Semivariograms and empirical (experimental) estimators for kriging interpolation.
Semivariogram models are created using nugget
, partial sill
, range
and in some cases beta
(exponent) parameters. All models can be fit to the empirical
(experimental) semivariogram which can be created by using a variety of the estimators.
Estimators calculate gamma
semivariogram for given bin h
(lag) (n
- number of pairs, diffs
- seq of differences).
Semivariograms and empirical (experimental) estimators for kriging interpolation. Semivariogram models are created using `nugget`, `partial sill`, `range` and in some cases `beta` (exponent) parameters. All models can be fit to the `empirical` (experimental) semivariogram which can be created by using a variety of the estimators. Estimators calculate `gamma` semivariogram for given bin `h` (lag) (`n` - number of pairs, `diffs` - seq of differences).
(->bessel)
(->bessel order)
Creator of the BesselJ semivariogram model.
Creator of the BesselJ semivariogram model.
(->hyperspherical)
(->hyperspherical order)
Creator of the hyperspherical semivariogram model.
Creator of the hyperspherical semivariogram model.
(->matern)
(->matern order)
Creator of the Matern semivariogram model.
Creator of the Matern semivariogram model.
(->quantile-estimator p)
Create a quantile (Armstrong and Delfiner) empirical semivariogram estimator for given p
.
Create a quantile (Armstrong and Delfiner) empirical semivariogram estimator for given `p`.
(->superspherical)
(->superspherical order)
Creator of the superspherical semivariogram model.
Creator of the superspherical semivariogram model.
(->tplstable)
(->tplstable H)
Creator of the superspherical semivariogram model.
Creator of the superspherical semivariogram model.
(bounding-box-diagonal xs)
Length of the diagonal of bounding box of spatial points.
Length of the diagonal of bounding box of spatial points.
(cauchy {:keys [nugget psill range beta]})
Generalized Cauchy semivariogram model.
Generalized Cauchy semivariogram model.
(circular {:keys [nugget psill range]})
Circular semivariogram model.
Circular semivariogram model.
(cressie-estimator n diffs)
Cressie (robust) empirical semivariogram estimator.
Cressie (robust) empirical semivariogram estimator.
(cubic {:keys [nugget psill range]})
Cubic semivariogram model.
Cubic semivariogram model.
(dowd-estimator _ diffs)
Dowd's empirical semivariogram estimator.
It's the same as quantile estimator for p
equal 0.5
.
Dowd's empirical semivariogram estimator. It's the same as quantile estimator for `p` equal `0.5`.
(empirical xs ys)
(empirical xs
ys
{:keys [cutoff diagonal-den bins estimator quantile remove-outliers?]
:or {bins 15
diagonal-den 3.0
estimator :classical
quantile 0.9
remove-outliers? false}})
Empirical (experimental) semivariogram.
Arguments:
xs
- positionsys
- values:bins
- number of bins, size of the semivariogram (default: 15
):cutoff
- semivariogram cutoff (default: bounding box diagonal divided by diagonal-den
):diagonal-den
- denomiator of bounding box diagonal (default: 3
):estimator
- estimator name or a function (default: :classical
):quantile
- quantile for quantile estimator (default: 0.9
):remove-outliers?
- should outliers be removed from raw data? (default: false
)Defined estimators are: :classical
/:matheron
(default), :cressie
, :genton
/:highly-robust
, :dowd
, :quantile
, :m-robust
.
:remove-outliers?
can be a true
value for Tukey's fences criterion or :mad
for median absolute deviation criterion.
Function return a list of maps sorted by lag h
, containing:
:n
- number of points in given bin:h
- average lag:gamma
- semivariogram estimationEmpirical (experimental) semivariogram. Arguments: * `xs` - positions * `ys` - values * parameters (optional): * `:bins` - number of bins, size of the semivariogram (default: `15`) * `:cutoff` - semivariogram cutoff (default: bounding box diagonal divided by `diagonal-den`) * `:diagonal-den` - denomiator of bounding box diagonal (default: `3`) * `:estimator` - estimator name or a function (default: `:classical`) * `:quantile` - quantile for quantile estimator (default: `0.9`) * `:remove-outliers?` - should outliers be removed from raw data? (default: `false`) Defined estimators are: `:classical`/`:matheron` (default), `:cressie`, `:genton`/`:highly-robust`, `:dowd`, `:quantile`, `:m-robust`. `:remove-outliers?` can be a `true` value for Tukey's fences criterion or `:mad` for median absolute deviation criterion. Function return a list of maps sorted by lag `h`, containing: * `:n` - number of points in given bin * `:h` - average lag * `:gamma` - semivariogram estimation
(exponential {:keys [nugget psill range]})
Exponential semivariogram model
Exponential semivariogram model
(expower {:keys [nugget psill range beta]})
Exponential-power (stable) semivariogram model.
