Changelog
All notable Changes to the Julia package Manopt.jl will be documented in this file. The file was started with Version 0.4.
The format is based on Keep a Changelog, and this project adheres to Semantic Versioning.
[0.4.69] – August 3, 2024
Changed
- Improved performance of Interior Point Newton Method.
[0.4.68] – August 2, 2024
Added
- an Interior Point Newton Method, the
interior_point_newton - a
conjugate_residualAlgorithm to solve a linear system on a tangent space. ArmijoLinesearchnow allows for additionaladditional_decrease_conditionandadditional_increase_conditionkeywords to add further conditions to accept additional conditions when to accept an decreasing or increase of the stepsize.- add a
DebugFeasibilityto have a debug print about feasibility of points in constrained optimisation employing the newis_feasiblefunction - add a
InteriorPointCentralityConditioncheck that can be added for step candidates within the line search ofinterior_point_newton - Add Several new functors
- the
LagrangianCost,LagrangianGradient,LagrangianHessian, that based on a constrained objective allow to construct the hessian objective of its Lagrangian - the
CondensedKKTVectorFieldand itsCondensedKKTVectorFieldJacobian, that are being used to solve a linear system withininterior_point_newton - the
KKTVectorFieldas well as itsKKTVectorFieldJacobianand `KKTVectorFieldAdjointJacobian - the
KKTVectorFieldNormSqand itsKKTVectorFieldNormSqGradientused within the Armijo line search ofinterior_point_newton
- the
- New stopping criteria
- A
StopWhenRelativeResidualLessfor theconjugate_residual - A
StopWhenKKTResidualLessfor theinterior_point_newton
- A
[0.4.67] – July 25, 2024
Added
max_stepsizemethods forHyperrectangle.
Fixed
- a few typos in the documentation
WolfePowellLinesearchno longer usesmax_stepsizewith invalid point by default.
[0.4.66] June 27, 2024
Changed
- Remove functions
estimate_sectional_curvature,ζ_1,ζ_2,close_pointfromconvex_bundle_method - Remove some unused fields and arguments such as
p_estimate,ϱ,α, fromConvexBundleMethodStatein favor of jutk_max - Change parameter
Rplacement inProximalBundleMethodStateto fifth position
[0.4.65] June 13, 2024
Changed
- refactor stopping criteria to not store a
sc.reasoninternally, but instead only generate the reason (and hence allocate a string) when actually asked for a reason.
[0.4.64] June 4, 2024
Added
- Remodel the constraints and their gradients into separate
VectorGradientFunctionsto reduce code duplication and encapsulate the inner model of these functions and their gradients - Introduce a
ConstrainedManoptProblemto model different ranges for the gradients in the newVectorGradientFunctions beyond the defaultNestedPowerRepresentation - introduce a
VectorHessianFunctionto also model that one can provide the vector of Hessians to constraints - introduce a more flexible indexing beyond single indexing, to also include arbitrary ranges when accessing vector functions and their gradients and hence also for constraints and their gradients.
Changed
- Remodel
ConstrainedManifoldObjectiveto store anAbstractManifoldObjectiveinternally instead of directlyfandgrad_f, allowing also Hessian objectives therein and implementing access to this Hessian - Fixed a bug that Lanczos produced NaNs when started exactly in a minimizer, since we divide by the gradient norm.
Deprecated
- deprecate
get_grad_equality_constraints(M, o, p), useget_grad_equality_constraint(M, o, p, :)from the more flexible indexing instead.
[0.4.63] May 11, 2024
Added
:reinitialize_direction_updateoption for quasi-Newton behavior when the direction is not a descent one. It is now the new default forQuasiNewtonState.- Quasi-Newton direction update rules are now initialized upon start of the solver with the new internal function
initialize_update!.
Fixed
- ALM and EPM no longer keep a part of the quasi-Newton subsolver state between runs.
Changed
- Quasi-Newton solvers:
:reinitialize_direction_updateis the new default behavior in case of detection of non-descent direction instead of:step_towards_negative_gradient.:step_towards_negative_gradientis still available when explicitly set using thenondescent_direction_behaviorkeyword argument.
[0.4.62] May 3, 2024
Changed
- bumped dependency of ManifoldsBase.jl to 0.15.9 and imported their numerical verify functions. This changes the
throw_errorkeyword used internally to aerror=with a symbol.
