# `interval_select` — iPLS — Interval PLS (moving-window)
_Group_: **Variable selector** · _Registry tolerance_: `1e-06`
## Description
Interval/iPLS forward selection (§18 Phase 5b)
From the `pls4all.sklearn.IntervalSelector` docstring:
> Forward interval PLS (iPLS, Nørgaard 2000).
> **Registry note** — R `mdatools::ipls(method='forward')`. Default `_interval_select_pls4all` path mirrors the same R call with identical interval grid and venetian CV, giving bit-exact mask parity. The C++ contiguous-fold kernel is opt-in via `legacy=True`.
### Parameters
| Name | Type | Default | Notes |
|------|------|---------|-------|
| `n_components` | `int` | `2` | Number of latent components extracted (k). |
| `interval_width` | `int` | `10` | Width (in variables) of each contiguous spectral interval. |
| `step` | `int` | `5` | Stride between consecutive forward-iPLS intervals. |
| `n_folds` | `int` | `3` | Number of cross-validation folds used inside the selector. |
| `interval_step` | `int` | `2` | registry benchmark cell value |
## Explanations
### Bibliographic source
Nørgaard, L., Saudland, A., Wagner, J., Nielsen, J. P., Munck, L. & Engelsen, S. B. (2000). *Interval partial least-squares regression (iPLS): a comparative chemometric study with an example from near-infrared spectroscopy*. Applied Spectroscopy 54(3), 413–419.
### Mathematical principle
Slide a fixed-width window of $w$ consecutive wavelengths across the spectrum, fit PLS on each window alone, evaluate by CV-RMSE. The window with the lowest CV-RMSE is returned as the selected interval.
iPLS is the simplest **interval** selector — it returns a single contiguous band rather than scattered wavelengths. The output is therefore directly interpretable as a spectroscopic feature (functional group, electronic transition, …). For multi-band selection use biPLS or siPLS.
The window width $w$ is the main tunable; cross-validating $w$ jointly with the window position is the standard extension.
### Implementation
`n4m_interval_select`. Reference: R `plsVarSel`.
### Usage
Every pls4all binding tab dispatches into the same C kernel; the external libraries listed at the bottom of the page are the parity references registered in `benchmarks.parity_timing.registry`. Switch tabs to read the same fit in your language. The R package now ships drop-in-compatible facades for the CRAN `pls` package (`plsr`, `pcr`, `mvr`) and for the `mdatools::pls(x, y, ...)` matrix idiom — those tabs appear only on the methods that have a meaningful equivalence.
**pls4all bindings**
::::{tab-set}
:class: pls4all-bindings
:::{tab-item} C ABI · libn4m
:sync: c
:class-label: lang-c
```c
/* C ABI — libn4m */
n4m_context_t* ctx = n4m_context_create();
n4m_config_t* cfg = n4m_config_create();
n4m_method_result_t* res = NULL;
n4m_interval_select_fit(ctx, cfg, &x_view, &y_view, /* hyperparams */, &res);
/* … read coefficients / mask / scores via */
/* n4m_method_result_get_double_matrix / vector / scalar … */
n4m_method_result_destroy(res);
n4m_config_destroy(cfg);
n4m_context_destroy(ctx);
```
:::
:::{tab-item} Python · pls4all (raw)
:sync: python-raw
:class-label: lang-python
```python
import pls4all
from pls4all._methods import interval_select_fit
with pls4all.Context() as ctx, pls4all.Config() as cfg:
res = interval_select_fit(ctx, cfg, X, y, n_components=4)
# then: res.matrix("predictions"), res.matrix("coefficients"),
# res.vector("mask"), res.scalar("intercept"), …
```
:::
:::{tab-item} Python · pls4all.sklearn
:sync: python-sklearn
:class-label: lang-python
```python
from pls4all.sklearn import IntervalSelector
mdl = IntervalSelector(n_components=2, interval_width=10, step=5, n_folds=3)
mdl.fit(X, y)
y_hat = mdl.predict(X_test)
```
:::
:::{tab-item} R · pls4all_method()
:sync: r-dispatcher
:class-label: lang-r
```r
library(pls4all)
# Unified low-level dispatcher (May 2026 R cleanup):
res <- pls4all_method("interval_select", X, y,
n_components = 4L, params = list(interval_width = 5L, interval_step = 2L))
# res is a named list with MethodResult arrays/scalars.
# selected_indices / top_k_intervals are 1-based.
```
:::
:::{tab-item} MATLAB · pls4all (MEX)
:sync: matlab-mex
:class-label: lang-matlab
```matlab
res = pls4all.interval_select(X, y, 4);
% see header of bindings/matlab/+pls4all/interval_select.m for full
% parameter surface:
% res = interval_select(X, Y, n_components, interval_width, step)
yhat = predict(res, Xtest);
```
:::
:::{tab-item} MATLAB · pls4all (classdef)
:sync: matlab-classdef
:class-label: lang-matlab
_No idiomatic classdef wrapper — invoke `pls4all.fit("interval_select", X, y, …)` directly from the unified MEX factory._
:::
::::
**Registry parity references** 📐
:::{card}
:class-card: external-refs
- 📐 **`ref.r_mdatools`** (R · r) — `mdatools` 0.15.0 · strict (rmse_rel ≤ 1e-06) — R `mdatools::ipls` forward-iPLS — returns the union of selected interval variables. pls4all's `interval_select` uses a slightly different scoring (fold-RMSE on a fixed validation plan), so set/index overlap is the metric of interest.
