pls_diagnostic_dmodx — DModX (distance to the model in X)

Group: Diagnostic · Registry tolerance: 1e-08

Description

PLS Distance-to-Model X (§9)

Registry note — mdatools has no native DModX; the R script computes it from $xdecomp$Q and the same dof formula pls4all uses.

Parameters

Name	Type	Default	Notes
n_components	int	4	registry benchmark cell value

Explanations

Bibliographic source

Eriksson, L., Byrne, T., Johansson, E., Trygg, J. & Vikström, C. (2013). Multi- and Megavariate Data Analysis. Basic Principles and Applications, 3rd ed., Umetrics Academy, §4.7. Verified primary catalogue: https://search.worldcat.org/title/891362497.

Mathematical principle

Let Q be an observation’s squared X reconstruction residual and let a be the number of components. The implementation reports \(\sqrt{Q/(p-a)}/\sigma\), where \(\sigma=\sqrt{\sum Q_{ref}/((p-a)(n_{ref}-a-1))}\) when a reference set is supplied.

Appropriate uses

Standardizing X reconstruction distance for model-population screening.

Limits and validation

The implementation uses p-a degrees of freedom and a reference residual scale; without reference data sigma is fixed to one.

Implementation

Valid degrees of freedom require p>a and, for reference scaling, n_ref>a+1. With no reference residuals the implementation sets sigma to one rather than estimating a model-population scale.

Sources and provenance

Current implementation: cpp/src/core/pls_diagnostics.cpp.

API and bindings

C ABI (ABI 2): n4m_metrics_pls_diagnostics_compute. Use the linked public header for the exact signature, configuration, and result handles.

Python: no current AST-verified public n4m re-export was found for this method. The linked C ABI above is the documented surface in this checkout.

R: no current source-verified entry point was found for this catalog method.

MATLAB / Octave: no current source-verified entry point was found for this catalog method.

Registry parity references 📐

• 📐 ref.r_mdatools (R · r) — mdatools 0.15.0 · strict (rmse_rel ≤ 1e-08) — R mdatools::pls with predict()$xdecomp$T2 / $Q. DModX is derived locally from $Q + DOF. mdatools uses different SIMPLS deflation / normalization conventions than pls4all, so cross-implementation parity is qualitative.

Benchmarks

Archived measurement identity. Backend labels in this table are the raw IDs recorded when the benchmark ran (including historical pls4all.* IDs). They preserve measurement provenance and do not describe a current public Python, R, or MATLAB binding; use the source-verified API and bindings section above for current entry points.

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 = archived binding-harness result 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; archived language-harness rows show binding parity against the C++ backend. Hover the icon for role and tolerance band.

1 thread

Backend	Parity	200×30 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp	✓ ref 2e-15	1.25 ms
Python · archived pls4all benchmark
pls4all.python	✓ bind	1.25 ms🏆
pls4all.sklearn	✓ bind	1.41 ms
R · archived pls4all benchmark
pls4all.R	✓ 7e-16	4.16 ms
pls4all.R.formula	✓ 7e-16	4.79 ms
pls4all.R.mdatools	✓ 7e-16	5.71 ms
pls4all.R.pls	✓ 7e-16	4.47 ms
R · external
📐ref.r_mdatools	source	19.8 ms

3 threads

Backend	Parity	200×30 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp	✓ ref 2e-15	1.28 ms
Python · archived pls4all benchmark
pls4all.python	✓ bind	1.25 ms🏆
pls4all.sklearn	✓ bind	1.41 ms
R · archived pls4all benchmark
pls4all.R	✓ 7e-16	6.86 ms
pls4all.R.formula	✓ 7e-16	20.8 ms
pls4all.R.mdatools	✓ 7e-16	14.5 ms
pls4all.R.pls	✓ 7e-16	18.2 ms
R · external
📐ref.r_mdatools	source	43.6 ms

10 threads

Backend	Parity	200×30 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp	✓ ref 2e-15	6.12 ms
Python · archived pls4all benchmark
pls4all.python	✓ bind	2.29 ms
pls4all.sklearn	✓ bind	1.45 ms🏆
R · archived pls4all benchmark
pls4all.R	✓ 7e-16	3.74 ms
pls4all.R.formula	✓ 7e-16	4.94 ms
pls4all.R.mdatools	✓ 7e-16	5.32 ms
pls4all.R.pls	✓ 7e-16	4.64 ms
R · external
📐ref.r_mdatools	source	21.1 ms

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See also: benchmark overview · methods index · interactive dashboard