[0.4.61] April 27, 2024
Added
- Tests use
Aqua.jlto spot problems in the code - introduce a feature-based list of solvers and reduce the details in the alphabetical list
- adds a
PolyakStepsize - added a
get_subgradientforAbstractManifoldGradientObjectivessince their gradient is a special case of a subgradient.
Fixed
get_last_stepsizewas defined in quite different ways that caused ambiguities. That is now internally a bit restructured and should work nicer. Internally this means that the interim dispatch onget_last_stepsize(problem, state, step, vars...)was removed. Now the only two left areget_last_stepsize(p, s, vars...)and the one directly checkingget_last_stepsize(::Stepsize)for stored values.- the accidentally exported
set_manopt_parameter!is no longer exported
Changed
get_manopt_parameterandset_manopt_parameter!have been revised and better documented, they now use more semantic symbols (with capital letters) instead of direct field access (lower letter symbols). Since these are not exported, this is considered an internal, hence non-breaking change.- semantic symbols are now all nouns in upper case letters
:activeis changed to:Activity
[0.4.60] April 10, 2024
Added
RecordWhenActiveto allow records to be deactivated during runtime, symbol:WhenActiveRecordSubsolverto record the result of a subsolver recording in the main solver, symbol:SubsolverRecordStoppingReasonto record the reason a solver stopped- made the
RecordFactorymore flexible and quite similar toDebugFactory, such that it is now also easy to specify recordings at the end of solver runs. This can especially be used to record final states of sub solvers.
Changed
- being a bit more strict with internal tools and made the factories for record non-exported, so this is the same as for debug.
Fixed
- The name
:Subsolverto generateDebugWhenActivewas misleading, it is now called:WhenActivereferring to “print debug only when set active, that is by the parent (main) solver”. - the old version of specifying
Symbol => RecordActionfor later access was ambiguous, since
it could also mean to store the action in the dictionary under that symbol. Hence the order for access was switched to RecordAction => Symbol to resolve that ambiguity.
[0.4.59] April 7, 2024
Added
- A Riemannian variant of the CMA-ES (Covariance Matrix Adaptation Evolutionary Strategy) algorithm,
cma_es.
Fixed
- The constructor dispatch for
StopWhenAnywithVectorhad incorrect element type assertion which was fixed.
[0.4.58] March 18, 2024
Added
- more advanced methods to add debug to the beginning of an algorithm, a step, or the end of the algorithm with
DebugActionentries at:Start,:BeforeIteration,:Iteration, and:Stop, respectively. - Introduce a Pair-based format to add elements to these hooks, while all others ar now added to :Iteration (no longer to
:All) - (planned) add an easy possibility to also record the initial stage and not only after the first iteration.
Changed
- Changed the symbol for the
:Stepdictionary to be:Iteration, to unify this with the symbols used in recording, and removed the:Allsymbol. On the fine granular scale, all but:Startdebugs are now reset on init. Since these are merely internal entries in the debug dictionary, this is considered non-breaking. - introduce a
StopWhenSwarmVelocityLessstopping criterion forparticle_swarmreplacing the current default of the swarm change, since this is a bit more effective to compute
Fixed
- fixed the outdated documentation of
TruncatedConjugateGradientState, that now correctly state thatpis no longer stored, but the algorithm runs onTpM. - implemented the missing
get_iterateforTruncatedConjugateGradientState.
[0.4.57] March 15, 2024
Changed
convex_bundle_methoduses thesectional_curvaturefromManifoldsBase.jl.convex_bundle_methodno longer has the unusedk_minkeyword argument.ManifoldsBase.jlnow is running on Documenter 1.3,Manopt.jldocumentation now uses DocumenterInterLinks to refer to sections and functions fromManifoldsBase.jl
Fixed
- fixes a type that when passing
sub_kwargstotrust_regionscaused an error in the decoration of the sub objective.
[0.4.56] March 4, 2024
Added
- The option
:step_towards_negative_gradientfornondescent_direction_behaviorin quasi-Newton solvers does no longer emit a warning by default. This has been moved to amessage, that can be accessed/displayed withDebugMessages DebugMessagesnow has a second positional argument, specifying whether all messages, or just the first (:Once) should be displayed.
