""" Wavelet band decomposition (CWT + synchrosqueezed variant), ported near-verbatim from c:\\DataS\\InstrumentSimulator\\backend\\app\\wavelet.py (project "Macro Causal Lab"). No project-specific dependencies — pure numpy/ssqueezepy, safe to call from any service. """ import logging import warnings import numpy as np from ssqueezepy import cwt, icwt from ssqueezepy.utils.cwt_utils import center_frequency logger = logging.getLogger(__name__) MIN_SCALES_PER_BAND = 4 # Fixed period (days) lower-bounds for bands 0..5, independent of the analysis # window's length. Without this, dividing [scales.min(), scales.max()] into # num_levels *equal* log-spaced buckets means "band i" covers a totally # different real-world period range depending on how much history is fed in # (a longer window resolves longer scales, which shifts every intermediate # boundary upward) - so the same band index is not comparable across window # lengths. Anchoring to absolute day-periods keeps "band i" meaning the same # oscillation whether the window is 3 months or 3 years; only the last band's # upper bound stays open, since a longer window can genuinely resolve slower # cycles a short one cannot. CANONICAL_PERIOD_EDGES_DAYS = [0.3, 1.5, 4.0, 12.0, 35.0, 90.0] def _period_to_log_scale_fn(wavelet, scales, n, num_calib_points=16): """Build an interpolation from log(period_days) to log(scale) by sampling center_frequency at a handful of scales (not every scale - it's not vectorized and can be slow over hundreds/thousands of scales). """ log_scales_full = np.log(scales) calib_log_scales = np.linspace(log_scales_full.min(), log_scales_full.max(), min(num_calib_points, len(scales))) calib_periods = np.array([1 / center_frequency(wavelet, scale=float(np.exp(s)), N=n) for s in calib_log_scales]) calib_log_periods = np.log(calib_periods) def period_to_log_scale(period_days): return float(np.interp(np.log(period_days), calib_log_periods, calib_log_scales)) return period_to_log_scale def band_decompose( values: list[float], dates: list[str], num_levels: int = 4, wavelet: str = "gmw", ) -> dict: x = np.asarray(values, dtype=float) n = len(x) if n < 32: raise ValueError("Serie trop courte pour une analyse ondelette (32 points minimum).") x_mean = float(x.mean()) xc = x - x_mean Wx, scales = cwt(xc, wavelet=wavelet) log_scales = np.log(scales) period_to_log_scale = _period_to_log_scale_fn(wavelet, scales, n) period_edges = list(CANONICAL_PERIOD_EDGES_DAYS[:num_levels]) while len(period_edges) < num_levels: period_edges.append(period_edges[-1] * 2.5) # scales[0] = smallest scale = highest frequency = shortest period (impulses/noise); # scales[-1] = largest scale = lowest frequency = longest period (slow trend). bands = [] for i in range(num_levels): lo = period_to_log_scale(period_edges[i]) hi = period_to_log_scale(period_edges[i + 1]) if i + 1 < len(period_edges) else log_scales.max() mask = (log_scales >= lo) & (log_scales <= hi if i == num_levels - 1 else log_scales < hi) scales_band = scales[mask] reconstruction_failed = False if len(scales_band) >= MIN_SCALES_PER_BAND: try: recon = icwt(Wx[mask, :], wavelet=wavelet, scales=scales_band, x_len=n) except Exception: # Root-caused: icwt's internal scaletype inference recursively splits # `scales` looking for a log/linear transition point (infer_scaletype -> # logscale_transition_idx), and on a masked SUBSET of the original CWT # scales that recursive sub-slice can come out too short, crashing with # "attempt to get argmax of an empty sequence" instead of a clean error. # Confirmed by reproducing it directly against ssqueezepy 0.6.6: retrying # with a regenerated, exactly log-uniform array over the same range/count # sidesteps the fragile inference entirely (trivially satisfies its "is # this log-spaced" check) and reliably recovers a real reconstruction — # verified on 5 independently reproduced failures, all recovered. try: clean_scales = np.geomspace(scales_band.min(), scales_band.max(), len(scales_band)) recon = icwt(Wx[mask, :], wavelet=wavelet, scales=clean_scales, x_len=n) logger.warning( "band_decompose: icwt failed for band %d with original scales (n=%d, wavelet=%s) — " "recovered using a regenerated log-uniform scale array", i, len(scales_band), wavelet, ) except Exception: logger.warning( "band_decompose: icwt failed for band %d (n=%d scales, wavelet=%s) even after " "retry — falling back to a zero band", i, len(scales_band), wavelet, exc_info=True, ) recon = np.zeros(n) reconstruction_failed = True scale_lo, scale_hi = float(scales_band.min()), float(scales_band.max()) else: # Too few scales in this bucket for a stable reconstruction; report a # flat zero band (its content ends up folded into the residual) so the # band list always stays num_levels long. logger.warning( "band_decompose: only %d scale(s) in band %d (< %d minimum) — falling back to a zero band", len(scales_band), i, MIN_SCALES_PER_BAND, ) recon = np.zeros(n) reconstruction_failed = True scale_lo, scale_hi = float(np.exp(lo)), float(np.exp(hi)) freq_at_scale_hi = center_frequency(wavelet, scale=scale_hi, N=n) freq_at_scale_lo = center_frequency(wavelet, scale=scale_lo, N=n) period_low_days = round(1 / freq_at_scale_lo, 1) if freq_at_scale_lo else None period_high_days = round(1 / freq_at_scale_hi, 1) if freq_at_scale_hi else None label = ( f"{period_low_days}-{period_high_days}j" if period_low_days is not None and period_high_days is not None else f"bande {i + 1}" ) bands.append( { "index": i, "label": label, "period_low_days": period_low_days, "period_high_days": period_high_days, "series": [round(float(v), 6) for v in recon], "reconstruction_failed": reconstruction_failed, } ) reconstructed_total = x_mean + sum(np.array(band["series"]) for band in bands) residual = x - reconstructed_total return { "dates": dates, "original": [round(float(v), 6) for v in x], "mean": round(x_mean, 6), "bands": bands, "residual": [round(float(v), 6) for v in residual], "wavelet": wavelet, } def windowed_band_decompose( values: list[float], dates: list[str], window_size: int, num_levels: int = 4, wavelet: str = "gmw", ) -> dict: """Decompose a long series by running band_decompose independently on consecutive slices of `window_size` points, then concatenating the results. Each slice is analyzed on its own terms (own local mean, own CWT scale range), so precision near the reconstructed curve stays high even over a long history; the trade-off is a visible discontinuity at each slice boundary, which is acceptable for this diagnostic view. """ n = len(values) window_size = max(32, min(window_size, n)) if window_size else n if n <= window_size: result = band_decompose(values, dates, num_levels, wavelet) result["window_size"] = window_size result["chunks"] = 1 return result all_dates: list[str] = [] all_original: list[float] = [] all_residual: list[float] = [] band_series: list[list[float]] = [[] for _ in range(num_levels)] band_meta: list[dict | None] = [None] * num_levels band_failed: list[bool] = [False] * num_levels chunk_count = 0 start = 0 while start < n: end = min(start + window_size, n) if 0 < n - end < 32: # Don't leave a too-short trailing slice: fold the remainder in. end = n chunk = band_decompose(values[start:end], dates[start:end], num_levels, wavelet) chunk_count += 1 all_dates.extend(chunk["dates"]) all_original.extend(chunk["original"]) all_residual.extend(chunk["residual"]) for band in chunk["bands"]: band_series[band["index"]].extend(band["series"]) band_meta[band["index"]] = band # OR across chunks: if any slice couldn't reconstruct this band, flag the # whole concatenated series as unreliable rather than losing that signal # when a later chunk happens to succeed and overwrites band_meta. band_failed[band["index"]] = band_failed[band["index"]] or band.get("reconstruction_failed", False) start = end bands = [] for i in range(num_levels): meta = band_meta[i] or {"label": f"bande {i + 1}", "period_low_days": None, "period_high_days": None} bands.append( { "index": i, "label": meta["label"], "period_low_days": meta["period_low_days"], "period_high_days": meta["period_high_days"], "series": band_series[i], "reconstruction_failed": band_failed[i], } ) return { "dates": all_dates, "original": all_original, "mean": round(float(np.mean(all_original)), 6) if all_original