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2026-07-09 05:08:16 +08:00

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"""
Comparison tests: ferro_ta vs pandas-ta (Priority 4 - requires pandas-ta).
This module validates ferro_ta against pandas-ta for indicators, using 500-bar data
for proper convergence of EMA-seeded indicators. Documents known formula differences
and expected tolerances.
Requirements
------------
Install pandas-ta before running these tests::
pip install pandas-ta
The tests are automatically skipped when pandas-ta is not installed.
"""
from __future__ import annotations
import numpy as np
import pytest
# ---------------------------------------------------------------------------
# Skip the whole module when pandas-ta is not available
# ---------------------------------------------------------------------------
pandas_ta = pytest.importorskip(
"pandas_ta", reason="pandas-ta not installed; skipping comparison tests"
)
pd = pytest.importorskip("pandas", reason="pandas required for pandas-ta")
import ferro_ta # noqa: E402
# ---------------------------------------------------------------------------
# Shared test data from conftest.py
# ---------------------------------------------------------------------------
# Use shared 500-bar fixture from conftest.py
# ---------------------------------------------------------------------------
# Helpers
# ---------------------------------------------------------------------------
def _nan_count(arr: np.ndarray) -> int:
"""Return count of NaN values."""
return int(np.sum(np.isnan(arr)))
def _valid_mask(*arrays: np.ndarray) -> np.ndarray:
"""Return boolean mask for positions where *all* arrays are finite."""
mask = np.ones(len(arrays[0]), dtype=bool)
for a in arrays:
mask &= ~np.isnan(a)
return mask
def _allclose(
a: np.ndarray, b: np.ndarray, atol: float = 1e-6, tail_fraction: float = 1.0
) -> bool:
"""Compare arrays within tolerance, optionally only comparing tail.
Parameters
----------
a, b : np.ndarray
Arrays to compare
atol : float
Absolute tolerance
tail_fraction : float
Fraction of tail to compare (1.0 = all, 0.3 = last 30%)
Returns
-------
bool
True if arrays match within tolerance
"""
mask = _valid_mask(a, b)
if not mask.any():
return False
if tail_fraction < 1.0:
# Only compare last tail_fraction of data
n = len(a)
start_idx = int(n * (1 - tail_fraction))
mask[:start_idx] = False
if not mask.any():
return False
return bool(np.allclose(a[mask], b[mask], atol=atol))
# ---------------------------------------------------------------------------
# Overlap Studies
# ---------------------------------------------------------------------------
class TestSMAVsPandasTA:
"""SMA — Exact match (deterministic)."""
def test_sma_exact_match(self, ohlcv_500):
"""SMA should match pandas-ta exactly."""
close = ohlcv_500["close"]
period = 20
ft = ferro_ta.SMA(close, timeperiod=period)
pt = pandas_ta.sma(pd.Series(close), length=period).to_numpy()
assert _allclose(ft, pt, atol=1e-8)
class TestEMAVsPandasTA:
"""EMA — Tail 30% match (seed difference).
ferro_ta starts EMA from bar 0, pandas-ta may use SMA seed.
After 350+ bars of decay, values should converge.
"""
def test_ema_tail_convergence(self, ohlcv_500):
"""EMA should converge in tail 30% of data."""
close = ohlcv_500["close"]
period = 20
ft = ferro_ta.EMA(close, timeperiod=period)
pt = pandas_ta.ema(pd.Series(close), length=period).to_numpy()
# Compare only last 30%
assert _allclose(ft, pt, atol=1e-4, tail_fraction=0.3)
def test_ema_shorter_period_tighter(self, ohlcv_500):
"""Shorter period EMA should have tighter convergence."""
close = ohlcv_500["close"]
period = 10
ft = ferro_ta.EMA(close, timeperiod=period)
pt = pandas_ta.ema(pd.Series(close), length=period).to_numpy()
# Shorter period converges faster
assert _allclose(ft, pt, atol=1e-5, tail_fraction=0.3)
class TestWMAVsPandasTA:
"""WMA — Exact match (deterministic)."""
def test_wma_exact_match(self, ohlcv_500):
"""WMA should match pandas-ta exactly."""
close = ohlcv_500["close"]
period = 20
ft = ferro_ta.WMA(close, timeperiod=period)
pt = pandas_ta.wma(pd.Series(close), length=period).to_numpy()
assert _allclose(ft, pt, atol=1e-8)
class TestBBANDSVsPandasTA:
"""BBANDS — Approximate match (ferro_ta uses population std; pandas-ta uses sample std)."""
def test_bbands_approximate_match(self, ohlcv_500):
"""BBANDS middle band matches exactly; upper/lower match within std-formula tolerance.
ferro_ta follows TA-Lib convention: std = population std (ddof=0).
pandas-ta uses sample std (ddof=1). Middle band (SMA) is identical.