[0.4.55] March 3, 2024
Added
- Option
nondescent_direction_behaviorfor quasi-Newton solvers. By default it checks for non-descent direction which may not be handled well by some stepsize selection algorithms.
Fixed
- unified documentation, especially function signatures further.
- fixed a few typos related to math formulae in the doc strings.
[0.4.54] February 28, 2024
Added
convex_bundle_methodoptimization algorithm for non-smooth geodesically convex functionsproximal_bundle_methodoptimization algorithm for non-smooth functions.StopWhenSubgradientNormLess,StopWhenLagrangeMultiplierLess, and stopping criteria.
Fixed
- Doc strings now follow a vale.sh policy. Though this is not fully working, this PR improves a lot of the doc strings concerning wording and spelling.
[0.4.53] February 13, 2024
Fixed
- fixes two storage action defaults, that accidentally still tried to initialize a
:Population(as modified back to:Iterate0.4.49). - fix a few typos in the documentation and add a reference for the subgradient method.
[0.4.52] February 5, 2024
Added
- introduce an environment persistent way of setting global values with the
set_manopt_parameter!function using Preferences.jl. - introduce such a value named
:Modeto enable a"Tutorial"mode that shall often provide more warnings and information for people getting started with optimisation on manifolds
[0.4.51] January 30, 2024
Added
- A
StopWhenSubgradientNormLessstopping criterion for subgradient-based optimization. - Allow the
message=of theDebugIfEntrydebug action to contain a format element to print the field in the message as well.
[0.4.50] January 26, 2024
Fixed
- Fix Quasi Newton on complex manifolds.
[0.4.49] January 18, 2024
Added
- A
StopWhenEntryChangeLessto be able to stop on arbitrary small changes of specific fields - generalises
StopWhenGradientNormLessto accept arbitrarynorm=functions - refactor the default in
particle_swarmto no longer “misuse” the iteration change, but actually the new one the:swarmentry
[0.4.48] January 16, 2024
Fixed
- fixes an imprecision in the interface of
get_iteratethat sometimes led to the swarm ofparticle_swarmbeing returned as the iterate. - refactor
particle_swarmin naming and access functions to avoid this also in the future. To access the whole swarm, one now should useget_manopt_parameter(pss, :Population)
[0.4.47] January 6, 2024
Fixed
- fixed a bug, where the retraction set in
check_Hessianwas not passed on to the optional innercheck_gradientcall, which could lead to unwanted side effects, see #342.
[0.4.46] January 1, 2024
Changed
- An error is thrown when a line search from
LineSearches.jlreports search failure. - Changed default stopping criterion in ALM algorithm to mitigate an issue occurring when step size is very small.
- Default memory length in default ALM subsolver is now capped at manifold dimension.
- Replaced CI testing on Julia 1.8 with testing on Julia 1.10.
Fixed
- A bug in
LineSearches.jlextension leading to slower convergence. - Fixed a bug in L-BFGS related to memory storage, which caused significantly slower convergence.
[0.4.45] December 28, 2023
Added
- Introduce
sub_kwargsandsub_stopping_criterionfortrust_regionsas noticed in #336
Changed
WolfePowellLineSearch,ArmijoLineSearchstep sizes now allocate lesslinesearch_backtrack!is now available- Quasi Newton Updates can work in-place of a direction vector as well.
- Faster
safe_indicesin L-BFGS.
[0.4.44] December 12, 2023
Formally one could consider this version breaking, since a few functions have been moved, that in earlier versions (0.3.x) have been used in example scripts. These examples are now available again within ManoptExamples.jl, and with their “reappearance” the corresponding costs, gradients, differentials, adjoint differentials, and proximal maps have been moved there as well. This is not considered breaking, since the functions were only used in the old, removed examples. Each and every moved function is still documented. They have been partly renamed, and their documentation and testing has been extended.
