feat: add cubic spline, damped pseudo-inverse, incremental QR least squares and SE(3) transform by gabrielfrasantos · Pull Request #357 · embedded-pro/numerical-toolbox-cpp

gabrielfrasantos · 2026-10-23T16:22:55Z

Summary

Tier 3 of the roadmap items added in #353.

chore: create a sync pid #61 Cubic spline (math): vector-valued C² spline with clamped or natural ends. All channels share one TridiagonalSolver factorization (from feat: add angle utilities, tridiagonal solver, friction compensation, symplectic integrators and motion profiles #355). Evaluation uses a binary interval search.
build(deps): bump the patch-minor-action-updates group with 2 updates #62 Damped pseudo-inverse (solvers): from one SVD (tall or wide), the damped least-squares solve σ/(σ² + λ²) plus the exact, undamped null-space projector.
build(deps): bump actions/upload-artifact from 4.6.2 to 5.0.0 #63 Incremental QR least squares (estimators/offline): streaming Givens QR in fixed memory, with a rank-revealing SVD solve that returns the minimum-norm solution, the rank, the identifiable row space and the residual RMS.
build(deps): bump github/codeql-action from 3.28.16 to 4.30.8 #53 SE(3) transform (math): twists (v; ω), wrenches (f; n), adjoint, exp/log, SO(3) log and the base-frame pose error.

Spec corrections (SE(3), float accuracy)

Exp: coefficients are computed on the unnormalised axis, sin φ/φ, (1 − cos φ)/φ² in half-angle form and (φ − sin φ)/φ³, with Taylor series below φ = 0.1. There is no ω = 0 branch and no small-angle cancellation.
Log: the axis comes from the symmetric part of R for every φ > π/2, not only within ε of π. With the spec's near-π-only switch, Exp∘Log errors reached 3.5e-5 just outside the band. Now they are ≈6e-7 for every φ ≤ π.

Verification

Unit tests pass on host GCC and Clang. Randomized cross-checks against independent references, run outside the repo:

Spline: knots reproduced, end conditions held, and C¹/C² continuity at interior knots exact to ≈1e-13 in double (2000 random fits).
Damped pseudo-inverse: agrees with the closed-form (AᵀA + λ²I)⁻¹Aᵀb or Aᵀ(AAᵀ + λ²I)⁻¹b to ≈1e-5 on random 2×3, 6×7, 7×6 and 4×4 matrices; P² − P ≈ 1e-6.
Incremental QR: agrees with double-precision normal equations to ≈3e-6 (300 problems, 5–205 rows).
SE(3): Exp agrees with a double-precision 4×4 matrix exponential to ≈6e-7, and Exp∘Log round-trips to ≈6e-7, over 3000 random twists including φ ≈ 1e-4 and φ ∈ [3, 3.1405].

Coverage with template instances merged is ≥ 96% on all four headers. CI's gcovr counts the spec's unexercised 6×7 pseudo-inverse instantiation separately, as it already does for the SVD header.

Stack

Base: main (#355 merged). Merge before #358, which targets this branch.

Generated by Claude Code

github-actions · 2026-10-23T16:24:33Z

✅⚠️MegaLinter analysis: Success with warnings

Descriptor	Linter	Files	Fixed	Errors	Elapsed time
✅ ACTION	actionlint	7		0	0.29s
✅ CPP	clang-format	468	11	0	2.63s
✅ CPP	cppcheck	468		0	5.46s
✅ DOCKERFILE	hadolint	1		0	0.39s
✅ JSON	jsonlint	8		0	0.08s
✅ JSON	prettier	8	8	0	0.29s
⚠️ MARKDOWN	markdownlint	148	2	157	2.03s
✅ MARKDOWN	markdown-table-formatter	148	12	0	0.21s
⚠️ SPELL	lychee	259		23	22.6s
✅ YAML	prettier	12	3	0	0.4s
✅ YAML	yamllint	12		0	0.4s

