% fields, Tools for spatial data
% Copyright 2004-2011, Institute for Mathematics Applied Geosciences
% University Corporation for Atmospheric Research
% Licensed under the GPL -- www.gpl.org/licenses/gpl.html

\name{predict.Krig}
\alias{predict.Krig}
\alias{predict.derivative.Krig}

\title{
  Evaluation of Krig spatial process estimate.  
}
\description{
Provides predictions from the Krig spatial process estimate at arbitrary
points, new data (Y) or other values of the smoothing parameter (lambda)
including a GCV estimate. 
}
\usage{
\method{predict}{Krig}(
object, x = NULL, Z = NULL, drop.Z = FALSE, just.fixed
                 = FALSE, lambda = NA, df = NA, model = NA,
                 eval.correlation.model = TRUE, y = NULL, yM = NULL,
                 verbose = FALSE, ...)
\method{predict.derivative}{Krig}(object, x = NULL,  verbose = FALSE,...)

}
\arguments{
\item{object}{
Fit object from the Krig or Tps function. 
}
\item{x}{
Matrix of x values on which to evaluate the kriging surface. 
If omitted, the data x values, i.e. out\$x  will be used. 
}
\item{Z}{ Vector/Matrix of additional covariates to be included in 
fixed part of spatial model}
\item{drop.Z}{ If TRUE only spatial fixed part of model is evaluated. 
i.e. Z covariates are not used. 
}
\item{just.fixed}{
Only fixed part of model is evaluated}

\item{lambda}{
Smoothing parameter. If omitted, out\$lambda will be used. 
(See also df and gcv arguments)
}
\item{df}{
Effective degrees of freedom for the predicted surface. This can be used
in place of lambda ( see the function Krig.df.to.lambda)
}
\item{model}{
Generic argument that may be used to pass a different lambda.  
}
\item{eval.correlation.model}{
If true ( the default) will multiply the predicted function by marginal
sd's
and add the mean function. This usually what one wants. If false will
return predicted surface in the standardized scale. The main use of this
option is a call from Krig to find MLE's of rho and sigma2     
}
\item{y}{
Evaluate the estimate using the new data vector y (in the same order as
the old data). This is equivalent
to recomputing the Krig object with this new data but is more efficient
because many pieces can be reused. Note that the x values are assumed to
be the same. 
}
\item{yM}{
If not NULL evaluate the estimate using this vector as the replicate mean 
data. That is, assume the full data has been collapsed into replicate 
means in the same order as xM. The replicate weights are assumed to be 
the same as the original data. (weightsM)
}

 \item{verbose}{
Print out all kinds of intermediate stuff for debugging 
}

\item{\dots}{Other arguments passed to predict.}
}
\value{
Vector of predicted responses or a matrix of the partial derivatives. 
}
\details{
 The main goal in this function is to reuse the Krig object to rapidly 
evaluate different estimates. Thus there is flexibility in changing the 
value of lambda and also the independent data without having to 
recompute the matrices associated with the Krig object. The reason this 
is possible is that most on the calculations depend on the observed 
locations not on lambda or the observed data. Note the version for 
evaluating partial derivatives does not provide the same flexibility as 
\code{predict.Krig} and makes some assumptions about the null model 
(as a low order polynomial) and can not handle the correlation model form.

}
\seealso{
Krig, predict.surface gcv.Krig 
}

\examples{
  Krig(ozone$x,ozone$y, theta=50) ->fit
  predict( fit) # gives predicted values at data points should agree with fitted.values
                #  in fit object 

# predict at the coordinate (-5,10)
  x0<- cbind( -5,10) # has to be a  1X2 matrix
  predict( fit,x= x0)

# redoing predictions at data locations:
   predict( fit, x=ozone$x)

# only the fixed part of the model
  predict( fit, just.fixed=TRUE) 

# evaluating estimate at a grid of points 
  grid<- make.surface.grid( list( seq( -40,40,,15), seq( -40,40,,15)))
  look<- predict(fit,grid) # evaluate on a grid of points

# some useful graphing functions for these gridded predicted values
  out.p<- as.surface( grid, look) # reformat into $x $y $z image-type object
  contour( out.p) 

# see also the functions predict.surface and surface 
# for functions that combine these steps 
   

# refit with 10 degrees of freedom in surface
  look<- predict(fit,grid, df=15)
# refit with random data 
  look<- predict( fit, grid, y= rnorm( 20))


# finding partial derivatives of the estimate
#
# find the partial derivatives at observation locations
# returned object is a two column matrix. 
# this does not make sense for the exponential covariance
# but can illustrate this with a thin plate spline with
# a high enough order ( i.e. need m=3 or greater)
# 
  data(ozone2)
# the 16th day of this ozone spatial dataset
  fit0<- Tps( ozone2$lon.lat, ozone2$y[16,], m=3)
  look1<- predict.derivative.Krig( fit0)
# for extra credit compare this to
  look2<- predict.derivative.Krig( fit0, x=ozone2$lon.lat)  
# (why are there more values in look2) 


}
\keyword{spatial}
% docclass is function
% Converted by Sd2Rd version 1.21.