# `rosa` — ROSA (Response-Oriented Sequential Alternation)
_Group_: **Multi-block / cross-modal** · _Registry tolerance_: `1e-06`
## Description
ROSA — Response-Oriented Sequential Alternation (§19)
From the `pls4all.sklearn.ROSARegression` docstring:
> Response-Oriented Sequential Alternation (Liland & Næs 2016).
> **Registry note** — Canonical multiblock ROSA (Liland, Næs & Indahl 2016). Both references implement the canonical formulation; pls4all matches them bit-for-bit (max_abs < 1e-6) for single-target Y. The R reference centers multi-target Y incorrectly (recycles `colMeans(y)` rather than broadcasting), so multi-target parity is intentionally evaluated against the NumPy reference.
### Parameters
| Name | Type | Default | Notes |
|------|------|---------|-------|
| `n_components` | `int` | `2` | Number of latent components extracted (k). |
| `block_sizes` | `—` | `None` | Sequence of contiguous block widths defining the X-block partition (columns of X). |
| `n_targets` | `int` | `1` | registry benchmark cell value |
| `n_blocks` | `int` | `3` | registry benchmark cell value |
## Explanations
### Bibliographic source
Liland, K. H. & Næs, T. (2016). *Response-oriented sequential alternation: a fast multiblock regression algorithm*. Journal of Chemometrics 30(11), 651–662.
### Mathematical principle
ROSA is a forward-greedy multi-block PLS: at each component extraction step, it tries one new component from **every block** and keeps the block whose new component most reduces residual variance in $\mathbf{y}$. The component sequence is therefore data-driven rather than pre-specified by the user.
This auto-attribution makes ROSA a strong default when the analyst has no prior on which block matters most: the block budget is allocated dynamically. ROSA is also much faster than SO-PLS for large block counts because it adds one component per iteration rather than refitting an inner PLS per block.
Output includes the **block-attribution vector** — the sequence of block indices selected — which is the main interpretive artefact: it tells you which block contributed which component, in order.
### Implementation
`n4m_rosa_fit`. Reference: CRAN `multiblock 0.8.10`.
MATLAB header (`bindings/matlab/+pls4all/rosa.m`):
```text
pls4all.rosa Response-Oriented Sequential Alternation (Liland & Næs 2016).
```
### 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_rosa_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 rosa_fit
with pls4all.Context() as ctx, pls4all.Config() as cfg:
res = rosa_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 ROSARegression
mdl = ROSARegression(n_components=2, block_sizes=None)
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("rosa", X, y,
n_components = 4L, params = list(n_targets = 1L, n_blocks = 3L))
# 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.rosa(X, y, 4);
% see header of bindings/matlab/+pls4all/rosa.m for full
% parameter surface:
% res = rosa(X, Y, n_components, block_sizes)
yhat = predict(res, Xtest);
```
:::
:::{tab-item} MATLAB · pls4all (classdef)
:sync: matlab-classdef
:class-label: lang-matlab
_No idiomatic classdef wrapper — invoke `pls4all.fit("rosa", X, y, …)` directly from the unified MEX factory._
:::
::::
**Registry parity references** 📐
:::{card}
:class-card: external-refs
- 📐 **`ref.python_numpy`** (python · python) — `numpy` 2.3.5 · strict (rmse_rel ≤ 1e-06) — Canonical multiblock ROSA in NumPy (Liland, Næs & Indahl 2016). Reproduces R `multiblock::rosa(canonical=TRUE)` exactly for single-target Y; for q >= 2 it uses proper column-mean centering and diverges from R `multiblock` because that package recycles `colMeans(y)` incorrectly. pls4all matches this NumPy reference for q == 1 at IEEE round-off.
- 📐 **`ref.r_multiblock`** (R · r) — `multiblock` 0.8.10 · strict (rmse_rel ≤ 1e-06) — R `multiblock::rosa 0.8.10` (Liland, Næs & Indahl 2016). ROSA's greedy block-selection-per-component may diverge from pls4all's ordering — tolerance widened.
