"""
Numerical/mathemetical related functions.
.. versionadded:: 2.1.0
"""
import math
import operator
import pydash as pyd
from .helpers import UNSET, iterator, iterator_with_default, iteriteratee
__all__ = (
"add",
"ceil",
"clamp",
"divide",
"floor",
"max_",
"max_by",
"mean",
"mean_by",
"median",
"min_",
"min_by",
"moving_mean",
"multiply",
"power",
"round_",
"scale",
"slope",
"std_deviation",
"sum_",
"sum_by",
"subtract",
"transpose",
"variance",
"zscore",
)
INFINITY = float("inf")
[docs]def add(a, b):
"""
Adds two numbers.
Args:
a (number): First number to add.
b (number): Second number to add.
Returns:
number
Example:
>>> add(10, 5)
15
.. versionadded:: 2.1.0
.. versionchanged:: 3.3.0
Support adding two numbers when passed as positional arguments.
.. versionchanged:: 4.0.0
Only support two argument addition.
"""
return a + b
[docs]def sum_(collection):
"""
Sum each element in `collection`.
Args:
collection (list|dict|number): Collection to process or first number to add.
Returns:
number: Result of summation.
Example:
>>> sum_([1, 2, 3, 4])
10
.. versionadded:: 2.1.0
.. versionchanged:: 3.3.0
Support adding two numbers when passed as positional arguments.
.. versionchanged:: 4.0.0
Move iteratee support to :func:`sum_by`. Move two argument addition to
:func:`add`.
"""
return sum_by(collection)
[docs]def sum_by(collection, iteratee=None):
"""
Sum each element in `collection`. If iteratee is passed, each element of `collection` is passed
through a iteratee before the summation is computed.
Args:
collection (list|dict|number): Collection to process or first number to add.
iteratee (mixed|number, optional): Iteratee applied per iteration or second number to add.
Returns:
number: Result of summation.
Example:
>>> sum_by([1, 2, 3, 4], lambda x: x ** 2)
30
.. versionadded:: 4.0.0
"""
return sum(result[0] for result in iteriteratee(collection, iteratee))
[docs]def mean(collection):
"""
Calculate arithmetic mean of each element in `collection`.
Args:
collection (list|dict): Collection to process.
Returns:
float: Result of mean.
Example:
>>> mean([1, 2, 3, 4])
2.5
.. versionadded:: 2.1.0
.. versionchanged:: 4.0.0
- Removed ``average`` and ``avg`` aliases.
- Moved iteratee functionality to :func:`mean_by`.
"""
return mean_by(collection)
[docs]def mean_by(collection, iteratee=None):
"""
Calculate arithmetic mean of each element in `collection`. If iteratee is passed, each element
of `collection` is passed through a iteratee before the mean is computed.
Args:
collection (list|dict): Collection to process.
iteratee (mixed, optional): Iteratee applied per iteration.
Returns:
float: Result of mean.
Example:
>>> mean_by([1, 2, 3, 4], lambda x: x ** 2)
7.5
.. versionadded:: 4.0.0
"""
return sum_by(collection, iteratee) / len(collection)
[docs]def ceil(x, precision=0):
"""
Round number up to precision.
Args:
x (number): Number to round up.
precision (int, optional): Rounding precision. Defaults to ``0``.
Returns:
int: Number rounded up.
Example:
>>> ceil(3.275) == 4.0
True
>>> ceil(3.215, 1) == 3.3
True
>>> ceil(6.004, 2) == 6.01
True
.. versionadded:: 3.3.0
"""
return rounder(math.ceil, x, precision)
[docs]def clamp(x, lower, upper=None):
"""
Clamps number within the inclusive lower and upper bounds.
Args:
x (number): Number to clamp.
lower (number, optional): Lower bound.
upper (number): Upper bound
Returns:
number
Example:
>>> clamp(-10, -5, 5)
-5
>>> clamp(10, -5, 5)
5
>>> clamp(10, 5)
5
>>> clamp(-10, 5)
-10
.. versionadded:: 4.0.0
"""
if upper is None:
upper = lower
lower = x
if x < lower:
x = lower
elif x > upper:
x = upper
return x
[docs]def divide(dividend, divisor):
"""
Divide two numbers.
Args:
dividend (int/float): The first number in a division.
divisor (int/float): The second number in a division.
Returns:
int/float: Returns the quotient.
Example:
>>> divide(20, 5)
4.0
>>> divide(1.5, 3)
0.5
>>> divide(None, None)
1.0
>>> divide(5, None)
5.0
.. versionadded:: 4.0.0
"""
return call_math_operator(dividend, divisor, operator.truediv, 1)
[docs]def floor(x, precision=0):
"""
Round number down to precision.
Args:
x (number): Number to round down.
precision (int, optional): Rounding precision. Defaults to ``0``.