Upper/lower differ by a sqrt(N/(N-1)) factor (~0.5% for N=20), capped at atol=0.1.
"""
close = ohlcv_500["close"]
period = 20
ft_upper, ft_middle, ft_lower = ferro_ta.BBANDS(
close, timeperiod=period, nbdevup=2.0, nbdevdn=2.0
)
# pandas-ta >= 0.3 returns columns named BBL_{period}_{std}_{std}
pt_bbands = pandas_ta.bbands(pd.Series(close), length=period, std=2.0)
# Locate columns robustly (column names vary across pandas-ta versions)
lower_col = next(c for c in pt_bbands.columns if c.startswith("BBL_"))
middle_col = next(c for c in pt_bbands.columns if c.startswith("BBM_"))
upper_col = next(c for c in pt_bbands.columns if c.startswith("BBU_"))
pt_lower = pt_bbands[lower_col].to_numpy()
pt_middle = pt_bbands[middle_col].to_numpy()
pt_upper = pt_bbands[upper_col].to_numpy()
# Middle band (SMA) must be identical
assert _allclose(ft_middle, pt_middle, atol=1e-8), (
"BBands middle (SMA) must match"
)
# Upper/lower: differ due to ddof=0 vs ddof=1
assert _allclose(ft_upper, pt_upper, atol=0.1)
assert _allclose(ft_lower, pt_lower, atol=0.1)
class TestTRIMAVsPandasTA:
"""TRIMA — Approximate match (implementations differ slightly in boundary handling)."""
def test_trima_approximate_match(self, ohlcv_500):
"""TRIMA should be close to pandas-ta (both are SMA-of-SMA but boundary handling differs).
Note: ferro_ta follows TA-Lib's TRIMA formula while pandas-ta uses a slightly
different implementation. Observed max difference is ~0.4 price units on
typical equity prices (~100), which is < 0.5%. We verify tail convergence
with atol=0.5 and confirm correct NaN warm-up length.
"""
close = ohlcv_500["close"]
period = 20
ft = ferro_ta.TRIMA(close, timeperiod=period)
pt = pandas_ta.trima(pd.Series(close), length=period).to_numpy()
assert _allclose(ft, pt, atol=0.5, tail_fraction=0.5)
class TestMACDVsPandasTA:
"""MACD — Tail 30% match (EMA seed difference)."""
def test_macd_tail_convergence(self, ohlcv_500):
"""MACD should converge in tail 30% of data."""
close = ohlcv_500["close"]
ft_macd, ft_signal, ft_hist = ferro_ta.MACD(
close, fastperiod=12, slowperiod=26, signalperiod=9
)
# pandas-ta returns DataFrame
pt_macd = pandas_ta.macd(pd.Series(close), fast=12, slow=26, signal=9)
pt_macd_line = pt_macd["MACD_12_26_9"].to_numpy()
pt_signal_line = pt_macd["MACDs_12_26_9"].to_numpy()
pt_hist = pt_macd["MACDh_12_26_9"].to_numpy()
# Compare tail 30%
assert _allclose(ft_macd, pt_macd_line, atol=1e-2, tail_fraction=0.3)
assert _allclose(ft_signal, pt_signal_line, atol=1e-2, tail_fraction=0.3)
assert _allclose(ft_hist, pt_hist, atol=1e-2, tail_fraction=0.3)
# ---------------------------------------------------------------------------
# Momentum Indicators
# ---------------------------------------------------------------------------
class TestRSIVsPandasTA:
"""RSI — Tail 30% match (Wilder seed difference)."""
def test_rsi_tail_convergence(self, ohlcv_500):
"""RSI should converge in tail 30% of data."""
close = ohlcv_500["close"]
period = 14
ft = ferro_ta.RSI(close, timeperiod=period)
pt = pandas_ta.rsi(pd.Series(close), length=period).to_numpy()
assert _allclose(ft, pt, atol=1e-3, tail_fraction=0.3)
class TestSTOCHVsPandasTA:
"""STOCH — Tail 30% match."""
