Description Usage Arguments Note References See Also Examples

`pdMedian`

calculates a weighted intrinsic median of a sample of *(d,d)*-dimensional
HPD matrices based on a Weiszfeld algorithm intrinsic to the chosen metric.In the case of the
affine-invariant Riemannian metric as detailed in e.g., \insertCiteB09pdSpecEst[Chapter 6] or
\insertCitePFA05pdSpecEst, the intrinsic Weiszfeld algorithm in \insertCiteF09pdSpecEst is used.
By default, the unweighted intrinsic median is computed.

1 | ```
pdMedian(M, w, metric = "Riemannian", maxit = 1000, reltol)
``` |

`M` |
a |

`w` |
an |

`metric` |
the distance measure, one of |

`maxit` |
maximum number of iterations in gradient descent algorithm. Defaults to |

`reltol` |
optional tolerance parameter in gradient descent algorithm. Defaults to |

The function does not check for positive definiteness of the input matrices, and (depending on the specified metric) may fail if matrices are close to being singular.

1 2 3 4 5 6 7 8 9 10 11 | ```
## Generate random sample of HPD matrices
m <- function(){
X <- matrix(complex(real=rnorm(9), imaginary=rnorm(9)), nrow=3)
t(Conj(X)) %*% X
}
M <- replicate(100, m())
## Generate random weight vector
z <- rnorm(100)
w <- abs(z)/sum(abs(z))
## Compute weighted intrinsic (Riemannian) median
pdMedian(M, w)
``` |

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