/**
* Copyright (C) 2013 - present by OpenGamma Inc. and the OpenGamma group of companies
*
* Please see distribution for license.
*/
package com.opengamma.strata.math.impl.util;
/**
* Taylor expansion epsilon.
*/
public final class Epsilon {
// Coefficients for the Taylor expansion of (e^x-1)/x and its first two derivatives
private static final double[] COEFF1 = new double[] {1 / 24., 1 / 6., 1 / 2., 1 };
private static final double[] COEFF2 = new double[] {1 / 144., 1 / 30., 1 / 8., 1 / 3., 1 / 2. };
private static final double[] COEFF3 = new double[] {1 / 168., 1 / 36., 1 / 10., 1 / 4., 1 / 3. };
//-------------------------------------------------------------------------
/**
* This is the Taylor expansion of $$\frac{\exp(x)-1}{x}$$ - note for $$|x| > 10^{-10}$$ the expansion is note used .
*
* @param x the value
* @return the result
*/
public static double epsilon(double x) {
if (Math.abs(x) > 1e-10) {
return Math.expm1(x) / x;
}
return taylor(x, COEFF1);
}
/**
* This is the Taylor expansion of the first derivative of $$\frac{\exp(x)-1}{x}$$.
*
* @param x the value
* @return the result
*/
public static double epsilonP(double x) {
if (Math.abs(x) > 1e-7) {
return ((x - 1) * Math.expm1(x) + x) / x / x;
}
return taylor(x, COEFF2);
}
/**
* This is the Taylor expansion of the second derivative of $$\frac{\exp(x)-1}{x}$$.
*
* @param x the value
* @return the result
*/
public static double epsilonPP(double x) {
if (Math.abs(x) > 1e-5) {
double x2 = x * x;
double x3 = x * x2;
return (Math.expm1(x) * (x2 - 2 * x + 2) + x2 - 2 * x) / x3;
}
return taylor(x, COEFF3);
}
private static double taylor(double x, double[] coeff) {
double sum = coeff[0];
int n = coeff.length;
for (int i = 1; i < n; i++) {
sum = coeff[i] + x * sum;
}
return sum;
}
//-------------------------------------------------------------------------
// restricted constructor
private Epsilon() {
}
}