def test_stoch_tail_convergence(self, ohlcv_500):
"""Stochastic should converge in tail 30% of data."""
high = ohlcv_500["high"]
low = ohlcv_500["low"]
close = ohlcv_500["close"]
ft_slowk, ft_slowd = ferro_ta.STOCH(
high, low, close, fastk_period=14, slowk_period=3, slowd_period=3
)
# pandas-ta returns DataFrame
pt_stoch = pandas_ta.stoch(
pd.Series(high), pd.Series(low), pd.Series(close), k=14, d=3, smooth_k=3
)
pt_slowk = pt_stoch["STOCHk_14_3_3"].to_numpy()
pt_slowd = pt_stoch["STOCHd_14_3_3"].to_numpy()
assert _allclose(ft_slowk, pt_slowk, atol=1e-2, tail_fraction=0.3)
assert _allclose(ft_slowd, pt_slowd, atol=1e-2, tail_fraction=0.3)
class TestCCIVsPandasTA:
"""CCI — Exact match (deterministic rolling formula)."""
def test_cci_exact_match(self, ohlcv_500):
"""CCI should match manually-computed reference (pandas-ta CCI has a formula bug)."""
high = ohlcv_500["high"]
low = ohlcv_500["low"]
close = ohlcv_500["close"]
period = 14
ft = ferro_ta.CCI(high, low, close, timeperiod=period)
# Compute CCI manually: (TP - SMA(TP)) / (0.015 * MeanAbsDev(TP))
tp = (pd.Series(high) + pd.Series(low) + pd.Series(close)) / 3.0
mean_tp = tp.rolling(period).mean()
mad_tp = tp.rolling(period).apply(
lambda x: np.mean(np.abs(x - x.mean())), raw=True
)
pt = ((tp - mean_tp) / (0.015 * mad_tp)).to_numpy()
assert _allclose(ft, pt, atol=1e-8)
class TestWILLRVsPandasTA:
"""WILLR — Exact match (deterministic)."""
def test_willr_exact_match(self, ohlcv_500):
"""Williams %R should match pandas-ta exactly."""
high = ohlcv_500["high"]
low = ohlcv_500["low"]
close = ohlcv_500["close"]
period = 14
ft = ferro_ta.WILLR(high, low, close, timeperiod=period)
df = pd.DataFrame({"high": high, "low": low, "close": close})
pt = df.ta.willr(length=period).to_numpy()
assert _allclose(ft, pt, atol=1e-8)
class TestMOMVsPandasTA:
"""MOM — Exact match."""
def test_mom_exact_match(self, ohlcv_500):
"""MOM should match pandas-ta exactly."""
close = ohlcv_500["close"]
period = 10
ft = ferro_ta.MOM(close, timeperiod=period)
pt = pandas_ta.mom(pd.Series(close), length=period).to_numpy()
assert _allclose(ft, pt, atol=1e-8)
class TestROCVsPandasTA:
"""ROC — Exact match."""
def test_roc_exact_match(self, ohlcv_500):
"""ROC should match pandas-ta exactly."""
close = ohlcv_500["close"]
period = 10
ft = ferro_ta.ROC(close, timeperiod=period)
pt = pandas_ta.roc(pd.Series(close), length=period).to_numpy()
assert _allclose(ft, pt, atol=1e-8)
class TestMFIVsPandasTA:
"""MFI — Exact match."""
def test_mfi_exact_match(self, ohlcv_500):
"""MFI should match pandas-ta exactly."""
high = ohlcv_500["high"]
low = ohlcv_500["low"]
close = ohlcv_500["close"]
volume = ohlcv_500["volume"]
period = 14
ft = ferro_ta.MFI(high, low, close, volume, timeperiod=period)
df = pd.DataFrame({"high": high, "low": low, "close": close, "volume": volume})
pt = df.ta.mfi(length=period).to_numpy()
assert _allclose(ft, pt, atol=1e-8)
class TestAROONVsPandasTA:
"""AROON — Exact match."""
def test_aroon_exact_match(self, ohlcv_500):
"""AROON should match pandas-ta exactly."""
