The Krig engines and support {fields} | R Documentation |
These are internal functions to Krig that compute the basic matrix decompositions or solve the linear systems needed to evaluate the Krig/Tps estimate. Others listed below do some simple housekeeping and formatting. Typically they are called from within Krig but can also be used directly if passed a Krig object list.
Krig.engine.default(out, verbose = FALSE) Krig.engine.knots(out, verbose = FALSE) Krig.engine.fixed( out, verbose=FALSE, lambda=NA) Krig.coef(out, lambda = out$lambda, y = NULL, yM = NULL, verbose = FALSE) Krig.check.xY(x, Y,Z, weights, na.rm, verbose = FALSE) Krig.cor.Y(obj, verbose = FALSE) Krig.transform.xY(obj, knots, verbose = FALSE) Krig.make.W( out, verbose=FALSE) Krig.make.Wi ( out, verbose=FALSE)
out |
A complete or partial Krig object. If partial it must have all the information accumulated to this calling point within the Krig function. |
obj |
Same as out . |
verbose |
If TRUE prints out intermediate results for debugging. |
lambda |
Value of smoothing parameter "hard wired" into decompositions.
Default is NA, i.e. use the value in out\$lambda . |
y |
New y vector for recomputing coefficients. OR for %d*% a vector or matrix. |
yM |
New y vector for recomputing coefficients but the values have already been collapsed into replicate group means. |
Y |
raw data Y vector |
x |
raw x matrix of spatial locations OR In the case of %d*%, y is either a matrix or a vector. As a vector, y, is interpreted to be the elements of a digaonal matrix. |
weights |
Raw weights vector passed to Krig |
Z |
Raw vector or matrix of additional covariates. |
na.rm |
NA action logical values passed to Krig |
knots |
Raw knots matrix passed to Krig |
ENGINES:
The engines are the code modules that handle the basic linear algebra needed to computed the estimated curve or surface coefficients. All the engine work on the data that has been reduced to unique locations and possibly replicate group means with the weights adjusted accordingly. All information needed for the decomposition are components in the Krig object passed to these functions.
Krig.engine.default
finds the decompositions for a Universal
Kriging estimator. by simultaneously diagonalizing the linear system
system for the coefficients of the estimator. The main advantage of this
form is that it is fairly stable numerically, even with ill-conditioned
covariance matrices with lambda > 0. (i.e. provided there is a "nugget"
or measure measurement error. Also the eigendecomposition allows for
rapid evaluation of the likelihood, GCV and coefficients for new data
vectors under different values of the smoothing parameter, lambda.
Krig.engine.knots
finds the decompositions in the case that the
covariance is evaluated at arbitrary locations possibly different than
the data locations (called knots). The intent of these decompositions is
to facilitate the evaluation at different values for lambda. There will
be computational savings when the number of knots is less than the
number of unique locations. (But the knots are as densely distributed as
the structure in the underlying spatial process.) This function call
fields.diagonalize, a function that computes the matrix and eigenvalues
that simultaneous diagonalize a nonnegative definite and a positive
definite matrix. These decompositions also facilitate multiple
evaluations of the likelihood and GCV functions in estimating a
smoothing parameter and also multiple solutions for different y vectors.
Krig.engine.fixed
are specific decomposition based on the Cholesky
factorization assuming that the smoothing parameter is fixed. This
is the only case that works in the sparse matrix.
Both knots and the full set of locations can be handled by this case.
The difference between the "knots" engine above is that only a single value
of lambda is considered in the fixed engine.
OTHER FUNCTIONS:
Krig.coef
Computes the "c" and "d" coefficients to represent the
estimated curve. These coefficients are used by the predict functions for
evaluations. Krig.coef can be used outside of the call to Krig to
recompute the fit with different Y values and possibly with different
lambda values. If new y values are not passed to this function then the yM
vector in the Krig object is used. The internal function
Krig.ynew
sorts out the logic of what to do and use based on the
passed arguments.
Krig.check.xY
Checks for removes missing values (NAs).
Krig.cor.Y
Standardizes the data vector Y based on a correlation model.
Krig.transform.xY
Finds all replicates and collapse to unique
locations and mean response and pooled variances and weights. These are
the xM, yM and weightsM used in the engines. Also scales the x locations
and the knots according to the transformation.
Krig.make.W
and Krig.make.Wi
These functions create an
off-diagonal weight matrix and its symmetric square root or the inverse
of the weight matrix based on the information passed to Krig. If
out$nondiag
is TRUE W is constructed based on a call to the passed
function wght.function along with additional arguments. If this flag is
FALSE then W is just diag(out$weightsM)
and the square root and inverse
are computed directly.
%d*%
Is a simple way to implement efficient diagonal
multiplications. x%d*%y is interpreted to mean diag(x)%*% y
if x is a vector. If x is a matrix then this becomes the same as the usual
matrix multiplication.
ENGINES:
The returned value is a list with the matrix decompositions and other information. These are incorporated into the complete Krig object.
Common to all engines:
Krig.engine.default
:
Krig.engine.knots
:
Krig.engine.fixed
:
Using all data locations
Using knot locations
OTHER FUNCTIONS:
Krig.coef
Krig.make.W
Krig.make.Wi
Doug Nychka
Krig( ozone$x, ozone$y)-> out Krig.engine.default( out)-> stuff # compare "stuff" to components in out$matrices Krig.coef( out)$c # compare to out$c Krig.coef( out, yM = ozone$y)$c # better be the same even though we pass as new data!