Returns:
int: Number rounded down.
Example:
>>> floor(3.75) == 3.0
True
>>> floor(3.215, 1) == 3.2
True
>>> floor(0.046, 2) == 0.04
True
.. versionadded:: 3.3.0
"""
return rounder(math.floor, x, precision)
[docs]def max_(collection, default=UNSET):
"""
Retrieves the maximum value of a `collection`.
Args:
collection (list|dict): Collection to iterate over.
default (mixed, optional): Value to return if `collection` is empty.
Returns:
mixed: Maximum value.
Example:
>>> max_([1, 2, 3, 4])
4
>>> max_([], default=-1)
-1
.. versionadded:: 1.0.0
.. versionchanged:: 4.0.0
Moved iteratee iteratee support to :func:`max_by`.
"""
return max_by(collection, default=default)
[docs]def max_by(collection, iteratee=None, default=UNSET):
"""
Retrieves the maximum value of a `collection`.
Args:
collection (list|dict): Collection to iterate over.
iteratee (mixed, optional): Iteratee applied per iteration.
default (mixed, optional): Value to return if `collection` is empty.
Returns:
mixed: Maximum value.
Example:
>>> max_by([1.0, 1.5, 1.8], math.floor)
1.0
>>> max_by([{'a': 1}, {'a': 2}, {'a': 3}], 'a')
{'a': 3}
>>> max_by([], default=-1)
-1
.. versionadded:: 4.0.0
"""
if isinstance(collection, dict):
collection = collection.values()
return max(iterator_with_default(collection, default), key=pyd.iteratee(iteratee))
[docs]def min_(collection, default=UNSET):
"""
Retrieves the minimum value of a `collection`.
Args:
collection (list|dict): Collection to iterate over.
default (mixed, optional): Value to return if `collection` is empty.
Returns:
mixed: Minimum value.
Example:
>>> min_([1, 2, 3, 4])
1
>>> min_([], default=100)
100
.. versionadded:: 1.0.0
.. versionchanged:: 4.0.0
Moved iteratee iteratee support to :func:`min_by`.
"""
return min_by(collection, default=default)
[docs]def min_by(collection, iteratee=None, default=UNSET):
"""
Retrieves the minimum value of a `collection`.
Args:
collection (list|dict): Collection to iterate over.
iteratee (mixed, optional): Iteratee applied per iteration.
default (mixed, optional): Value to return if `collection` is empty.
Returns:
mixed: Minimum value.
Example:
>>> min_by([1.8, 1.5, 1.0], math.floor)
1.8
>>> min_by([{'a': 1}, {'a': 2}, {'a': 3}], 'a')
{'a': 1}
>>> min_by([], default=100)
100
.. versionadded:: 4.0.0
"""
if isinstance(collection, dict):
collection = collection.values()
return min(iterator_with_default(collection, default), key=pyd.iteratee(iteratee))
[docs]def moving_mean(array, size):
"""
Calculate moving mean of each element of `array`.
Args:
array (list): List to process.
size (int): Window size.
Returns:
list: Result of moving average.
Example:
>>> moving_mean(range(10), 1)
[0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0]
>>> moving_mean(range(10), 5)
[2.0, 3.0, 4.0, 5.0, 6.0, 7.0]
>>> moving_mean(range(10), 10)
[4.5]
.. versionadded:: 2.1.0
.. versionchanged:: 4.0.0
Rename to ``moving_mean`` and remove ``moving_average`` and ``moving_avg`` aliases.
"""
result = []
size = int(size)
for i in range(size - 1, len(array) + 1):
window = array[i - size : i]
if len(window) == size:
result.append(mean(window))
return result
[docs]def multiply(multiplier, multiplicand):
"""
Multiply two numbers.
Args:
multiplier (int/float): The first number in a multiplication.
multiplicand (int/float): The second number in a multiplication.
Returns:
int/float: Returns the product.
Example:
>>> multiply(4, 5)
20
>>> multiply(10, 4)
40
>>> multiply(None, 10)
10
>>> multiply(None, None)
1
.. versionadded:: 4.0.0
"""
return call_math_operator(multiplier, multiplicand, operator.mul, 1)
[docs]def power(x, n):
"""
Calculate exponentiation of `x` raised to the `n` power.
Args:
x (number): Base number.
n (number): Exponent.
Returns:
number: Result of calculation.
Example:
>>> power(5, 2)
25
>>> power(12.5, 3)
1953.125
.. versionadded:: 2.1.0
.. versionchanged:: 4.0.0
Removed alias ``pow_``.
"""
if pyd.is_number(x):
result = pow(x, n)
elif pyd.is_list(x):
result = [pow(item, n) for item in x]
else:
result = None
return result
[docs]def round_(x, precision=0):
"""
Round number to precision.
