mirrors/cpython
1
0
Fork 0
mirror of https://github.com/python/cpython.git synced 2025-07-24 11:44:31 +00:00
Code Issues Projects Releases Packages Wiki Activity Actions 8

Misc itertool recipe improvements, mostly docstrings and comments (gh-109555)

Browse source
This commit is contained in:
Raymond Hettinger 2023-09-19 07:39:44 -05:00 • committed by GitHub
parent 94c95d42a3
commit f2636d2c45
No known key found for this signature in database
GPG key ID: 4AEE18F83AFDEB23
1 changed files with 73 additions and 65 deletions
Download patch file Download diff file Expand all files Collapse all files

138
Doc/library/itertools.rst
View file

@ -844,6 +844,7 @@ which incur interpreter overhead.
return next(islice(iterable, n, None), default)
def quantify(iterable, pred=bool):
"Given a predicate that returns True or False, count the True results."
"Count how many times the predicate is True"
return sum(map(pred, iterable))
@ -1028,6 +1029,77 @@ The following recipes have a more mathematical flavor:
s = list(iterable)
return chain.from_iterable(combinations(s, r) for r in range(len(s)+1))
def sum_of_squares(it):
"Add up the squares of the input values."
# sum_of_squares([10, 20, 30]) -> 1400
return math.sumprod(*tee(it))
def transpose(it):
"Swap the rows and columns of the input."
# transpose([(1, 2, 3), (11, 22, 33)]) --> (1, 11) (2, 22) (3, 33)
return zip(*it, strict=True)
def matmul(m1, m2):
"Multiply two matrices."
# matmul([(7, 5), (3, 5)], [(2, 5), (7, 9)]) --> (49, 80), (41, 60)
n = len(m2[0])
return batched(starmap(math.sumprod, product(m1, transpose(m2))), n)
def convolve(signal, kernel):
"""Discrete linear convolution of two iterables.
The kernel is fully consumed before the calculations begin.
The signal is consumed lazily and can be infinite.
Convolutions are mathematically commutative.
If the signal and kernel are swapped,
the output will be the same.
Article: https://betterexplained.com/articles/intuitive-convolution/
Video: https://www.youtube.com/watch?v=KuXjwB4LzSA
"""
# convolve(data, [0.25, 0.25, 0.25, 0.25]) --> Moving average (blur)
# convolve(data, [1/2, 0, -1/2]) --> 1st derivative estimate
# convolve(data, [1, -2, 1]) --> 2nd derivative estimate
kernel = tuple(kernel)[::-1]
n = len(kernel)
padded_signal = chain(repeat(0, n-1), signal, repeat(0, n-1))
windowed_signal = sliding_window(padded_signal, n)
return map(math.sumprod, repeat(kernel), windowed_signal)
def polynomial_from_roots(roots):
"""Compute a polynomial's coefficients from its roots.
(x - 5) (x + 4) (x - 3) expands to: x³ -4x² -17x + 60
"""
# polynomial_from_roots([5, -4, 3]) --> [1, -4, -17, 60]
factors = zip(repeat(1), map(operator.neg, roots))
return list(functools.reduce(convolve, factors, [1]))
def polynomial_eval(coefficients, x):
"""Evaluate a polynomial at a specific value.
Computes with better numeric stability than Horner's method.
"""
# Evaluate x³ -4x² -17x + 60 at x = 2.5
# polynomial_eval([1, -4, -17, 60], x=2.5) --> 8.125
n = len(coefficients)
if not n:
return type(x)(0)
powers = map(pow, repeat(x), reversed(range(n)))
return math.sumprod(coefficients, powers)
def polynomial_derivative(coefficients):
"""Compute the first derivative of a polynomial.
f(x) = x³ -4x² -17x + 60
f'(x) = 3x² -8x -17
"""
# polynomial_derivative([1, -4, -17, 60]) -> [3, -8, -17]
n = len(coefficients)
powers = reversed(range(1, n))
return list(map(operator.mul, coefficients, powers))
def sieve(n):
"Primes less than n."
# sieve(30) --> 2 3 5 7 11 13 17 19 23 29
@ -1056,70 +1128,6 @@ The following recipes have a more mathematical flavor:
if n > 1:
yield n
def sum_of_squares(it):
"Add up the squares of the input values."
# sum_of_squares([10, 20, 30]) -> 1400
return math.sumprod(*tee(it))
def transpose(it):
"Swap the rows and columns of the input."
# transpose([(1, 2, 3), (11, 22, 33)]) --> (1, 11) (2, 22) (3, 33)
return zip(*it, strict=True)
def matmul(m1, m2):
"Multiply two matrices."
# matmul([(7, 5), (3, 5)], [(2, 5), (7, 9)]) --> (49, 80), (41, 60)
n = len(m2[0])
return batched(starmap(math.sumprod, product(m1, transpose(m2))), n)
def convolve(signal, kernel):
"""Linear convolution of two iterables.
Article: https://betterexplained.com/articles/intuitive-convolution/
Video: https://www.youtube.com/watch?v=KuXjwB4LzSA
"""
# convolve(data, [0.25, 0.25, 0.25, 0.25]) --> Moving average (blur)
# convolve(data, [1, -1]) --> 1st finite difference (1st derivative)
# convolve(data, [1, -2, 1]) --> 2nd finite difference (2nd derivative)
kernel = tuple(kernel)[::-1]
n = len(kernel)
padded_signal = chain(repeat(0, n-1), signal, repeat(0, n-1))
windowed_signal = sliding_window(padded_signal, n)
return map(math.sumprod, repeat(kernel), windowed_signal)
def polynomial_from_roots(roots):
"""Compute a polynomial's coefficients from its roots.
(x - 5) (x + 4) (x - 3) expands to: x³ -4x² -17x + 60
"""
# polynomial_from_roots([5, -4, 3]) --> [1, -4, -17, 60]
factors = zip(repeat(1), map(operator.neg, roots))
return list(functools.reduce(convolve, factors, [1]))
def polynomial_eval(coefficients, x):
"""Evaluate a polynomial at a specific value.
Computes with better numeric stability than Horner's method.
"""
# Evaluate x³ -4x² -17x + 60 at x = 2.5
# polynomial_eval([1, -4, -17, 60], x=2.5) --> 8.125
n = len(coefficients)
if n == 0:
return x * 0 # coerce zero to the type of x
powers = map(pow, repeat(x), reversed(range(n)))
return math.sumprod(coefficients, powers)
def polynomial_derivative(coefficients):
"""Compute the first derivative of a polynomial.
f(x) = x³ -4x² -17x + 60
f'(x) = 3x² -8x -17
"""
# polynomial_derivative([1, -4, -17, 60]) -> [3, -8, -17]
n = len(coefficients)
powers = reversed(range(1, n))
return list(map(operator.mul, coefficients, powers))
def nth_combination(iterable, r, index):
"Equivalent to list(combinations(iterable, r))[index]"
pool = tuple(iterable)
@ -1295,7 +1303,7 @@ The following recipes have a more mathematical flavor:
>>> polynomial_eval([], Fraction(2, 3))
Fraction(0, 1)
>>> polynomial_eval([], Decimal('1.75'))
Decimal('0.00')
Decimal('0')
>>> polynomial_eval([11], 7) == 11
True
>>> polynomial_eval([11, 2], 7) == 11 * 7 + 2