2019/08/math-for-programmers/ about blog-comments HOT 2 CLOSED

X = [1, 2, 3]

from statistics import mean, fmean
mean(X)

# may or may not be preferable to
sum(X) / len(X)

import operator
from functools import reduce
# from itertools import accumulate
reduce(operator.mul, X)

from numpy import linalg as LA
LA.norm(X)

from numbers import Number
from fractions import Fraction
from decimal import Decimal
x_fraction = Fraction("1/2") or Fraction(1, 2)
x_decimal = Decimal("0.3")
assert isinstance(x_fraction, Fraction)
assert isinstance(x_fraction, Number)
assert type(x_decimal) == Decimal
assert type(1j) == complex

from numbers import Number
from typing import Callable, Iterable, Optional, Union

def sum(a: int, b: int) -> int:
    return a + b

def sum(a: float, b: Number) -> Number:
    return a + b

def sum(a: Number, b: Number) -> Union[Number, None]:
    return a + b if not (a is None or b is None) else None

def sum(a: Number, b: Number) -> Optional[Number]:
    return a + b if not (a is None or b is None) else None

def sum(a: Number, b: Number) -> Optional[Number]:
    if not isinstance(a, Number):
        raise TypeError(("a is not a", Number))
    return a + b if not (a is None or b is None) else None

def map(function: Callable, sequence: Iterable) -> Iterable:
    return (function(x) for x in sequence)

def sum(a: Number, b: Number) -> Optional[Number]:
    # preconditions
    if not isinstance(a, Number):
        raise TypeError(("a is not a", Number, "a is a", type(a)))
    if a < 0:
        raise ValueError(("a is < 0", a))

    # function ("command" in Hoare Logic)
    if b is None:
        return None
    a_ = a
    output = a_ + b

    # postconditions
    assert isinstance(output, (Number,  bool, int, float, complex, Fraction, Decimal))
    assert a == a_  # "invariance"
    # a['num1'] += 1; assert a['num1'] == a['num1']

    return output

import pytest

def test_sum():
    assert sum(False, True) == 1

    with pytest.raises(TypeError):
        sum(None, 0)
    with pytest.raises(ValueError):
        sum(-1, 0)

    assert sum(1, None) == None

# !pip install pytest-cov
# !pytest -v --cov=this_file --cov-report=term-missing ./this_file.py
test_sum()

Y = [4, 5, 6]
np.dot(X, Y)

X / np.linalg.norm(X)

x**3    # x*x*x
x**1/2  # math.sqrt(x)

x^2   # x XOR 2
x^3   # operator.xor(x, 3)

import numpy as np
a = np.matrix([[1, 0], [0, 1]])
b = np.matrix([[4, 1], [2, 2]])
assert a @ b == np.matmul(a, b)
p.testing.assert_equal(np.matmul(a,b), a @ b)