Monotonic smoothing splines for the JVM
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README.md

snowball

Monotonic smoothing splines for the JVM ecosystem and Apache Commons Math.

Documentation

API javadoc is available at: https://erikerlandson.github.io/snowball/java/api/

A few examples are below.

Features

  • Fit monotonic interpolating splines to data, including data that has noise or is otherwise non-monotonic.
  • Enforce equality constraints of the form s(x) = y, where s is the spline function
  • Enforce gradient constraints of the form ds(x)/dx = g

How to use snowball in your project

The snowball package is implemented in java, and so it can be used in both java and scala. It is built on, and designed to work with, Apache Commons Math 3.6

snowball expects you to provide commons-math3 and gibbous dependencies, as shown here:

resolvers += "manyangled" at "https://dl.bintray.com/manyangled/maven/"

libraryDependencies ++= Seq(
  "com.manyangled" % "snowball" % "0.1.1",
  "com.manyangled" % "gibbous" % "0.1.1",
  "org.apache.commons" % "commons-math3" % "3.6.1")

Examples

Java

import org.apache.commons.math3.analysis.polynomials.PolynomialSplineFunction;
import com.manyangled.snowball.analysis.interpolation.MonotonicSplineInterpolator;

double[] x = { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0 };
double[] y = { 0.0, 0.05, 0.02, 0.3, 0.5, 0.7, 0.99, 0.95, 1.0 };
MonotonicSplineInterpolator interpolator = new MonotonicSplineInterpolator();
PolynomialSplineFunction s = interpolator.interpolate(x, y);

Scala REPL

scala> import com.manyangled.snowball.analysis.interpolation._, com.manyangled.gnuplot4s._
import com.manyangled.snowball.analysis.interpolation._
import com.manyangled.gnuplot4s._

scala> val interpolator = new MonotonicSplineInterpolator()
interpolator: com.manyangled.snowball.analysis.interpolation.MonotonicSplineInterpolator = com.manyangled.snowball.analysis.interpolation.MonotonicSplineInterpolator@6834fd1b

scala> val xdata = Array(1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0)
xdata: Array[Double] = Array(1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0)

scala> val ydata = Array(0.0, 0.2, 0.05, 0.3, 0.5, 0.7, 0.95, 0.8, 1.0)
ydata: Array[Double] = Array(0.0, 0.2, 0.05, 0.3, 0.5, 0.7, 0.95, 0.8, 1.0)

scala> val s = interpolator.interpolate(xdata, ydata)
s: org.apache.commons.math3.analysis.polynomials.PolynomialSplineFunction = org.apache.commons.math3.analysis.polynomials.PolynomialSplineFunction@5852d898

scala> Session().block("data", xdata.zip(ydata)).block("spline", (1.0 to 9.0 by 0.1).map { x => (x, s.value(x)) }).plot(Plot().block("data").using(1,2).style(PlotStyle.Points)).plot(Plot().block("spline").using(1,2).style(PlotStyle.Lines)).term(Dumb().size(80,40)).render

scala> 
                                                                                       
                                                                                
    1 +-+------+--------+-------+--------+--------+--------+-------+------+-A   
      +        +        +       +        +        +        +       +     ####   
      |                                             $data uAing 1:2   #A#   |   
      |                                           $spline using 1:######### |   
      |                                                        ###          |   
      |                                                     ###             |   
      |                                                   ##                |   
  0.8 +-+                                                ##        A      +-+   
      |                                               ###                   |   
      |                                             ##                      |   
      |                                           A#                        |   
      |                                           #                         |   
      |                                         ##                          |   
      |                                       ##                            |   
  0.6 +-+                                    #                            +-+   
      |                                     #                               |   
      |                                    #                                |   
      |                                  A#                                 |   
      |                                 ##                                  |   
      |                                #                                    |   
      |                               #                                     |   
  0.4 +-+                            #                                    +-+   
      |                            ##                                       |   
      |                          ##                                         |   
      |                         A                                           |   
      |                        #                                            |   
      |                      ##                                             |   
      |                   ###                                               |   
  0.2 +-+      A        ##                                                +-+   
      |                ##                                                   |   
      |             ###                                                     |   
      |          ###                                                        |   
      |      ####                                                           |   
      |   ###           A                                                   |   
      ####     +        +       +        +        +        +       +        +   
    0 A-+------+--------+-------+--------+--------+--------+-------+------+-+   
      1        2        3       4        5        6        7       8        9   
                                                                                

References:

  1. H. Fujioka and H. Kano: Monotone smoothing spline curves using normalized uniform cubic B-splines, Trans. Institute of Systems, Control and Information Engineers, Vol. 26, No. 11, pp. 389–397, 2013

  2. Hiroyuki KANO, Hiroyuki FUJIOKA, and Clyde F. MARTIN, Optimal Smoothing Spline with Constraints on Its Derivatives, SICE Journal of Control, Measurement, and System Integration, Vol.7, No. 2, pp. 104–111, March 2014

  3. M. Nagahara, Y. Yamamoto, C. Martin, Quadratic Programming for Monotone Control Theoretic Splines, SICE, 2010.

  4. M. Egerstedt and C. Martin. Monotone Smoothing Splines. Mathematical Theory of Networks and Systems. Perpignan, France, June 2000.