File size: 14,121 Bytes
a59bdc5 |
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 |
from numba import jit
import numpy as np
from pyrqa.computation import RPComputation, RQAComputation
from pyrqa.time_series import TimeSeries, EmbeddedSeries
from pyrqa.settings import Settings
from pyrqa.analysis_type import Classic
from pyrqa.metric import EuclideanMetric
# from pyrqa.metric import Sigmoid
# from pyrqa.metric import Cosine
from pyrqa.neighbourhood import Unthresholded,FixedRadius
def get_results(recurrence_matrix,
minimum_diagonal_line_length,
minimum_vertical_line_length,
minimum_white_vertical_line_length):
number_of_vectors = recurrence_matrix.shape[0]
diagonal = diagonal_frequency_distribution(recurrence_matrix)
vertical = vertical_frequency_distribution(recurrence_matrix)
white = white_vertical_frequency_distribution(recurrence_matrix)
number_of_vert_lines = number_of_vertical_lines(vertical, minimum_vertical_line_length)
number_of_vert_lines_points = number_of_vertical_lines_points(vertical, minimum_vertical_line_length)
RR = recurrence_rate(recurrence_matrix)
DET = determinism(number_of_vectors, diagonal, minimum_diagonal_line_length)
L = average_diagonal_line_length(number_of_vectors, diagonal, minimum_diagonal_line_length)
Lmax = longest_diagonal_line_length(number_of_vectors, diagonal)
DIV = divergence(Lmax)
Lentr = entropy_diagonal_lines(number_of_vectors, diagonal, minimum_diagonal_line_length)
DET_RR = ratio_determinism_recurrence_rate(DET, RR)
LAM = laminarity(number_of_vectors, vertical, minimum_vertical_line_length)
V = average_vertical_line_length(number_of_vectors, vertical, minimum_vertical_line_length)
Vmax = longest_vertical_line_length(number_of_vectors, vertical)
Ventr = entropy_vertical_lines(number_of_vectors, vertical, minimum_vertical_line_length)
LAM_DET = laminarity_determinism(LAM, DET)
W = average_white_vertical_line_length(number_of_vectors, white, minimum_white_vertical_line_length)
Wmax = longest_white_vertical_line_length(number_of_vectors, white)
Wentr = entropy_white_vertical_lines(number_of_vectors, white, minimum_white_vertical_line_length)
TT = trapping_time(number_of_vert_lines_points, number_of_vert_lines)
return [RR, DET, L, Lmax, DIV, Lentr, DET_RR, LAM, V, Vmax, Ventr, LAM_DET, W, Wmax, Wentr, TT]
@jit(nopython=True)
def diagonal_frequency_distribution(recurrence_matrix):
# Calculating the number of states - N
number_of_vectors = recurrence_matrix.shape[0]
diagonal_frequency_distribution = np.zeros(number_of_vectors + 1)
# Calculating the diagonal frequency distribution - P(l)
for i in range(number_of_vectors - 1, -1, -1):
diagonal_line_length = 0
for j in range(0, number_of_vectors - i):
if recurrence_matrix[i + j, j] == 1:
diagonal_line_length += 1
if j == (number_of_vectors - i - 1):
diagonal_frequency_distribution[diagonal_line_length] += 1.0
else:
if diagonal_line_length != 0:
diagonal_frequency_distribution[diagonal_line_length] += 1.0
diagonal_line_length = 0
for k in range(1, number_of_vectors):
diagonal_line_length = 0
for i in range(number_of_vectors - k):
j = i + k
if recurrence_matrix[i, j] == 1:
diagonal_line_length += 1
if j == (number_of_vectors - 1):
diagonal_frequency_distribution[diagonal_line_length] += 1.0
else:
if diagonal_line_length != 0:
diagonal_frequency_distribution[diagonal_line_length] += 1.0
diagonal_line_length = 0
return diagonal_frequency_distribution
@jit(nopython=True)
def vertical_frequency_distribution(recurrence_matrix):
number_of_vectors = recurrence_matrix.shape[0]
# Calculating the vertical frequency distribution - P(v)
vertical_frequency_distribution = np.zeros(number_of_vectors + 1)
for i in range(number_of_vectors):
vertical_line_length = 0
for j in range(number_of_vectors):
if recurrence_matrix[i, j] == 1:
vertical_line_length += 1
if j == (number_of_vectors - 1):
vertical_frequency_distribution[vertical_line_length] += 1.0
else:
if vertical_line_length != 0:
vertical_frequency_distribution[vertical_line_length] += 1.0
vertical_line_length = 0
