KrigingEstimators.ExternalDriftKriging
— TypeExternalDriftKriging(γ, drifts)
ExternalDriftKriging(X, z, γ, drifts)
External Drift Kriging with variogram model γ
and external drifts
functions.
Optionally, pass the coordinates X
and values z
to the fit
function.
Notes
- External drift functions should be smooth
- Kriging system with external drift is often unstable
- Include a constant drift (e.g.
x->1
) for unbiased estimation OrdinaryKriging
is recovered fordrifts = [x->1]
- For polynomial mean, see
UniversalKriging
KrigingEstimators.FittedKriging
— TypeFittedKriging(estimator, state)
An object that can be used for making predictions using the parameters in estimator
and the current Kriging state
.
KrigingEstimators.Kriging
— TypeKriging(var₁=>param₁, var₂=>param₂, ...)
A polyalgorithm Kriging estimation solver.
Each pair var=>param
specifies the KrigingParam
param
for the Kriging variable var
. In order to avoid boilerplate code, the constructor expects pairs of Symbol
and NamedTuple
instead.
Parameters
variogram
- Variogram model (default toGaussianVariogram()
)mean
- Simple Kriging meandegree
- Universal Kriging degreedrifts
- External Drift Kriging drift functions
Latter options override former options. For example, by specifying drifts
, the user is telling the algorithm to ignore degree
and mean
. If no option is specified, Ordinary Kriging is used by default with the variogram
only.
maxneighbors
- Maximum number of neighbors (default tonothing
)neighborhood
- Search neighborhood (default tonothing
)distance
- Distance used to find nearest neighbors (default toEuclidean()
)
The maxneighbors
option can be used to perform approximate Kriging with a subset of data points per estimation location. Two neighborhood search methods are available depending on the value of neighborhood
:
If a
neighborhood
is provided, local Kriging is performed by sliding theneighborhood
in the domain.If
neighborhood
is not provided, the Kriging system is built usingmaxneighbors
nearest neighbors according to adistance
.
Examples
Solve the variable :var₁
with Simple Kriging by specifying the mean
, and the variable :var₂
with Universal Kriging by specifying the degree
and the variogram
model.
julia> Kriging(
:var₁ => (mean=1.,),
:var₂ => (degree=1, variogram=SphericalVariogram(range=20.))
)
Solve all variables of the problem with the default parameters (i.e. Ordinary Kriging with unit Gaussian variogram):
julia> Kriging()
KrigingEstimators.KrigingEstimator
— TypeKrigingEstimator
A Kriging estimator (e.g. Simple Kriging).
KrigingEstimators.KrigingJointParam
— TypeKriging(var₁=>param₁, var₂=>param₂, ...)
A polyalgorithm Kriging estimation solver.
Each pair var=>param
specifies the KrigingParam
param
for the Kriging variable var
. In order to avoid boilerplate code, the constructor expects pairs of Symbol
and NamedTuple
instead.
Parameters
variogram
- Variogram model (default toGaussianVariogram()
)mean
- Simple Kriging meandegree
- Universal Kriging degreedrifts
- External Drift Kriging drift functions
Latter options override former options. For example, by specifying drifts
, the user is telling the algorithm to ignore degree
and mean
. If no option is specified, Ordinary Kriging is used by default with the variogram
only.
maxneighbors
- Maximum number of neighbors (default tonothing
)neighborhood
- Search neighborhood (default tonothing
)distance
- Distance used to find nearest neighbors (default toEuclidean()
)
The maxneighbors
option can be used to perform approximate Kriging with a subset of data points per estimation location. Two neighborhood search methods are available depending on the value of neighborhood
:
If a
neighborhood
is provided, local Kriging is performed by sliding theneighborhood
in the domain.If
neighborhood
is not provided, the Kriging system is built usingmaxneighbors
nearest neighbors according to adistance
.
Examples
Solve the variable :var₁
with Simple Kriging by specifying the mean
, and the variable :var₂
with Universal Kriging by specifying the degree
and the variogram
model.
julia> Kriging(
:var₁ => (mean=1.,),
:var₂ => (degree=1, variogram=SphericalVariogram(range=20.))
)
Solve all variables of the problem with the default parameters (i.e. Ordinary Kriging with unit Gaussian variogram):
julia> Kriging()
KrigingEstimators.KrigingParam
— TypeKriging(var₁=>param₁, var₂=>param₂, ...)
A polyalgorithm Kriging estimation solver.
Each pair var=>param
specifies the KrigingParam
param
for the Kriging variable var
. In order to avoid boilerplate code, the constructor expects pairs of Symbol
and NamedTuple
instead.
Parameters
variogram
- Variogram model (default toGaussianVariogram()
)mean
- Simple Kriging meandegree
- Universal Kriging degreedrifts
- External Drift Kriging drift functions
Latter options override former options. For example, by specifying drifts
, the user is telling the algorithm to ignore degree
and mean
. If no option is specified, Ordinary Kriging is used by default with the variogram
only.
maxneighbors
- Maximum number of neighbors (default tonothing
)neighborhood
- Search neighborhood (default tonothing
)distance
- Distance used to find nearest neighbors (default toEuclidean()
)
The maxneighbors
option can be used to perform approximate Kriging with a subset of data points per estimation location. Two neighborhood search methods are available depending on the value of neighborhood
:
If a
neighborhood
is provided, local Kriging is performed by sliding theneighborhood
in the domain.If
neighborhood
is not provided, the Kriging system is built usingmaxneighbors
nearest neighbors according to adistance
.
Examples
Solve the variable :var₁
with Simple Kriging by specifying the mean
, and the variable :var₂
with Universal Kriging by specifying the degree
and the variogram
model.
julia> Kriging(
:var₁ => (mean=1.,),
:var₂ => (degree=1, variogram=SphericalVariogram(range=20.))
