"""
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 :math:`[0, 1]` or
:math:`[0, n]`, where :math:`n` is some number that makes the
plotted object overflow the plotting area.
Although a scale may be able handle the :math:`[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. :math:`[0.1, 1]`. Similarly you can restrict the upper bound
-- using these functions.
"""
from __future__ import annotations
import datetime
import sys
import typing
from copy import copy
from typing import overload
import numpy as np
import pandas as pd
from .utils import get_null_value, is_vector
if typing.TYPE_CHECKING:
from typing import Any, Optional, Sequence
from mizani.typing import (
FloatArrayLike,
FloatSeries,
NDArrayFloat,
TupleFloat2,
TupleFloat4,
)
__all__ = [
"censor",
"expand_range",
"rescale",
"rescale_max",
"rescale_mid",
"squish_infinite",
"zero_range",
"expand_range_distinct",
"squish",
]
EPSILON = sys.float_info.epsilon
[docs]
def rescale(
x: FloatArrayLike,
to: TupleFloat2 = (0, 1),
_from: Optional[TupleFloat2] = None,
) -> NDArrayFloat:
"""
Rescale numeric vector to have specified minimum and maximum.
Parameters
----------
x : array_like | numeric
1D vector of values to manipulate.
to : tuple
output range (numeric vector of length two)
_from : tuple
input range (numeric vector of length two).
If not given, is calculated from the range of x
Returns
-------
out : 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. ])
"""
__from = (np.min(x), np.max(x)) if _from is None else _from
return np.interp(x, __from, to)
[docs]
def rescale_mid(
x: FloatArrayLike,
to: TupleFloat2 = (0, 1),
_from: Optional[TupleFloat2] = None,
mid: float = 0,
) -> NDArrayFloat:
"""
Rescale numeric vector to have specified minimum, midpoint,
and maximum.
Parameters
----------
x : array_like
1D vector of values to manipulate.
to : tuple
output range (numeric vector of length two)
_from : tuple
input range (numeric vector of length two).
If not given, is calculated from the range of x
mid : numeric
mid-point of input range
Returns
-------
out : 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. ])
"""
__from: NDArrayFloat = np.array(
(np.min(x), np.max(x)) if _from is None else _from
)
if zero_range(__from) or zero_range(to): # type: ignore
out = np.repeat(np.mean(to), len(x))
else:
extent = 2 * np.max(np.abs(__from - mid))
out = (np.asarray(x) - mid) / extent * np.diff(to) + np.mean(to)
return out
[docs]
def rescale_max(
x: FloatArrayLike,
to: TupleFloat2 = (0, 1),
_from: Optional[TupleFloat2] = None,
) -> NDArrayFloat:
"""
Rescale numeric vector to have specified maximum.
Parameters
----------
x : array_like
1D vector of values to manipulate.
to : tuple
output range (numeric vector of length two)
_from : 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
-------
out : array_like
Rescaled values
Examples
--------
>>> x = np.array([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 :python:`max(x) < _from[1]` then values will be
scaled beyond the requested maximum (:python:`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(np.array([5, 5, 5]))
array([1., 1., 1.])
>>> rescale_max(np.array([0, 0, 0]))
array([1, 1, 1])
"""
x = np.asarray(x)
if _from is None:
_from = np.min(x), np.max(x) # type: ignore
assert _from is not None # type narrowing
if np.any(x < 0):
out = rescale(x, (0, to[1]), _from)
elif np.all(x == 0) and _from[1] == 0:
out = np.repeat(to[1], len(x))
else:
out = x / _from[1] * to[1]
return out
[docs]
def squish_infinite(
x: FloatArrayLike, range: TupleFloat2 = (0, 1)
) -> NDArrayFloat:
"""
Truncate infinite values to a range.
Parameters
----------
x : array_like
Values that should have infinities squished.
range : tuple
The range onto which to squish the infinites.
Must be of size 2.
Returns
-------
out : array_like
Values with infinites squished.
Examples
--------
>>> arr1 = np.array([0, .5, .25, np.inf, .44])
>>> arr2 = np.array([0, -np.inf, .5, .25, np.inf])
>>> list(squish_infinite(arr1))
[0.0, 0.5, 0.25, 1.0, 0.44]
>>> list(squish_infinite(arr2, (-10, 9)))
[0.0, -10.0, 0.5, 0.25, 9.0]
"""
_x = np.asarray(x)
_x[np.isneginf(_x)] = range[0]
_x[np.isposinf(_x)] = range[1]
return _x
[docs]
def squish(
x: FloatArrayLike, range: TupleFloat2 = (0, 1), only_finite: bool = True
) -> NDArrayFloat:
"""
Squish values into range.
Parameters
----------
x : array_like
Values that should have out of range values squished.
range : tuple
The range onto which to squish the values.
only_finite: boolean
When true, only squishes finite values.
Returns
-------
out : array_like
Values with out of range values squished.
Examples
--------
>>> list(squish([-1.5, 0.2, 0.8, 1.0, 1.2]))
[0.0, 0.2, 0.8, 1.0, 1.0]
>>> list(squish([-np.inf, -1.5, 0.2, 0.8, 1.0, np.inf], only_finite=False))
[0.0, 0.0, 0.2, 0.8, 1.0, 1.0]
"""
_x = np.asarray(x)
finite = np.isfinite(_x) if only_finite else True
_x[np.logical_and(_x < range[0], finite)] = range[0]
_x[np.logical_and(_x > range[1], finite)] = range[1]
return _x
@overload
def censor(
x: NDArrayFloat | Sequence[float],
range: TupleFloat2 = (0, 1),
only_finite: bool = True,
) -> NDArrayFloat: ...
