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Changelog

All notable changes to this project will be documented in this file.

The format is based on Keep a Changelog, and this project adheres to Semantic Versioning.

0.11.0 (2025-10-02)

Added

  • a function metric(M) analogous to embedding(M) and connection(M) that returns the metric of the manifold M.
  • a DefaultMetric() type to specify that the manifold uses some specific metric, that is not further named.

Changed

  • Switch to using Runic.jl as code formatter
  • refactored all manifolds to use a parameter order of {๐”ฝ, T} where ๐”ฝ is the number type and T the type of size parameter (either a TypeParameter or a Tuple). this changed internally
    • ArraySphere{T<:Tuple,๐”ฝ} to ArraySphere{๐”ฝ, T<:Tuple}
    • CenteredMatrices{T, ๐”ฝ} to CenteredMatrices{๐”ฝ, T}
    • Euclidean{T, ๐”ฝ} to Euclidean{๐”ฝ, T}
    • FixedRankMatrices{T, ๐”ฝ} to FixedRankMatrices{๐”ฝ, T}
    • GeneralizedGrassmann{T, ๐”ฝ, B} to GeneralizedGrassmann{๐”ฝ, T, B}
    • GeneralizedStiefel{T, ๐”ฝ, B} to GeneralizedStiefel{๐”ฝ, T, B}
    • Grassmann{T, ๐”ฝ, B} to Grassmann{๐”ฝ, T, B}
    • GeneralUnitaryMatrices{T, ๐”ฝ, S} to GeneralUnitaryMatrices{๐”ฝ, T, S}
    • GraphManifold{G <: AbstractGraph, ๐”ฝ, TM, T <: GraphManifoldType} to GraphManifold{๐”ฝ, G <: AbstractGraph, TM, T <: GraphManifoldType}
    • Grassmann{T, ๐”ฝ} to Grassmann{๐”ฝ, T}
    • HamiltonianMatrices{T, ๐”ฝ} to HamiltonianMatrices{๐”ฝ, T}
    • Oblique{T, ๐”ฝ, S} to Oblique{๐”ฝ, T, S}
    • SkewHermitianMatrices{T, ๐”ฝ} to SkewHermitianMatrices{๐”ฝ, T}
    • Sphere{T, ๐”ฝ} to Sphere{๐”ฝ, T}
    • SphereSymmetricMatrices{T, ๐”ฝ} to SphereSymmetricMatrices{๐”ฝ, T}
    • Stiefel{T, ๐”ฝ} to Stiefel{๐”ฝ, T}
    • SymmetricMatrices{T, ๐”ฝ} to SymmetricMatrices{๐”ฝ, T}
    • SymplecticGrassmann{T, ๐”ฝ} to SymplecticGrassmann{๐”ฝ, T}
    • SymplecticStiefel{T, ๐”ฝ} to SymplecticStiefel{๐”ฝ, T}
    • Tucker{T, D, ๐”ฝ} to Tucker{๐”ฝ, T, D}
    • UnitaryMatrices{T, ๐”ฝ} to UnitaryMatrices{๐”ฝ, T}
  • the functions canoncial_project, differential_canonical_project, horizontal_lift, horizontal_component, get_total_space, and vertical_component have been moved upstream to ManifoldsBase.jl

Removed

  • the trait system that was present additionally to the wrapper types for metric, embedding and connections. Those were moved to default_X functions and the dispatch was adapted to still obtain the same logic/behaviour.
  • the QuotientManifold type, since it was not really used and its proper definition would require functionality from LieGroups.jl
  • all functions related to the GroupManifolds type and corresponding traits using the old trait system have been removed here after being deprecated for a while now. These have been redesigned and introduced in the new package LieGroups.jl, see their How to transition from GroupManifolds tutorial for all details.
  • all deprecated tangent vector types that had TVector in their name
    • instead of HyperboloidTVectoruseHyperboloidTangentVector
    • instead of OrthogonalTVector useOrthogonalTangentVector
    • instead of PoincareBallTVector use PoincareBallTangentVector
    • instead of PoincareHalfSpaceTVector use PoincareHalfSpaceTangentVector
    • instead of ProjectorTVector use ProjectorTangentVector
    • instead of StiefelTVector use StiefelTangentVector
    • instead of TuckerTVector use TuckerTangentVector
    • instead of UMVTVector use UMVTangentVector
  • The QuotientManifold type has been removed, the API for general (implicit) quotient manifolds is now already in ManifoldsBase.jl.
  • The retract_exp_ode! and retract_exp_ode_fused! functions were removed. The cases in which they were correct are covered by solve_chart_exp_ode, and it was too easy to use retract_exp_ode! incorrectly.