return vertical_frequency_distribution
@jit(nopython=True)
def white_vertical_frequency_distribution(recurrence_matrix):
number_of_vectors = recurrence_matrix.shape[0]
# Calculating the white vertical frequency distribution - P(w)
white_vertical_frequency_distribution = np.zeros(number_of_vectors + 1)
for i in range(number_of_vectors):
white_vertical_line_length = 0
for j in range(number_of_vectors):
if recurrence_matrix[i, j] == 0:
white_vertical_line_length += 1
if j == (number_of_vectors - 1):
white_vertical_frequency_distribution[white_vertical_line_length] += 1.0
else:
if white_vertical_line_length != 0:
white_vertical_frequency_distribution[white_vertical_line_length] += 1.0
white_vertical_line_length = 0
return white_vertical_frequency_distribution
@jit(nopython=True)
def recurrence_rate(recurrence_matrix):
# Calculating the recurrence rate - RR
number_of_vectors = recurrence_matrix.shape[0]
return np.float(np.sum(recurrence_matrix)) / np.power(number_of_vectors, 2)
def determinism(number_of_vectors, diagonal_frequency_distribution_, minimum_diagonal_line_length):
# Calculating the determinism - DET
numerator = np.sum(
[l * diagonal_frequency_distribution_[l] for l in range(minimum_diagonal_line_length, number_of_vectors)])
denominator = np.sum([l * diagonal_frequency_distribution_[l] for l in range(1, number_of_vectors)])
return numerator / denominator
def average_diagonal_line_length(number_of_vectors, diagonal_frequency_distribution_, minimum_diagonal_line_length):
# Calculating the average diagonal line length - L
numerator = np.sum(
[l * diagonal_frequency_distribution_[l] for l in range(minimum_diagonal_line_length, number_of_vectors)])
denominator = np.sum(
[diagonal_frequency_distribution_[l] for l in range(minimum_diagonal_line_length, number_of_vectors)])
return numerator / denominator
@jit(nopython=True)
def longest_diagonal_line_length(number_of_vectors, diagonal_frequency_distribution_):
# Calculating the longest diagonal line length - Lmax
for l in range(number_of_vectors - 1, 0, -1):
if diagonal_frequency_distribution_[l] != 0:
longest_diagonal_line_length = l
break
return longest_diagonal_line_length
@jit(nopython=True)
def divergence(longest_diagonal_line_length_):
# Calculating the divergence - DIV
return 1. / longest_diagonal_line_length_
@jit(nopython=True)
def entropy_diagonal_lines(number_of_vectors, diagonal_frequency_distribution_, minimum_diagonal_line_length):
# Calculating the entropy diagonal lines - Lentr
sum_diagonal_frequency_distribution = np.float(
np.sum(diagonal_frequency_distribution_[minimum_diagonal_line_length:-1]))
entropy_diagonal_lines = 0
for l in range(minimum_diagonal_line_length, number_of_vectors):
if diagonal_frequency_distribution_[l] != 0:
entropy_diagonal_lines += (diagonal_frequency_distribution_[
l] / sum_diagonal_frequency_distribution) * np.log(
diagonal_frequency_distribution_[l] / sum_diagonal_frequency_distribution)
entropy_diagonal_lines *= -1
return entropy_diagonal_lines
@jit(nopython=True)
def ratio_determinism_recurrence_rate(determinism_, recurrence_rate_):
# Calculating the divergence - DIV
return determinism_ / recurrence_rate_
def laminarity(number_of_vectors, vertical_frequency_distribution_, minimum_vertical_line_length):
# Calculating the laminarity - LAM
numerator = np.sum(
[v * vertical_frequency_distribution_[v] for v in range(minimum_vertical_line_length, number_of_vectors + 1)])
denominator = np.sum([v * vertical_frequency_distribution_[v] for v in range(1, number_of_vectors + 1)])
return numerator / denominator
def average_vertical_line_length(number_of_vectors, vertical_frequency_distribution_, minimum_vertical_line_length):
# Calculating the average vertical line length - V
numerator = np.sum(
[v * vertical_frequency_distribution_[v] for v in range(minimum_vertical_line_length, number_of_vectors + 1)])
denominator = np.sum(
[vertical_frequency_distribution_[v] for v in range(minimum_vertical_line_length, number_of_vectors + 1)])
return numerator / denominator
