Packages

object Integral

The Integral object provides implementations for five basic integration methods:

∫f(x)dx on interval [a, b]

trap - trapezoidal method - linear simpson - Simpson method - quadratic simpson38 - 3/8 Simpson method - cubic boole - Boole Method - quartic romberg - Romberg method - recursive, uses trap

The first four are Composite Newton-Coates type integrators.

See also

en.wikipedia.org/wiki/Newton%E2%80%93Cotes_formulas

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  5. def boole(a: Double, b: Double, f: FunctionS2S, sd: Int = SUBDIV): Double

    Integrate '∫f(x)dx' on interval '[a, b]' using the Boole method.

    Integrate '∫f(x)dx' on interval '[a, b]' using the Boole method.

    a

    the start of the integration interval

    b

    the end of the integration interval

    f

    the function to be integrated

    sd

    the number of subdivision (intervals) of [a, b]

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  11. def hashCode(): Int
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  12. def integrate(on: Interval, f: FunctionS2S): Double

    Integrate '∫f(x)dx' on interval 'on' using the default method.

    Integrate '∫f(x)dx' on interval 'on' using the default method.

    on

    the interval of integration, e.g., (0.0, 2.0)

    f

    the function to be integrated

  13. final def isInstanceOf[T0]: Boolean
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  17. def romberg(a: Double, b: Double, f: FunctionS2S, iter: Int = ITER): Double

    Integrate '∫f(x)dx' on interval '[a, b]' using the Romberg method.

    Integrate '∫f(x)dx' on interval '[a, b]' using the Romberg method. Translation of Java code from the site below to Scala.

    a

    the start of the integration interval

    b

    the end of the integration interval

    f

    the function to be integrated

    iter

    the number of iterative steps

    See also

    cs.roanoke.edu/Spring2012/CPSC402A/Integrate.java FIX: shouldn't need a 2D array/matrix.

  18. def simpson(a: Double, b: Double, f: FunctionS2S, sd: Int = SUBDIV): Double

    Integrate '∫f(x)dx' on interval '[a, b]' using the Simpson method.

    Integrate '∫f(x)dx' on interval '[a, b]' using the Simpson method.

    a

    the start of the integration interval

    b

    the end of the integration interval

    f

    the function to be integrated

    sd

    the number of subdivision (intervals) of [a, b]

  19. def simpson38(a: Double, b: Double, f: FunctionS2S, sd: Int = SUBDIV): Double

    Integrate '∫f(x)dx' on interval '[a, b]' using the 3/8 Simpson method.

    Integrate '∫f(x)dx' on interval '[a, b]' using the 3/8 Simpson method.

    a

    the start of the integration interval

    b

    the end of the integration interval

    f

    the function to be integrated

    sd

    the number of subdivision (intervals) of [a, b]

  20. final def synchronized[T0](arg0: ⇒ T0): T0
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  21. def test(a: Double, b: Double, f: FunctionS2S, ans: Double, sd: Int = SUBDIV): Unit

    Test each of the numerical integrators: '∫f(x)dx' on interval '[a, b]'.

    Test each of the numerical integrators: '∫f(x)dx' on interval '[a, b]'.

    a

    the start of the integration interval

    b

    the end of the integration interval

    f

    the function to be integrated

    ans

    the answer to the integration problem, if known (for % error)

    sd

    the number of subdivision (intervals) of [a, b]

  22. def toString(): String
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  23. def trap(a: Double, b: Double, f: FunctionS2S, sd: Int = SUBDIV): Double

    Integrate '∫f(x)dx' on interval '[a, b]' using the trapezoidal method.

    Integrate '∫f(x)dx' on interval '[a, b]' using the trapezoidal method.

    a

    the start of the integration interval

    b

    the end of the integration interval

    f

    the function to be integrated

    sd

    the number of subdivision (intervals) of [a, b]

  24. final def wait(): Unit
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  27. def ∫(on: Interval, f: FunctionS2S): Double

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