0.10.23 (2025-07-19)

Fixed

  • fix a small bug in the point checks of general unitary matrices.

0.10.22 (2025-06-25)

Fixed

  • Support for ForwardDiff.jl v1

0.10.21 (2025-06-24)

Added

  • Support for ForwardDiff.jl v1

0.10.20 (2025-06-16)

Fixed

  • Fix in-place computation of exp! for GeneralLinear.

0.10.19 (2025-06-14)

Added

  • riemannian_gradient for the GeneralLinear manifold
  • riemannian_gradient method for ProductManifold.

Fixed

  • Fix the projection and embedding of tangent vectors on GeneralLinear.

0.10.18 (2025-05-29)

Fixed

  • Fix the supertype of PoincareBallTangentVector to be AbstractTangentVector
  • Fix the supertype of StiefelTangentVector to be AbstractTangentVector
  • Fix riemannian_gradient for fixed rank matrices, which did not work due to a small bug in the default fallback and a missing metric specification.

0.10.17 (2025-04-21)

Changed

Note that while it is currently not so easy to use Manifolds.jl and LieGroups.jl together due to the common definitions that are here now deprecated, it might still take a reasonable time to do a breaking release here, since we do not have a very good reason to yet.

0.10.16 (2025-04-08)

Changed

  • Added all [compat] entries also for the docs/ and tutorials/ environments
  • get_vector on Circle no longer returns SArray when no static arrays are passed as arguments.

Fixed

  • a copy pase error in the new determinant one manifold from the last release.

0.10.15 (2025-03-28)

Added

  • a DeterminantOneMatrices manifold of matrices of determinant one.

Changed

  • the following internal types were renamed since their super type also uses the singular
    • AbsoluteDeterminantOneMatrices to AbsoluteDeterminantOneMatrixType
    • DeterminantOneMatrices to DeterminantOneMatrixType

Fixed

  • fix rand! to also work on the Circle(โ„‚)

0.10.14 (- 2025-02-18)

Changed

  • Introduced new implementation of parallel transport on Rotations(3) based on Rodrigues' rotation

formula.

0.10.13 (- 2025-02-10)

Changed

  • Bumped dependency of ManifoldsBase.jl to 1.0, split exp into exp (without optional argument t) and exp_fused (with argument t) and similarly retract to retract and retract_fused.
  • ManifoldsBase.jl 1.0 also moved from TVector to TangentVectors in type names. The following names are adapted
    • Renamed HyperboloidTVector (now deprecated) to HyperboloidTangentVector
    • Renamed OrthogonalTVector (now deprecated) to OrthogonalTangentVector
    • Renamed PoincareBallTVector (now deprecated) to PoincareBallTangentVector
    • Renamed PoincareHalfSpaceTVector (now deprecated) to PoincareHalfSpaceTangentVector
    • Renamed ProjectorTVector (now deprecated) to ProjectorTangentVector
    • Renamed StiefelTVector (now deprecated) to StiefelTangentVector
    • Renamed TuckerTVector (now deprecated) to TuckerTangentVector
    • Renamed UMVTVector (now deprecated) to UMVTangentVector
  • The internal access array_value is now called internal_value, compare to its renaming in ManifoldsBase

0.10.12 (- 2025-01-10)

Added

  • Orthonormal bases for CholeskySpace and LogCholesky metric for SymmetricPositiveDefinite.
  • rand for CholeskySpace.

Changed

  • Improved performance of selected get_vector and get_coordinates methods for complex Euclidean manifold.

0.10.11 (- 2025-01-02)

Added

  • Bases and rand for HeisenbergMatrices and InvertibleMatrices.

0.10.10 (- 2024-12-20)

Added

  • the Segre manifold
  • the WarpedMetric for the Segremanifold

0.10.9 (- 2024-12-16)

Added

  • the Segre manifold
  • the WarpedMetric for the Segremanifold
  • The manifold HeisenbergMatrices as the underlying manifold of HeisenbergGroup.

Changed

  • about.md now also lists contributors of manifolds and a very short history of the package.

0.10.8 (โ€“ 2024-11-27)

Changed

  • Some methods related to get_vector for GeneralUnitaryMatrices now have AbstractVector upper bound for coefficients.
  • Minimum Julia version is now 1.10 (the LTS which replaced 1.6)
  • The dependency ManifoldDiff.jl has been upgraded from v0.3 to v0.4, to bring compatibility with DifferentiationInterface.jl.