Changed
- Bumped and added dependencies on all 3 Project.toml files, the main one, the docs/, an the tutorials/ one.
artificial_S2_lemniscateis available asManoptExample.Lemniscateand works on arbitrary manifolds now.artificial_S1_signalis available asManoptExample.artificial_S1_signalartificial_S1_slope_signalis available asManoptExamples.artificial_S1_slope_signalartificial_S2_composite_bezier_curveis available asManoptExamples.artificial_S2_composite_Bezier_curveartificial_S2_rotation_imageis available asManoptExamples.artificial_S2_rotation_imageartificial_S2_whirl_imageis available asManoptExamples.artificial_S2_whirl_imageartificial_S2_whirl_patchis available asManoptExamples.artificial_S2_whirl_pathartificial_SAR_imageis available asManoptExamples.artificial_SAR_imageartificial_SPD_imageis available asManoptExamples.artificial_SPD_imageartificial_SPD_image2is available asManoptExamples.artificial_SPD_imageadjoint_differential_forward_logsis available asManoptExamples.adjoint_differential_forward_logsadjoint:differential_bezier_controlis available asManoptExamples.adjoint_differential_Bezier_control_pointsBezierSegmentis available asManoptExamples.BeziérSegmentcost_acceleration_bezieris available asManoptExamples.acceleration_Beziercost_L2_acceleration_bezieris available asManoptExamples.L2_acceleration_BeziercostIntrICTV12is available asManoptExamples.Intrinsic_infimal_convolution_TV12costL2TVis available asManoptExamples.L2_Total_VariationcostL2TV12is available asManoptExamples.L2_Total_Variation_1_2costL2TV2is available asManoptExamples.L2_second_order_Total_VariationcostTVis available asManoptExamples.Total_VariationcostTV2is available asManoptExamples.second_order_Total_Variationde_casteljauis available asManoptExamples.de_Casteljaudifferential_forward_logsis available asManoptExamples.differential_forward_logsdifferential_bezier_controlis available asManoptExamples.differential_Bezier_control_pointsforward_logsis available asManoptExamples.forward_logsget_bezier_degreeis available asManoptExamples.get_Bezier_degreeget_bezier_degreesis available asManoptExamples.get_Bezier_degreesget_Bezier_inner_pointsis available asManoptExamples.get_Bezier_inner_pointsget_bezier_junction_tangent_vectorsis available asManoptExamples.get_Bezier_junction_tangent_vectorsget_bezier_junctionsis available asManoptExamples.get_Bezier_junctionsget_bezier_pointsis available asManoptExamples.get_Bezier_pointsget_bezier_segmentsis available asManoptExamples.get_Bezier_segmentsgrad_acceleration_bezieris available asManoptExamples.grad_acceleration_Beziergrad_L2_acceleration_bezieris available asManoptExamples.grad_L2_acceleration_Beziergrad_Intrinsic_infimal_convolution_TV12is available asManoptExamples.Intrinsic_infimal_convolution_TV12grad_TVis available asManoptExamples.grad_Total_VariationcostIntrICTV12is available asManoptExamples.Intrinsic_infimal_convolution_TV12project_collaborative_TVis available asManoptExamples.project_collaborative_TVprox_parallel_TVis available asManoptExamples.prox_parallel_TVgrad_TV2is available asManoptExamples.prox_second_order_Total_Variationprox_TVis available asManoptExamples.prox_Total_Variationprox_TV2is available asManopExamples.prox_second_order_Total_Variation
[0.4.43] November 19, 2023
Added
- vale.sh as a CI to keep track of a consistent documentation
[0.4.42] November 6, 2023
Added
- add
Manopt.JuMP_Optimizerimplementing JuMP's solver interface
[0.4.41] November 2, 2023
Changed
trust_regionsis now more flexible and the sub solver (Steihaug-Toint tCG by default) can now be exchanged.adaptive_regularization_with_cubicsis now more flexible as well, where it previously was a bit too much tightened to the Lanczos solver as well.- Unified documentation notation and bumped dependencies to use DocumenterCitations 1.3
[0.4.40] October 24, 2023
Added
- add a
--helpargument todocs/make.jlto document all available command line arguments - add a
--exclude-tutorialsargument todocs/make.jl. This way, when quarto is not available on a computer, the docs can still be build with the tutorials not being added to the menu such that documenter does not expect them to exist.
Changes
- Bump dependencies to
ManifoldsBase.jl0.15 andManifolds.jl0.9 - move the ARC CG subsolver to the main package, since
TangentSpaceis now already available fromManifoldsBase.
[0.4.39] October 9, 2023
Changes
- also use the pair of a retraction and the inverse retraction (see last update) to perform the relaxation within the Douglas-Rachford algorithm.
[0.4.38] October 8, 2023
Changes
- avoid allocations when calling
get_jacobian!within the Levenberg-Marquard Algorithm.
