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fastmath.interpolation

1d, 2d interpolation functions.

See more:

Note: Smile interpolators also extrapolate values outside range.

Input data

You provide data as sequence or double array.

1d interpolation

You provide two sequences:

  • xs - x axis coorditanes, strictly monotonic (increasing)
  • ys - function values

See kriging-spline-interpolator

2d interpolation

This is grid based interpolation.

  • xs - x axis coordinates, strictly monotonic (increasing)
  • ys - y axis coordinates, strictly monotonic (increasing)
  • vs - sequence of sequences of values (2d array) for all possible pairs. Array is column-wise: [ [first column] [second column] ...].

See cubic-2d-interpolator

Examples

Examples below use following functions:

1d

1d

2d

2d

Categories

Code snippets

1d interpolation

(defn interpolate
  [f params & opts]
  (let [fun (fn [x] (m/sin (* x (* 0.5 (m/cos (inc x))))))
        xs [0.69 1.73 2.0 2.28 3.46 4.18 4.84 5.18 5.53 5.87 6.22]
        ys (map fun xs)
        interpolator ((apply partial f params) xs ys)]
    (interpolator 5.0)))

2d interpolation

(defn interpolate2d
  [f params & opts]
  (let [fun (fn [x y]
              (m/sin (* (/ (- x 100.0) 10.0) (m/cos (/ y 20.0)))))
        xs [20 50 58 66 100 121 140 150 160 170 180]
        ys [20 30 58 66 90 121 140 152 170 172 180]
        vs (partition (count ys) (for [x xs y ys] (fun x y)))
        interpolator ((apply partial f params) xs ys vs)]
    (interpolator 105 155)))

akima-spline

(akima-spline xs ys)

Create cubic spline interpolator using Akima algorithm. Minimum number of points: 5

xs[n] < xs[n+1] for all n.

Source: Apache Commons Math.

Examples

Usage

(interpolate akima-spline ...)
;;=> 0.6825735245080953

Akima spline plot

view source

b-spline

(b-spline xs ys)(b-spline degree-or-knots xs ys)

B-spline for given points, default degree equals samples count - 1.

more

Examples

Usage

(interpolate b-spline ...)
;;=> 0.5600852765013091

B-Spline plot

B-Spline plot (degree=1)

B-Spline plot (with knots)

view source

b-spline-interp

(b-spline-interp xs ys)(b-spline-interp degree xs ys)(b-spline-interp degree h xs ys)

B-spline interpolation.

See:

  • 2 or 3 arity - exact interpolation using b-spline, default degree = 3 (more)
  • 4 arity - approximated b-spline interpolation with precision parameter h (more)

Examples

Usage

(interpolate b-spline-interp ...)
;;=> 0.6903406231405653

B-Spline interpolation plot

B-Spline interpolation plot (degree=5)

B-Spline interpolation plot (degree=3, h=6)

view source

bicubic

(bicubic xs ys vs)

Bicubic 2d.

Grid based.

Source: Apache Commons Math.

Examples

Usage

(interpolate2d bicubic ...)
;;=> 0.07081337259133846

Bicubic plot

view source

bicubic-smile

(bicubic-smile xs ys vs)

Bicubic 2d.

Grid based.

Source: Smile.

Examples

Usage

(interpolate2d bicubic-smile ...)
;;=> 0.07081337259133846

Bicubic (Smile) plot

view source

bilinear

(bilinear xs ys vs)

Bilinear 2d.

Grid based.

Source: Smile.

Examples

Usage

(interpolate2d bilinear ...)
;;=> 0.062068616254939334

Bilinear plot

view source

cubic-2d

(cubic-2d xs ys vs)

Cubic spline 2d.

Grid based.

Source: Smile.

Examples

Usage

(interpolate2d cubic-2d ...)
;;=> 0.053984474655155074

Cubic-2d plot

view source

cubic-spline

(cubic-spline xs ys)

Cubic spline interpolation.

Source: Smile.

Examples

Usage

(interpolate cubic-spline ...)
;;=> 0.6809644344471792

Cubic spline plot

view source

divided-difference

(divided-difference xs ys)

Create Divided Difference Algorithm for interpolation.

Source: Apache Commons Math.

Examples

Usage

(interpolate divided-difference ...)
;;=> 0.6789478287835669

Divided difference plot

view source

interpolators-1d-list

Map of 1d interpolation functions

Examples

List of names

(keys interpolators-1d-list)
;;=> (:linear-smile :divided-difference :rbf
;;=>                :neville :step-after
;;=>                :kriging-spline :cubic-spline
;;=>                :spline :b-spline
;;=>                :loess :step-before
;;=>                :polynomial :shepard
;;=>                :linear :microsphere
;;=>                :monotone :step
;;=>                :b-spline-interp :akima)
view source

interpolators-2d-list

Map of 2d interpolation functions

Examples

List of names

(keys interpolators-2d-list)
;;=> (:bicubic :piecewise-bicubic
;;=>           :microsphere-2d :bilinear
;;=>           :bicubic-smile :cubic-2d)
view source

kriging-spline

(kriging-spline xs ys)

Kriging interpolation.

Source: Smile.

