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fastmath.kernel.variogram

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).
raw docstring

->besselclj

(->bessel)
(->bessel order)

Creator of the BesselJ semivariogram model.

Creator of the BesselJ semivariogram model.
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->hypersphericalclj

(->hyperspherical)
(->hyperspherical order)

Creator of the hyperspherical semivariogram model.

Creator of the hyperspherical semivariogram model.
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->maternclj

(->matern)
(->matern order)

Creator of the Matern semivariogram model.

Creator of the Matern semivariogram model.
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->quantile-estimatorclj

(->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`.
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->supersphericalclj

(->superspherical)
(->superspherical order)

Creator of the superspherical semivariogram model.

Creator of the superspherical semivariogram model.
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->tplstableclj

(->tplstable)
(->tplstable H)

Creator of the superspherical semivariogram model.

Creator of the superspherical semivariogram model.
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bounding-box-diagonalclj

(bounding-box-diagonal xs)

Length of the diagonal of bounding box of spatial points.

Length of the diagonal of bounding box of spatial points.
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cauchyclj

(cauchy {:keys [nugget psill range beta]})

Generalized Cauchy semivariogram model.

Generalized Cauchy semivariogram model.
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circularclj

(circular {:keys [nugget psill range]})

Circular semivariogram model.

Circular semivariogram model.
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cressie-estimatorclj

(cressie-estimator n diffs)

Cressie (robust) empirical semivariogram estimator.

Cressie (robust) empirical semivariogram estimator.
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cubicclj

(cubic {:keys [nugget psill range]})

Cubic semivariogram model.

Cubic semivariogram model.
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dowd-estimatorclj

(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`.
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empiricalclj

(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 - 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
Empirical (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
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exponentialclj

(exponential {:keys [nugget psill range]})

Exponential semivariogram model

Exponential semivariogram model
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expowerclj

(expower {:keys [nugget psill range beta]})

Exponential-power (stable) semivariogram model.

Exponential-power (stable) semivariogram model.
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fitclj

(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
  • 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.

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.
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fit-paramsclj

(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.
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gaussianclj

(gaussian {:keys [nugget psill range]})

Gaussian semivariogram model.

Gaussian semivariogram model.
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highly-robust-estimatorclj

(highly-robust-estimator n diffs)

Genton's higly robust empirical semivariogram estimator.

Genton's higly robust empirical semivariogram estimator.
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holeclj

(hole {:keys [nugget psill range]})

Hole effect semivariogram model.

Hole effect semivariogram model.
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linearclj

(linear {:keys [nugget psill range]})

Linear semivariogram model.

Linear semivariogram model.
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matheron-estimatorclj

(matheron-estimator _ diffs)

Matheron (classical) empirical semivariogram estimator.

Matheron (classical) empirical semivariogram estimator.
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pentasphericalclj

(pentaspherical {:keys [nugget psill range]})

Pentaspherical semivariogram model.

Pentaspherical semivariogram model.
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powerclj

(power {:keys [nugget psill range beta]})

Power semivariogram model.

Power semivariogram model.
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rationalclj

(rational {:keys [nugget psill range beta]})

Rational semivariogram model.

Rational semivariogram model.
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rbf->variogramclj

(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`.
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remove-outliers-fenceclj

(remove-outliers-fence combined ys)

Removes outliers using Tukey's fences (k=1.5).

Removes outliers using Tukey's fences (`k`=1.5).
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remove-outliers-madclj

(remove-outliers-mad combined ys)

Removes outliers using median absolute deviation.

Removes outliers using median absolute deviation.
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robust-m-estimatorclj

(robust-m-estimator n diffs)

Robust M-estimator (Gunst and Hartfield) for empirical semivariogram.

Robust M-estimator (Gunst and Hartfield) for empirical semivariogram.
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sphericalclj

(spherical {:keys [nugget psill range]})

Spherical semivariogram model.

Spherical semivariogram model.
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tpowerclj

(tpower {:keys [nugget psill range beta]})

Trunctated power semivariogram model.

Trunctated power semivariogram model.
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