Class StandardInterval
- java.lang.Object
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- dev.nm.analysis.integration.univariate.riemann.substitution.StandardInterval
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- All Implemented Interfaces:
SubstitutionRule
public class StandardInterval extends Object implements SubstitutionRule
This transformation is for mapping integral region from [a, b] to [-1, 1]. The substitution rule is \[ \int_{a}^{b}f(x)dx = \int_{-1}^{1}\frac{b-a}{2}f(\frac{(b-a)t+(a+b)}{2})dt \]
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Constructor Summary
Constructors Constructor Description StandardInterval(double a, double b)
Construct aStandardInterval
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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