else 0.0, "bands": bands, "residual": all_residual, "wavelet": wavelet, "window_size": window_size, "chunks": chunk_count, } def rolling_causal_bands( values: list[float], dates: list[str], start_idx: int, lookback: int, num_levels: int = 4, wavelet: str = "gmw", step: int = 1, ) -> dict: """Walk-forward band decomposition with no look-ahead: the band value reported for day `t` is computed from a CWT run only on the trailing `lookback` points ending at `t` (never anything after `t`). This is deliberately much slower than `band_decompose` (one CWT per day instead of one for the whole range) - that cost is the point: a single whole-range CWT lets every point "see" the entire future through the transform's global/symmetric support, which makes any backtest built on it meaningless (the peaks/troughs it finds were computed with hindsight). `step` > 1 re-runs the CWT every `step` days and holds the last computed value in between, trading fidelity for speed on long ranges. """ n = len(values) out_dates: list[str] = [] out_original: list[float] = [] band_series: list[list[float]] = [[] for _ in range(num_levels)] band_labels = [f"bande {i + 1}" for i in range(num_levels)] band_failed = [False] * num_levels last_tip: list[float] | None = None recomputations = 0 for t in range(start_idx, n): window_start = t - lookback + 1 if window_start < 0: continue # not enough trailing history yet for a full lookback window if last_tip is None or (t - start_idx) % step == 0: window_values = values[window_start:t + 1] window_dates = dates[window_start:t + 1] result = band_decompose(window_values, window_dates, num_levels, wavelet) last_tip = [band["series"][-1] for band in result["bands"]] band_labels = [band["label"] for band in result["bands"]] for i, band in enumerate(result["bands"]): band_failed[i] = band_failed[i] or band.get("reconstruction_failed", False) recomputations += 1 out_dates.append(dates[t]) out_original.append(values[t]) for i in range(num_levels): band_series[i].append(last_tip[i]) bands = [ { "index": i, "label": band_labels[i], "period_low_days": None, "period_high_days": None, "series": band_series[i], "reconstruction_failed": band_failed[i], } for i in range(num_levels) ] return { "dates": out_dates, "original": out_original, "bands": bands, "wavelet": wavelet, "lookback": lookback, "step": step, "recomputations": recomputations, } # --------------------------------------------------------------------------- # Synchrosqueezed variant (opt-in, method="ssq"). Everything above this line # is completely untouched by what follows: band_decompose, windowed_band_decompose # and rolling_causal_bands are the exact same functions used when method="cwt" # (the default), so any existing simulation re-run with its original config # hits the same code path and produces byte-identical results as before. # # Rationale: plain cwt/icwt smears a single true frequency's energy across # several neighboring scales (that's *why* band_decompose needs canonical period # edges and a minimum-scales guard - the boundaries are fuzzy). Synchrosqueezing # reassigns that smeared energy onto its estimated true instantaneous frequency # before splitting into bands, which should reduce cross-band leakage. It also # exposes two things plain cwt does not: per-band energy |Tx|^2 (how dominant # that cycle is *right now*, independent of direction) and a dominant-frequency # ridge (which cycle length is currently winning, tracked over time). # # Separate period edges from the cwt path's CANONICAL_PERIOD_EDGES_DAYS: with # fs=1.0 (one sample = one day, matching our daily data), ssq_cwt has a hard # Nyquist floor at exactly 2.0 days (max resolvable frequency = fs/2). The cwt # path's edges start at 0.3 days - below that floor, so reusing them here would # leave the fastest band permanently empty. This does mean "band 0" covers a # different absolute range under ssq than under cwt; that's an inherent # consequence of ssq's stricter frequency floor, not a rounding choice. # --------------------------------------------------------------------------- CANONICAL_PERIOD_EDGES_DAYS_SSQ = [2.0, 4.0, 10.0, 25.0, 