@jit(nopython=True)
def longest_vertical_line_length(number_of_vectors, vertical_frequency_distribution_):
# Calculating the longest vertical line length - Vmax
longest_vertical_line_length_ = 0
for v in range(number_of_vectors, 0, -1):
if vertical_frequency_distribution_[v] != 0:
longest_vertical_line_length_ = v
break
return longest_vertical_line_length_
@jit(nopython=True)
def entropy_vertical_lines(number_of_vectors, vertical_frequency_distribution_, minimum_vertical_line_length):
# Calculating the entropy vertical lines - Ventr
sum_vertical_frequency_distribution = np.float(
np.sum(vertical_frequency_distribution_[minimum_vertical_line_length:]))
entropy_vertical_lines_ = 0
for v in range(minimum_vertical_line_length, number_of_vectors + 1):
if vertical_frequency_distribution_[v] != 0:
entropy_vertical_lines_ += (vertical_frequency_distribution_[
v] / sum_vertical_frequency_distribution) * np.log(
vertical_frequency_distribution_[v] / sum_vertical_frequency_distribution)
entropy_vertical_lines_ *= -1
return entropy_vertical_lines_
@jit(nopython=True)
def laminarity_determinism(laminarity_, determinism_):
# Calculating the ratio laminarity_determinism - LAM/DET
return laminarity_ / determinism_
def average_white_vertical_line_length(number_of_vectors, white_vertical_frequency_distribution_,
minimum_white_vertical_line_length):
# Calculating the average white vertical line length - W
numerator = np.sum([w * white_vertical_frequency_distribution_[w] for w in
range(minimum_white_vertical_line_length, number_of_vectors + 1)])
denominator = np.sum([white_vertical_frequency_distribution_[w] for w in
range(minimum_white_vertical_line_length, number_of_vectors + 1)])
return numerator / denominator
@jit(nopython=True)
def longest_white_vertical_line_length(number_of_vectors, white_vertical_frequency_distribution_):
# Calculating the longest white vertical line length - Wmax
longest_white_vertical_line_length_ = 0
for w in range(number_of_vectors, 0, -1):
if white_vertical_frequency_distribution_[w] != 0:
longest_white_vertical_line_length_ = w
break
return longest_white_vertical_line_length_
@jit(nopython=True)
def entropy_white_vertical_lines(number_of_vectors, white_vertical_frequency_distribution_,
minimum_white_vertical_line_length):
# Calculating the entropy white vertical lines - Wentr
sum_white_vertical_frequency_distribution = np.float(
np.sum(white_vertical_frequency_distribution_[minimum_white_vertical_line_length:]))
entropy_white_vertical_lines_ = 0
for w in range(minimum_white_vertical_line_length, number_of_vectors + 1):
if white_vertical_frequency_distribution_[w] != 0:
entropy_white_vertical_lines_ += (white_vertical_frequency_distribution_[
w] / sum_white_vertical_frequency_distribution) * np.log(
white_vertical_frequency_distribution_[w] / sum_white_vertical_frequency_distribution)
entropy_white_vertical_lines_ *= -1
return entropy_white_vertical_lines_
def number_of_vertical_lines(vertical_frequency_distribution_, minimum_vertical_line_length):
if minimum_vertical_line_length > 0:
return np.sum(vertical_frequency_distribution_[minimum_vertical_line_length - 1:])
return np.uint(0)
def number_of_vertical_lines_points(vertical_frequency_distribution_, minimum_vertical_line_length):
if minimum_vertical_line_length > 0:
return np.sum(
((np.arange(vertical_frequency_distribution_.size) + 1) * vertical_frequency_distribution_)[minimum_vertical_line_length - 1:])
return np.uint(0)
@jit(nopython=True)
def trapping_time(number_of_vertical_lines_points_, number_of_vertical_lines_):
"""
Trapping time (TT).
"""
try:
return np.float32(number_of_vertical_lines_points_ / number_of_vertical_lines_)
except:
return 0
def return_pyRQA_results(signal, nbr):
time_series = EmbeddedSeries(signal)
settings = Settings(time_series,
analysis_type=Classic,
neighbourhood=FixedRadius(nbr),
similarity_measure=EuclideanMetric,
theiler_corrector=1)
computation = RQAComputation.create(settings,
verbose=True)
result = computation.run()
return result
|