high = ohlcv_500["high"]
low = ohlcv_500["low"]
period = 14
ft_down, ft_up = ferro_ta.AROON(high, low, timeperiod=period)
df = pd.DataFrame({"high": high, "low": low})
pt_aroon = df.ta.aroon(length=period)
pt_down = pt_aroon[f"AROOND_{period}"].to_numpy()
pt_up = pt_aroon[f"AROONU_{period}"].to_numpy()
assert _allclose(ft_down, pt_down, atol=1e-8)
assert _allclose(ft_up, pt_up, atol=1e-8)
# ---------------------------------------------------------------------------
# Volume/Volatility
# ---------------------------------------------------------------------------
class TestOBVVsPandasTA:
"""OBV — Incremental match (offset constant, verify diffs)."""
def test_obv_incremental_match(self, ohlcv_500):
"""OBV differences should match (absolute values may have offset)."""
close = ohlcv_500["close"]
volume = ohlcv_500["volume"]
ft = ferro_ta.OBV(close, volume)
df = pd.DataFrame({"close": close, "volume": volume})
pt = df.ta.obv().to_numpy()
# OBV can have different starting values, compare differences
ft_diff = np.diff(ft)
pt_diff = np.diff(pt)
# Remove NaN values from comparison
mask = ~np.isnan(ft_diff) & ~np.isnan(pt_diff)
assert np.allclose(ft_diff[mask], pt_diff[mask], atol=1e-8)
class TestATRVsPandasTA:
"""ATR — Tail 30% match (Wilder seed difference)."""
def test_atr_tail_convergence(self, ohlcv_500):
"""ATR should converge in tail 30% of data."""
high = ohlcv_500["high"]
low = ohlcv_500["low"]
close = ohlcv_500["close"]
period = 14
ft = ferro_ta.ATR(high, low, close, timeperiod=period)
df = pd.DataFrame({"high": high, "low": low, "close": close})
pt = df.ta.atr(length=period).to_numpy()
assert _allclose(ft, pt, atol=1e-2, tail_fraction=0.3)
class TestADXVsPandasTA:
"""ADX — Tail 30% match (two levels of Wilder smoothing)."""
def test_adx_tail_convergence(self, ohlcv_500):
"""ADX should converge in tail 30% of data."""
high = ohlcv_500["high"]
low = ohlcv_500["low"]
close = ohlcv_500["close"]
period = 14
ft = ferro_ta.ADX(high, low, close, timeperiod=period)
df = pd.DataFrame({"high": high, "low": low, "close": close})
pt = df.ta.adx(length=period)[f"ADX_{period}"].to_numpy()
assert _allclose(ft, pt, atol=5e-2, tail_fraction=0.3)
# ---------------------------------------------------------------------------
# Extended Indicators (no prior validation)
# ---------------------------------------------------------------------------
class TestVWAPVsPandasTA:
"""VWAP — Validate rolling VWAP against a reference numpy implementation."""
def test_vwap_rolling_match(self, ohlcv_500):
"""Rolling VWAP should match a reference implementation using numpy."""
high = ohlcv_500["high"]
low = ohlcv_500["low"]
close = ohlcv_500["close"]
volume = ohlcv_500["volume"]
period = 20
ft = ferro_ta.VWAP(high, low, close, volume, timeperiod=period)
# Reference: rolling VWAP = sum(typical_price * volume, N) / sum(volume, N)
tp = (np.array(high) + np.array(low) + np.array(close)) / 3.0
vol = np.array(volume)
n = len(tp)
ref = np.full(n, np.nan)
for i in range(period - 1, n):
w = tp[i - period + 1 : i + 1]
v = vol[i - period + 1 : i + 1]
ref[i] = np.dot(w, v) / v.sum()
assert _allclose(ft, ref, atol=1e-8)
class TestDONCHIANVsPandasTA:
"""DONCHIAN — Exact match (rolling max(H), min(L), mean)."""
def test_donchian_exact_match(self, ohlcv_500):
"""Donchian Channels should match pandas-ta exactly."""
high = ohlcv_500["high"]
low = ohlcv_500["low"]
period = 20
ft_upper, ft_middle, ft_lower = ferro_ta.DONCHIAN(high, low, timeperiod=period)
df = pd.DataFrame({"high": high, "low": low, "close": ohlcv_500["close"]})
pt_donchian = df.ta.donchian(lower_length=period, upper_length=period)
pt_lower = pt_donchian[f"DCL_{period}_{period}"].to_numpy()
pt_middle = pt_donchian[f"DCM_{period}_{period}"].to_numpy()
pt_upper = pt_donchian[f"DCU_{period}_{period}"].to_numpy()
assert _allclose(ft_upper, pt_upper, atol=1e-8)
assert _allclose(ft_middle, pt_middle, atol=1e-8)
assert _allclose(ft_lower, pt_lower, atol=1e-8)
class TestHULL_MAVsPandasTA:
"""HULL_MA — Exact match (WMA composition: deterministic)."""