:::
### 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-06`).
Rows tagged with **📐** are the canonical parity references for this method (declared in [`parity_timing.registry`](../benchmarks/methodology.md)). C++ and external rows show reference parity; pls4all language bindings show binding parity against the C++ backend. Hover the icon for role and tolerance band.
::::{tab-set}
:class: parity-tabs
:::{tab-item} 1 thread
:sync: threads-1
| Backend | Parity | 50×250 (ms) | 100×50 (ms) | 100×500 (ms) | 100×2500 (ms) | 200×40 (ms) | 250×50 (ms) | 500×50 (ms) | 500×500 (ms) | 500×2500 (ms) | 2500×50 (ms) | 2500×500 (ms) | 2500×2500 (ms) | 10000×50 (ms) | 10000×500 (ms) |
|---|
| C++ native · libn4m |
|---|
pls4all.cpp.blas | ✗ +8e-01 | 2.6 s | 1.3 s | 9.1 s | 44.4 s | 966.4 ms | 1.2 s | 1.6 s | 23.4 s🏆 | 207.7 s | 3.2 s | 59.3 s | 324.1 s | 14.7 s | 867.9 s |
pls4all.cpp.blas+omp | ✗ +8e-01 | 2.8 s | 1.4 s | 9.0 s🏆 | 46.7 s | 966.0 ms | 1.2 s | 1.6 s🏆 | 23.6 s | 208.9 s | 3.2 s | 58.9 s | 328.5 s | 14.4 s | 864.8 s🏆 |
pls4all.cpp.omp | ✗ +8e-01 | 2.6 s | 1.4 s | 9.2 s | 43.5 s🏆 | 966.2 ms | 1.2 s | 1.6 s | 23.8 s | 208.5 s | 3.2 s | 58.8 s | 323.9 s🏆 | 14.4 s | 866.4 s |
pls4all.cpp.ref | ✗ +8e-01 | 2.7 s | 1.3 s | 9.0 s | 43.6 s | 952.8 ms | 1.3 s | 1.6 s | 23.7 s | 205.8 s🏆 | 3.2 s🏆 | 58.6 s🏆 | 326.1 s | 14.4 s🏆 | 874.4 s |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | 2.8 s | — | — | — | 970.1 ms | 1.3 s | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +1e+00 | 4.38 ms | — | — | — | 2.46 ms | 4.02 ms | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +1e+00 | 12.0 ms | — | — | — | 7.59 ms | 12.1 ms | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +1e+00 | 22.1 ms | — | — | — | 8.72 ms | 11.2 ms | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +1e+00 | 20.8 ms | — | — | — | 7.71 ms | 9.88 ms | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +1e+00 | 20.3 ms | — | — | — | 7.70 ms | 10.2 ms | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +1e+00 | 5.43 ms | — | — | — | 3.42 ms | 5.81 ms | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +1e+00 | 6.17 ms | — | — | — | 3.64 ms | 6.13 ms | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_mdatools | source | 2.4 s🏆 | — | — | — | 454.0 ms🏆 | 813.0 ms🏆 | — | — | — | — | — | — | — | — |
:::
:::{tab-item} 3 threads
:sync: threads-3
| Backend | Parity | 50×250 (ms) | 100×50 (ms) | 100×500 (ms) | 100×2500 (ms) | 200×40 (ms) | 250×50 (ms) | 500×50 (ms) | 500×500 (ms) | 500×2500 (ms) | 2500×50 (ms) | 2500×500 (ms) | 2500×2500 (ms) | 10000×50 (ms) | 10000×500 (ms) |
|---|
| C++ native · libn4m |
|---|
pls4all.cpp.blas | ✓ ref | — | — | — | — | 835.0 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ✓ ref | — | — | — | — | 828.8 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ✓ ref | — | — | — | — | 833.8 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ✓ ref | — | — | — | — | 831.8 ms | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | — | — | — | — | 854.9 ms | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +1e+00 | — | — | — | — | 2.36 ms | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +1e+00 | — | — | — | — | 5.92 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +1e+00 | — | — | — | — | 6.89 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +1e+00 | — | — | — | — | 6.71 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +1e+00 | — | — | — | — | 6.36 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +1e+00 | — | — | — | — | 2.94 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +1e+00 | — | — | — | — | 3.52 ms | — | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_mdatools | source | — | — | — | — | 383.1 ms🏆 | — | — | — | — | — | — | — | — | — |
:::
:::{tab-item} 10 threads
:sync: threads-10
| Backend | Parity | 50×250 (ms) | 100×50 (ms) | 100×500 (ms) | 100×2500 (ms) | 200×40 (ms) | 250×50 (ms) | 500×50 (ms) | 500×500 (ms) | 500×2500 (ms) | 2500×50 (ms) | 2500×500 (ms) | 2500×2500 (ms) | 10000×50 (ms) | 10000×500 (ms) |
|---|
| C++ native · libn4m |
|---|
pls4all.cpp.blas | ✓ ref | — | — | — | — | 703.6 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ✓ ref | — | — | — | — | 689.1 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ✓ ref | — | — | — | — | 686.7 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ✓ ref | — | — | — | — | 718.5 ms | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | — | — | — | — | 686.5 ms | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +1e+00 | — | — | — | — | 2.03 ms | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +1e+00 | — | — | — | — | 4.36 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +1e+00 | — | — | — | — | 5.25 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +1e+00 | — | — | — | — | 5.77 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +1e+00 | — | — | — | — | 5.01 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +1e+00 | — | — | — | — | 2.75 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +1e+00 | — | — | — | — | 3.03 ms | — | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_mdatools | source | — | — | — | — | 317.9 ms🏆 | — | — | — | — | — | — | — | — | — |
:::
::::
---
_See also_: [benchmark overview](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)