# `di_pls` — Domain-Invariant PLS (di-PLS)
_Group_: **Calibration transfer** · _Registry tolerance_: `1e-06`
## Description
Domain-invariant PLS
From the `pls4all.sklearn.DIPLSRegression` docstring:
> Domain-invariant PLS (Nikzad-Langerodi 2018).
> **Registry note** — Python `diPLSlib.models.DIPLS` (B-Analytics; Nikzad-Langerodi 2018 authors). pls4all `di_pls_fit` defaults to the diPLSlib algorithm (centered NIPALS, convex-relaxation penalty, target-mean rescale) — bit-for-bit parity with `DIPLS(centering=True, rescale='Target')`. Set `cfg.di_pls_legacy = 1` to fall back to the pre-0.97.4 SIMPLS direction projection.
### Parameters
| Name | Type | Default | Notes |
|------|------|---------|-------|
| `n_components` | `int` | `2` | Number of latent components extracted (k). |
| `di_lambda` | `float` | `1.0` | Domain-invariance penalty weight balancing covariance alignment vs response fit. |
## Explanations
### Bibliographic source
Nikzad-Langerodi, R., Zellinger, W., Saminger-Platz, S. & Moser, B. A. (2018). *Domain-invariant partial-least-squares regression*. Analytical Chemistry 90(11), 6693–6701.
### Mathematical principle
Calibration transfer methods reconcile spectra acquired on different instruments or under different environmental conditions. di-PLS does this by augmenting the PLS objective with a domain-discrepancy penalty: $\mathcal{L}(\mathbf{w}) = -\operatorname{Cov}(\mathbf{X}_s\mathbf{w}, \mathbf{y}_s)^2 + \lambda \,\mathrm{MMD}^2(\mathbf{X}_s\mathbf{w}, \mathbf{X}_t\mathbf{w})$, where $(\mathbf{X}_s, \mathbf{y}_s)$ is a labelled source domain, $\mathbf{X}_t$ is an unlabelled target domain and MMD is the maximum mean discrepancy.
Minimising $\mathcal{L}$ produces latent directions $\mathbf{w}$ that simultaneously **predict $y$ in the source** and have **matched distributions across domains**. The model is therefore robust to drift between calibration and prediction sets without requiring labels on the target domain.
Computational cost is dominated by the MMD term, which is $O((n_s + n_t)^2)$ in a naive implementation; pls4all uses a linear-kernel MMD which reduces this to $O((n_s + n_t) p)$.
$\lambda$ controls the bias–transferability trade-off: $\lambda = 0$ recovers vanilla PLS on the source, large $\lambda$ shrinks toward a domain-aligned but potentially under-predictive model.
### Implementation
`n4m_di_pls_fit` — requires `X_target` at fit time. Reference: Python `diPLSlib.models.DIPLS` (Nikzad-Langerodi authors). The pls4all variant matches diPLSlib's `rescale='Target'` source-centred default.
MATLAB header (`bindings/matlab/+pls4all/DiPlsRegression.m`):
```text
pls4all.DiPlsRegression Domain-Invariant PLS regression.
```
### 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_di_pls_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 di_pls_fit
with pls4all.Context() as ctx, pls4all.Config() as cfg:
res = di_pls_fit(ctx, cfg, X, y, n_components=4, X_target=X_target)
# 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 DIPLSRegression
mdl = DIPLSRegression(n_components=2, di_lambda=1.0)
mdl.fit(X, y, X_target=X_target)
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("di_pls", X, y,
n_components = 4L, params = list(di_lambda = 1.0))
# 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.di_pls(X, y, 4);
% see header of bindings/matlab/+pls4all/di_pls.m for full
% parameter surface:
% res = di_pls(X_source, Y_source, n_components, X_target, di_lambda)
yhat = predict(res, Xtest);
```
:::
:::{tab-item} MATLAB · pls4all (classdef)
:sync: matlab-classdef
:class-label: lang-matlab
```matlab
mdl = pls4all.fit("di_pls", X, y, "NumComponents", 4);
yhat = predict(mdl, Xtest);
```
:::
::::
**Registry parity references** 📐
:::{card}
:class-card: external-refs
- 📐 **`ref.python_diplslib`** (python · python) — `diPLSlib` 2.5.0 · strict (rmse_rel ≤ 1e-06) — Python `diPLSlib.models.DIPLS` (B-Analytics; Nikzad-Langerodi 2018 authors). Same di-PLS penalty applied during deflation; centering / target rescaling differ slightly, so tolerance is 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) | 200×50 (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-13 | 77.6 ms | 2.56 ms | 1.0 s🏆 | 586.8 s | 2.92 ms | 3.67 ms | 12.7 ms🏆 | 1.5 s🏆 | 503.8 s | 53.1 ms | 2.2 s🏆 | 575.2 s | 217.7 ms | 4.1 s🏆 |
