Class Exponential
- java.lang.Object
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- dev.nm.analysis.integration.univariate.riemann.substitution.Exponential
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- 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 \[ \int_{a}^{\infty}f(x)dx = \int_{0}^{e^a}f(-\log (t))\frac{\mathrm{d} t}{t} \]
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Constructor Summary
Constructors Constructor Description Exponential(double a)
Construct anExponential
substitution rule.
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Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description UnivariateRealFunction
dx()
the first order derivative of the transformation: x'(t) = dx(t)/dtdouble
ta()
Get the lower limit of the integral.double
tb()
Get the upper limit of the integral.UnivariateRealFunction
x()
the transformation: x(t)
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Method Detail
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x
public UnivariateRealFunction x()
Description copied from interface:SubstitutionRule
the transformation: x(t)- Specified by:
x
in interfaceSubstitutionRule
- Returns:
- x(t)
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dx
public UnivariateRealFunction dx()
Description copied from interface:SubstitutionRule
the first order derivative of the transformation: x'(t) = dx(t)/dt- Specified by:
dx
in interfaceSubstitutionRule
- Returns:
- x'(t) = dx(t)/dt
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ta
public double ta()
Description copied from interface:SubstitutionRule
Get the lower limit of the integral.- Specified by:
ta
in interfaceSubstitutionRule
- Returns:
- the lower limit
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tb
public double tb()
Description copied from interface:SubstitutionRule
Get the upper limit of the integral.- Specified by:
tb
in interfaceSubstitutionRule
- Returns:
- the upper limit
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