Class MappedExpander

java.lang.Object

com.github.gbenroscience.math.numericalmethods.MappedExpander

public class MappedExpander
extends Object

How to use these in your Platform When you want the derivative of a badly behaved function at a point : Map x to u using toChebyshev(x). Compute the derivative of the Chebyshev series at (standard algorithm). Multiply that result by map.derivativeFactor(u). When you want the integral: Sample f(x) at mapped nodes. Multiply by map.dx_du(u). Sum using Clenshaw-Curtis weights. Pro-Tip for Precision In the SemiInfiniteMap, as * , * . In your code, you should clamp to something like 0.9999999999 if you hit a NaN in the physical domain to prevent the platform from crashing on a hard infinity. Would you like the Clenshaw-Curtis weight generator to ensure your integration reaches full 16-digit precision?

Author:

GBEMIRO

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static final class	MappedExpander.CCWeightGenerator
static interface	MappedExpander.DomainMap
static class	MappedExpander.DoubleLogarithmicMap	A DomainMap that clusters nodes tightly at BOTH the lower bound (a) and the upper bound (b).
static class	MappedExpander.LinearMap
static class	MappedExpander.LogarithmicMap
static class	MappedExpander.ReversedLogarithmicMap	Logarithmic map that clusters nodes near the upper bound B.
static class	MappedExpander.SemiInfiniteMap	Algebraic map for the semi-infinite interval [0, infinity) Hardens against functions with "tails".
static final class	MappedExpander.SubDomainMap

Field Summary

Fields

Modifier and Type	Field	Description
static final int	MAX_DEPTH

Constructor Summary

Constructors

Constructor	Description
MappedExpander(Function function, MappedExpander.DomainMap map, int N)	Uses Chebyshev Extrema nodes: u_k = cos(k * PI / N) for k = 0...N.

Method Summary

Modifier and Type	Method	Description
MappedExpander.DomainMap	autoSelectMap(Function f, double a, double b)	Detection heuristic
double	evaluate(double x)
double	getTailError()
double	integrate()
double	integrateAdaptive(Function f, MappedExpander.DomainMap map, double tol, int depth)
double	integrateFinal(double[] ccWeights)	O(N) Integration: Direct sum using pre-sampled values and CC weights.
double	integrateSeamless()
boolean	isAliasing()
static void	main(String[] args)

Methods inherited from class java.lang.Object

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

Field Details

MAX_DEPTH

public static final int MAX_DEPTH

See Also:

• Constant Field Values

Constructor Details

MappedExpander

public MappedExpander(Function function,
 MappedExpander.DomainMap map,
 int N)

Uses Chebyshev Extrema nodes: u_k = cos(k * PI / N) for k = 0...N. This matches Clenshaw-Curtis weights perfectly.

Method Details

getTailError

public double getTailError()

evaluate

public double evaluate(double x)

integrate

public double integrate()

integrateSeamless

public double integrateSeamless()

integrateFinal

public double integrateFinal(double[] ccWeights)

O(N) Integration: Direct sum using pre-sampled values and CC weights.

integrateAdaptive

public double integrateAdaptive(Function f,
 MappedExpander.DomainMap map,
 double tol,
 int depth)

isAliasing

public boolean isAliasing()

autoSelectMap

public MappedExpander.DomainMap autoSelectMap(Function f,
 double a,
 double b)

Detection heuristic

Parameters:

f -

a -

b -

Returns:

main

public static void main(String[] args)