Class Exponential
- java.lang.Object
-
- dev.nm.analysis.integration.univariate.riemann.substitution.Exponential
-
- All Implemented Interfaces:
SubstitutionRule
public class Exponential extends Object implements SubstitutionRule
This transformation is good for when the lower limit is finite, the upper limit is infinite, and the integrand falls off exponentially. The integrator for this substitution should use an OPEN formula to avoid computing for the end point where t = 0. The substitution is \[ \int_{a}^{\infty}f(x)dx = \int_{0}^{e^a}f(-\log (t))\frac{\mathrm{d} t}{t} \]
-
-
Constructor Summary
Constructors Constructor Description Exponential(double a)Construct anExponentialsubstitution rule.
-
Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description UnivariateRealFunctiondx()the first order derivative of the transformation: x'(t) = dx(t)/dtdoubleta()Get the lower limit of the integral.doubletb()Get the upper limit of the integral.UnivariateRealFunctionx()the transformation: x(t)
-
-
-
Method Detail
-
x
public UnivariateRealFunction x()
Description copied from interface:SubstitutionRulethe transformation: x(t)- Specified by:
xin interfaceSubstitutionRule- Returns:
- x(t)
-
dx
public UnivariateRealFunction dx()
Description copied from interface:SubstitutionRulethe first order derivative of the transformation: x'(t) = dx(t)/dt- Specified by:
dxin interfaceSubstitutionRule- Returns:
- x'(t) = dx(t)/dt
-
ta
public double ta()
Description copied from interface:SubstitutionRuleGet the lower limit of the integral.- Specified by:
tain interfaceSubstitutionRule- Returns:
- the lower limit
-
tb
public double tb()
Description copied from interface:SubstitutionRuleGet the upper limit of the integral.- Specified by:
tbin interfaceSubstitutionRule- Returns:
- the upper limit
-
-