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17b7ba4 | 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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 | """DR-TS-SL-LIB: Operator-based Basis Library + FAISS Candidate Selection.
This module implements a decomposition approach using a pre-computed library of
basis functions (polynomials, sinusoids, logistic curves) with FAISS for fast
candidate retrieval and sparse regression for coefficient optimization.
Decomposition form:
x_t ≈ Σ_i c_i φ_i(t) + r_t
Where φ_i are basis functions from a trend or seasonal library.
"""
from __future__ import annotations
from dataclasses import dataclass, field
from pathlib import Path
from typing import Any, Dict, List, Optional, Tuple
import numpy as np
from scipy.optimize import nnls
try:
import faiss
_HAS_FAISS = True
except ImportError:
_HAS_FAISS = False
faiss = None
@dataclass
class SLLibConfig:
"""Configuration for SL-LIB decomposition.
Attributes
----------
library_size : int
Total number of basis functions in the library.
n_trend_bases : int
Number of trend basis functions.
n_seasonal_bases : int
Number of seasonal basis functions.
n_candidates : int
Number of candidates to retrieve from FAISS.
sparsity_lambda : float
L1 regularization for sparse coefficients.
max_poly_degree : int
Maximum polynomial degree for trend bases.
min_period : int
Minimum period for sinusoidal bases.
max_period : int
Maximum period for sinusoidal bases.
"""
library_size: int = 500
n_trend_bases: int = 200
n_seasonal_bases: int = 300
n_candidates: int = 100 # v1.1.0: increased from 50
sparsity_lambda: float = 0.001 # v1.1.0: reduced from 0.01
max_poly_degree: int = 5
min_period: int = 4
max_period: int = 128
def _generate_polynomial_bases(length: int, n_bases: int, max_degree: int = 5) -> np.ndarray:
"""Generate polynomial trend basis functions.
Returns
-------
bases : np.ndarray of shape (n_bases, length)
"""
t = np.linspace(-1, 1, length)
bases = []
# Standard polynomials
for degree in range(max_degree + 1):
bases.append(t ** degree)
# Chebyshev-like bases
while len(bases) < n_bases // 2:
d = len(bases) % (max_degree + 1)
offset = len(bases) // (max_degree + 1) * 0.1
bases.append(np.cos(d * np.arccos(np.clip(t + offset, -1, 1))))
# Logistic-style bases
while len(bases) < n_bases * 3 // 4:
k = 1.0 + len(bases) * 0.5 # steepness
midpoint = (len(bases) - n_bases // 2) / (n_bases // 4) - 0.5
bases.append(1.0 / (1.0 + np.exp(-k * (t - midpoint))))
# Smoothed random-walk bases (cumulative sums of smooth noise)
rng = np.random.RandomState(42)
while len(bases) < n_bases:
noise = rng.randn(length)
# Smooth the noise
kernel = np.ones(max(3, length // 20)) / max(3, length // 20)
smooth_noise = np.convolve(noise, kernel, mode='same')
cumsum = np.cumsum(smooth_noise)
# Normalize
cumsum = (cumsum - cumsum.mean()) / (cumsum.std() + 1e-8)
bases.append(cumsum)
bases = np.array(bases[:n_bases])
# Normalize each basis
norms = np.linalg.norm(bases, axis=1, keepdims=True) + 1e-8
return bases / norms
def _generate_sinusoidal_bases(
length: int,
n_bases: int,
min_period: int = 4,
max_period: int = 128,
) -> np.ndarray:
"""Generate sinusoidal seasonal basis functions.
