pp_second_derivative — Second derivative

Group: Preprocessing · Binding: n4m.sklearn.SecondDerivative · C ABI: n4m_pp_second_derivative_*

Description

Two passes of np.gradient (shape-preserving).

Parameters

Name	Type	Default
delta	float	1.0
edge_order	int	2

Explanations

Bibliographic source

Standard finite-difference / gap derivative; see Savitzky & Golay (1964) and Norris & Williams (1984).

Mathematical principle

Approximates \(\mathrm{d}^2\mathbf{x}/\mathrm{d}\lambda^2\). The second derivative removes both constant and linear baselines and resolves overlapping peaks into sharp negative lobes at the original band positions, at the cost of amplifying high-frequency noise (hence it is usually paired with smoothing).

Implementation

C ABI n4m_pp_second_derivative_* in libn4m (create / apply / destroy lifecycle), wrapped by n4m.sklearn.SecondDerivative. The same numerical kernel backs every language binding.

Usage

from n4m.sklearn import SecondDerivative
op = SecondDerivative()
X_transformed = op.fit_transform(X)

Benchmarks

Adaptive wall-clock per cell measured against full_matrix.csv. Only backends that implement this method are listed; libraries without the method are omitted.

Verdict  ·  ✓ ref / ≈ ref / ~ shape mark a reference-gate pass at strict / relaxed / qualitative tolerance  ·  ✓ bind = pls4all binding agrees with the C++ baseline  ·  ⇄ cross-check = documented by-design selector/RNG/model, noncanonical API/facade convention, or secondary oracle  ·  ✗ divergent  ·  ⚠ error  ·  — not run. The fastest backend per column is marked 🏆.

Reference gate: strict — numeric equivalence (rmse_rel_tol ≤ 1e-12).

1 thread

Backend	Parity	50×250 (ms)	250×50 (ms)
C++ native · libn4m
pls4all.cpp.blas	✓ ref	—	—
pls4all.cpp.blas+omp	✓ ref	0.01 ms🏆	0.01 ms🏆
pls4all.cpp.omp	✓ ref	—	—
pls4all.cpp.ref	✓ ref	0.01 ms	0.01 ms
Python · pls4all
pls4all.python	✓ bind	0.02 ms	0.02 ms
pls4all.sklearn	✓ bind	0.02 ms	0.02 ms
Python · external
nirs4all	source	0.07 ms	0.08 ms
ref.python_numpy	source	—	—

---

See also: methods index · interactive dashboard