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

Class GaussLegendreQuadratureIntegrator1D

java.lang.Object

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

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

com.opengamma.strata.math.impl.integration.GaussLegendreQuadratureIntegrator1D

All Implemented Interfaces:

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

public class GaussLegendreQuadratureIntegrator1D
extends GaussianQuadratureIntegrator1D

Gauss-Legendre quadrature approximates the value of integrals of the form $$ \begin{align*} \int_{-1}^{1} f(x) dx \end{align*} $$ The weights and abscissas are generated by GaussLegendreWeightAndAbscissaFunction.

The function to integrate is scaled in such a way as to allow any values for the limits of the integrals.

Constructor Summary

Constructors

Constructor	Description
GaussLegendreQuadratureIntegrator1D(int n)

Method Summary

Modifier and Type	Method	Description
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.
Double[]	getLimits()	Gets the limits.

Methods inherited from class com.opengamma.strata.math.impl.integration.GaussianQuadratureIntegrator1D

equals, hashCode, integrate, integrateFromPolyFunc

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

GaussLegendreQuadratureIntegrator1D

public GaussLegendreQuadratureIntegrator1D(int n)

Parameters:

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

Method Detail

getLimits

public Double[] getLimits()

Description copied from class: GaussianQuadratureIntegrator1D

Gets the limits.

Specified by:

getLimits in class GaussianQuadratureIntegrator1D

Returns:

The lower and upper limits for which the quadrature is valid

getIntegralFunction

public 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. To evaluate an integral over $[a, b]$, a change of interval must be performed: $$ \begin{align*} \int_a^b f(x)dx &= \frac{b - a}{2}\int_{-1}^1 f(\frac{b - a}{2} x + \frac{a + b}{2})dx\\ &\approx \frac{b - a}{2}\sum_{i=1}^n w_i f(\frac{b - a}{2} x + \frac{a + b}{2}) \end{align*} $$

Specified by:

getIntegralFunction in class GaussianQuadratureIntegrator1D

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