pls4all.cpp.blas+omp | ≈ +7e-13 | 74.2 ms | 2.19 ms🏆 | 1.3 s | 560.2 s🏆 | 2.88 ms🏆 | 4.28 ms | 12.7 ms | 1.6 s | 496.1 s🏆 | 52.2 ms🏆 | 2.2 s | 571.4 s🏆 | 216.6 ms🏆 | 4.1 s |
pls4all.cpp.omp | ≈ +7e-13 | 83.2 ms | 2.68 ms | 1.2 s | 585.7 s | 3.77 ms | 4.98 ms | 14.9 ms | 2.0 s | 546.8 s | 67.0 ms | 4.3 s | 715.5 s | 268.4 ms | 12.5 s |
pls4all.cpp.ref | ≈ +7e-13 | 86.2 ms | 2.98 ms | 1.2 s | 606.5 s | 3.78 ms | 4.81 ms | 15.0 ms | 1.9 s | 531.9 s | 67.5 ms | 4.3 s | 743.7 s | 278.1 ms | 12.7 s |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | 76.3 ms | — | — | — | 3.00 ms | 3.64 ms🏆 | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✓ 4e-15 | 76.2 ms | — | — | — | 5.20 ms | 3.80 ms | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +7e-02 | 24.9 ms | — | — | — | 35.9 ms | 16.6 ms | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +7e-02 | 33.8 ms | — | — | — | 37.1 ms | 16.0 ms | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +7e-02 | 31.0 ms | — | — | — | 38.6 ms | 16.3 ms | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +7e-02 | 33.8 ms | — | — | — | 36.0 ms | 17.6 ms | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +9e+00 | 87.2 ms | — | — | — | 7.41 ms | 9.25 ms | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +9e+00 | 101.0 ms | — | — | — | 8.51 ms | 11.0 ms | — | — | — | — | — | — | — | — |
| Python · external |
|---|
📐ref.python_diplslib | source | 37.5 ms🏆 | — | — | — | 4.93 ms | 5.57 ms | — | — | — | — | — | — | — | — |
:::
:::{tab-item} 3 threads
:sync: threads-3
| Backend | Parity | 50×250 (ms) | 100×50 (ms) | 100×500 (ms) | 100×2500 (ms) | 200×50 (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 8e-15 | — | — | — | — | 4.30 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ✓ ref 8e-15 | — | — | — | — | 3.24 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ✓ ref 8e-15 | — | — | — | — | 3.59 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ✓ ref 8e-15 | — | — | — | — | 5.48 ms | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ 6e-15 | — | — | — | — | 3.15 ms🏆 | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✓ 4e-15 | — | — | — | — | 3.37 ms | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✓ 1e-13 | — | — | — | — | 28.5 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✓ 1e-13 | — | — | — | — | 32.2 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✓ 1e-13 | — | — | — | — | 42.5 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✓ 1e-13 | — | — | — | — | 30.0 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +9e+00 | — | — | — | — | 11.2 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +9e+00 | — | — | — | — | 12.0 ms | — | — | — | — | — | — | — | — | — |
| Python · external |
|---|
📐ref.python_diplslib | source | — | — | — | — | 4.55 ms | — | — | — | — | — | — | — | — | — |
:::
:::{tab-item} 10 threads
:sync: threads-10
| Backend | Parity | 50×250 (ms) | 100×50 (ms) | 100×500 (ms) | 100×2500 (ms) | 200×50 (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 8e-15 | — | — | — | — | 2.67 ms🏆 | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ✓ ref 8e-15 | — | — | — | — | 2.74 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ✓ ref 8e-15 | — | — | — | — | 3.28 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ✓ ref 8e-15 | — | — | — | — | 3.39 ms | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ 6e-15 | — | — | — | — | 2.72 ms | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✓ 4e-15 | — | — | — | — | 2.89 ms | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✓ 1e-13 | — | — | — | — | 24.5 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✓ 1e-13 | — | — | — | — | 27.6 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✓ 1e-13 | — | — | — | — | 26.9 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✓ 1e-13 | — | — | — | — | 27.1 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +9e+00 | — | — | — | — | 6.52 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +9e+00 | — | — | — | — | 6.94 ms | — | — | — | — | — | — | — | — | — |
| Python · external |
|---|
📐ref.python_diplslib | source | — | — | — | — | 4.15 ms | — | — | — | — | — | — | — | — | — |
:::
::::
---
_See also_: [benchmark overview](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)