Description Usage Arguments Value References See Also Examples

`pdParTrans`

computes the parallel transport on the manifold of HPD matrices
equipped with the affine-invariant Riemannian metric as described in e.g., Chapter 2 of \insertCiteC18pdSpecEst. That is,
the function computes the parallel transport of a Hermitian matrix `W`

in the tangent space
at the HPD matrix `P`

along a geodesic curve in the direction of the Hermitian matrix `V`

in the tangent space at `P`

for a unit time step.

1 | ```
pdParTrans(P, V, W)
``` |

`P` |
a |

`V` |
a |

`W` |
a |

a *(d,d)*-dimensional Hermitian matrix corresponding to the parallel transportation of `W`

in
the direction of `V`

along a geodesic curve for a unit time step.

1 2 3 4 5 6 7 8 | ```
## Transport the vector W to the tangent space at the identity
W <- matrix(complex(real = rnorm(9), imaginary = rnorm(9)), nrow = 3)
diag(W) <- rnorm(3)
W[lower.tri(W)] <- t(Conj(W))[lower.tri(W)]
p <- matrix(complex(real = rnorm(9), imaginary = rnorm(9)), nrow = 3)
P <- t(Conj(p)) %*% p
pdParTrans(P, Logm(P, diag(3)), W) ## whitening transport
``` |

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