:::
### 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) | 200×30 (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 | ≈ +7e-16 | 3.13 ms | 2.12 ms | 12.4 ms🏆 | 58.8 ms | 1.23 ms🏆 | 2.90 ms | 6.79 ms | 60.4 ms | 306.6 ms🏆 | 29.5 ms🏆 | 313.9 ms | 1.8 s | 130.3 ms | 1.4 s🏆 |
pls4all.cpp.blas+omp | ≈ +7e-16 | 2.59 ms | 1.29 ms | 13.2 ms | 59.0 ms | 1.24 ms | 2.61 ms🏆 | 5.64 ms🏆 | 60.2 ms🏆 | 311.5 ms | 30.5 ms | 293.8 ms🏆 | 1.8 s🏆 | 130.2 ms | 1.4 s |
pls4all.cpp.omp | ≈ +7e-16 | 2.58 ms🏆 | 1.17 ms🏆 | 12.4 ms | 57.3 ms | 1.24 ms | 2.70 ms | 6.33 ms | 60.7 ms | 315.4 ms | 31.0 ms | 305.8 ms | 1.8 s | 125.4 ms🏆 | 1.4 s |
pls4all.cpp.ref | ≈ +7e-16 | 2.60 ms | 1.43 ms | 13.4 ms | 55.4 ms🏆 | 1.26 ms | 2.90 ms | 6.90 ms | 60.8 ms | 309.1 ms | 30.0 ms | 309.2 ms | 1.8 s | 130.0 ms | 1.4 s |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | 2.62 ms | — | — | — | 1.30 ms | 2.89 ms | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✓ bind | 3.28 ms | — | — | — | 1.59 ms | 6.17 ms | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✓ bind | 12.7 ms | — | — | — | 4.34 ms | 11.4 ms | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✓ bind | 21.1 ms | — | — | — | 6.92 ms | 11.8 ms | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✓ bind | 23.9 ms | — | — | — | 6.26 ms | 12.1 ms | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✓ bind | 22.4 ms | — | — | — | 5.23 ms | 14.2 ms | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +9e+00 | 5.35 ms | — | — | — | 2.15 ms | 4.02 ms | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +9e+00 | 6.08 ms | — | — | — | 2.65 ms | 5.19 ms | — | — | — | — | — | — | — | — |
| Python · external |
|---|
📐ref.python_numpy | source | 3.04 ms | — | — | — | 1.58 ms | 3.47 ms | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_multiblock | ✓ ref 2e-15 | 1.4 s | — | — | — | 1.3 s | 1.4 s | — | — | — | — | — | — | — | — |
:::
:::{tab-item} 3 threads
:sync: threads-3
| Backend | Parity | 50×250 (ms) | 100×50 (ms) | 100×500 (ms) | 100×2500 (ms) | 200×30 (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 2e-16 | — | — | — | — | 2.02 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ✓ ref 2e-16 | — | — | — | — | 1.83 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ✓ ref 2e-16 | — | — | — | — | 2.23 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ✓ ref 2e-16 | — | — | — | — | 2.25 ms | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | — | — | — | — | 1.22 ms🏆 | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✓ bind | — | — | — | — | 1.49 ms | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✓ bind | — | — | — | — | 4.70 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✓ bind | — | — | — | — | 5.04 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✓ bind | — | — | — | — | 5.00 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✓ bind | — | — | — | — | 4.64 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +9e+00 | — | — | — | — | 2.57 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +9e+00 | — | — | — | — | 2.60 ms | — | — | — | — | — | — | — | — | — |
| Python · external |
|---|
📐ref.python_numpy | source | — | — | — | — | 1.60 ms | — | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_multiblock | ✓ ref 1e-15 | — | — | — | — | 1.3 s | — | — | — | — | — | — | — | — | — |
:::
:::{tab-item} 10 threads
:sync: threads-10
| Backend | Parity | 50×250 (ms) | 100×50 (ms) | 100×500 (ms) | 100×2500 (ms) | 200×30 (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 2e-16 | — | — | — | — | 1.14 ms🏆 | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ✓ ref 2e-16 | — | — | — | — | 1.17 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ✓ ref 2e-16 | — | — | — | — | 1.19 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ✓ ref 2e-16 | — | — | — | — | 1.16 ms | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | — | — | — | — | 1.81 ms | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✓ bind | — | — | — | — | 1.44 ms | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✓ bind | — | — | — | — | 3.33 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✓ bind | — | — | — | — | 3.96 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✓ bind | — | — | — | — | 3.84 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✓ bind | — | — | — | — | 3.96 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +9e+00 | — | — | — | — | 1.90 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +9e+00 | — | — | — | — | 2.27 ms | — | — | — | — | — | — | — | — | — |
| Python · external |
|---|
📐ref.python_numpy | source | — | — | — | — | 1.36 ms | — | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_multiblock | ✓ ref 1e-15 | — | — | — | — | 1.1 s | — | — | — | — | — | — | — | — | — |
:::
::::
---
_See also_: [benchmark overview](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)