Returns
-------
bases : np.ndarray of shape (n_bases, length)
"""
t = np.arange(length, dtype=float)
bases = []
# Generate periods logarithmically spaced
periods = np.logspace(np.log10(min_period), np.log10(min(max_period, length // 2)), n_bases // 2)
for period in periods:
freq = 2 * np.pi / period
# Sine and cosine at this frequency
bases.append(np.sin(freq * t))
bases.append(np.cos(freq * t))
# Harmonics
if len(bases) < n_bases:
bases.append(np.sin(2 * freq * t))
if len(bases) < n_bases:
bases.append(np.cos(2 * freq * t))
# Multi-harmonic combinations
rng = np.random.RandomState(123)
while len(bases) < n_bases:
n_harmonics = rng.randint(2, 5)
base_period = rng.uniform(min_period, max_period)
combo = np.zeros(length)
for h in range(1, n_harmonics + 1):
amp = rng.uniform(0.5, 1.5) / h
phase = rng.uniform(0, 2 * np.pi)
combo += amp * np.sin(h * 2 * np.pi / base_period * t + phase)
bases.append(combo)
bases = np.array(bases[:n_bases])
# Normalize
norms = np.linalg.norm(bases, axis=1, keepdims=True) + 1e-8
return bases / norms
def build_basis_library(
length: int,
config: Optional[SLLibConfig] = None,
) -> Tuple[np.ndarray, np.ndarray, Dict[str, Any]]:
"""Build the basis function library.
Parameters
----------
length : int
Length of the time series.
config : SLLibConfig, optional
Configuration for library generation.
Returns
-------
trend_bases : np.ndarray of shape (n_trend, length)
seasonal_bases : np.ndarray of shape (n_seasonal, length)
metadata : dict
Library metadata.
"""
cfg = config or SLLibConfig()
trend_bases = _generate_polynomial_bases(
length,
cfg.n_trend_bases,
max_degree=cfg.max_poly_degree,
)
seasonal_bases = _generate_sinusoidal_bases(
length,
cfg.n_seasonal_bases,
min_period=cfg.min_period,
max_period=cfg.max_period,
)
metadata = {
'length': length,
'n_trend': trend_bases.shape[0],
'n_seasonal': seasonal_bases.shape[0],
}
return trend_bases, seasonal_bases, metadata
def _build_faiss_index(bases: np.ndarray) -> Any:
"""Build a FAISS index for the basis library.
Parameters
----------
bases : np.ndarray of shape (n_bases, length)
Basis functions as feature vectors.
Returns
-------
index : faiss.IndexFlatIP
FAISS inner product index.
"""
if not _HAS_FAISS:
return None
# Normalize for inner product search
bases_norm = bases / (np.linalg.norm(bases, axis=1, keepdims=True) + 1e-8)
bases_norm = bases_norm.astype(np.float32)
d = bases_norm.shape[1]
index = faiss.IndexFlatIP(d)
index.add(bases_norm)
return index
def _search_candidates_faiss(
query: np.ndarray,
index: Any,
k: int,
) -> np.ndarray:
"""Search for k nearest basis candidates using FAISS."""
query_norm = query / (np.linalg.norm(query) + 1e-8)
query_norm = query_norm.astype(np.float32).reshape(1, -1)
_, indices = index.search(query_norm, k)
return indices[0]
def _search_candidates_numpy(
query: np.ndarray,
bases: np.ndarray,
k: int,
) -> np.ndarray:
"""Fallback search using numpy correlation."""
query_norm = query / (np.linalg.norm(query) + 1e-8)
bases_norm = bases / (np.linalg.norm(bases, axis=1, keepdims=True) + 1e-8)
# Inner products
scores = bases_norm @ query_norm
indices = np.argsort(-np.abs(scores))[:k]
return indices
def _sparse_regression(
y: np.ndarray,
B: np.ndarray,
lambda_l1: float = 0.01,
max_iter: int = 100,
) -> np.ndarray:
"""Solve sparse regression: min ||y - Bc||² + λ||c||₁
Uses iteratively reweighted least squares (IRLS) approximation.
"""
# Expect B shape (length, n_bases)
n_bases = B.shape[1]
if n_bases == 0:
return np.array([])
# Initial non-negative least squares (simple but works)
# For speed, use OLS then threshold
BT = B.T
BTB = BT @ B
BTy = BT @ y
# Add small regularization for stability
reg = lambda_l1 * np.eye(BTB.shape[0])
try:
c = np.linalg.solve(BTB + reg, BTy)
except np.linalg.LinAlgError:
c = np.linalg.lstsq(BTB + reg, BTy, rcond=None)[0]
# Soft threshold for L1
threshold = lambda_l1 * 0.5
c = np.sign(c) * np.maximum(np.abs(c) - threshold, 0)
return c
def sl_lib_decompose(
y: np.ndarray,
config: Optional[Dict[str, Any]] = None,
fs: float = 1.0,
meta: Optional[Dict[str, Any]] = None,
) -> "DecompResult":
"""SL-LIB decomposition using basis library and FAISS selection.