Examples

Usage

(interpolate kriging-spline ...)
;;=> 0.6863915017789594

Kriging spline plot

view source

linear

(linear xs ys)

Create Divided Difference Algorithm for inqterpolation.

Source: Apache Commons Math.

Examples

Usage

(interpolate linear ...)
;;=> 0.6843915831251183

Linear (Apache) plot

view source

linear-smile

(linear-smile xs ys)

Linear interpolation from Smile library.

Source: Smile.

Examples

Usage

(interpolate linear-smile ...)
;;=> 0.6843915831251183

Linear (Smile) plot

view source

loess

(loess xs ys)(loess bandwidth robustness-iters xs ys)(loess bandwidth robustness-iters accuracy xs ys)

Local Regression Algorithm

  • bandwidth: 0.2-1.0 (optimal: 0.25-0.5, default: 0.4)
  • robustness-iters: 0-4 (optimal: 0, default: 2)
  • accuracy: double (default: 1e-12)

Source: Apache Commons Math.

Examples

Usage

(interpolate loess ...)
;;=> 0.6878279262016764

Loess plot

Usage (0.7, 2.0)

(interpolate loess 0.7 2 ...)
;;=> 0.5834139882299265

Loess (0.7, 2.0) plot

Usage (0.2, 1.0)

(interpolate loess 0.2 1 ...)
;;=> 0.6809644344471794

Loess (0.2, 1.0) plot

view source

microsphere-2d-projection

(microsphere-2d-projection elements max-dark-friction dark-threshold background exponent shared-sphere? no-interpolation-tolerance xs ys vs)

Microsphere projection interpolator - 2d version

Grid based.

Source: Apache Commons Math.

Examples

Usage

(interpolate2d microsphere-2d-projection
               10 0.5
               1.0E-4 0.5
               1.5 false
               0.1 ...)
;;=> 0.047755559862045736

Microsphere 2d plot

view source

microsphere-projection

(microsphere-projection elements max-dark-friction dark-threshold background exponent shared-sphere? no-interpolation-tolerance xs ys)

Microsphere projection interpolator - 1d version

Source: Apache Commons Math.

Examples

Usage

(interpolate microsphere-projection 6 0.1 0.1 0.1 1.5 false 0.01 ...)
;;=> 0.640659702573876

Microsphere plot

view source

monotone

(monotone xs ys)

Monotone interpolation

https://gist.github.com/lecho/7627739

Examples

Usage

(interpolate monotone ...)
;;=> 0.7094972531399422

Monotone plot

view source

neville

(neville xs ys)

Neville algorithm

Source: Apache Commons Math.

Examples

Usage

(interpolate neville ...)
;;=> 0.6789478287835672

Neville plot

view source

piecewise-bicubic

(piecewise-bicubic xs ys vs)

Piecewise bicubic 2d.

Grid based.

Source: Apache Commons Math.

Examples

Usage

(interpolate2d piecewise-bicubic ...)
;;=> 0.06876424996210916

Piecewise bicubic plot

view source

polynomial

(polynomial xs ys)

Polynomial interpolation.

more

Examples

Usage

(interpolate polynomial ...)
;;=> 0.6789478287861641

Polynomial plot

view source

rbf

(rbf xs ys)(rbf rbf-fn normalize? xs ys)(rbf rbf-fn xs ys)

RBF (Radial Basis Function) interpolation.

Default kernel: :gaussian

Source: Smile

Examples

Usage

(interpolate rbf ...)
;;=> 0.6773457006293545

Rbf plot

Usage (mattern-c0 kernel)

(interpolate rbf (k/rbf :mattern-c0) ...)
;;=> 0.6747315645069647

Rbf (mattern-c0 kernel) plot

Usage (gaussian kernel, normalized)

(interpolate rbf (k/rbf :gaussian) true ...)
;;=> 0.6883452896663522

Rbf (gaussian kernel, normalized) plot

Usage (truncated-power kernel)

(interpolate rbf (k/rbf :truncated-power 3 0.3) ...)
;;=> 0.11727096867681523

Rbf (truncated-power kernel) plot

Usage (wendland-53 kernel)

(interpolate rbf (k/rbf :wendland-53) ...)
;;=> 0.74837576670325

Rbf (wendland-53 kernel) plot

view source

shepard

(shepard xs ys)(shepard p xs ys)

Shepard interpolation.

Source: Smile.

Examples

Usage

(interpolate shepard ...)
;;=> 0.6717576636886534

Shepard plot

Usage (0.9)

(interpolate shepard 0.9 ...)
;;=> 0.5225345022349268

Shepard (0.9) plot

view source

spline

(spline xs ys)

Cubic spline interpolation

Source: Apache Commons Math.

Examples

Usage

(interpolate spline ...)
;;=> 0.6809644344471794

Spline plot

view source

step

(step xs ys)

Step function.

Examples

Usage

(interpolate step ...)
;;=> 0.8165378262982225

Step plot

view source

step-after

(step-after xs ys)

Step function.

Examples

Usage

(interpolate step-after ...)
;;=> 0.8165378262982225

Step (after) plot

view source

step-before

(step-before xs ys)

Step function.

Examples

Usage

(interpolate step-before ...)
;;=> 0.5357270595553765

Step (before) plot

view source