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finmath lib is a Mathematical Finance Library in Java.
It provides algorithms and methodologies related to mathematical finance.
/*
* (c) Copyright Christian P. Fries, Germany. Contact: [email protected].
*
* Created on 26.01.2018
*/
package net.finmath.interpolation;
import java.util.Arrays;
import java.util.function.BiFunction;
/**
* Simple bi-linear interpolation of data points \( z_{i,j} \) over a Cartesian grid \( (x_{i},y_{j}) \).
*
* The interpolation function is
* \[
* z = f(x,y) =
* \alpha_{x} \alpha_{y} z_{k_{x},k_{y}} +
* \alpha_{x} (1-\alpha_{y}) z_{k_{x},k_{y}+1} +
* (1-\alpha_{x}) \alpha_{y} z_{k_{x}+1,k_{y}} +
* (1-\alpha_{x}) (1-\alpha_{y}) z_{k_{x}+1,k_{y}+1}
* \]
* where \( x_{k_{x}} \leq x \leq x_{k_{x}+1} \) and \( y_{k_{y}} \leq y \leq y_{k_{x}+1} \) and \( \alpha_{x} = (x_{k_{x}+1}-x)/(x_{k_{x}+1}-x_{k_{x}}) \) and \( \alpha_{y} = (x_{k_{y}+1}-x)/(x_{k_{y}+1}-x_{k_{y}}) \).
*
* @author Christian Fries
* @version 1.0
*/
public class BiLinearInterpolation implements BiFunction {
private final double[] x;
private final double[] y;
private final double[][] z;
public BiLinearInterpolation(final double[] x, final double[] y, final double[][] z) {
super();
this.x = x;
this.y = y;
this.z = z;
}
@Override
public Double apply(final Double x, final Double y) {
return getValue(x, y);
}
double getValue(final double x, final double y) {
int indexGreaterOrEqualX = Arrays.binarySearch(this.x, x);
if(indexGreaterOrEqualX < 0) {
indexGreaterOrEqualX = -indexGreaterOrEqualX-1;
}
int upperIndexX = Math.min(Math.max(indexGreaterOrEqualX, 0), this.x.length-1);
final int lowerIndexX = Math.min(Math.max(upperIndexX-1, 0), this.x.length-1);
int indexGreaterOrEqualY = Arrays.binarySearch(this.y, y);
if(indexGreaterOrEqualY < 0) {
indexGreaterOrEqualY = -indexGreaterOrEqualY-1;
}
int upperIndexY = Math.min(Math.max(indexGreaterOrEqualY, 0), this.y.length-1);
final int lowerIndexY = Math.min(Math.max(upperIndexY-1, 0), this.y.length-1);
if(upperIndexX == lowerIndexX) {
upperIndexX++;
}
if(upperIndexY == lowerIndexY) {
upperIndexY++;
}
final double alphaX = (this.x[upperIndexX]-x)/(this.x[upperIndexX]-this.x[lowerIndexX]);
final double alphaY = (this.y[upperIndexY]-y)/(this.y[upperIndexY]-this.y[lowerIndexY]);
final double interpolatedValue =
alphaX * alphaY * z[lowerIndexX][lowerIndexY] +
alphaX * (1.0-alphaY) * z[lowerIndexX][upperIndexY] +
(1-alphaX) * alphaY * z[upperIndexX][lowerIndexY] +
(1-alphaX) * (1-alphaY) * z[upperIndexX][upperIndexY];
return interpolatedValue;
}
}