MatrixLieGroup implementation and traits

[dellaert]

UPDATE: took timing and new vecs out of this PR for easier review, avoid segafult in #2191 .

This PR introduces a significant refactoring of how matrix Lie groups are handled in GTSAM, aiming to reduce code duplication and improve consistency:

• New MatrixLieGroup Concept: A new CRTP helper class MatrixLieGroup has been introduced in gtsam/base/MatrixLieGroup.h. This class provides generic implementations for common matrix Lie group operations like vec() (vectorization of the matrix representation) and AdjointMap().
• Refactoring of Lie.h: Existing MatrixLieGroup related definitions and functions have been moved from gtsam/base/Lie.h to the new gtsam/base/MatrixLieGroup.h. The AdjointMap assignment in IsLieGroup concept check in Lie.h was also corrected.
• Migration of Geometry Classes: Numerous geometry classes (e.g., Gal3, Pose2, Pose3, Rot2, SO3, SO4, SO, Similarity2, Similarity3, NavState) have been updated to inherit from MatrixLieGroup instead of LieGroup.
• Removal of Redundant Implementations: Individual vec() and AdjointMap() implementations in various geometry classes have been removed, as they now leverage the generic implementations provided by MatrixLieGroup.
• Updated traits Specializations: The traits specializations for the migrated classes have been updated to use internal::MatrixLieGroup.
• New Tests: Added tests verify the correctness of the generic AdjointMap() and vec() implementations for various matrix Lie groups.
• FrobeniusFactor Updates: FrobeniusFactor and FrobeniusBetweenFactor now utilize the generic traits::Vec and traits::AdjointMap methods.

[Copilot]

Pull Request Overview

This PR refactors how matrix Lie groups are implemented by introducing a generic MatrixLieGroup CRTP helper and migrating existing geometry and dynamics classes to use it, removing duplicate vectorization and adjoint implementations, and updating dependent factors and tests.

• Introduce MatrixLieGroup concept in gtsam/base/MatrixLieGroup.h with default implementations of vec() and AdjointMap().
• Migrate geometry classes (SO3, Pose2, Pose3, Gal3, NavState, etc.) to inherit from MatrixLieGroup instead of LieGroup, removing their specialized vec() and AdjointMap() code.
• Update FrobeniusFactor and FrobeniusBetweenFactor to assert IsMatrixLieGroup<T> and use traits<T>::Vec / traits<T>::AdjointMap for vectorization and adjoint computations.

Reviewed Changes

Copilot reviewed 36 out of 36 changed files in this pull request and generated no comments.

Show a summary per file

File	Description
gtsam/base/MatrixLieGroup.h	Added CRTP helper MatrixLieGroup with generic vec() and AdjointMap()
gtsam/slam/FrobeniusFactor.h	Added IsMatrixLieGroup asserts and switched to traits<T>::Vec/AdjointMap
gtsam/geometry/SO3.h	Changed SO3 to inherit from MatrixLieGroup<SO3,3,3> and removed old code
gtsam/geometry/Pose3.h	Switched Pose3 to MatrixLieGroup<Pose3,6,4> and removed vec() override
gtsam/navigation/NavState.h	Switched NavState to MatrixLieGroup<NavState,9,5> and updated traits

Comments suppressed due to low confidence (3)

gtsam/geometry/tests/testGal3.cpp:1202

• [nitpick] The test name uses lowercase 'vec' whereas other vec tests (e.g., TEST(Pose3, Vec)) use uppercase 'Vec' for consistency. Consider renaming to TEST(Gal3, Vec).

TEST(Gal3, AdjointMap) {

gtsam/geometry/SOn.h:54

• The generic implementation for SOn via MatrixLieGroup is introduced here, but there are no corresponding unit tests for SOn< N > (especially for N>4 or dynamic N). Consider adding tests for vec() and AdjointMap() to validate the generic code.

class SO : public MatrixLieGroup<SO<N>, internal::DimensionSO(N), N> {

gtsam/geometry/SOn.cpp:102

• [nitpick] There are large blocks of commented-out legacy vec() implementations across geometry sources (e.g., SOn.cpp). Since MatrixLieGroup now provides the generic implementation, these commented sections can be removed to improve code clarity.

  return result;

[dellaert]

@mkielo3 adding you to look at Gal3 changes. After this PR merges you should probably rebase your changes on this.