def test_hull_ma_exact_match(self, ohlcv_500):
"""Hull MA should match pandas-ta exactly."""
close = ohlcv_500["close"]
period = 16
ft = ferro_ta.HULL_MA(close, timeperiod=period)
pt = pandas_ta.hma(pd.Series(close), length=period).to_numpy()
assert _allclose(ft, pt, atol=1e-8)
class TestICHIMOKUVsPandasTA:
"""ICHIMOKU — Exact match for tenkan/kijun (rolling midpoint formula)."""
def test_ichimoku_tenkan_kijun_match(self, ohlcv_500):
"""Ichimoku tenkan and kijun should match pandas-ta."""
high = ohlcv_500["high"]
low = ohlcv_500["low"]
close = ohlcv_500["close"]
ft_tenkan, ft_kijun, ft_senkou_a, ft_senkou_b, ft_chikou = ferro_ta.ICHIMOKU(
high,
low,
close,
tenkan_period=9,
kijun_period=26,
senkou_b_period=52,
displacement=26,
)
df = pd.DataFrame({"high": high, "low": low, "close": close})
pt_ichimoku = df.ta.ichimoku(tenkan=9, kijun=26, senkou=52)[0]
pt_tenkan = pt_ichimoku["ITS_9"].to_numpy()
pt_kijun = pt_ichimoku["IKS_26"].to_numpy()
assert _allclose(ft_tenkan, pt_tenkan, atol=1e-8)
assert _allclose(ft_kijun, pt_kijun, atol=1e-8)
class TestKELTNER_CHANNELSVsPandasTA:
"""KELTNER_CHANNELS — Tail 30% match (Middle=EMA, bands=EMA±mult*ATR)."""
def test_keltner_tail_convergence(self, ohlcv_500):
"""Keltner Channels should converge in tail 30%."""
high = ohlcv_500["high"]
low = ohlcv_500["low"]
close = ohlcv_500["close"]
period = 20
atr_period = 10
multiplier = 2.0
ft_upper, ft_middle, ft_lower = ferro_ta.KELTNER_CHANNELS(
high,
low,
close,
timeperiod=period,
atr_period=atr_period,
multiplier=multiplier,
)
# Compute manually using pandas_ta EMA and ATR to match ferro_ta's exact formula
pt_ema = pandas_ta.ema(pd.Series(close), length=period).to_numpy()
pt_atr = pandas_ta.atr(
pd.Series(high), pd.Series(low), pd.Series(close), length=atr_period
).to_numpy()
pt_upper = pt_ema + multiplier * pt_atr
pt_middle = pt_ema
pt_lower = pt_ema - multiplier * pt_atr
assert _allclose(ft_upper, pt_upper, atol=1e-2, tail_fraction=0.3)
assert _allclose(ft_middle, pt_middle, atol=1e-2, tail_fraction=0.3)
assert _allclose(ft_lower, pt_lower, atol=1e-2, tail_fraction=0.3)
class TestVWMAVsPandasTA:
"""VWMA — Exact match (sum(c*v)/sum(v))."""
def test_vwma_exact_match(self, ohlcv_500):
"""VWMA should match pandas-ta exactly."""
close = ohlcv_500["close"]
volume = ohlcv_500["volume"]
period = 20
ft = ferro_ta.VWMA(close, volume, timeperiod=period)
df = pd.DataFrame({"close": close, "volume": volume})
pt = df.ta.vwma(length=period).to_numpy()
assert _allclose(ft, pt, atol=1e-8)
class TestCHOPPINESS_INDEXVsPandasTA:
"""CHOPPINESS_INDEX — Close match (log10-based formula)."""
def test_choppiness_index_close_match(self, ohlcv_500):
"""Choppiness Index should match pandas-ta closely."""
high = ohlcv_500["high"]
low = ohlcv_500["low"]
close = ohlcv_500["close"]
period = 14
ft = ferro_ta.CHOPPINESS_INDEX(high, low, close, timeperiod=period)
df = pd.DataFrame({"high": high, "low": low, "close": close})
pt = df.ta.chop(length=period).to_numpy()
assert _allclose(ft, pt, atol=1e-4)
class TestSUPERTRENDVsPandasTA:
"""SUPERTREND — Direction >80% agreement (path-dependent, ATR seeding differs)."""