Args:
x (number): Number to round.
precision (int, optional): Rounding precision. Defaults to ``0``.
Returns:
int: Rounded number.
Example:
>>> round_(3.275) == 3.0
True
>>> round_(3.275, 1) == 3.3
True
.. versionadded:: 2.1.0
.. versionchanged:: 4.0.0
Remove alias ``curve``.
"""
return rounder(round, x, precision)
[docs]def scale(array, maximum=1):
"""
Scale list of value to a maximum number.
Args:
array (list): Numbers to scale.
maximum (number): Maximum scale value.
Returns:
list: Scaled numbers.
Example:
>>> scale([1, 2, 3, 4])
[0.25, 0.5, 0.75, 1.0]
>>> scale([1, 2, 3, 4], 1)
[0.25, 0.5, 0.75, 1.0]
>>> scale([1, 2, 3, 4], 4)
[1.0, 2.0, 3.0, 4.0]
>>> scale([1, 2, 3, 4], 2)
[0.5, 1.0, 1.5, 2.0]
.. versionadded:: 2.1.0
"""
array_max = max(array)
factor = maximum / array_max
return [item * factor for item in array]
[docs]def slope(point1, point2):
"""
Calculate the slope between two points.
Args:
point1 (list|tuple): X and Y coordinates of first point.
point2 (list|tuple): X and Y cooredinates of second point.
Returns:
float: Calculated slope.
Example:
>>> slope((1, 2), (4, 8))
2.0
.. versionadded:: 2.1.0
"""
x1, y1 = point1[0], point1[1]
x2, y2 = point2[0], point2[1]
if x1 == x2:
result = INFINITY
else:
result = (y2 - y1) / (x2 - x1)
return result
[docs]def std_deviation(array):
"""
Calculate standard deviation of list of numbers.
Args:
array (list): List to process.
Returns:
float: Calculated standard deviation.
Example:
>>> round(std_deviation([1, 18, 20, 4]), 2) == 8.35
True
.. versionadded:: 2.1.0
.. versionchanged:: 4.0.0
Remove alias ``sigma``.
"""
return math.sqrt(variance(array))
[docs]def subtract(minuend, subtrahend):
"""
Subtracts two numbers.
Args:
minuend (int/float): Value passed in by the user.
subtrahend (int/float): Value passed in by the user.
Returns:
int/float: Result of the difference from the given values.
Example:
>>> subtract(10, 5)
5
>>> subtract(-10, 4)
-14
>>> subtract(2, 0.5)
1.5
.. versionadded:: 4.0.0
"""
return call_math_operator(minuend, subtrahend, operator.sub, 0)
[docs]def transpose(array):
"""
Transpose the elements of `array`.
Args:
array (list): List to process.
Returns:
list: Transposed list.
Example:
>>> transpose([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
[[1, 4, 7], [2, 5, 8], [3, 6, 9]]
.. versionadded:: 2.1.0
"""
trans = []
for y, row in iterator(array):
for x, col in iterator(row):
trans = pyd.set_(trans, [x, y], col)
return trans
[docs]def variance(array):
"""
Calculate the variance of the elements in `array`.
Args:
array (list): List to process.
Returns:
float: Calculated variance.
Example:
>>> variance([1, 18, 20, 4])
69.6875
.. versionadded:: 2.1.0
"""
avg = mean(array)
def var(x):
return power(x - avg, 2)
return pyd._(array).map_(var).mean().value()
[docs]def zscore(collection, iteratee=None):
"""
Calculate the standard score assuming normal distribution. If iteratee is passed, each element
of `collection` is passed through a iteratee before the standard score is computed.
Args:
collection (list|dict): Collection to process.
iteratee (mixed, optional): Iteratee applied per iteration.
Returns:
float: Calculated standard score.
Example:
>>> results = zscore([1, 2, 3])
# [-1.224744871391589, 0.0, 1.224744871391589]
.. versionadded:: 2.1.0
"""
array = pyd.map_(collection, iteratee)
avg = mean(array)
sig = std_deviation(array)
return [(item - avg) / sig for item in array]
#
# Utility methods not a part of the main API
#
def call_math_operator(value1, value2, op, default):
"""Return the result of the math operation on the given values."""
if not value1:
value1 = default
if not value2:
value2 = default
if not pyd.is_number(value1):
try:
value1 = float(value1)
except Exception:
pass
if not pyd.is_number(value2):
try:
value2 = float(value2)
except Exception:
pass
return op(value1, value2)
def rounder(func, x, precision):
precision = pow(10, precision)
def rounder_func(item):
return func(item * precision) / precision
result = None
if pyd.is_number(x):
result = rounder_func(x)
elif pyd.is_iterable(x):
try:
result = [rounder_func(item) for item in x]
except TypeError:
pass
return result