ExternalDriftKriging(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 for drifts = [x->1]
• For polynomial mean, see UniversalKriging

FittedKriging(estimator, state)

An object that can be used for making predictions using the parameters in estimator and the current Kriging state.

Kriging(var₁=>param₁, var₂=>param₂, ...)

A polyalgorithm Kriging estimation solver.

Each pair var=>param specifies the KrigingParamparam 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 to GaussianVariogram())
• mean - Simple Kriging mean
• degree - Universal Kriging degree
• drifts - 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 to nothing)
• neighborhood - Search neighborhood (default to nothing)
• distance - Distance used to find nearest neighbors (default to Euclidean())

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 the neighborhood in the domain.

• If neighborhood is not provided, the Kriging system is built using maxneighbors nearest neighbors according to a distance.

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()

KrigingEstimator

A Kriging estimator (e.g. Simple Kriging).

Kriging(var₁=>param₁, var₂=>param₂, ...)

A polyalgorithm Kriging estimation solver.

Each pair var=>param specifies the KrigingParamparam 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 to GaussianVariogram())
• mean - Simple Kriging mean
• degree - Universal Kriging degree
• drifts - 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 to nothing)
• neighborhood - Search neighborhood (default to nothing)
• distance - Distance used to find nearest neighbors (default to Euclidean())

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 the neighborhood in the domain.

• If neighborhood is not provided, the Kriging system is built using maxneighbors nearest neighbors according to a distance.

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()

Kriging(var₁=>param₁, var₂=>param₂, ...)

A polyalgorithm Kriging estimation solver.

Each pair var=>param specifies the KrigingParamparam 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 to GaussianVariogram())
• mean - Simple Kriging mean
• degree - Universal Kriging degree
• drifts - 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 to nothing)
• neighborhood - Search neighborhood (default to nothing)
• distance - Distance used to find nearest neighbors (default to Euclidean())

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 the neighborhood in the domain.

• If neighborhood is not provided, the Kriging system is built using maxneighbors nearest neighbors according to a distance.

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()

KrigingState(X, z, LHS, RHS)

A Kriging state stores information needed to perform estimation at any given location.

KrigingWeights(λ, ν)

An object storing Kriging weights λ and Lagrange multipliers ν.

OrdinaryKriging(γ)
OrdinaryKriging(X, z, γ)

Ordinary Kriging with variogram model γ.

Optionally, pass the coordinates X and values z to the fit function.

SeqGaussSim(var₁=>param₁, var₂=>param₂, ...)

A sequential Gaussian simulation solver.

Parameters

• variogram - Variogram model (default to GaussianVariogram())
• mean - Simple Kriging mean
• degree - Universal Kriging degree
• drifts - 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 neighbors
• maxneighbors - Maximum number of neighbors (default to 10)
• path - Simulation path (default to LinearPath())

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.

SeqGaussSim(var₁=>param₁, var₂=>param₂, ...)

A sequential Gaussian simulation solver.

Parameters

• variogram - Variogram model (default to GaussianVariogram())
• mean - Simple Kriging mean
• degree - Universal Kriging degree
• drifts - 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 neighbors
• maxneighbors - Maximum number of neighbors (default to 10)
• path - Simulation path (default to LinearPath())

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.

SeqGaussSim(var₁=>param₁, var₂=>param₂, ...)

A sequential Gaussian simulation solver.

Parameters

• variogram - Variogram model (default to GaussianVariogram())
• mean - Simple Kriging mean
• degree - Universal Kriging degree
• drifts - 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 neighbors
• maxneighbors - Maximum number of neighbors (default to 10)
• path - Simulation path (default to LinearPath())

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.

SimpleKriging(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

UniversalKriging(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

predict(estimator, xₒ)

Compute mean and variance for the estimator at coordinates xₒ.

status(fittedkrig)

Return the status of the fittedkrig object, meaning the factorization of the Kriging system was successful.

combine(estimator, weights, z)

Combine weights with values z to produce mean and variance.

factorize(estimator, LHS)

Factorize LHS of Kriging system with appropriate factorization method.

lhs(estimator, X)

Return LHS of Kriging system using spatial configuration X.

nconstraints(estimator)

Return number of constraints for estimator.

set_constraints_lhs!(estimator, LHS, X)

Set constraints in LHS of Kriging system.

set_constraints_rhs!(estimator, xₒ)

Set constraints in RHS of Kriging system.

set_rhs!(estimator, xₒ)

Set RHS of Kriging system at coodinates xₒ.

weights(estimator, xₒ)

Compute the weights λ (and Lagrange multipliers ν) for the estimator at coordinates xₒ.

fit(estimator, X, z)

Build Kriging system from coordinates X and values z and return a fitted estimator.