# `pls_diagnostic_dmodx` — DModX (distance to the model in X)
_Group_: **Diagnostic** · _Registry tolerance_: `5.0`
## 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.
### Mathematical principle
DModX is a **normalised** version of Q that accounts for the model's residual degrees of freedom: $\mathrm{DModX}_i = \sqrt{Q_i \,/\, (p - k - 1) \,\cdot\, (n - k - 1) / \bar{Q}_{\mathrm{cal}}}$ where $\bar{Q}_{\mathrm{cal}}$ is the average Q on the calibration set.
DModX is the diagnostic of choice in the SIMCA software (Umetrics) and is commonly used because the normalisation produces a unit-less quantity directly comparable across models with different $p$, $n$, $k$. Critical thresholds follow the F-distribution: DModX > 2 is the heuristic outlier cutoff in practice.
Conceptually equivalent to Q for monitoring purposes, but the normalisation is what makes it portable.
### Implementation
`n4m_pls_diagnostics_compute` with stat='dmodx'.
MATLAB header (`bindings/matlab/+pls4all/pls_diagnostics.m`):
```text
pls4all.pls_diagnostics Hotelling T2, Q residuals, DModX from a SIMPLS fit.
res = pls4all.pls_diagnostics(X, Y, n_components)
res = pls4all.pls_diagnostics(X, Y, n_components, X_reference)
Fits an internal SIMPLS model (store_scores=1) and evaluates row-wise
```
### 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_pls_diagnostics_compute(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 pls_diagnostics_compute
with pls4all.Context() as ctx, pls4all.Config() as cfg:
res = pls_diagnostics_compute(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 dmodx_score
result = dmodx_score(X, y, n_components=4)
```
:::
:::{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("pls_diagnostic_dmodx", X, y,
n_components = 4L)
# 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.pls_diagnostics(X, y, 4);
% see header of bindings/matlab/+pls4all/pls_diagnostics.m for full
% parameter surface:
% res = pls_diagnostics(X, Y, n_components, X_reference)
yhat = predict(res, Xtest);
```
:::
:::{tab-item} MATLAB · pls4all (classdef)
:sync: matlab-classdef
:class-label: lang-matlab
_No idiomatic classdef wrapper — invoke `pls4all.fit("pls_diagnostic_dmodx", X, y, …)` directly from the unified MEX factory._
:::
::::
**Registry parity references** 📐
:::{card}
:class-card: external-refs
- 📐 **`ref.r_mdatools`** (R · r) — `mdatools` 0.15.0 · qualitative (rmse_rel ≤ 5e+00) — 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
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+00` 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 | ≈ +2e-15 | 2.63 ms | 1.79 ms | 11.1 ms | 52.2 ms🏆 | 1.29 ms🏆 | 2.90 ms🏆 | 6.61 ms | 52.7 ms🏆 | 262.9 ms | 26.3 ms | 276.8 ms | 1.4 s🏆 | 115.3 ms | 1.2 s🏆 |
pls4all.cpp.blas+omp | ≈ +2e-15 | 3.11 ms | 2.07 ms | 8.46 ms🏆 | 53.1 ms | 1.34 ms | 3.17 ms | 5.31 ms🏆 | 54.8 ms | 272.9 ms | 24.9 ms | 281.2 ms | 1.5 s | 112.1 ms | 1.2 s |
pls4all.cpp.omp | ≈ +2e-15 | 2.68 ms | 1.58 ms🏆 | 11.3 ms | 53.7 ms | 1.41 ms | 4.10 ms | 5.53 ms | 55.5 ms | 270.3 ms | 24.5 ms🏆 | 287.7 ms | 1.5 s | 113.4 ms | 1.2 s |
pls4all.cpp.ref | ≈ +2e-15 | 3.90 ms | 1.78 ms | 10.4 ms | 53.8 ms | 1.30 ms | 3.82 ms | 5.59 ms | 56.1 ms | 260.9 ms🏆 | 28.6 ms | 267.1 ms🏆 | 1.5 s | 105.5 ms🏆 | 1.2 s |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | 2.61 ms🏆 | — | — | — | 1.44 ms | 3.03 ms | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✓ bind | 2.99 ms | — | — | — | 1.54 ms | 2.98 ms | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✓ 9e-16 | 18.3 ms | — | — | — | 4.10 ms | 15.8 ms | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✓ 9e-16 | 23.6 ms | — | — | — | 5.40 ms | 16.4 ms | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✓ 9e-16 | 22.0 ms | — | — | — | 5.59 ms | 14.8 ms | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✓ 9e-16 | 24.0 ms | — | — | — | 5.52 ms | 13.8 ms | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +5e-01 | 4.47 ms | — | — | — | 2.21 ms | 5.42 ms | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +5e-01 | 5.03 ms | — | — | — | 2.49 ms | 5.01 ms | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_mdatools | source | 39.2 ms | — | — | — | 21.8 ms | 30.7 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 2e-15 | — | — | — | — | 1.41 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ~ shape 2e-15 | — | — | — | — | 1.39 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ~ shape 2e-15 | — | — | — | — | 1.88 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ~ shape 2e-15 | — | — | — | — | 1.39 ms | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ 7e-16 | — | — | — | — | 1.24 ms🏆 | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✓ 7e-16 | — | — | — | — | 2.26 ms | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✓ bind | — | — | — | — | 5.04 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✓ bind | — | — | — | — | 4.76 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✓ bind | — | — | — | — | 5.06 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✓ bind | — | — | — | — | 4.97 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +5e-01 | — | — | — | — | 2.08 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +5e-01 | — | — | — | — | 2.61 ms | — | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_mdatools | source | — | — | — | — | 22.4 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 2e-15 | — | — | — | — | 1.24 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ~ shape 2e-15 | — | — | — | — | 1.18 ms🏆 | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ~ shape 2e-15 | — | — | — | — | 1.21 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ~ shape 2e-15 | — | — | — | — | 1.19 ms | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ 7e-16 | — | — | — | — | 1.23 ms | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✓ 7e-16 | — | — | — | — | 1.29 ms | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✓ bind | — | — | — | — | 3.02 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✓ bind | — | — | — | — | 3.76 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✓ bind | — | — | — | — | 3.59 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✓ bind | — | — | — | — | 3.56 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +5e-01 | — | — | — | — | 1.88 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +5e-01 | — | — | — | — | 2.19 ms | — | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_mdatools | source | — | — | — | — | 17.1 ms | — | — | — | — | — | — | — | — | — |
:::
::::
---
_See also_: [benchmark overview](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)