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Restructure docs
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mateuszbaran committed Dec 2, 2024
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# Basic usage

You can calculate Riemannian gradient of a function defined in its embedding in multiple ways.
For example, `rb_onb_fd51` corresponds to a finite differencing scheme and `rb_onb_fwdd` calculates gradient using [`ForwardDiff.jl`](https://github.com/JuliaDiff/ForwardDiff.jl). [`DifferentiationInterface.jl`](https://github.com/JuliaDiff/DifferentiationInterface.jl) is used to select the backend.
[`DifferentiationInterface.jl`](https://github.com/JuliaDiff/DifferentiationInterface.jl) can be used to select the backend.

```@example
using ManifoldDiff
Expand All @@ -24,4 +24,6 @@ println(ManifoldDiff.gradient(s2, f, q, rb_onb_fwdd))
println(ManifoldDiff.gradient(s2, f, q, rb_proj_zyg))
```

In this example `rb_onb_fd51` corresponds to a finite differencing scheme, `rb_onb_fwdd` calculates gradient using [`ForwardDiff.jl`](https://github.com/JuliaDiff/ForwardDiff.jl) and `rb_proj_zyg` uses [`Zygote.jl`](https://github.com/FluxML/Zygote.jl) for reverse mode automatic differentiation.

[`TangentDiffBackend`](@ref) reduces dimensionality of the problem to the intrinsic dimension of the manifold, while [`RiemannianProjectionBackend`](@ref) relies on converting Euclidean gradient in the embedding to the Riemannian one.

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