Exponential-power (stable) semivariogram model.
(fit empirical-variogram semivariogram-model)
(fit empirical-variogram semivariogram-model parameters)
Fits semivariogram model parameter to a empirical semivariogram data.
Arguments:
empirical-semivariogram
- empirical semivariogram data as returned by empirical
function.semivariogram-model
- name of the semivariogram model:estimation
- estimation used to fit the model, :sq
- least squares (default), :abs
- least absolute values:weights
- fitting weights (default: nil
, no weights):parameter
- order for :bessel
, :matern
and :supershperical
, H for :tplstable
or d for :hyperspherical
semivariogram models:defaults
- a map containing semivariogram model parameters which should be a fixed value, fitting will be done for the lacking ones only.Weights can be a sequence of weights or one of the following methods:
:n
- N, number of points in a bin:nhh
- N divided by a squared lag (h):ngg
- N divided by a squared gamma (estimated from a model):ngg2
-N divided by a cubed gamma (estimated from a model) and multiplied by empirical gamma.Fit is done by using L-BFGS-B numerical optimization.
Returns fitted semivariogram model.
Fits semivariogram model parameter to a empirical semivariogram data. Arguments: * `empirical-semivariogram` - empirical semivariogram data as returned by `empirical` function. * `semivariogram-model` - name of the semivariogram model * parameters: * `:estimation` - estimation used to fit the model, `:sq` - least squares (default), `:abs` - least absolute values * `:weights` - fitting weights (default: `nil`, no weights) * `:parameter` - order for `:bessel`, `:matern` and `:supershperical`, H for `:tplstable` or d for `:hyperspherical` semivariogram models * `:defaults` - a map containing semivariogram model parameters which should be a fixed value, fitting will be done for the lacking ones only. Weights can be a sequence of weights or one of the following methods: * `:n` - N, number of points in a bin * `:nhh` - N divided by a squared lag (h) * `:ngg` - N divided by a squared gamma (estimated from a model) * `:ngg2` -N divided by a cubed gamma (estimated from a model) and multiplied by empirical gamma. Fit is done by using L-BFGS-B numerical optimization. Returns fitted semivariogram model.
(fit-params empirical-semivariogram semivariogram-model)
(fit-params empirical-semivariogram
semivariogram-model
{:keys [estimation weights defaults parameter]
:or {estimation :sq}})
Fits a model and a pair of selected semivariogram model and fitted parameters.
Fits a model and a pair of selected semivariogram model and fitted parameters.
(gaussian {:keys [nugget psill range]})
Gaussian semivariogram model.
Gaussian semivariogram model.
(highly-robust-estimator n diffs)
Genton's higly robust empirical semivariogram estimator.
Genton's higly robust empirical semivariogram estimator.
(hole {:keys [nugget psill range]})
Hole effect semivariogram model.
Hole effect semivariogram model.
(linear {:keys [nugget psill range]})
Linear semivariogram model.
Linear semivariogram model.
(matheron-estimator _ diffs)
Matheron (classical) empirical semivariogram estimator.
Matheron (classical) empirical semivariogram estimator.
(pentaspherical {:keys [nugget psill range]})
Pentaspherical semivariogram model.
Pentaspherical semivariogram model.
(power {:keys [nugget psill range beta]})
Power semivariogram model.
Power semivariogram model.
(rational {:keys [nugget psill range beta]})
Rational semivariogram model.
Rational semivariogram model.
(rbf->variogram kernel)
Build semivariogram model based on RBF kernel.
Selected kernel should has a value 1.0
at zero and should be 0.0
at infinity. For example :matern-c2
will work but :thin-plate
will not. range
parameter acts as reciprocal of RBF's shape
.
Build semivariogram model based on RBF kernel. Selected kernel should has a value `1.0` at zero and should be `0.0` at infinity. For example `:matern-c2` will work but `:thin-plate` will not. `range` parameter acts as reciprocal of RBF's `shape`.
(remove-outliers-fence combined ys)
Removes outliers using Tukey's fences (k
=1.5).
Removes outliers using Tukey's fences (`k`=1.5).
(remove-outliers-mad combined ys)
Removes outliers using median absolute deviation.
Removes outliers using median absolute deviation.
(robust-m-estimator n diffs)
Robust M-estimator (Gunst and Hartfield) for empirical semivariogram.
Robust M-estimator (Gunst and Hartfield) for empirical semivariogram.
(spherical {:keys [nugget psill range]})
Spherical semivariogram model.
Spherical semivariogram model.
(tpower {:keys [nugget psill range beta]})
Trunctated power semivariogram model.
Trunctated power semivariogram model.
cljdoc is a website building & hosting documentation for Clojure/Script libraries
× close