Package com.opengamma.strata.math.impl.integration

Class GaussianQuadratureIntegrator1D

java.lang.Object

com.opengamma.strata.math.impl.integration.Integrator1D<Double,Double>

com.opengamma.strata.math.impl.integration.GaussianQuadratureIntegrator1D

All Implemented Interfaces:

Integrator<Double,Double,Function<Double,Double>>

Direct Known Subclasses:

GaussHermiteQuadratureIntegrator1D, GaussJacobiQuadratureIntegrator1D, GaussLaguerreQuadratureIntegrator1D, GaussLegendreQuadratureIntegrator1D

public abstract class GaussianQuadratureIntegrator1D
extends Integrator1D<Double,Double>

Class that performs integration using Gaussian quadrature.

If a function $f(x)$ can be written as $f(x) = W(x)g(x)$, where $g(x)$ is approximately polynomial, then for suitably chosen weights $w_i$ and points $x_i$, the integral can be approximated as: $$ \begin{align*} \int_{-1}^1 f(x)dx &=\int_{-1}^1 W(x)g(x)dx\\ &\approx \sum_{\i=1}^{n} w_i f(x_i) \end{align*} $$ The evaluation points, weights and valid limits of integration depend on the type of orthogonal polynomials that are used (see OrthogonalPolynomialFunctionGenerator and GaussLaguerreWeightAndAbscissaFunction).

Constructor Summary

Constructors

Constructor	Description
GaussianQuadratureIntegrator1D(int n, QuadratureWeightAndAbscissaFunction generator)	Creates an instance.

Method Summary

Modifier and Type	Method	Description
boolean	equals(Object obj)
abstract Function<Double,Double>	getIntegralFunction(Function<Double,Double> function, Double lower, Double upper)	Returns a function that is valid for both the type of quadrature and the limits of integration.
abstract Double[]	getLimits()	Gets the limits.
int	hashCode()
Double	integrate(Function<Double,Double> function, Double lower, Double upper)	1-D integration method.
double	integrateFromPolyFunc(Function<Double,Double> polyFunction)	If a function $g(x)$ can be written as $W(x)f(x)$, where the weight function $W(x)$ corresponds to one of the Gaussian quadrature forms, then we may approximate the integral of $g(x)$ over a specific range as $\int^b_a g(x) dx =\int^b_a W(x)f(x) dx \approx \sum_{i=0}^{N-1} w_i f(x_i)$, were the abscissas $x_i$ and the weights $w_i$ have been precomputed.

Methods inherited from class com.opengamma.strata.math.impl.integration.Integrator1D

integrate

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

GaussianQuadratureIntegrator1D

public GaussianQuadratureIntegrator1D(int n,
                                      QuadratureWeightAndAbscissaFunction generator)

Creates an instance.

Parameters:

n - The number of sample points to be used in the integration, not negative or zero

generator - The generator of weights and abscissas

Method Detail

integrate

public Double integrate(Function<Double,Double> function,
                        Double lower,
                        Double upper)

1-D integration method.

Specified by:

integrate in class Integrator1D<Double,Double>

Parameters:

function - The function to integrate, not null

lower - The lower bound, not null

upper - The upper bound, not null

Returns:

The result of the integration

integrateFromPolyFunc

public double integrateFromPolyFunc(Function<Double,Double> polyFunction)

If a function $g(x)$ can be written as $W(x)f(x)$, where the weight function $W(x)$ corresponds to one of the Gaussian quadrature forms, then we may approximate the integral of $g(x)$ over a specific range as $\int^b_a g(x) dx =\int^b_a W(x)f(x) dx \approx \sum_{i=0}^{N-1} w_i f(x_i)$, were the abscissas $x_i$ and the weights $w_i$ have been precomputed. This is accurate if $f(x)$ can be approximated by a polynomial.

Parameters:

polyFunction - The function $f(x)$ rather than the full function $g(x) = W(x)f(x)$ This should be well approximated by a polynomial.

Returns:

The integral

getLimits

public abstract Double[] getLimits()

Gets the limits.

Returns:

The lower and upper limits for which the quadrature is valid

getIntegralFunction

public abstract Function<Double,Double> getIntegralFunction(Function<Double,Double> function,
                                                                  Double lower,
                                                                  Double upper)

Returns a function that is valid for both the type of quadrature and the limits of integration.

Parameters:

function - The function to be integrated, not null

lower - The lower integration limit, not null

upper - The upper integration limit, not null

Returns:

A function in the appropriate form for integration

hashCode

public int hashCode()

Overrides:

hashCode in class Object

equals

public boolean equals(Object obj)

Overrides:

equals in class Object