Interpolation over an array (or two)

Question

I\'m looking for a java library or some help to write my own interpolation function. That is I have two arrays of doubles which are potentially different sizes, but are ord

Answer 1

Designed for ONE Dimension data array

import java.util.ArrayList;

public class Interpolator {

public static Float CosineInterpolate(Float y1,Float y2,Float mu)
{
    double mu2;

    mu2 = (1.0f-Math.cos(mu*Math.PI))/2.0f;
    Float f_mu2 = new Float(mu2);
    return(y1*(1.0f-f_mu2)+y2*f_mu2);
}

public static Float LinearInterpolate(Float y1,Float y2,Float mu)
{
    return(y1*(1-mu)+y2*mu);
}


public static Float[] Interpolate(Float[] a, String mode) {

    // Check that have at least the very first and very last values non-null
    if (!(a[0] != null && a[a.length-1] != null)) return null;

    ArrayList<Integer> non_null_idx = new ArrayList<Integer>();
    ArrayList<Integer> steps = new ArrayList<Integer>();

    int step_cnt = 0;
    for (int i=0; i<a.length; i++)
    {
        if (a[i] != null)
        {
            non_null_idx.add(i);
            if (step_cnt != 0) {
                steps.add(step_cnt);
                System.err.println("aDDed step >> " + step_cnt);
            }
            step_cnt = 0;
        }
        else
        {
            step_cnt++;
        }
    }

    Float f_start = null;
    Float f_end = null;
    Float f_step = null;
    Float f_mu = null;

    int i = 0;
    while (i < a.length - 1) // Don't do anything for the very last element (which should never be null)
    {
        if (a[i] != null && non_null_idx.size() > 1 && steps.size() > 0)
        {
            f_start = a[non_null_idx.get(0)];
            f_end = a[non_null_idx.get(1)];
            f_step = new Float(1.0) / new Float(steps.get(0) + 1);
            f_mu = f_step;
            non_null_idx.remove(0);
            steps.remove(0);
        }
        else if (a[i] == null)
        {
            if (mode.equalsIgnoreCase("cosine"))
                a[i] = CosineInterpolate(f_start, f_end, f_mu);
            else
                a[i] = LinearInterpolate(f_start, f_end, f_mu);
            f_mu += f_step;
        }
        i++;
    }

    return a;
}
}

Don't know if it helps... It is very fast coded, so if anyone has a nicer / more performing way to do the same, thank for contributing.

USAGE:

input : Float[] a = {1.0f, null, null, 2.0f, null, null, null, 15.0f};

call : Interpolator.Interpolate(a, "Linear");

output : 1.0|1.3333333|1.6666667|2.0|5.25|8.5|11.75|15.0

Answer 2

You need to get the x-values corresponding to the y-values. Otherwise no algorithm will be able to determine whether [1, 16, 81] is x^2 for [1, 4, 9] or x^4 for [1, 2, 3]. Would you interpolate six values or none?

And then, when you're given the x-values, you can use some sort of interpolation (linear, kubic spline, you name it) to approximate the missing values.