)
Solve all variables of the problem with the default parameters (i.e. Ordinary Kriging with unit Gaussian variogram):
julia> Kriging()
KrigingEstimators.KrigingState
— TypeKrigingState(X, z, LHS, RHS)
A Kriging state stores information needed to perform estimation at any given location.
KrigingEstimators.KrigingWeights
— TypeKrigingWeights(λ, ν)
An object storing Kriging weights λ
and Lagrange multipliers ν
.
KrigingEstimators.OrdinaryKriging
— TypeOrdinaryKriging(γ)
OrdinaryKriging(X, z, γ)
Ordinary Kriging with variogram model γ
.
Optionally, pass the coordinates X
and values z
to the fit
function.
KrigingEstimators.SeqGaussSim
— TypeSeqGaussSim(var₁=>param₁, var₂=>param₂, ...)
A sequential Gaussian simulation solver.
Parameters
variogram
- Variogram model (default toGaussianVariogram()
)mean
- Simple Kriging meandegree
- Universal Kriging degreedrifts
- External Drift Kriging drift functions
Latter options override former options. For example, by specifying drifts
, the user is telling the algorithm to ignore degree
and mean
. If no option is specified, Ordinary Kriging is used by default with the variogram
only.
neighborhood
- Neighborhood on which to search neighborsmaxneighbors
- Maximum number of neighbors (default to 10)path
- Simulation path (default toLinearPath()
)
For each location in the simulation path
, a maximum number of neighbors maxneighbors
is used to fit a Gaussian distribution. The neighbors are searched according to a neighborhood
.
KrigingEstimators.SeqGaussSimJointParam
— TypeSeqGaussSim(var₁=>param₁, var₂=>param₂, ...)
A sequential Gaussian simulation solver.
Parameters
variogram
- Variogram model (default toGaussianVariogram()
)mean
- Simple Kriging meandegree
- Universal Kriging degreedrifts
- External Drift Kriging drift functions
Latter options override former options. For example, by specifying drifts
, the user is telling the algorithm to ignore degree
and mean
. If no option is specified, Ordinary Kriging is used by default with the variogram
only.
neighborhood
- Neighborhood on which to search neighborsmaxneighbors
- Maximum number of neighbors (default to 10)path
- Simulation path (default toLinearPath()
)
For each location in the simulation path
, a maximum number of neighbors maxneighbors
is used to fit a Gaussian distribution. The neighbors are searched according to a neighborhood
.
KrigingEstimators.SeqGaussSimParam
— TypeSeqGaussSim(var₁=>param₁, var₂=>param₂, ...)
A sequential Gaussian simulation solver.
Parameters
variogram
- Variogram model (default toGaussianVariogram()
)mean
- Simple Kriging meandegree
- Universal Kriging degreedrifts
- External Drift Kriging drift functions
Latter options override former options. For example, by specifying drifts
, the user is telling the algorithm to ignore degree
and mean
. If no option is specified, Ordinary Kriging is used by default with the variogram
only.
neighborhood
- Neighborhood on which to search neighborsmaxneighbors
- Maximum number of neighbors (default to 10)path
- Simulation path (default toLinearPath()
)
For each location in the simulation path
, a maximum number of neighbors maxneighbors
is used to fit a Gaussian distribution. The neighbors are searched according to a neighborhood
.
KrigingEstimators.SimpleKriging
— TypeSimpleKriging(γ, μ)
SimpleKriging(X, z, γ, μ)
Simple Kriging with variogram model γ
and constant mean μ
.
Optionally, pass the coordinates X
and values z
to the fit
function.
Notes
- Simple Kriging requires stationary variograms
KrigingEstimators.UniversalKriging
— TypeUniversalKriging(γ, degree, dim)
UniversalKriging(X, z, γ, degree)
Universal Kriging with variogram model γ
and polynomial degree
on a spatial domain of dimension dim
.
Optionally, pass the coordinates X
and values z
to the fit
function.
Notes
OrdinaryKriging
is recovered for 0th degree polynomial- For non-polynomial mean, see
ExternalDriftKriging
GeoStatsBase.predict
— Methodpredict(estimator, xₒ)
Compute mean and variance for the estimator
at coordinates xₒ
.
GeoStatsBase.status
— Methodstatus(fittedkrig)
Return the status of the fittedkrig
object, meaning the factorization of the Kriging system was successful.
KrigingEstimators.combine
— Methodcombine(estimator, weights, z)
Combine weights
with values z
to produce mean and variance.
KrigingEstimators.factorize
— Methodfactorize(estimator, LHS)
Factorize LHS of Kriging system with appropriate factorization method.
KrigingEstimators.lhs
— Methodlhs(estimator, X)
Return LHS of Kriging system using spatial configuration X
.
KrigingEstimators.nconstraints
— Methodnconstraints(estimator)
Return number of constraints for estimator
.
KrigingEstimators.set_constraints_lhs!
— Methodset_constraints_lhs!(estimator, LHS, X)
Set constraints in LHS of Kriging system.
KrigingEstimators.set_constraints_rhs!
— Methodset_constraints_rhs!(estimator, xₒ)
Set constraints in RHS of Kriging system.
KrigingEstimators.set_rhs!
— Methodset_rhs!(estimator, xₒ)
Set RHS of Kriging system at coodinates xₒ
.
KrigingEstimators.weights
— Methodweights(estimator, xₒ)
Compute the weights λ (and Lagrange multipliers ν) for the estimator
at coordinates xₒ
.
StatsBase.fit
— Methodfit(estimator, X, z)
Build Kriging system from coordinates X
and values z
and return a fitted estimator.