@overload
def censor(
x: FloatSeries, range: TupleFloat2 = (0, 1), only_finite: bool = True
) -> FloatSeries: ...
[docs]
def censor(
x: NDArrayFloat | Sequence[float] | FloatSeries,
range: TupleFloat2 = (0, 1),
only_finite: bool = True,
) -> NDArrayFloat | FloatSeries:
"""
Convert any values outside of range to a **NULL** type object.
Parameters
----------
x : array_like
Values to manipulate
range : tuple
(min, max) giving desired output range
only_finite : bool
If True (the default), will only modify
finite values.
Returns
-------
x : array_like
Censored array
Examples
--------
>>> a = np.array([1, 2, np.inf, 3, 4, -np.inf, 5])
>>> list(censor(a, (0, 10)))
[1.0, 2.0, inf, 3.0, 4.0, -inf, 5.0]
>>> list(censor(a, (0, 10), False))
[1.0, 2.0, nan, 3.0, 4.0, nan, 5.0]
>>> list(censor(a, (2, 4)))
[nan, 2.0, inf, 3.0, 4.0, -inf, nan]
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**.
- :class:`float` - :py:`float('nan')`
- :class:`int` - :py:`float('nan')`
- :class:`datetime.datetime` : :py:`np.datetime64(NaT)`
- :class:`datetime.timedelta` : :py:`np.timedelta64(NaT)`
"""
if not len(x):
return np.array([])
if not is_vector(x):
x = np.asarray(x)
null = get_null_value(x)
if only_finite:
try:
finite = np.isfinite(x)
except TypeError:
finite = np.repeat(True, len(x))
else:
finite = np.repeat(True, len(x))
# Ignore RuntimeWarning when x contains nans
with np.errstate(invalid="ignore"):
outside = (x < range[0]) | (x > range[1])
bool_idx = finite & outside
res = copy(x)
if bool_idx.any():
if res.dtype.kind == "i":
res = np.asarray(res, dtype=float)
res[bool_idx] = null
return res
[docs]
def zero_range(x: tuple[Any, Any], tol: float = EPSILON * 100) -> bool:
"""
Determine if range of vector is close to zero.
Parameters
----------
x : array_like
Value(s) to check. If it is an array_like, it
should be of length 2.
tol : float
Tolerance. Default tolerance is the `machine epsilon`_
times :math:`10^2`.
Returns
-------
out : bool
Whether ``x`` has zero range.
Examples
--------
>>> zero_range([1, 1])
True
>>> zero_range([1, 2])
False
>>> zero_range([1, 2], tol=2)
True
.. _machine epsilon: https://en.wikipedia.org/wiki/Machine_epsilon
"""
if x[0] > x[1]:
x = x[1], x[0]
# datetime - pandas, cpython
if isinstance(x[0], (pd.Timestamp, datetime.datetime)):
from mizani._core.dates import datetime_to_num
l, h = datetime_to_num(x)
return l == h
# datetime - numpy
elif isinstance(x[0], np.datetime64):
return x[0] == x[1]
# timedelta - pandas, cpython
elif isinstance(x[0], (pd.Timedelta, datetime.timedelta)):
return x[0].total_seconds() == x[1].total_seconds()
# timedelta - numpy
elif isinstance(x[0], np.timedelta64):
return x[0] == x[1]
elif not isinstance(x[0], (float, int, np.number)):
raise TypeError(
"zero_range objects cannot work with objects "
"of type '{}'".format(type(x[0]))
)
else:
low, high = x
if any(np.isnan((low, high))):
return True
if low == high:
return True
if any(np.isinf((low, high))):
return False
low_abs = np.abs(low)
if low_abs == 0:
return False
return ((high - low) / low_abs) < tol
[docs]
def expand_range(
range: TupleFloat2, mul: float = 0, add: float = 0, zero_width: float = 1
) -> TupleFloat2:
"""
Expand a range with a multiplicative or additive constant
Parameters
----------
range : tuple
Range of data. Size 2.
mul : int | float
Multiplicative constant
add : int | float | timedelta
Additive constant
zero_width : int | float | timedelta
Distance to use if range has zero width
Returns
-------
out : tuple
Expanded range
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)
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
:mod:`datetime` module.
"""
x = range
low, high = x
# The expansion cases
if zero_range(x):
new = low - zero_width / 2, low + zero_width / 2
else:
dx = (high - low) * mul + add
new = low - dx, high + dx
return new
[docs]
def expand_range_distinct(
range: TupleFloat2,
expand: TupleFloat2 | TupleFloat4 = (0, 0, 0, 0),
zero_width: float = 1,
) -> TupleFloat2:
"""
Expand a range with a multiplicative or additive constants
Similar to :func:`expand_range` but both sides of the range
expanded using different constants
Parameters
----------
range : tuple
Range of data. Size 2
expand : 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_width : int | float | timedelta
Distance to use if range has zero width
Returns
-------
out : 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)
"""
if len(expand) == 2:
low_mul = high_mul = expand[0]
low_add = high_add = expand[1]
else:
low_mul, low_add, high_mul, high_add = expand
lower = expand_range(range, low_mul, low_add, zero_width)[0]
upper = expand_range(range, high_mul, high_add, zero_width)[1]
return (lower, upper)