def test_supertrend_direction_agreement(self, ohlcv_500):
"""SUPERTREND direction should agree >80% of the time."""
high = ohlcv_500["high"]
low = ohlcv_500["low"]
close = ohlcv_500["close"]
period = 7
multiplier = 3.0
ft_line, ft_dir = ferro_ta.SUPERTREND(
high, low, close, timeperiod=period, multiplier=multiplier
)
df = pd.DataFrame({"high": high, "low": low, "close": close})
pt_supertrend = df.ta.supertrend(length=period, multiplier=multiplier)
pt_dir = pt_supertrend[f"SUPERTd_{period}_{multiplier}"].to_numpy()
# Convert directions to same format (1 = up, -1 = down)
# pandas-ta: 1 = uptrend, -1 = downtrend
# ferro_ta: 1 = uptrend, -1 = downtrend (assuming same convention)
# Remove NaN values
mask = ~np.isnan(ft_dir) & ~np.isnan(pt_dir)
agreement_rate = np.mean(ft_dir[mask] == pt_dir[mask])
assert agreement_rate > 0.80, f"Direction agreement rate: {agreement_rate:.2%}"
class TestCHANDELIER_EXITVsPandasTA:
"""CHANDELIER_EXIT — Exact structure (rolling_max(H)-mult*ATR)."""
def test_chandelier_exit_structure_match(self, ohlcv_500):
"""Chandelier Exit should match pandas-ta structure."""
high = ohlcv_500["high"]
low = ohlcv_500["low"]
close = ohlcv_500["close"]
period = 22
multiplier = 3.0
ft_long, ft_short = ferro_ta.CHANDELIER_EXIT(
high, low, close, timeperiod=period, multiplier=multiplier
)
# Compute manually: long = rolling_max(H, n) - mult*ATR; short = rolling_min(L, n) + mult*ATR
pt_atr = pandas_ta.atr(
pd.Series(high), pd.Series(low), pd.Series(close), length=period
).to_numpy()
rolling_high = pd.Series(high).rolling(period).max().to_numpy()
rolling_low = pd.Series(low).rolling(period).min().to_numpy()
pt_long = rolling_high - multiplier * pt_atr
pt_short = rolling_low + multiplier * pt_atr
assert _allclose(ft_long, pt_long, atol=1e-2, tail_fraction=0.3)
assert _allclose(ft_short, pt_short, atol=1e-2, tail_fraction=0.3)
class TestPIVOT_POINTSVsPandasTA:
"""PIVOT_POINTS — Exact match for Classic (arithmetic formula)."""
def test_pivot_points_classic_exact(self, ohlcv_500):
"""Classic Pivot Points should match manually-computed reference."""
high = ohlcv_500["high"]
low = ohlcv_500["low"]
close = ohlcv_500["close"]
ft_pivot, ft_r1, ft_s1, ft_r2, ft_s2 = ferro_ta.PIVOT_POINTS(
high, low, close, method="classic"
)
# ferro_ta PIVOT_POINTS uses previous bar's H/L/C (1-bar forward shift).
# Reference values are computed from bar i-1 to match index i output.
pivot = np.empty_like(high, dtype=float)
pivot[0] = np.nan
pivot[1:] = (high[:-1] + low[:-1] + close[:-1]) / 3.0
r1 = np.empty_like(high, dtype=float)
r1[0] = np.nan
r1[1:] = 2 * pivot[1:] - low[:-1]
s1 = np.empty_like(high, dtype=float)
s1[0] = np.nan
s1[1:] = 2 * pivot[1:] - high[:-1]
r2 = np.empty_like(high, dtype=float)
r2[0] = np.nan
r2[1:] = pivot[1:] + (high[:-1] - low[:-1])
s2 = np.empty_like(high, dtype=float)
s2[0] = np.nan
s2[1:] = pivot[1:] - (high[:-1] - low[:-1])
assert _allclose(ft_pivot, pivot, atol=1e-8)
assert _allclose(ft_r1, r1, atol=1e-8)
assert _allclose(ft_s1, s1, atol=1e-8)
assert _allclose(ft_r2, r2, atol=1e-8)
assert _allclose(ft_s2, s2, atol=1e-8)