0.10.7 (โ€“ 2024-11-16)

Added

  • adjoint_matrix for Lie groups, with optimized implementations for SO(2), SO(3), SE(2) and SE(3).

0.10.6 (โ€“ 2024-11-06)

Added

  • Two new actions: ComplexPlanarRotation, QuaternionRotation.
  • New function quaternion_rotation_matrix for converting quaternions to rotation matrices.
  • make.jl script now has more command line arguments, for example --exclude-tutorials when you do not want to build the tutorials but still look at the docs. See make.jl --help for more information.

0.10.5 (โ€“ 2024-10-24)

Added

  • the manifold InvertibleMatrices of invertible matrices

Changed

  • rewrote the CONTRIBUTING.md and adapt it to today's links and references.

0.10.4 (- 2024-10-20)

Added

  • uniform_distribution now has an error hint explaining what has to be done to make it work.
  • Euclidean now follows the new has_components function from ManifoldsBase.jl (0.15.18) and can handle also the r-norms now.
  • Union type MatrixGroup
  • Columnwise group action with arbitrary matrix groups
  • uniform_distribution now has an error hint explaining what has to be done to make it work.
  • lie_bracket is exactly zero on orthogonal Lie algebra in 2D

0.10.3 (- 2024-10-04)

Changed

  • Mildly breaking: the number system parameter now corresponds to the coefficients standing in front of basis vectors in a linear combination instead of components of a vector. For example, DefaultOrthonormalBasis() == DefaultOrthonormalBasis(โ„) of Euclidean(3, field=โ„‚) now has 6 vectors, and DefaultOrthonormalBasis(โ„‚) of the same manifold has 3 basis vectors.

Fixed

  • Fixed solve_exp_ode only returning the starting position (#744)
  • Fixed documentation of solve_exp_ode function signature (#740)

0.10.2 (- 2024-09-24)

Added

  • GroupManifold can now be called with two arguments, the third one defaulting to LeftInvariantRepresentation.

Changed

  • fixes a few typographical errors.

0.10.1 (โ€“ 2024-08-29)

Changed

  • identity_element on ProductManifold without RecursiveArrayTools.jl now prints a useful error message.

0.10.0 (โ€“ 2024-08-24)

Changed

  • Distributions.jl, RecursiveArrayTools.jl and HybridArrays.jl were moved to weak dependencies to reduce load time and improve extensibility.
  • translate_diff, inv_diff and thus apply_diff_group, are available for all the groups with invariant tangent vector storage.
  • SpecialEuclidean group now has a different default tangent vector representation, the left-invariant one; to get the old representation pass vectors=HybridTangentRepresentation() to the constructor of SpecialEuclidean.
  • adjoint_action takes a direction argument; by default it is LeftAction.
  • adjoint_action! is the necessary method to implement in groups with left-invariant tangent vector representation.
  • Fixed a few typos in the doc string of the SPD fixed determinant description.
  • Random point on the MultinomialSymmetricPositiveDefinite manifold was improved to make it more robust.

Added

  • Introduced exp_inv and log_inv based on exp_lie and log_lie. They are invariant to the group operation.
  • A tutorial about usage of group-related functionality.

Removed

  • Deprecated bindings:
    • ExtrinsicEstimation() (should be replaced with ExtrinsicEstimation(EfficientEstimator())),
    • Symplectic (renamed to SymplecticMatrices),
    • SymplecticMatrix (renamed to SymplecticElement).
    • AbstractEstimationMethod (renamed to AbstractApproximationMethod).
    • VectorBundleVectorTransport (renamed to FiberBundleProductVectorTransport).
    • rand on SymplecticMatrices and SymplecticStiefel no longer accepts hamiltonian_norm as an alias for ฯƒ.
    • mean! and median! no longer accept extrinsic_method (should be replaced with e = ExtrinsicEstimation(extrinsic_method)).
  • As a result of making Distributions.jl and RecursiveArrayTools.jl weak dependencies the following symbols are no longer exported from Manifolds.jl. Essential functionality is still available but distribution-related features may change in the future without a breaking release.
    • ArrayPartition (RecursiveArrayTools.jl needs to be explicitly imported),
    • ProjectedPointDistribution (not exported),
    • normal_tvector_distribution (not exported),
    • projected_distribution (not exported),
    • uniform_distribution (not exported).
  • Ability to create non-real SymplecticStiefel and SymplecticGrassmann manifolds; essential functionality was missing so it was removed until a more developed version is developed.

