# `ds` — Direct Standardisation
_Group_: **Calibration transfer** · _Registry tolerance_: `0.5`
## Description
DS — Direct Standardization (§13)
From the `pls4all.sklearn.DSTransformer` docstring:
> Direct Standardization — full-band cross-instrument regression.
> **Registry note** — Base R per-band `lm.fit` with window_half_width=0 — Direct Standardization is just per-band linear regression.
_No tunable parameters declared at the binding level._
## Explanations
### Bibliographic source
Wang, Y., Veltkamp, D. J. & Kowalski, B. R. (1991). *Multivariate instrument standardisation*. Analytical Chemistry 63(23), 2750–2756.
### Mathematical principle
Direct Standardisation (DS) learns a **single global transfer matrix** $\mathbf{F}$ that maps secondary-instrument spectra back onto the primary instrument: $\hat{\mathbf{X}}_{\mathrm{primary}} = \mathbf{X}_{\mathrm{secondary}} \mathbf{F}$. The matrix is fit by least squares on a small set of transfer-standard samples measured on both instruments, typically with a Tikhonov ridge for stability.
DS is the simplest member of the calibration-transfer family and works well when the inter-instrument response is approximately linear and stationary — i.e. when instrument differences amount to a constant linear transformation that is invariant across the spectrum. When the transformation varies across wavelength bands (common in dispersive vs FT spectrometers) the global transfer matrix produces band-mixing artefacts and PDS should be used instead.
A canonical workflow: fit DS on $\le 30$ transfer standards, apply $\mathbf{F}$ to all subsequent secondary-instrument spectra, then use a single PLS model fit only on primary data.
### Implementation
`n4m_ds_fit` (TransformerMixin in tier 2). Reference: R `chemometrics::stdize`.
MATLAB header (`bindings/matlab/+pls4all/ds.m`):
```text
pls4all.ds Direct Standardization (calibration transfer).
```
### 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_ds_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 ds_fit
with pls4all.Context() as ctx, pls4all.Config() as cfg:
res = ds_fit(ctx, cfg, X, y, 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 DSTransformer
mdl = DSTransformer(n_components=2)
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("ds", X, y,
n_components = 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.ds(X, y, 2);
% see header of bindings/matlab/+pls4all/ds.m for full
% parameter surface:
% res = ds(X_source, X_target)
yhat = predict(res, Xtest);
```
:::
:::{tab-item} MATLAB · pls4all (classdef)
:sync: matlab-classdef
:class-label: lang-matlab
_No idiomatic classdef wrapper — invoke `pls4all.fit("ds", X, y, …)` directly from the unified MEX factory._
:::
::::
**Registry parity references** 📐
:::{card}
:class-card: external-refs
- 📐 **`ref.r_base`** (R · r) — `base` R 4.3.3 · qualitative (rmse_rel ≤ 5e-01) — Base R `lm` per spectral band — closest installable analog to Wang 1991 Piecewise Direct Standardization. With window_half_width=0 this reduces to Direct Standardization.
:::
### 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**: qualitative — shape/smoke comparison only. The external library and pls4all do not produce numerically equivalent output for this method (see the MethodSpec notes); the `rmse_rel_tol ≤ 5e-01` budget is set wide on purpose. Treat ~ shape as *“we ran both, both finished”*, not as numerical agreement.
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 | ≈ +6e-09 | 15.2 ms | 1.50 ms | 119.2 ms | 91.0 s | 1.47 ms | 3.71 ms | 13.6 ms | 532.5 ms | 66.2 s | 52.1 ms | 11.8 s🏆 | 482.7 s | 295.1 ms | 60.3 s |
pls4all.cpp.blas+omp | ≈ +6e-09 | 12.4 ms | 1.52 ms | 127.7 ms | 89.5 s🏆 | 1.60 ms | 3.69 ms | 13.7 ms | 532.3 ms | 65.6 s | 47.6 ms🏆 | 12.7 s | 460.1 s🏆 | 304.9 ms | 47.4 s |
pls4all.cpp.omp | ≈ +6e-09 | 12.9 ms | 1.43 ms🏆 | 103.1 ms🏆 | 91.6 s | 1.61 ms | 3.44 ms | 13.1 ms🏆 | 482.8 ms🏆 | 66.4 s | 52.0 ms | 12.0 s | 520.6 s | 294.1 ms🏆 | 51.4 s |
pls4all.cpp.ref | ≈ +6e-09 | 14.3 ms | 1.49 ms | 118.5 ms | 92.3 s | 1.38 ms🏆 | 3.28 ms🏆 | 13.7 ms | 539.6 ms | 65.2 s🏆 | 47.8 ms | 13.4 s | 605.1 s | 297.2 ms | 43.5 s🏆 |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | 11.9 ms🏆 | — | — | — | 1.42 ms | 3.36 ms | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✓ 4e-15 | 13.3 ms | — | — | — | 1.94 ms | 4.26 ms | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✓ bind | 39.7 ms | — | — | — | 9.27 ms | 22.0 ms | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✓ bind | 50.8 ms | — | — | — | 10.0 ms | 25.3 ms | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✓ bind | 47.8 ms | — | — | — | 10.7 ms | 20.1 ms | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✓ bind | 51.7 ms | — | — | — | 11.7 ms | 19.1 ms | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +6e+00 | 19.7 ms | — | — | — | 4.22 ms | 9.20 ms | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +6e+00 | 19.6 ms | — | — | — | 4.51 ms | 9.75 ms | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_base | source | 55.7 ms | — | — | — | 28.9 ms | 48.2 ms | — | — | — | — | — | — | — | — |
:::
:::{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 | ~ shape 6e-09 | — | — | — | — | 1.42 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ~ shape 6e-09 | — | — | — | — | 1.70 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ~ shape 6e-09 | — | — | — | — | 1.47 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ~ shape 6e-09 | — | — | — | — | 1.41 ms | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | — | — | — | — | 1.36 ms🏆 | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✓ 9e-16 | — | — | — | — | 1.66 ms | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✓ bind | — | — | — | — | 8.15 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✓ bind | — | — | — | — | 10.1 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✓ bind | — | — | — | — | 9.86 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✓ bind | — | — | — | — | 9.74 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +6e+00 | — | — | — | — | 4.28 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +6e+00 | — | — | — | — | 4.62 ms | — | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_base | source | — | — | — | — | 32.1 ms | — | — | — | — | — | — | — | — | — |
:::
:::{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 | ~ shape 6e-09 | — | — | — | — | 1.34 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ~ shape 6e-09 | — | — | — | — | 1.29 ms🏆 | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ~ shape 6e-09 | — | — | — | — | 1.35 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ~ shape 6e-09 | — | — | — | — | 1.37 ms | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | — | — | — | — | 2.49 ms | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✓ 9e-16 | — | — | — | — | 1.45 ms | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✓ bind | — | — | — | — | 6.26 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✓ bind | — | — | — | — | 6.94 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✓ bind | — | — | — | — | 6.95 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✓ bind | — | — | — | — | 7.04 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +6e+00 | — | — | — | — | 3.77 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +6e+00 | — | — | — | — | 4.09 ms | — | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_base | source | — | — | — | — | 23.1 ms | — | — | — | — | — | — | — | — | — |
:::
::::
---
_See also_: [benchmark overview](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)