Description Usage Arguments Details Value See Also Examples

`npf`

returns a completed Euclidean Distance Matrix D, with dimension d,
from a partial Euclidean Distance Matrix using the methods of Fang & O'Leary (2012)

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`D` |
An nxn partial-distance matrix to be completed. D must satisfy a list of conditions (see details), with unkown entries set to NA. |

`A` |
a weight matrix, with |

`d` |
the dimension of the resulting completion |

`dmax` |
the maximum dimension to consider during dimension relaxation |

`decreaseDim` |
during dimension reduction, the number of dimensions to decrease each step |

`stretch` |
should the distance matrix be multiplied by a scalar constant? If no, stretch = NULL, otherwise stretch is a positive scalar |

`method` |
The method used for dimension reduction, one of "Linear" or "NLP". |

`toler` |
convergence tolerance for the algorithm |

This is an implementation of the Nonconvex Position Formulation (npf) for Euclidean Distance Matrix Completion, as proposed in 'Euclidean Distance Matrix Completion Problems' (Fang & O'Leary, 2012).

The method seeks to minimize the following:

*||A \cdot (D - K(XX'))||_{F}^{2}*

where the function K() is that described in gram2edm, and the norm is Frobenius. Minimization is over X, the nxp matrix of node locations.

The matrix D is a partial-distance matrix, meaning some of its entries are unknown. It must satisfy the following conditions in order to be completed:

diag(D) = 0

If

*a_{ij}*is known,*a_{ji} = a_{ij}*If

*a_{ij}*is unknown, so is*a_{ji}*The graph of D must be connected. If D can be decomposed into two (or more) subgraphs, then the completion of D can be decomposed into two (or more) independent completion problems.

`D` |
an nxn matrix of the completed Euclidean distances |

`optval` |
the minimum value achieved of the target function during minimization |

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