0.9.20 (โ€“ 2024-06-17)

Added

  • implemented parallel transport on the Grassmann manifold with respect to Stiefel representation

Changed

  • since now all exp/log/parallel transport are available for all representations of Grassmann, these are now also set as defaults, since they are more exact.

0.9.19 (โ€“ 2024-06-12)

Changed

  • Updated Project.toml compatibility entries.
  • Updated CI for Julia 1.11-beta

Fixed

  • a few typos in the doc string of the SPD fixed determinant description
  • several other typographical errors throughout the documentation

0.9.18 (โ€“ 2024-05-07)

Added

  • added the injectivity radius for the Stiefel manifold with Euclidean metric

0.9.17 (โ€“ 2024-04-23)

Added

  • Hyperrectangle manifold with boundary.

0.9.16 (โ€“ 2024-04-01)

Changed

  • NonlinearSolve.jl and PythonCall.jl are no longer an upper bounded dependency (bugs were fixed).

0.9.15 (โ€“ 2024-03-24)

Added

  • using DocumenterInterLinks for links to other Julia packages documentation.
  • Implementation of sectional_curvature, sectional_curvature_min and sectional_curvature_max for several manifolds.
  • sectional_curvature_matrix function and a tutorial on coordinate-free curvature.

Changed

  • default_vector_transport_method for GeneralUnitaryMatrices other than Rotations was changed to ProjectionTransport.

Fixed

  • typographical errors in tutorials/working-in-charts.jl.
  • several typographical errors in the docs
  • unifies to use two backticks `` for math instead of $ further in the docs

0.9.14 (โ€“ 2024-01-31)

Added

  • rand on UnitaryMatrices
  • rand on arbitrary GroupManifolds and manifolds with IsGroupManifold trait generating points and elements from the Lie algebra, respectively

0.9.13 (โ€“ 2024-01-24)

Added

  • added the real symplectic Grassmann manifold SymplecticGrassmann
  • Introduce the manifold of HamiltonianMatrices and a wrapper for Hamiltonian matrices
  • introduce rand(:HamiltonianMatrices)
  • extend rand to also rand! for HamiltonianMatrices, SymplecticMatrices and SymplecticStiefel
  • implement riemannian_gradient conversion for SymplecticMatrices and SymplecticGrassmann
  • the new manifold of MultinomialSymmetricPositiveDefinite matrices
  • rand! for MultinomialDoublyStochastic and MultinomialSymmetric

Deprecated

  • Rename Symplectic to SimplecticMatrices in order to have a Symplectic wrapper for such matrices as well in the future for the next breaking change.
  • Rename SymplecticMatrix to SymplecticElement to clarify that it is the special matrix $J_{2n}$ and not an arbitrary symplectic matrix.

Fixed

  • a bug that cause project for tangent vectors to return wrong results on MultinomialDoublyStochastic

0.9.12 (โ€“ 2024-01-21)

Fixed

  • Fixed var on TranslationGroup.

0.9.11 (โ€“ 2023-12-27)

Fixed

  • Fixed mixed array index number in-place parallel_transport_to! on zero-index Euclidean, on Julia 1.6.

0.9.10 (โ€“ 2023-12-27)

Added

  • Compatibility with RecursiveArrayTools v3.

Fixed

  • Fixed mixed array index number in-place parallel_transport_to! on real Circle, on Julia 1.6.
  • Violations of MD004 lint rule in this file.

0.9.9 (โ€“ 2023-12-25)

Fixed

  • introduced a nonzero atol for all point and vector checks that compre to zero. This makes those checks a bit more relaxed by default and resolves #630.
  • default_estimation_method(M, f) is deprecated, use default_approximation_method(M, f) for your specific method f on the manifold M.
  • AbstractEstimationMethod is deprecated, use AbstractApproximationMethod instead.

0.9.8 (- 2023-11-17)

Fixed

  • Improved distribution of random vector generation for rotation matrices and complex circle.

0.9.7 (โ€“ 2023-11-14)

Fixed

0.9.6 (- 2023-11-09)

Fixed

0.9.5 (- 2023-11-08)

Changed

  • identity_element now returns a complex matrix for unitary group.
  • number_of_coordinates is now exported.

0.9.4 (- 2023-11-06)

Added

  • Functions inv_diff, inv_diff!, adjoint_inv_diff and adjoint_inv_diff! that correspond to differentials and pullbacks of group inversion.
  • Julia 1.10-rc CI workflow.

Changed

  • Documentation project files are marked as compatible with BoundaryValueDiffEq v5.

Fixed

  • Fixed issue with incorrect implementation of apply_diff_group in GroupOperationAction with left backward and right forward action #669.

