BandedCholesky: Cholesky factor of a band matrix in
\(O(n b^2)\). IncompleteCholesky: IC(0) on the sparsity pattern
(entries above drop_tol) with its relative Frobenius error.
WendlandTaper: Wendland's compactly supported correlation, as
fields::Wendland. TaperedSimulate: simulation from the
tapered covariance. LmcCosimulate: joint simulation of
coregionalised fields (linear model of coregionalisation).
SimulationSensitivity: realisations under several ranges or sills
with common random numbers. NestedDecomposition: a nested model
simulated as independent components with variance shares.
RefinedSolve: Cholesky solve with iterative refinement.
BlockLuSimulate: block-sequential LU simulation of a grid, each
tile conditioned on simulated nodes within halo. Identical to the
Python arm morie.fn.cholext.
Usage
BandedCholesky(A, bandwidth)
IncompleteCholesky(A, drop_tol = 0)
WendlandTaper(d, theta, dimension = 2L, k = 1L)
TaperedSimulate(coords, model, theta, k = 1L, nsim = 1L, seed = 1, mean = 0)
LmcCosimulate(coords, components, nsim = 1L, seed = 1, means = NULL)
SimulationSensitivity(coords, model, ranges = NULL, sills = NULL, seed = 1)
NestedDecomposition(coords, components, seed = 1)
RefinedSolve(A, b, iterations = 3L)
BlockLuSimulate(xs, ys, model, block = 4L, halo = 1, seed = 1, mean = 0)Arguments
- A
Symmetric positive-definite matrix.
- bandwidth
Half-bandwidth.
- drop_tol
Sparsity threshold.
- d
Distances.
- theta
Taper range.
- dimension
Space dimension.
- k
Wendland smoothness (0 to 3).
- coords
Coordinates.
- model
Covariance model (as
KrigingCovariance).- nsim
Realisations.
- seed
Philox seed.
- mean
Mean.
- components
List of
list(B, model)(LmcCosimulate) or of covariance components (NestedDecomposition).- means
Field means.
- ranges, sills
Parameter values.
- b
Right-hand side.
- iterations
Refinement steps.
- xs, ys
Grid coordinates.
- block
Tile size.
- halo
Conditioning radius.
References
Golub, G. H. and Van Loan, C. F. (2013). Matrix Computations, 4th edn. Johns Hopkins University Press.
Wendland, H. (1995). Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree. Advances in Computational Mathematics 4, 389-396.
Furrer, R., Genton, M. G. and Nychka, D. (2006). Covariance tapering for interpolation of large spatial datasets. JCGS 15, 502-523.
Davis, M. W. (1987). Production of conditional simulations via the LU triangular decomposition of the covariance matrix. Mathematical Geology 19, 91-98.