from __future__ import annotations from functools import lru_cache import hashlib import inspect import math import numpy as np from typing import TYPE_CHECKING if TYPE_CHECKING: from typing import Callable, TypeVar from manimlib.typing import FloatArray Scalable = TypeVar("Scalable", float, FloatArray) def sigmoid(x: float | FloatArray): return 1.0 / (1 + np.exp(-x)) @lru_cache(maxsize=10) def choose(n: int, k: int) -> int: return math.comb(n, k) def gen_choose(n: int, r: int) -> int: return int(np.prod(range(n, n - r, -1)) / math.factorial(r)) def get_num_args(function: Callable) -> int: return len(get_parameters(function)) def get_parameters(function: Callable) -> list: return list(inspect.signature(function).parameters.keys()) # Just to have a less heavyweight name for this extremely common operation # # We may wish to have more fine-grained control over division by zero behavior # in the future (separate specifiable values for 0/0 and x/0 with x != 0), # but for now, we just allow the option to handle indeterminate 0/0. def clip(a: float, min_a: float, max_a: float) -> float: if a < min_a: return min_a elif a > max_a: return max_a return a def arr_clip(arr: np.ndarray, min_a: float, max_a: float) -> np.ndarray: arr[arr < min_a] = min_a arr[arr > max_a] = max_a return arr def fdiv(a: Scalable, b: Scalable, zero_over_zero_value: Scalable | None = None) -> Scalable: if zero_over_zero_value is not None: out = np.full_like(a, zero_over_zero_value) where = np.logical_or(a != 0, b != 0) else: out = None where = True return np.true_divide(a, b, out=out, where=where) def binary_search(function: Callable[[float], float], target: float, lower_bound: float, upper_bound: float, tolerance:float = 1e-4) -> float | None: lh = lower_bound rh = upper_bound mh = (lh + rh) / 2 while abs(rh - lh) > tolerance: lx, mx, rx = [function(h) for h in (lh, mh, rh)] if lx == target: return lx if rx == target: return rx if lx <= target and rx >= target: if mx > target: rh = mh else: lh = mh elif lx > target and rx < target: lh, rh = rh, lh else: return None mh = (lh + rh) / 2 return mh def hash_string(string: str) -> str: # Truncating at 16 bytes for cleanliness hasher = hashlib.sha256(string.encode()) return hasher.hexdigest()[:16]