# `pp_savgol` — Savitzky–Golay smoothing / derivative

_Group_: **Preprocessing** · _Binding_: `n4m.sklearn.SavitzkyGolay` · _C ABI_: `n4m_pp_savgol_*`

## Description

scipy.signal.savgol_filter parity.

### Parameters

| Name | Type | Default |
|------|------|---------|
| `window_length` | `int` | `5` |
| `polyorder` | `int` | `2` |
| `deriv` | `int` | `0` |
| `delta` | `float` | `1.0` |
| `mode` | `str` | `'mirror'` |
| `cval` | `float` | `0.0` |

## Explanations

### Bibliographic source

Savitzky, A. & Golay, M. J. E. (1964). *Smoothing and Differentiation of Data by Simplified Least Squares Procedures*. Analytical Chemistry 36(8), 1627–1639.

### Mathematical principle

Within a sliding window of odd length $w$, a polynomial of order $p$ is fit by least squares; the smoothed value (or its $d$-th derivative) at the window centre is a fixed linear combination of the windowed points. Because the convolution coefficients are precomputed, SG simultaneously denoises and differentiates while preserving peak shape far better than a moving average.

### Implementation

C ABI `n4m_pp_savgol_*` in libn4m (create / apply / destroy lifecycle), wrapped by `n4m.sklearn.SavitzkyGolay`. The same numerical kernel backs every language binding.

### Usage

```python
from n4m.sklearn import SavitzkyGolay
op = SavitzkyGolay()
X_transformed = op.fit_transform(X)
```

### Benchmarks

Adaptive wall-clock per cell measured against [`full_matrix.csv`](../benchmarks/overview.md). 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  ·  ✗ divergent  ·  ⚠ error  ·  — not run. The fastest backend per column is marked 🏆.

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

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:class: parity-tabs

:::{tab-item} 1 thread
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<div class="parity-table-wrap">
<table class="docutils parity-grouped">
<thead><tr><th scope="col">Backend</th><th scope="col">Parity</th><th class="size-col" scope="col">50×250 (ms)</th><th class="size-col" scope="col">250×50 (ms)</th></tr></thead>
<tbody class="lang-band lang-cpp"><tr class="lang-band-row" data-lang="cpp"><th colspan="4" scope="rowgroup"><span class="lang-band-dot"></span>C++ native · libn4m</th></tr>
<tr class="bk-row"><td class="bk-name"><code>pls4all.cpp.blas+omp</code></td><td class="parity parity-ref-strict">✓ ref</td><td class="ms">—</td><td class="ms">—</td></tr>
</tbody>
<tbody class="lang-band lang-python"><tr class="lang-band-row" data-lang="python"><th colspan="4" scope="rowgroup"><span class="lang-band-dot"></span>Python · external</th></tr>
<tr class="bk-row"><td class="bk-name"><code>ref.python_numpy</code></td><td class="parity parity-ref-source">source</td><td class="ms">—</td><td class="ms">—</td></tr>
</tbody>
</table>
</div>

:::

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_See also_: [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)