/**
* Copyright (C) 2009 - present by OpenGamma Inc. and the OpenGamma group of companies
*
* Please see distribution for license.
*/
package com.opengamma.analytics.math.integration;
import org.apache.commons.lang.Validate;
import com.opengamma.analytics.math.function.Function1D;
/**
* Gauss-Hermite quadrature approximates the value of integrals of the form
* $$
* \begin{align*}
* \int_{-\infty}^{\infty} e^{-x^2} g(x) dx
* \end{align*}
* $$
* The weights and abscissas are generated by {@link GaussHermiteWeightAndAbscissaFunction}.
* <p>
* At present, this integrator can only be used for the limits $\pm\infty$. The
* function to integrate is scaled in such a way as to allow any values for the
* limits of integration.
*/
public class GaussHermiteQuadratureIntegrator1D extends GaussianQuadratureIntegrator1D {
private static final Double[] LIMITS = new Double[] {Double.NEGATIVE_INFINITY, Double.POSITIVE_INFINITY };
private static final GaussHermiteWeightAndAbscissaFunction GENERATOR = new GaussHermiteWeightAndAbscissaFunction();
/**
* @param n The number of sample points to use in the integration
*/
public GaussHermiteQuadratureIntegrator1D(final int n) {
super(n, GENERATOR);
}
/**
* {@inheritDoc}
*/
@Override
public Double[] getLimits() {
return LIMITS;
}
/**
* {@inheritDoc}
* The function $f(x)$ that is to be integrated is transformed into a form
* suitable for this quadrature method using:
* $$
* \begin{align*}
* \int_{-\infty}^{\infty} f(x) dx
* &= \int_{-\infty}^{\infty} f(x) e^{x^2} e^{-x^2} dx\\
* &= \int_{-\infty}^{\infty} g(x) e^{-x^2} dx
* \end{align*}
* $$
* @throws UnsupportedOperationException If the lower limit is not $-\infty$ or the upper limit is not $\infty$
*/
@Override
public Function1D<Double, Double> getIntegralFunction(final Function1D<Double, Double> function, final Double lower, final Double upper) {
Validate.notNull(function, "function");
Validate.notNull(lower, "lower");
Validate.notNull(upper, "upper");
if (lower.equals(LIMITS[0]) && upper.equals(LIMITS[1])) {
return new Function1D<Double, Double>() {
@Override
public Double evaluate(final Double x) {
return Math.exp(x * x) * function.evaluate(x);
}
};
}
throw new UnsupportedOperationException("Limits for this integration method are +/-infinity");
}
}