Parameters
----------
y : np.ndarray
Input time series.
config : dict, optional
Configuration for the method.
fs : float
Sampling frequency.
meta : dict, optional
Metadata from scenario.
Returns
-------
DecompResult
Decomposition result.
"""
from .decomp_methods import DecompResult
y_arr = np.asarray(y, dtype=float).ravel()
n = len(y_arr)
cfg_dict = dict(config or {})
# Build config
lib_cfg = SLLibConfig(
library_size=int(cfg_dict.get('library_size', 500)),
n_trend_bases=int(cfg_dict.get('n_trend_bases', 200)),
n_seasonal_bases=int(cfg_dict.get('n_seasonal_bases', 300)),
n_candidates=int(cfg_dict.get('n_candidates', 100)), # v1.1.0
sparsity_lambda=float(cfg_dict.get('sparsity_lambda', 0.001)), # v1.1.0
max_poly_degree=int(cfg_dict.get('max_poly_degree', 5)),
min_period=int(cfg_dict.get('min_period', 4)),
max_period=int(cfg_dict.get('max_period', min(128, n // 2))),
)
# Build library
trend_bases, seasonal_bases, lib_meta = build_basis_library(n, lib_cfg)
# Normalize input for search
y_centered = y_arr - np.mean(y_arr)
y_norm = y_centered / (np.std(y_centered) + 1e-8)
# Step 1: Find trend candidates and fit trend
if _HAS_FAISS:
trend_index = _build_faiss_index(trend_bases)
trend_cand_idx = _search_candidates_faiss(
y_norm, trend_index, min(lib_cfg.n_candidates, trend_bases.shape[0])
)
else:
trend_cand_idx = _search_candidates_numpy(
y_norm, trend_bases, min(lib_cfg.n_candidates, trend_bases.shape[0])
)
B_trend = trend_bases[trend_cand_idx].T
c_trend = _sparse_regression(y_arr, B_trend, lib_cfg.sparsity_lambda)
if len(c_trend) > 0:
trend = B_trend @ c_trend
else:
trend = np.zeros(n)
# Step 2: Find seasonal candidates on residual
residual_after_trend = y_arr - trend
if _HAS_FAISS:
seasonal_index = _build_faiss_index(seasonal_bases)
seasonal_cand_idx = _search_candidates_faiss(
residual_after_trend, seasonal_index, min(lib_cfg.n_candidates, seasonal_bases.shape[0])
)
else:
seasonal_cand_idx = _search_candidates_numpy(
residual_after_trend, seasonal_bases, min(lib_cfg.n_candidates, seasonal_bases.shape[0])
)
B_seasonal = seasonal_bases[seasonal_cand_idx].T
c_seasonal = _sparse_regression(residual_after_trend, B_seasonal, lib_cfg.sparsity_lambda)
if len(c_seasonal) > 0:
seasonal = B_seasonal @ c_seasonal
else:
seasonal = np.zeros(n)
# Ensure seasonal is zero-mean
seasonal = seasonal - np.mean(seasonal)
# Final residual
residual = y_arr - trend - seasonal
extra = {
'method': 'sl_lib',
'n_trend_candidates': len(trend_cand_idx),
'n_seasonal_candidates': len(seasonal_cand_idx),
'n_active_trend': int(np.sum(np.abs(c_trend) > 1e-8)) if len(c_trend) > 0 else 0,
'n_active_seasonal': int(np.sum(np.abs(c_seasonal) > 1e-8)) if len(c_seasonal) > 0 else 0,
'used_faiss': _HAS_FAISS,
}
return DecompResult(
trend=trend,
season=seasonal,
residual=residual,
extra=extra,
)
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