Source code for deephyper.skopt.sampler.halton

Inspired by
import numpy as np
from .base import InitialPointGenerator
from import Space
from sklearn.utils import check_random_state

[docs]class Halton(InitialPointGenerator): """Creates `Halton` sequence samples. In statistics, Halton sequences are sequences used to generate points in space for numerical methods such as Monte Carlo simulations. Although these sequences are deterministic, they are of low discrepancy, that is, appear to be random for many purposes. They were first introduced in 1960 and are an example of a quasi-random number sequence. They generalise the one-dimensional van der Corput sequences. For ``dim == 1`` the sequence falls back to Van Der Corput sequence. Parameters ---------- min_skip : int Minimum skipped seed number. When `min_skip != max_skip` a random number is picked. max_skip : int Maximum skipped seed number. When `min_skip != max_skip` a random number is picked. primes : tuple, default=None The (non-)prime base to calculate values along each axis. If empty or None, growing prime values starting from 2 will be used. """ def __init__(self, min_skip=0, max_skip=0, primes=None): self.primes = primes self.min_skip = min_skip self.max_skip = max_skip
[docs] def generate(self, dimensions, n_samples, random_state=None): """Creates samples from Halton set. Parameters ---------- dimensions : list, shape (n_dims,) List of search space dimensions. Each search dimension can be defined either as - a `(lower_bound, upper_bound)` tuple (for `Real` or `Integer` dimensions), - a `(lower_bound, upper_bound, "prior")` tuple (for `Real` dimensions), - as a list of categories (for `Categorical` dimensions), or - an instance of a `Dimension` object (`Real`, `Integer` or `Categorical`). n_samples : int The order of the Halton sequence. Defines the number of samples. random_state : int, RandomState instance, or None (default) Set random state to something other than None for reproducible results. Returns ------- np.array, shape=(n_dim, n_samples) Halton set. """ rng = check_random_state(random_state) if self.primes is None: primes = [] else: primes = list(self.primes) space = Space(dimensions) n_dim = space.n_dims transformer = space.get_transformer() space.set_transformer("normalize") if len(primes) < n_dim: prime_order = 10 * n_dim while len(primes) < n_dim: primes = _create_primes(prime_order) prime_order *= 2 primes = primes[:n_dim] assert len(primes) == n_dim, "not enough primes" if self.min_skip == self.max_skip: skip = self.min_skip elif self.min_skip < 0 and self.max_skip < 0: skip = max(primes) elif self.min_skip < 0 or self.max_skip < 0: skip = np.max(self.min_skip, self.max_skip) else: skip = rng.randint(self.min_skip, self.max_skip) out = np.empty((n_dim, n_samples)) indices = [idx + skip for idx in range(n_samples)] for dim_ in range(n_dim): out[dim_] = _van_der_corput_samples(indices, number_base=primes[dim_]) out = space.inverse_transform(np.transpose(out)) space.set_transformer(transformer) return out
def _van_der_corput_samples(idx, number_base=2): """Create `Van Der Corput` low discrepancy sequence samples. A van der Corput sequence is an example of the simplest one-dimensional low-discrepancy sequence over the unit interval; it was first described in 1935 by the Dutch mathematician J. G. van der Corput. It is constructed by reversing the base-n representation of the sequence of natural numbers (1, 2, 3, ...). In practice, use Halton sequence instead of Van Der Corput, as it is the same, but generalized to work in multiple dimensions. Parameters ---------- idx (int, numpy.ndarray): The index of the sequence. If array is provided, all values in array is returned. number_base : int The numerical base from where to create the samples from. Returns ------- float, numpy.ndarray Van der Corput samples. """ assert number_base > 1 idx = np.asarray(idx).flatten() out = np.zeros(len(idx), dtype=float) base = float(number_base) active = np.ones(len(idx), dtype=bool) while np.any(active): out[active] += (idx[active] % number_base) / base idx //= number_base base *= number_base active = idx > 0 return out def _create_primes(threshold): """ Generate prime values using sieve of Eratosthenes method. Parameters ---------- threshold : int The upper bound for the size of the prime values. Returns ------ List All primes from 2 and up to ``threshold``. """ if threshold == 2: return [2] elif threshold < 2: return [] numbers = list(range(3, threshold + 1, 2)) root_of_threshold = threshold**0.5 half = int((threshold + 1) / 2 - 1) idx = 0 counter = 3 while counter <= root_of_threshold: if numbers[idx]: idy = int((counter * counter - 3) / 2) numbers[idy] = 0 while idy < half: numbers[idy] = 0 idy += counter idx += 1 counter = 2 * idx + 3 return [2] + [number for number in numbers if number]