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Fix a few typos. (#723)
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kellertuer authored May 24, 2024
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7 changes: 7 additions & 0 deletions NEWS.md
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Expand Up @@ -5,6 +5,13 @@ All notable changes to this project will be documented in this file.
The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/),
and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0.html).

## [0.9.19] – unreleased

### Changed

* fixed a few typos in the doc string of the SPD fixed determinant description.


## [0.9.18] – 2024-05-07

### Added
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13 changes: 7 additions & 6 deletions src/manifolds/SPDFixedDeterminant.jl
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Expand Up @@ -11,7 +11,9 @@ p ∈ ℝ^{n×n} \ \big|\ a^\mathrm{T}pa > 0 \text{ for all } a ∈ ℝ^{n}\back
\bigr\}.
````
This manifold is modelled as a submanifold of [`SymmetricPositiveDefinite`](@ref)`(n)`.
This manifold is modelled as a submanifold of [`SymmetricPositiveDefinite`](@ref)`(n)`,
see [`IsEmbeddedSubmanifold`](@ref `ManifoldsBase.IsEmbeddedSubmanifold`) for the implications,
but for example retractions and inverse retractions are all available
These matrices are sometimes also called [isochoric](https://en.wiktionary.org/wiki/isochoric), which refers to the interpretation of
the matrix representing an ellipsoid. All ellipsoids that represent points on this manifold have the same volume.
Expand All @@ -21,18 +23,18 @@ and consists of all symmetric matrices with zero trace
```math
T_p\mathcal P_d(n) =
\bigl\{
X \in \mathbb R^{n×n} \big|\ X=X^\mathrm{T} \text{ and } \operatorname{tr}(p) = 0
X \in \mathbb R^{n×n} \big|\ X=X^\mathrm{T} \text{ and } \operatorname{tr}(X) = 0
\bigr\},
```
since for a constant determinant we require that `0 = D\det(p)[Z] = \det(p)\operatorname{tr}(p^{-1}Z)` for all tangent vectors ``Z``.
Additionally we store the tangent vectors as `X=p^{-1}Z`, i.e. symmetric matrices.
since for a constant determinant we require that ``0 = D\det(p)[Z] = \det(p)\operatorname{tr}(p^{-1}Z)`` for all tangent vectors ``Z``.
Additionally we store the tangent vectors as ``X=p^{-1}Z``, i.e. symmetric matrices.
# Constructor
SPDFixedDeterminant(n::Int, d::Real=1.0; parameter::Symbol=:type)
Generate the manifold $\mathcal P_d(n) \subset \mathcal P(n)$ of determinant ``d``,
which defaults to 1.
which defaults to `1.0`.
`parameter`: whether a type parameter should be used to store `n`. By default size
is stored in type. Value can either be `:field` or `:type`.
Expand Down Expand Up @@ -154,7 +156,6 @@ end
Project the symmetric matrix `X` onto the tangent space at `p` of the
(sub-)manifold of s.p.d. matrices of determinant `M.d` (in place of `Y`),
by setting its diagonal (and hence its trace) to zero.
"""
project(M::SPDFixedDeterminant, p, X)

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