1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
|
"""
Lhs functions are inspired by
https://github.com/clicumu/pyDOE2/blob/
master/pyDOE2/doe_lhs.py
"""
import numpy as np
from scipy import spatial
from sklearn.utils import check_random_state
from ..space import Space
from .base import InitialPointGenerator
def _random_permute_matrix(h, random_state=None):
rng = check_random_state(random_state)
h_rand_perm = np.zeros_like(h)
samples, n = h.shape
for j in range(n):
order = rng.permutation(range(samples))
h_rand_perm[:, j] = h[order, j]
return h_rand_perm
class Lhs(InitialPointGenerator):
"""Latin hypercube sampling.
Parameters
----------
lhs_type : str, default='classic'
- 'classic' - a small random number is added
- 'centered' - points are set uniformly in each interval
criterion : str or None, default='maximin'
When set to None, the LHS is not optimized
- 'correlation' : optimized LHS by minimizing the correlation
- 'maximin' : optimized LHS by maximizing the minimal pdist
- 'ratio' : optimized LHS by minimizing the ratio
`max(pdist) / min(pdist)`
iterations : int
Defines the number of iterations for optimizing LHS
"""
def __init__(self, lhs_type="classic", criterion="maximin", iterations=1000):
self.lhs_type = lhs_type
self.criterion = criterion
self.iterations = iterations
def generate(self, dimensions, n_samples, random_state=None):
"""Creates latin hypercube samples.
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 LHS 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)
LHS set
"""
rng = check_random_state(random_state)
space = Space(dimensions)
transformer = space.get_transformer()
n_dim = space.n_dims
space.set_transformer("normalize")
if self.criterion is None or n_samples == 1:
h = self._lhs_normalized(n_dim, n_samples, rng)
h = space.inverse_transform(h)
space.set_transformer(transformer)
return h
else:
h_opt = self._lhs_normalized(n_dim, n_samples, rng)
h_opt = space.inverse_transform(h_opt)
if self.criterion == "correlation":
mincorr = np.inf
for _ in range(self.iterations):
# Generate a random LHS
h = self._lhs_normalized(n_dim, n_samples, rng)
r = np.corrcoef(np.array(h).T)
if (
len(np.abs(r[r != 1])) > 0
and np.max(np.abs(r[r != 1])) < mincorr
):
mincorr = np.max(np.abs(r - np.eye(r.shape[0])))
h_opt = h.copy()
h_opt = space.inverse_transform(h_opt)
elif self.criterion == "maximin":
maxdist = 0
# Maximize the minimum distance between points
for _ in range(self.iterations):
h = self._lhs_normalized(n_dim, n_samples, rng)
d = spatial.distance.pdist(np.array(h), 'euclidean')
if maxdist < np.min(d):
maxdist = np.min(d)
h_opt = h.copy()
h_opt = space.inverse_transform(h_opt)
elif self.criterion == "ratio":
minratio = np.inf
# Maximize the minimum distance between points
for _ in range(self.iterations):
h = self._lhs_normalized(n_dim, n_samples, rng)
p = spatial.distance.pdist(np.array(h), 'euclidean')
if np.min(p) == 0:
ratio = np.max(p) / 1e-8
else:
ratio = np.max(p) / np.min(p)
if minratio > ratio:
minratio = ratio
h_opt = h.copy()
h_opt = space.inverse_transform(h_opt)
else:
raise ValueError("Wrong criterion." "Got {}".format(self.criterion))
space.set_transformer(transformer)
return h_opt
def _lhs_normalized(self, n_dim, n_samples, random_state):
rng = check_random_state(random_state)
x = np.linspace(0, 1, n_samples + 1)
u = rng.rand(n_samples, n_dim)
h = np.zeros_like(u)
if self.lhs_type == "centered":
for j in range(n_dim):
h[:, j] = np.diff(x) / 2.0 + x[:n_samples]
elif self.lhs_type == "classic":
for j in range(n_dim):
h[:, j] = u[:, j] * np.diff(x) + x[:n_samples]
else:
raise ValueError(f"Wrong lhs_type. Got {self.lhs_type}")
return _random_permute_matrix(h, random_state=rng)
|
