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Changelog

All notable changes to Β΄Manifolds.jlΒ΄ will be documented in this file.

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

0.11.7 (2025-11-27)

Added

  • added a more structured version for the extension with Test.jl that now introduces (#839)
    • a complete test suite Manifolds.Test.test_manifold(M; kwargs...) it follows the structure of the one recently written for LieGroups.jl.
    • a lot of small test functions like Manifolds.Test.test_exp(M, p, X; kwargs...) with the goal of providing one test for each individual API function
  • New methods and functions for working in a chart: local_metric, inverse_local_metric, levi_civita_affine_connection!, christoffel_symbols_second.
  • Default implementation of get_vector! and get_coordinates! for InducedBasis using automatic differentiation.
  • A new tutorial that describes working with the Levi-Civita connection for a Riemannian metric defined through inner in a chart.

Fixed

  • the circle represented in angles (Circle()) had a wrong default and provided a project and embed method while not being an embedded manifold, this is now fixed, but might cause errors for some users. To fix the errors, note that the old behavior of embed(M, p) was just returning p, and the old behavior of project(M, p) was Manifolds.sym_rem(p). (#839)

0.11.6 (2025-11-19)

Changed

  • rand on Hyperrectangle returns valid points in the presence of -Inf and Inf.
  • check_point on Hyperrectangle checks that there are no NaNs.

0.11.5 (2025-11-13)

Added

  • rand for SkewHermitianMatrices

0.11.4 (2025-11-07)

Changed

  • Random tangent vectors on Hyperbolic are now much shorter (their norm is on the order of 1) to guide users away from numerical issues with long vectors.

0.11.3 (2025-11-04)

Fixed

  • fixes a few inconsistencies regarding get_embedding, which now consistently uses a point type as positional second argument.

0.11.2 (2025-10-30)

Fixed

  • fixed the default_retraction_method for AbstractSphere to be the stabilized exponential map to avoid accumulations of rounding errors when the tangent vector is not exactly tangent.
  • fixed the contributing.md to mention runic as the code formatter.

0.11.1 (2025-10-24)

Fixed

  • fix a few small errors regarding the forwarding of retract, retract_fused, and inverse_retract when using a MetricManifold.jl (cf (#823))
  • document why we kept that vector_transport_direction and vector_transport_to are not automatically forwarded in MetricManifold.jl

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 {𝔽, T} where 𝔽 is the number type and T the type of size parameter (either a TypeParameter or a Tuple). this changed internally
    • ArraySphere{T<:Tuple,𝔽} to ArraySphere{𝔽, T<:Tuple}
    • CenteredMatrices{T, 𝔽} to CenteredMatrices{𝔽, T}
    • Euclidean{T, 𝔽} to Euclidean{𝔽, T}
    • FixedRankMatrices{T, 𝔽} to FixedRankMatrices{𝔽, T}
    • GeneralizedGrassmann{T, 𝔽, B} to GeneralizedGrassmann{𝔽, T, B}
    • GeneralizedStiefel{T, 𝔽, B} to GeneralizedStiefel{𝔽, T, B}
    • Grassmann{T, 𝔽, B} to Grassmann{𝔽, T, B}
    • GeneralUnitaryMatrices{T, 𝔽, S} to GeneralUnitaryMatrices{𝔽, T, S}
    • GraphManifold{G <: AbstractGraph, 𝔽, TM, T <: GraphManifoldType} to GraphManifold{𝔽, G <: AbstractGraph, TM, T <: GraphManifoldType}
    • Grassmann{T, 𝔽} to Grassmann{𝔽, T}
    • HamiltonianMatrices{T, 𝔽} to HamiltonianMatrices{𝔽, T}
    • Oblique{T, 𝔽, S} to Oblique{𝔽, T, S}
    • SkewHermitianMatrices{T, 𝔽} to SkewHermitianMatrices{𝔽, T}
    • Sphere{T, 𝔽} to Sphere{𝔽, T}
    • SphereSymmetricMatrices{T, 𝔽} to SphereSymmetricMatrices{𝔽, T}
    • Stiefel{T, 𝔽} to Stiefel{𝔽, T}
    • SymmetricMatrices{T, 𝔽} to SymmetricMatrices{𝔽, T}
    • SymplecticGrassmann{T, 𝔽} to SymplecticGrassmann{𝔽, T}
    • SymplecticStiefel{T, 𝔽} to SymplecticStiefel{𝔽, T}
    • Tucker{T, D, 𝔽} to Tucker{𝔽, T, D}
    • UnitaryMatrices{T, 𝔽} to UnitaryMatrices{𝔽, 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(β„‚)

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 (– 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 (– 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 (– 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 (– 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(ℝ) of Euclidean(3, field=β„‚) now has 6 vectors, and DefaultOrthonormalBasis(β„‚) 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 (– 2024-08-29)

Changed

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

0.10.0 (– 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 Οƒ.
    • 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 (– 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 (– 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 (– 2024-05-07)

Added

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

0.9.17 (– 2024-04-23)

Added

  • Hyperrectangle manifold with boundary.

0.9.16 (– 2024-04-01)

Changed

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

0.9.15 (– 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 (– 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 (– 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 (– 2024-01-21)

Fixed

  • Fixed var on TranslationGroup.

0.9.11 (– 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 (– 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 (– 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 (– 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.