pds — Piecewise Direct Standardisation

Group: Calibration transfer · Registry tolerance: 0.5

Description

PDS — Piecewise Direct Standardization (§13)

From the pls4all.sklearn.PDSTransformer docstring:

Piecewise Direct Standardization (Wang 1991).

Registry note — Base R per-band lm.fit over a window of source bands — the canonical Wang 1991 PDS algorithm with no extra deps. Same algorithm as pls4all’s pds_fit modulo CSV-roundtrip precision.

Parameters

Name

Type

Default

Notes

window_half_width

int

5

Half-width (in channels) of the PDS local regression window.

Explanations

Bibliographic source

Wang, Y., Veltkamp, D. J. & Kowalski, B. R. (1991). Multivariate instrument standardization. Analytical Chemistry 63(23), 2750–2756. https://doi.org/10.1021/ac00023a016 — same paper as ds; PDS is introduced in §3 (piecewise local regression with a sliding window of width 2w+1).

Mathematical principle

PDS generalises DS by allowing the transfer to vary across wavelength bands. For each wavelength \(j\) on the primary instrument, a local regression maps a window of \(\pm w\) wavelengths from the secondary instrument: \(\hat{x}_{\mathrm{primary}, j} = \mathbf{x}_{\mathrm{secondary}, j-w:j+w} \cdot \mathbf{f}_j\). The full transfer matrix is then banded: only \(\pm w\) off-diagonal columns per row are non-zero.

PDS handles wavelength-dependent inter-instrument behaviour — wavelength-axis drift, resolution differences, detector non-linearities — that DS cannot. The window half-width \(w\) controls the locality: \(w=0\) recovers a diagonal-only transfer, \(w \to p/2\) recovers DS.

PDS is the de-facto standard in NIR / FT-IR calibration transfer; the prospectr R package’s implementation is considered canonical.

Implementation

n4m_pds_fit (TransformerMixin in tier 2). Reference: R prospectr::pds. Note: pls4all applies the transpose convention so that transform(X_secondary) returns the standardised primary-instrument estimate.

MATLAB header (bindings/matlab/+pls4all/pds.m):

pls4all.pds  Piecewise 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

/* C ABI — libn4m */
n4m_context_t* ctx = n4m_context_create();
n4m_config_t*  cfg = n4m_config_create();
n4m_method_result_t* res = NULL;
n4m_pds_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);

import pls4all
from pls4all._methods import pds_fit
with pls4all.Context() as ctx, pls4all.Config() as cfg:
    res = pds_fit(ctx, cfg, X, y, X_target=X_target)
# then: res.matrix("predictions"), res.matrix("coefficients"),
# res.vector("mask"), res.scalar("intercept"), …

from pls4all.sklearn import PDSTransformer
mdl = PDSTransformer(window_half_width=5)
mdl.fit(X, y, X_target=X_target)
y_hat = mdl.predict(X_test)

library(pls4all)
# Unified low-level dispatcher (May 2026 R cleanup):
res <- pls4all_method("pds", X, y,
                      n_components = 2L, params = list(window_half_width = 2L))
# res is a named list with MethodResult arrays/scalars.
# selected_indices / top_k_intervals are 1-based.

res = pls4all.pds(X, y, 2);
% see header of bindings/matlab/+pls4all/pds.m for full
% parameter surface:
%   res = pds(X_source, X_target, window_half_width)
yhat = predict(res, Xtest);

No idiomatic classdef wrapper — invoke pls4all.fit("pds", X, y, …) directly from the unified MEX factory.

Registry parity references 📐

  • 📐 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. 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  ·  ⇄ cross-check = documented by-design selector/RNG/model, noncanonical API/facade convention, or secondary oracle  ·  ✗ divergent  ·  ⚠ error  ·  — not run. The fastest backend per column is marked 🏆.

Reference gate: strict — numeric equivalence (rmse_rel_tol ≤ 1e-08).

Rows tagged with 📐 are the canonical parity references for this method (declared in parity_timing.registry). 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.

BackendParity200×30 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref 5e-091.37 ms🏆
Python · pls4all
pls4all.python✓ bind1.44 ms
pls4all.sklearn✓ 4e-161.86 ms
R · pls4all
pls4all.R✓ bind10.6 ms
pls4all.R.formula✓ bind10.1 ms
pls4all.R.mdatools✓ bind13.7 ms
pls4all.R.pls✓ bind14.2 ms
R · external
📐ref.r_basesource43.1 ms
BackendParity200×30 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref 5e-092.54 ms🏆
Python · pls4all
pls4all.python✓ bind2.67 ms
pls4all.sklearn✓ 4e-167.45 ms
R · pls4all
pls4all.R✓ bind34.6 ms
pls4all.R.formula✓ bind34.8 ms
pls4all.R.mdatools✓ bind42.9 ms
pls4all.R.pls✓ bind49.1 ms
R · external
📐ref.r_basesource112.2 ms
BackendParity200×30 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref 5e-096.67 ms
Python · pls4all
pls4all.python✓ bind3.05 ms
pls4all.sklearn✓ 4e-163.01 ms🏆
R · pls4all
pls4all.R✓ bind15.7 ms
pls4all.R.formula✓ bind18.9 ms
pls4all.R.mdatools✓ bind15.4 ms
pls4all.R.pls✓ bind10.5 ms
R · external
📐ref.r_basesource35.6 ms

See also: benchmark overview · methods index · interactive dashboard