fastmath.kernel.variogram — generateme/fastmath 3.0.0-alpha1

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 clj

(->bessel)

(->bessel order)

Creator of the BesselJ semivariogram model.

->hyperspherical clj

(->hyperspherical)

(->hyperspherical order)

Creator of the hyperspherical semivariogram model.

->matern clj

(->matern)

(->matern order)

Creator of the Matern semivariogram model.

->quantile-estimator clj

(->quantile-estimator p)

Create a quantile (Armstrong and Delfiner) empirical semivariogram estimator for given p.

->superspherical clj

(->superspherical)

(->superspherical order)

Creator of the superspherical semivariogram model.

->tplstable clj

(->tplstable)

(->tplstable H)

Creator of the superspherical semivariogram model.

bounding-box-diagonal clj

(bounding-box-diagonal xs)

Length of the diagonal of bounding box of spatial points.

cauchy clj

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

Generalized Cauchy semivariogram model.

circular clj

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

Circular semivariogram model.

cressie-estimator clj

(cressie-estimator n diffs)

Cressie (robust) empirical semivariogram estimator.

cubic clj

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

Cubic semivariogram model.

dowd-estimator clj

(dowd-estimator _ diffs)

Dowd's empirical semivariogram estimator.

It's the same as quantile estimator for p equal 0.5.

empirical clj

(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

exponential clj

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

Exponential semivariogram model

expower clj

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

Exponential-power (stable) semivariogram model.

fit clj

(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.

fit-params clj

(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.

gaussian clj

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

Gaussian semivariogram model.

highly-robust-estimator clj

(highly-robust-estimator n diffs)

Genton's higly robust empirical semivariogram estimator.

hole clj

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

Hole effect semivariogram model.

linear clj

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

Linear semivariogram model.

matheron-estimator clj

(matheron-estimator _ diffs)

Matheron (classical) empirical semivariogram estimator.

pentaspherical clj

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

Pentaspherical semivariogram model.

power clj

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

Power semivariogram model.

rational clj

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

Rational semivariogram model.

rbf->variogram clj

(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.

remove-outliers-fence clj

(remove-outliers-fence combined ys)

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

remove-outliers-mad clj

(remove-outliers-mad combined ys)

Removes outliers using median absolute deviation.

robust-m-estimator clj

(robust-m-estimator n diffs)

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

spherical clj

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

Spherical semivariogram model.

tpower clj

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

Trunctated power semivariogram model.