smile.math.rbf.MultiquadricRadialBasis Maven / Gradle / Ivy
/******************************************************************************
* Confidential Proprietary *
* (c) Copyright Haifeng Li 2011, All Rights Reserved *
******************************************************************************/
package smile.math.rbf;
/**
* Multiquadric RBF. φ(r) = (r2 + r20)1/2
* where r0 is a scale factor. Multiquadrics are said to be less
* sensitive to the choice of r0 than som other functional forms.
*
* In general, r0 should be larger than the typical separation of
* points but smaller than the "outer scale" or feature size of the function
* to interplate. There can be several orders of magnitude difference between
* the interpolation accuracy with a good choice for r0, versus a
* poor choice, so it is definitely worth some experimentation. One way to
* experiment is to construct an RBF interpolator omitting one data point
* at a time and measuring the interpolation error at the omitted point.
*
* @author Haifeng Li
*/
public class MultiquadricRadialBasis implements RadialBasisFunction {
private double r02;
/**
* Constructor.
*/
public MultiquadricRadialBasis() {
this(1.0);
}
/**
* Constructor.
*/
public MultiquadricRadialBasis(double scale) {
r02 = scale * scale;
}
@Override
public double f(double r) {
return Math.sqrt(r * r + r02);
}
}