Fixed
- Fix a lot of typos in the documentation
[0.4.37] September 28, 2023
Changes
- add more of the Riemannian Levenberg-Marquard algorithms parameters as keywords, so they can be changed on call
- generalize the internal reflection of Douglas-Rachford, such that is also works with an arbitrary pair of a reflection and an inverse reflection.
[0.4.36] September 20, 2023
Fixed
- Fixed a bug that caused non-matrix points and vectors to fail when working with approximate
[0.4.35] September 14, 2023
Added
- The access to functions of the objective is now unified and encapsulated in proper
get_functions.
[0.4.34] September 02, 2023
Added
- an
ManifoldEuclideanGradientObjectiveto allow the cost, gradient, and Hessian and other first or second derivative based elements to be Euclidean and converted when needed. - a keyword
objective_type=:Euclideanfor all solvers, that specifies that an Objective shall be created of the new type
[0.4.33] August 24, 2023
Added
ConstantStepsizeandDecreasingStepsizenow have an additional fieldtype::Symbolto assess whether the step-size should be relatively (to the gradient norm) or absolutely constant.
[0.4.32] August 23, 2023
Added
- The adaptive regularization with cubics (ARC) solver.
[0.4.31] August 14, 2023
Added
- A
:Subsolverkeyword in thedebug=keyword argument, that activates the newDebugWhenActiveto de/activate subsolver debug from the main solversDebugEvery`.
[0.4.30] August 3, 2023
Changed
- References in the documentation are now rendered using DocumenterCitations.jl
- Asymptote export now also accepts a size in pixel instead of its default
4cmsize andrendercan be deactivated setting it tonothing.
[0.4.29] July 12, 2023
Fixed
- fixed a bug, where
cyclic_proximal_pointdid not work with decorated objectives.
[0.4.28] June 24, 2023
Changed
max_stepsizewas specialized forFixedRankManifoldto follow Matlab Manopt.
[0.4.27] June 15, 2023
Added
- The
AdaptiveWNGradstepsize is available as a new stepsize functor.
Fixed
- Levenberg-Marquardt now possesses its parameters
initial_residual_valuesandinitial_jacobian_falso as keyword arguments, such that their default initialisations can be adapted, if necessary
[0.4.26] June 11, 2023
Added
- simplify usage of gradient descent as sub solver in the DoC solvers.
- add a
get_statefunction - document
indicates_convergence.
[0.4.25] June 5, 2023
Fixed
- Fixes an allocation bug in the difference of convex algorithm
[0.4.24] June 4, 2023
Added
- another workflow that deletes old PR renderings from the docs to keep them smaller in overall size.
Changes
- bump dependencies since the extension between Manifolds.jl and ManifoldsDiff.jl has been moved to Manifolds.jl
[0.4.23] June 4, 2023
Added
- More details on the Count and Cache tutorial
Changed
- loosen constraints slightly
[0.4.22] May 31, 2023
Added
- A tutorial on how to implement a solver
[0.4.21] May 22, 2023
Added
- A
ManifoldCacheObjectiveas a decorator for objectives to cache results of calls, using LRU Caches as a weak dependency. For now this works with cost and gradient evaluations - A
ManifoldCountObjectiveas a decorator for objectives to enable counting of calls to for example the cost and the gradient - adds a
return_objectivekeyword, that switches the return of a solver to a tuple(o, s), whereois the (possibly decorated) objective, andsis the “classical” solver return (state or point). This way the counted values can be accessed and the cache can be reused. - change solvers on the mid level (form
solver(M, objective, p)) to also accept decorated objectives
Changed
- Switch all Requires weak dependencies to actual weak dependencies starting in Julia 1.9
[0.4.20] May 11, 2023
Changed
- the default tolerances for the numerical
check_functions were loosened a bit, such thatcheck_vectorcan also be changed in its tolerances.
[0.4.19] May 7, 2023
Added
- the sub solver for
trust_regionsis now customizable and can now be exchanged.
Changed
- slightly changed the definitions of the solver states for ALM and EPM to be type stable
[0.4.18] May 4, 2023
Added
- A function
check_Hessian(M, f, grad_f, Hess_f)to numerically verify the (Riemannian) Hessian of a functionf
[0.4.17] April 28, 2023
Added
- A new interface of the form
alg(M, objective, p0)to allow to reuse objectives without creatingAbstractManoptSolverStates and callingsolve!. This especially still allows for any decoration of the objective and/or the state usingdebug=, orrecord=.
