fastmath.interpolation — generateme/fastmath 2.4.0

1d, 2d interpolation functions.

See more:

• Apache Commons Math
• [Smile Interpolation](http://haifengl.github.io/smile/api/java/smile/interpolation/package-summary.html
• SSJ B-Spline

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

2d

akima-spline clj

(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.

b-spline clj

(b-spline xs ys)

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

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

more

b-spline-interp clj

(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)

bicubic clj

(bicubic xs ys vs)

Bicubic 2d.

Grid based.

Source: Apache Commons Math.

bicubic-smile clj

(bicubic-smile xs ys vs)

Bicubic 2d.

Grid based.

Source: Smile.

bilinear clj

(bilinear xs ys vs)

Bilinear 2d.

Grid based.

Source: Smile.

cubic-2d clj

(cubic-2d xs ys vs)

Cubic spline 2d.

Grid based.

Source: Smile.

cubic-spline clj

(cubic-spline xs ys)

Cubic spline interpolation.

Source: Smile.

divided-difference clj

(divided-difference xs ys)

Create Divided Difference Algorithm for interpolation.

Source: Apache Commons Math.

interpolators-1d-list clj

Map of 1d interpolation functions

interpolators-2d-list clj

Map of 2d interpolation functions

kriging-spline clj

(kriging-spline xs ys)

Kriging interpolation.

Source: Smile.

linear clj

(linear xs ys)

Create Divided Difference Algorithm for inqterpolation.

Source: Apache Commons Math.

linear-smile clj

(linear-smile xs ys)

Linear interpolation from Smile library.

Source: Smile.

loess clj

(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.

microsphere-2d-projection clj

(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.

microsphere-projection clj

(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.

monotone clj

(monotone xs ys)

Monotone interpolation

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

neville clj

(neville xs ys)

Neville algorithm

Source: Apache Commons Math.

piecewise-bicubic clj

(piecewise-bicubic xs ys vs)

Piecewise bicubic 2d.

Grid based.

Source: Apache Commons Math.

polynomial clj

(polynomial xs ys)

Polynomial interpolation.

more

rbf clj

(rbf xs ys)

(rbf rbf-fn xs ys)

(rbf rbf-fn normalize? xs ys)

RBF (Radial Basis Function) interpolation.

Default kernel: :gaussian

Source: Smile

shepard clj

(shepard xs ys)

(shepard p xs ys)

Shepard interpolation.

Source: Smile.

spline clj

(spline xs ys)

Cubic spline interpolation

Source: Apache Commons Math.

step clj

(step xs ys)

Step function.

step-after clj

(step-after xs ys)

Step function.

step-before clj

(step-before xs ys)

Step function.