0.9.3 (- 2023-10-28)

Added

  • Support for BoundaryValueDiffEq v5.

0.9.2 (- 2023-10-27)

Added

  • rand(G; vector_at=Identity(G)) now works for translation, special orthogonal and special Euclidean groups G (issue #665).
  • get_embedding now works for GeneralUnitaryMultiplicationGroup.
  • Github action that checks for NEWS.md changes.

0.9.1 (- 2023-10-25)

Added

  • a new retraction and its inverse for the fixed Rank Manifolds, the orthographic retraction.

0.9.0 (- 2023-10-24)

Added

  • Vector bundles are generalized to fiber bundles. Old BundleFibers functionality was reworked to better match mathematical abstractions. Fiber bundle functionality is experimental and minor changes may happen without a breaking release, with the exception of TangentBundle which is considered to be stable.
  • RotationTranslationAction is introduced.

Changed

  • Sizes of all manifolds can now be either encoded in type or stored in a field to avoid over-specialization. The default is set to store the size in type parameter (except for PowerManifold and its variants), replicating the previous behavior. For field storage, pass the parameter=:field keyword argument to manifold constructor. For example statically sized CenteredMatrices{m,n} is now CenteredMatrices{TypeParameter{Tuple{m,n}}}, whereas the type of special Euclidean group with field-stored size is CenteredMatrices{Tuple{Int,Int}}. Similar change applies to:

    • CenteredMatrices{m,n},
    • CholeskySpace{N},
    • Elliptope{N,K},
    • Euclidean,
    • FixedRankMatrices{m,n,k},
    • KendallsPreShapeSpace{n,k},
    • KendallsShapeSpace{n,k},
    • GeneralLinear{n},
    • GeneralUnitaryMultiplicationGroup{n},
    • GeneralizedGrassmann{n,k},
    • GeneralizedStiefel{n,k},
    • Grassmann{n,k},
    • Heisenberg{n},
    • Hyperbolic{n},
    • MultinomialMatrices{N,M},
    • MultinomialDoublyStochastic{n},
    • MultinomialSymmetric{n},
    • Orthogonal{n},
    • PowerManifold,
    • PositiveArrays,
    • PositiveMatrices,
    • PositiveNumbers,
    • ProbabilitySimplex{n},
    • SPDFixedDeterminant{n},
    • SpecialLinear{n},
    • SpecialOrthogonal{n},
    • SpecialUnitary{n},
    • SpecialEuclidean{n},
    • SpecialEuclideanManifold{n},
    • Spectrahedron{n,k},
    • SphereSymmetricMatrices{N},
    • Stiefel{n,k},
    • SymmetricMatrices{N},
    • SymmetricPositiveDefinite{n},
    • SymmetricPositiveSemidefiniteFixedRank{n,k},
    • Symplectic{n},
    • SymplecticStiefel{n,k},
    • TranslationGroup,
    • Tucker.

    For example

    function Base.show(io::IO, ::CenteredMatrices{m,n}) where {m,n}
    return print(io, "CenteredMatrices($m, $n)")
end

    needs to be replaced with

    function Base.show(io::IO, ::CenteredMatrices{TypeParameter{Tuple{m,n}}}) where {m,n}
    return print(io, "CenteredMatrices($m, $n)")
end

    for statically-sized groups and

    function Base.show(io::IO, M::CenteredMatrices{Tuple{Int,Int}})
    m, n = get_parameter(M.size)
    return print(io, "CenteredMatrices($m, $n; parameter=:field)")
end

    for groups with size stored in field. Alternatively, you can use a single generic method like this:

    function Base.show(io::IO, M::CenteredMatrices{T}) where {T}
    m, n = get_parameter(M)
    if T <: TypeParameter
        return print(io, "CenteredMatrices($m, $n)")
    else
        return print(io, "CenteredMatrices($m, $n; parameter=:field)")
    end
end

  • Argument order for type aliases RotationActionOnVector and RotationTranslationActionOnVector: most often dispatched on argument is now first.

  • A more consistent handling of action direction was introduced. 4-valued ActionDirection was split into 2-valued ActionDirection (either left or right action) and GroupActionSide (action acting from the left or right side). See https://github.com/JuliaManifolds/Manifolds.jl/issues/637 for a design discussion.

Removed

  • ProductRepr is removed; please use ArrayPartition instead.
  • Default methods throwing "not implemented" ErrorException for some group-related operations. Standard MethodError is now thrown instead.
  • LinearAffineMetric was deprecated in a previous release and the symbol is now removed. Please use AffineInvariantMetric instead.