36 lines
1.4 KiB
Scala
36 lines
1.4 KiB
Scala
object NumericalIntegration {
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def leftRect(f:Double=>Double, a:Double, b:Double)=f(a)
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def midRect(f:Double=>Double, a:Double, b:Double)=f((a+b)/2)
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def rightRect(f:