60.0, 120.0] def band_decompose_ssq( values: list[float], dates: list[str], num_levels: int = 4, wavelet: str = "gmw", ) -> dict: from ssqueezepy import issq_cwt, ssq_cwt from ssqueezepy.ridge_extraction import extract_ridges x = np.asarray(values, dtype=float) n = len(x) if n < 32: raise ValueError("Serie trop courte pour une analyse ondelette (32 points minimum).") x_mean = float(x.mean()) xc = x - x_mean with warnings.catch_warnings(): warnings.simplefilter("ignore", RuntimeWarning) # fs=1.0: one sample = one day, so ssq_freqs comes out directly in # cycles/day and 1/ssq_freqs is a period in days with no extra # calibration step (unlike band_decompose's scale->period conversion, # which needs _period_to_log_scale_fn precisely because plain cwt's # scale axis has no absolute unit by itself). Tx, _Wx, ssq_freqs, _scales = ssq_cwt(xc, wavelet=wavelet, fs=1.0) ssq_freqs = np.asarray(ssq_freqs) periods = 1.0 / ssq_freqs period_edges = list(CANONICAL_PERIOD_EDGES_DAYS_SSQ[:num_levels]) while len(period_edges) < num_levels: period_edges.append(period_edges[-1] * 2.5) bands = [] for i in range(num_levels): lo_period = period_edges[i] hi_period = period_edges[i + 1] if i + 1 < len(period_edges) else float(periods.max()) mask = (periods >= lo_period) & (periods <= hi_period if i == num_levels - 1 else periods < hi_period) reconstruction_failed = False if mask.any(): try: Tx_band = np.zeros_like(Tx) Tx_band[mask, :] = Tx[mask, :] with warnings.catch_warnings(): warnings.simplefilter("ignore", RuntimeWarning) recon = np.real(issq_cwt(Tx_band, wavelet=wavelet)) except Exception: # Defensive, mirroring band_decompose: never let one band's edge # case fail the whole request — but log it and flag it (see # band_decompose's identical fix for why this used to be silent). logger.warning( "band_decompose_ssq: issq_cwt failed for band %d (wavelet=%s) — " "falling back to a zero band", i, wavelet, exc_info=True, ) recon = np.zeros(n) reconstruction_failed = True energy = np.sum(np.abs(Tx[mask, :]) ** 2, axis=0) else: logger.warning("band_decompose_ssq: no frequencies fall in band %d — falling back to a zero band", i) recon = np.zeros(n) energy = np.zeros(n) reconstruction_failed = True period_low_days = round(float(lo_period), 1) period_high_days = round(float(hi_period), 1) bands.append( { "index": i, "label": f"{period_low_days}-{period_high_days}j", "period_low_days": period_low_days, "period_high_days": period_high_days, "series": [round(float(v), 6) for v in recon], "energy": [round(float(v), 8) for v in energy], "reconstruction_failed": reconstruction_failed, } ) reconstructed_total = x_mean + sum(np.array(band["series"]) for band in bands) residual = x - reconstructed_total try: with warnings.catch_warnings(): warnings.simplefilter("ignore", RuntimeWarning) ridge_idxs = extract_ridges(Tx, ssq_freqs, n_ridges=1, bw=4) ridge_periods = 1.0 / ssq_freqs[ridge_idxs.ravel()] ridge_period_days = [round(float(v), 3) for v in ridge_periods] except Exception: ridge_period_days = [None] * n return { "dates": dates, "original": [round(float(v), 6) for v in x], "mean": round(x_mean, 6), "bands": bands, "residual": [round(float(v), 6) for v in residual], "wavelet": wavelet, "ridge_period_days": ridge_period_days, } def rolling_causal_bands_ssq( values: list[float], dates: list[str], start_idx: int, lookback: int, num_levels: int = 4, wavelet: str = "gmw", step: int = 1, ) -> dict: """Synchrosqueezed counterpart to rolling_causal_bands - identical walk-forward, no-look-ahead structure (same day-by-day trailing window, same step logic), just calling band_decompose_ssq instead of band_decompose. rolling_causal_bands itself is untouched. """ n = len(values) out_dates: list[str] = [] out_original: list[float] = [] band_series: list[list[float]] = [[] for _ in range(num_levels)] energy_series: list[list[float]] = [[] for _ in range(num_levels)] ridge_series: list[float | None] = [] band_labels = [f"bande {i + 1}" for i in range(num_levels)] band_failed = [False] * num_levels last_tip: list[float] | None = None last_energy_tip: list[float] | None = None last_ridge_tip: float | None = None recomputations = 0 for t in range(start_idx, n): window_start = t - lookback + 1 if window_start < 0: continue if last_tip is None or (t - start_idx) % step == 0: window_values = values[window_start:t + 1] window_dates = dates[window_start:t + 1] result = band_decompose_ssq(window_values, window_dates, num_levels, wavelet) last_tip = [band["series"][-1] for band in result["bands"]] last_energy_tip = [band["energy"][-1] for band in result["bands"]] last_ridge_tip = result["ridge_period_days"][-1] band_labels = [band["label"] for band in result["bands"]] for i, band in enumerate(result["bands"]): band_failed[i] = band_failed[i] or band.get("reconstruction_failed", False) recomputations += 1 out_dates.append(dates[t]) out_original.append(values[t]) for i in range(num_levels): band_series[i].append(last_tip[i]) energy_series[i].append(last_energy_tip[i]) ridge_series.append(last_ridge_tip) bands = [ { "index": i, "label": band_labels[i], "period_low_days": None, "period_high_days": None, "series": band_series[i], "energy": energy_series[i], "reconstruction_failed": band_failed[i], } for i in range(num_levels) ] return { "dates": out_dates, "original": out_original, "bands": bands, "wavelet": wavelet, "lookback": lookback, "step": step, "recomputations": recomputations, "method": "ssq", "ridge_period_days": ridge_series, } def _turning_points(series: list[float], smooth_days: int) -> list[tuple[int, int]]: """Indices (and new direction, +1/-1) where the sign of the `smooth_days`-lag slope of `series` flips. Using the raw day-to-day slope would flag noise as a "reversal"; lagging over a few days smooths that out.""" turns: list[tuple[int, int]] = [] prev_sign = 0 for t in range(smooth_days, len(series)): slope = series[t] - series[t - smooth_days] sign = 1 if slope > 0 else (-1 if slope < 0 else 0) if sign != 0: if prev_sign != 0 and sign != prev_sign: turns.append((t, sign)) prev_sign = sign return turns def _average_cycle_days(turn_points: list[tuple[int, int]]) -> float | None: """Empirical average gap (in days) between consecutive SAME-direction turning points — peak-to-peak or trough-to-trough, i.e. one full oscillation — measured from the actual reconstructed series rather than assumed from the band's theoretical period_low/high labels (which describe the wavelet scale bucket, not necessarily the real cycle length this specific window's price action produced). None if there aren't at least 2 same-direction turns to measure a gap from.""" peaks = [t for t, d in turn_points if d == -1] # a downturn = just passed a peak troughs = [t for t, d in turn_points if d == 1] # an upturn = just passed a trough gaps = [seq[i + 1] - seq[i] for seq in (peaks, troughs) for i in range(len(seq) - 1)] return sum(gaps) / len(gaps) if gaps else None def wavelet_reliability( values: list[float], dates: list[str], start_idx: int, lookback: int, num_levels: int = 4, wavelet: str = "gmw", method: str = "cwt", step: int = 1, smooth_days: int = 3, tolerance_pct: float = 0.10, min_confirm_horizon: int = 3, ) -> dict: """ For every turning point a CAUSAL (walk-forward, no look-ahead) decomposition flags — i.e. what a live signal would have shown on that date, using only data available up to then — checks whether redoing the decomposition later still shows a same-direction reversal near the original date. The fraction confirmed is a per-band confidence score: CWT/SSQ reconstructions are well known to be least reliable right at the edge of the available data — exactly where a live "the band just turned" reading gets made. A fixed confirm horizon (e.g. always +10 days) is meaningless across bands whose natural oscillation period can range from ~1 day to several weeks: 10 days is many cycles for a fast band (trivially "confirmed", inflating its score) but less than half a cycle for a slow one (never has time to actually turn back, deflating its score) — the exact pattern that shows up as fast bands scoring ~100% and the slow band scoring ~10% for no real reliability reason. Instead, per band: measure its own historical average peak-to-peak (or trough-to-trough) period from the causal series, and use `avg_cycle * (1 + tolerance_pct)` as a MAXIMUM horizon — a same-direction reversal confirms the original one if it shows up ANYWHERE in the forward window [original date, original date + that horizon], not just near one specific point in it. """ rolling_decomposer = rolling_causal_bands_ssq if method == "ssq" else rolling_causal_bands batch_decompose = band_decompose_ssq if method == "ssq" else band_decompose causal = rolling_decomposer( values, dates, start_idx=start_idx, lookback=lookback, num_levels=num_levels, wavelet=wavelet, step=step, ) causal_dates = causal["dates"] date_to_global = {d: i for i, d in enumerate(dates)} bands_out = [] for band in causal["bands"]: turn_points = _turning_points(band["series"], smooth_days) avg_cycle_days = _average_cycle_days(turn_points) if avg_cycle_days is None: bands_out.append({ "label": band["label"], "n_tested": 0, "n_confirmed": 0, "confidence_pct": None, "avg_cycle_days": None, "confirm_horizon": None, "turns": [], }) continue confirm_horizon = max(min_confirm_horizon, round(avg_cycle_days * (1 + tolerance_pct))) tested = [] for t, direction in turn_points: d_date = causal_dates[t] g_idx = date_to_global.get(d_date) if g_idx is None or g_idx + confirm_horizon >= len(values): continue # not enough real future data yet to judge this one end_idx = g_idx + confirm_horizon window_start = end_idx - lookback + 1 if window_start < 0: continue window_values = values[window_start:end_idx + 1] window_dates = dates[window_start:end_idx + 1] try: hindsight = batch_decompose(window_values, window_dates, num_levels, wavelet) except ValueError: continue h_series = hindsight["bands"][band["index"]]["series"] # Forward-only window [original date, original date + horizon] — the reversal # can be confirmed anywhere in it, not just near a specific point. window_values # was built to end exactly at end_idx = g_idx + confirm_horizon, so h_series's # last index already IS "original date + horizon"; no separate bound needed. d_pos = g_idx - window_start hindsight_turns = _turning_points(h_series, smooth_days) matches = [idx for idx, new_dir in hindsight_turns if idx >= d_pos and new_dir == direction] confirmed = bool(matches) # Actual delay = how many days after the original date the confirming reversal # showed up (earliest match) — compared against avg_cycle_days below to check # whether "one cycle" is actually a well-calibrated horizon, or systematically # too long/short relative to how quickly a real reversal actually confirms. actual_delay = None height_diff = None if confirmed: confirm_idx = min(matches) actual_delay = confirm_idx - d_pos # Direction agreeing doesn't mean the peak/trough had the same amplitude — # the live (causal) reading can be a real reversal but distorted in height by # edge effects. Compare the band's own value at the original causal turning # point against its value at the confirming point in the hindsight # reconstruction (same units as the band, e.g. price terms). height_diff = abs(band["series"][t] - h_series[confirm_idx]) tested.append({ "date": d_date, "confirmed": confirmed, "actual_delay_days": actual_delay, "height_diff": height_diff, }) n_tested = len(tested) n_confirmed = sum(1 for t in tested if t["confirmed"]) delays = [t["actual_delay_days"] for t in tested if t["actual_delay_days"] is not None] avg_actual_delay = round(sum(delays) / len(delays), 1) if delays else None calibration_gap = round(sum(abs(avg_cycle_days - d) for d in delays) / len(delays), 1) if delays else None heights = [t["height_diff"] for t in tested if t["height_diff"] is not None] avg_height_diff = round(sum(heights) / len(heights), 6) if heights else None bands_out.append({ "label": band["label"], "n_tested": n_tested, "n_confirmed": n_confirmed, "confidence_pct": round(n_confirmed / n_tested * 100, 1) if n_tested else None, "avg_cycle_days": round(avg_cycle_days, 1), "confirm_horizon": confirm_horizon, "avg_actual_delay_days": avg_actual_delay, "calibration_gap_days": calibration_gap, "avg_height_diff": avg_height_diff, "turns": tested, }) return { "bands": bands_out, "smooth_days": smooth_days, "tolerance_pct": tolerance_pct, "method": method, }