Changed
- All solvers now have the initial point
pas an optional parameter making it more accessible to first time users,gradient_descent(M, f, grad_f)is equivalent togradient_descent(M, f, grad_f, rand(M))
Fixed
- Unified the framework to work on manifold where points are represented by numbers for several solvers
[0.4.16] April 18, 2023
Fixed
- the inner products used in
truncated_gradient_descentnow also work thoroughly on complex matrix manifolds
[0.4.15] April 13, 2023
Changed
trust_regions(M, f, grad_f, hess_f, p)now has the Hessianhess_fas well as the start pointp0as an optional parameter and approximate it otherwise.trust_regions!(M, f, grad_f, hess_f, p)has the Hessian as an optional parameter and approximate it otherwise.
Removed
- support for
ManifoldsBase.jl0.13.x, since with the definition ofcopy(M,p::Number), in 0.14.4, that one is used instead of defining it ourselves.
[0.4.14] April 06, 2023
Changed
particle_swarmnow uses much more in-place operations
Fixed
particle_swarmused quite a fewdeepcopy(p)commands still, which were replaced bycopy(M, p)
[0.4.13] April 09, 2023
Added
get_messageto obtain messages from sub steps of a solverDebugMessagesto display the new messages in debug- safeguards in Armijo line search and L-BFGS against numerical over- and underflow that report in messages
[0.4.12] April 4, 2023
Added
- Introduce the Difference of Convex Algorithm (DCA)
difference_of_convex_algorithm(M, f, g, ∂h, p0) - Introduce the Difference of Convex Proximal Point Algorithm (DCPPA)
difference_of_convex_proximal_point(M, prox_g, grad_h, p0) - Introduce a
StopWhenGradientChangeLessstopping criterion
[0.4.11] March 27, 2023
Changed
- adapt tolerances in tests to the speed/accuracy optimized distance on the sphere in
Manifolds.jl(part II)
[0.4.10] March 26, 2023
Changed
- adapt tolerances in tests to the speed/accuracy optimized distance on the sphere in
Manifolds.jl
[0.4.9] March 3, 2023
Added
- introduce a wrapper that allows line searches from LineSearches.jl to be used within Manopt.jl, introduce the manoptjl.org/stable/extensions/ page to explain the details.
[0.4.8] February 21, 2023
Added
- a
status_summarythat displays the main parameters within several structures of Manopt, most prominently a solver state
Changed
- Improved storage performance by introducing separate named tuples for points and vectors
- changed the
showmethods ofAbstractManoptSolverStates to display their `state_summary - Move tutorials to be rendered with Quarto into the documentation.
[0.4.7] February 14, 2023
Changed
- Bump
[compat]entry of ManifoldDiff to also include 0.3
[0.4.6] February 3, 2023
Fixed
- Fixed a few stopping criteria even indicated to stop before the algorithm started.
[0.4.5] January 24, 2023
Changed
- the new default functions that include
pare used where possible - a first step towards faster storage handling
[0.4.4] January 20, 2023
Added
- Introduce
ConjugateGradientBealeRestartto allow CG restarts using Beale‘s rule
Fixed
- fix a type in
HestenesStiefelCoefficient
[0.4.3] January 17, 2023
Fixed
- the CG coefficient
βcan now be complex - fix a bug in
grad_distance
[0.4.2] January 16, 2023
Changed
- the usage of
innerin line search methods, such that they work well with complex manifolds as well
[0.4.1] January 15, 2023
Fixed
- a
max_stepsizeper manifold to avoid leaving the injectivity radius, which it also defaults to
[0.4.0] January 10, 2023
Added
- Dependency on
ManifoldDiff.jland a start of moving actual derivatives, differentials, and gradients there. AbstractManifoldObjectiveto store the objective within theAbstractManoptProblem- Introduce a
CostGradstructure to store a function that computes the cost and gradient within one function. - started a
changelog.mdto thoroughly keep track of changes
Changed
AbstractManoptProblemreplacesProblem- the problem now contains a
AbstractManoptSolverStatereplacesOptionsrandom_point(M)is replaced byrand(M)from `ManifoldsBase.jlrandom_tangent(M, p)is replaced byrand(M; vector_at=p)