https://github.com/cran/fields
Tip revision: 8eab500c3dad2103092ff68706417414fe53e16b authored by Doug Nychka on 22 September 2009, 20:23:49 UTC
version 6.01
version 6.01
Tip revision: 8eab500
fields.diagonalize.R
# fields, Tools for spatial data
# Copyright 2004-2007, Institute for Mathematics Applied Geosciences
# University Corporation for Atmospheric Research
# Licensed under the GPL -- www.gpl.org/licenses/gpl.html
"fields.diagonalize" <- function(A, B) {
hold <- eigen(A, symmetric = TRUE)
# square root of A
hold2 <- (t(hold$vectors) * sqrt(1/hold$values))
#
# note: interated transposes are a quick way to post multiply by a
# diagonal matrix
#
#
# A.inv.sqrt = hold2
# A.inv = hold%*% t(hold2)
#
# eigen decomp of A.inv.sqrt B t( A.inv.sqrt)
#
hold <- eigen((hold2) %*% B %*% t(hold2), symmetric = TRUE)
# the magic G matrix used throughout fields.
G <- t(hold2) %*% hold$vectors
#
# Note:
# G simultaneously diagonalizes two matrices:
#
# G^T A G= I
# G^T B G= D
#
# and in terms of application we also have the useful
# diagonalization
#
# (A +lambda B)^{-1} = G( I + lambda D)^{-1} G^T
list(G = G, D = hold$values)
}