Description Usage Arguments Details Value Note Author(s) References See Also Examples

Functions that deal with the singular value decomposition of an output Y, for use with Gaussian process lists

1 2 3 4 | ```
pcweights(Y, weights.num = NULL, cutoff = 99)
getSingularValues(Y)
singularValueImportance(Y)
numSingularValues(Y, cutoff = 99)
``` |

`Y` |
the output to decompose, where each column of |

`weights.num` |
optionally, the number of principle component weights to keep |

`cutoff` |
if specified, |

Utilizes the singular value decomposition (SVD) of `Y`

, Y = UDVprime. Columns of `Y`

should correspond to a single k-dimensional observation (e.g., functional output of a computer model, evaluated at a particular input).

For a k x m matrix `Y`

, and r = min(k,m), in the complete SVD, `U`

is k x r, `D`

is r x r, containing the singular values along the diagonal, and `Vprime`

is r x m. The output `Y`

is approximated by keeping l < r singular values, keeping a UD matrix of dimension k x l, and the `Vprime`

matrix of dimension l x m. Each column of `Vprime`

now contains l principle component weights, which can be used to reconstruct the functional output.

`pcweights`

returns a list with components:

`UD` |
the UD matrix corresponding to the number of principle components kept |

`Vprime` |
The Vprime matrix corresponding to the number of principle components kept |

Note: the number of principle component weights kept is equal to dim(UD)[2]

`getSingularValues`

returns a matrix containing the singular values of `Y`

`numSingularValues`

returns the minimum number of singular values accounting for `cutoff`

percent of the variation in `Y`

`singularValueImportance`

returns a matrix where element i corresponds to the percentage of total variation in `Y`

accounted for by the first i singular values

these functions are utilized by `mlegp`

to fit Gaussian processes to principle component weights

Garrett M. Dancik dancikg@easternct.edu

Heitmann, K., Higdon, D., Nakhleh, C., Habib, S., 2006. Cosmic Calibration. The Astrophysical Journal, 646, 2, L1-L4.

https://github.com/gdancik/mlegp/

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