Detailed Issues

⚠️ SPELL / lychee - 23 errors

📝 Summary
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🔍 Total..........603
🔗 Unique.........452
✅ Successful.....568
⏳ Timeouts.........0
🔀 Redirected.....151
👻 Excluded........11
❓ Unknown..........0
🚫 Errors..........23
⛔ Unsupported.....23

Errors in .github/workflows/static-analysis.yml
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Errors in CHANGELOG.md
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Errors in doc/filters/active/AhrsMadgwickMahony.md
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Errors in doc/filters/active/KalmanFilter.md
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[ERROR] file://doc/filters/solvers/DiscreteAlgebraicRiccatiEquation.md (at 134:3) | File not found. Check if file exists and path is correct

Errors in doc/performance-optimization/README.md
[403] https://developer.arm.com/documentation/100166/latest/ (at 472:3) | Rejected status code: 403 Forbidden
[403] https://developer.arm.com/documentation/dui0473/latest (at 474:3) | Rejected status code: 403 Forbidden

Errors in README.md
[ERROR] file:///releases/latest (at 39:14) | File not found. Check if file exists and path is correct
[404] https://embedded-pro.github.io/embedded-dsp-control/ (at 38:1) | Rejected status code: 404 Not Found

Hint: Followed 151 redirects. You might want to consider replacing redirecting URLs with the resolved URLs. Use verbose mode (`-v`/`-vv`) to see redirection details.
Hint: You can configure accepted/rejected response codes with `-a` or `--accept`

⚠️ MARKDOWN / markdownlint - 157 errors

ne-h1 First line in a file should be a top-level heading [Context: "Canonical rules: `AGENTS.md`. ..."]
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doc/solvers/JacobiEigenSolver.md:5:401 error MD013/line-length Line length [Expected: 400; Actual: 443]
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doc/solvers/JacobiEigenSolver.md:45:401 error MD013/line-length Line length [Expected: 400; Actual: 427]
doc/solvers/RungeKuttaIntegrators.md:9:401 error MD013/line-length Line length [Expected: 400; Actual: 509]
doc/solvers/SpectralRadius.md:5:401 error MD013/line-length Line length [Expected: 400; Actual: 665]
doc/solvers/SymplecticIntegrators.md:7:401 error MD013/line-length Line length [Expected: 400; Actual: 486]
doc/solvers/SymplecticIntegrators.md:35:401 error MD013/line-length Line length [Expected: 400; Actual: 476]
doc/solvers/SymplecticIntegrators.md:63:401 error MD013/line-length Line length [Expected: 400; Actual: 431]
doc/windowing/window.md:5:401 error MD013/line-length Line length [Expected: 400; Actual: 415]
README.md:1 error MD041/first-line-heading/first-line-h1 First line in a file should be a top-level heading [Context: "[![Quality Gate Status](https:..."]
README.md:9:401 error MD013/line-length Line length [Expected: 400; Actual: 442]
README.md:17:401 error MD013/line-length Line length [Expected: 400; Actual: 472]
roadmap/README.md:11 error MD040/fenced-code-language Fenced code blocks should have a language specified [Context: "```"]

(Truncated to last 20000 characters out of 20595)

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Deploy roadmap item 61: C² cubic spline through up to MaxKnots knots with clamped or natural ends. All channels share the abscissa and one TridiagonalSolver factorization. Evaluate clamps x to the knot range, finds the interval by binary search and returns value, slope and curvature per channel. Checked on 2000 random fits beyond the unit tests: knots reproduced, one-sided first and second derivatives agree at interior knots (≈1e-13 in double), and end conditions hold. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01Q53m7MZDmHwocmKbhhd2o5

Deploy roadmap item 62. One SVD (tall or wide) gives the damped least-squares solve Σ σ/(σ² + λ²)(uᵢᵀb)vᵢ, which falls back to a thresholded undamped inverse for λ = 0, plus the exact orthogonal null-space projector I − Σ_{i<r} vᵢvᵢᵀ. The projector is left undamped so that A·P stays zero whatever λ is. Checked against closed-form (AᵀA + λ²I)⁻¹Aᵀb / Aᵀ(AAᵀ + λ²I)⁻¹b in double on random 2×3, 6×7, 7×6 and 4×4 matrices (≈1e-5 agreement, P² − P ≈ 1e-6). Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01Q53m7MZDmHwocmKbhhd2o5

