IterativeLegendreGaussIntegrator instead.@Deprecated public class LegendreGaussIntegrator extends BaseAbstractUnivariateIntegrator
Legendre-Gauss integrators are efficient integrators that can accurately integrate functions with few function evaluations. A Legendre-Gauss integrator using an n-points quadrature formula can integrate 2n-1 degree polynomials exactly.
These integrators evaluate the function on n carefully chosen abscissas in each step interval (mapped to the canonical [-1,1] interval). The evaluation abscissas are not evenly spaced and none of them are at the interval endpoints. This implies the function integrated can be undefined at integration interval endpoints.
The evaluation abscissas xi are the roots of the degree n Legendre polynomial. The weights ai of the quadrature formula integrals from -1 to +1 ∫ Li2 where Li (x) = ∏ (x-xk)/(xi-xk) for k != i.
DEFAULT_ABSOLUTE_ACCURACY, DEFAULT_MAX_ITERATIONS_COUNT, DEFAULT_MIN_ITERATIONS_COUNT, DEFAULT_RELATIVE_ACCURACY, iterations| Constructor and Description |
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LegendreGaussIntegrator(int n,
double relativeAccuracy,
double absoluteAccuracy)
Deprecated.
Build a Legendre-Gauss integrator with given accuracies.
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LegendreGaussIntegrator(int n,
double relativeAccuracy,
double absoluteAccuracy,
int minimalIterationCount,
int maximalIterationCount)
Deprecated.
Build a Legendre-Gauss integrator with given accuracies and iterations counts.
|
LegendreGaussIntegrator(int n,
int minimalIterationCount,
int maximalIterationCount)
Deprecated.
Build a Legendre-Gauss integrator with given iteration counts.
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| Modifier and Type | Method and Description |
|---|---|
protected double |
doIntegrate()
Deprecated.
Method for implementing actual integration algorithms in derived
classes.
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computeObjectiveValue, getAbsoluteAccuracy, getEvaluations, getIterations, getMax, getMaximalIterationCount, getMin, getMinimalIterationCount, getRelativeAccuracy, incrementCount, integrate, setuppublic LegendreGaussIntegrator(int n,
double relativeAccuracy,
double absoluteAccuracy,
int minimalIterationCount,
int maximalIterationCount)
throws MathIllegalArgumentException,
NotStrictlyPositiveException,
NumberIsTooSmallException
n - number of points desired (must be between 2 and 5 inclusive)relativeAccuracy - relative accuracy of the resultabsoluteAccuracy - absolute accuracy of the resultminimalIterationCount - minimum number of iterationsmaximalIterationCount - maximum number of iterationsMathIllegalArgumentException - if number of points is out of [2; 5]NotStrictlyPositiveException - if minimal number of iterations
is not strictly positiveNumberIsTooSmallException - if maximal number of iterations
is lesser than or equal to the minimal number of iterationspublic LegendreGaussIntegrator(int n,
double relativeAccuracy,
double absoluteAccuracy)
throws MathIllegalArgumentException
n - number of points desired (must be between 2 and 5 inclusive)relativeAccuracy - relative accuracy of the resultabsoluteAccuracy - absolute accuracy of the resultMathIllegalArgumentException - if number of points is out of [2; 5]public LegendreGaussIntegrator(int n,
int minimalIterationCount,
int maximalIterationCount)
throws MathIllegalArgumentException
n - number of points desired (must be between 2 and 5 inclusive)minimalIterationCount - minimum number of iterationsmaximalIterationCount - maximum number of iterationsMathIllegalArgumentException - if number of points is out of [2; 5]NotStrictlyPositiveException - if minimal number of iterations
is not strictly positiveNumberIsTooSmallException - if maximal number of iterations
is lesser than or equal to the minimal number of iterationsprotected double doIntegrate()
throws MathIllegalArgumentException,
TooManyEvaluationsException,
MaxCountExceededException
doIntegrate in class BaseAbstractUnivariateIntegratorTooManyEvaluationsException - if the maximal number of evaluations
is exceeded.MaxCountExceededException - if the maximum iteration count is exceeded
or the integrator detects convergence problems otherwiseMathIllegalArgumentExceptionCopyright © 2003–2016 The Apache Software Foundation. All rights reserved.