Differentials

Manopt.differential_forward_logsMethod
Y = differential_forward_logs(M, p, X)

compute the differenital of forward_logs $F$ on the PowerManifold manifold M at p and direction X , in the power manifold array, the differential of the function

\[F_i(x) = \sum_{j ∈ \mathcal I_i} \log_{p_i} p_j$, \quad i ∈ \mathcal G,\]

where $\mathcal G$ is the set of indices of the PowerManifold manifold M and $\mathcal I_i$ denotes the forward neighbors of $i$.

Input

  • M – a PowerManifold manifold
  • p – a point.
  • X – a tangent vector.

Ouput

  • Y – resulting tangent vector in $T_x\mathcal N$ representing the differentials of the logs, where $\mathcal N$ is thw power manifold with the number of dimensions added to size(x).
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