Deploy roadmap item 63: streaming linear least squares in fixed memory. Each row is rotated into an upper-triangular factor with Givens rotations, so YᵀY is never formed. Solve runs a rank-revealing SVD of that factor and returns the minimum-norm parameters, the rank, the identifiable row space and the residual RMS. Checked against double-precision normal equations on 300 random 3-parameter problems with 5–205 rows (parameters agree to ≈3e-6). Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01Q53m7MZDmHwocmKbhhd2o5

Deploy roadmap item 53 with linear-first 6-vectors: twists (v; ω), wrenches (f; n). Covers composition, closed-form inverse, adjoint, twist/wrench transforms, exponential, logarithm, SO(3) log and a base-frame pose error. Two changes from the spec, both for float accuracy: - Exp uses unnormalised-axis coefficients sin φ/φ, (1 − cos φ)/φ² (in half-angle form) and (φ − sin φ)/φ³, with short series below φ = 0.1. There is no ω = 0 branch and no cancellation at small angles. - LogRotation takes the axis from the symmetric part of R for every φ > π/2, not only within ε of π. Exp∘Log then round-trips to ≈6e-7 for all φ ≤ π; the near-π-only switch left 3.5e-5 errors at φ ≈ π − 2e-3. Exp matches a double-precision 4×4 matrix exponential to ≈6e-7 on 3000 random twists. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01Q53m7MZDmHwocmKbhhd2o5

Apply markdown-table-formatter's layout to the tables this tier adds or edits, as suggested by MegaLinter. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01Q53m7MZDmHwocmKbhhd2o5

Define operator* as an inline friend, matching Quaternion, Matrix and Complex, as flagged by SonarCloud (cpp:S2807). Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01Q53m7MZDmHwocmKbhhd2o5

sonarqubecloud · 2026-10-23T17:49:33Z

Quality Gate passed

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97.4% Coverage on New Code
0.0% Duplication on New Code

See analysis details on SonarQube Cloud

gabrielfrasantos mentioned this pull request Oct 23, 2026

feat: add Levenberg–Marquardt and Goldfarb–Idnani active-set QP #358

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gabrielfrasantos force-pushed the claude/brave-einstein-5nj7y6-tier2 branch from 690f252 to 3f9b2c4 Compare October 23, 2026 16:26

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gabrielfrasantos mentioned this pull request Oct 23, 2026

feat: add angle utilities, tridiagonal solver, friction compensation, symplectic integrators and motion profiles #355

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Base automatically changed from claude/brave-einstein-5nj7y6-tier1 to main October 23, 2026 17:25

claude added 6 commits October 23, 2026 17:46

docs: align markdown tables

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Apply markdown-table-formatter's layout to the tables this tier adds or edits, as suggested by MegaLinter. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01Q53m7MZDmHwocmKbhhd2o5

gabrielfrasantos force-pushed the claude/brave-einstein-5nj7y6-tier3 branch from cef9e71 to 920b43d Compare October 23, 2026 17:47

gabrielfrasantos merged commit fd49d30 into main Oct 23, 2026
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gabrielfrasantos deleted the claude/brave-einstein-5nj7y6-tier3 branch October 23, 2026 17:52

embedded-releaser-app Bot mentioned this pull request Oct 23, 2026

chore(main): release 4.0.0 #327

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feat: add cubic spline, damped pseudo-inverse, incremental QR least squares and SE(3) transform - #357

feat: add cubic spline, damped pseudo-inverse, incremental QR least squares and SE(3) transform#357
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Summary

Spec corrections (SE(3), float accuracy)

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sonarqubecloud Bot commented Oct 23, 2026

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