Monotonic smoothing splines for the JVM ecosystem and Apache Commons Math.
API javadoc is available at: https://erikerlandson.github.io/snowball/java/api/
A few examples are below.
- 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
- Enforce inequality constraints of the form s(x) < y and s(x) > y
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.
libraryDependencies ++= Seq(
"com.manyangled" % "snowball" % "0.3.0"
)<dependency>
<groupId>com.manyangled</groupId>
<artifactId>snowball</artifactId>
<version>0.3.0</version>
<type>pom</type>
</dependency>
<dependency>
<groupId>com.manyangled</groupId>
<artifactId>gibbous</artifactId>
<version>0.3.0</version>
<type>pom</type>
</dependency>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);$ sbt test:consolescala> 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
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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
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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
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M. Nagahara, Y. Yamamoto, C. Martin, Quadratic Programming for Monotone Control Theoretic Splines, SICE, 2010.
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M. Egerstedt and C. Martin. Monotone Smoothing Splines. Mathematical Theory of Networks and Systems. Perpignan, France, June 2000.