From e6e3b1b27d08bfe77b5e19b41fbb006fe7bfed36 Mon Sep 17 00:00:00 2001 From: Raymond Hettinger Date: Tue, 21 Mar 2023 13:44:32 -0500 Subject: [3.11] Backport itertool recipe updates (GH-102881) --- Doc/library/itertools.rst | 24 ++++++++++++++++++------ 1 file changed, 18 insertions(+), 6 deletions(-) diff --git a/Doc/library/itertools.rst b/Doc/library/itertools.rst index 5fe93fd..e1ffd39 100644 --- a/Doc/library/itertools.rst +++ b/Doc/library/itertools.rst @@ -805,7 +805,7 @@ which incur interpreter overhead. if n < 1: raise ValueError('n must be at least one') it = iter(iterable) - while (batch := tuple(islice(it, n))): + while batch := tuple(islice(it, n)): yield batch def grouper(iterable, n, *, incomplete='fill', fillvalue=None): @@ -861,11 +861,23 @@ which incur interpreter overhead. (x - 5) (x + 4) (x - 3) expands to: x³ -4x² -17x + 60 """ # polynomial_from_roots([5, -4, 3]) --> [1, -4, -17, 60] - roots = list(map(operator.neg, roots)) - return [ - sum(map(math.prod, combinations(roots, k))) - for k in range(len(roots) + 1) - ] + expansion = [1] + for r in roots: + expansion = convolve(expansion, (1, -r)) + return list(expansion) + + 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 sumprod(coefficients, powers) def iter_index(iterable, value, start=0): "Return indices where a value occurs in a sequence or iterable." -- cgit v0.12