuple

The range onto which to squish the values.

only_finite: boolean

When true, only squishes finite values.

Returns:

outnumpy:array_like

Values with out of range values squished.

Examples

>>> squish([-1.5, 0.2, 0.5, 0.8, 1.0, 1.2])
[0.0, 0.2, 0.5, 0.8, 1.0, 1.0]

>>> squish([-np.inf, -1.5, 0.2, 0.5, 0.8, 1.0, np.inf], only_finite=False)
[0.0, 0.0, 0.2, 0.5, 0.8, 1.0, 1.0]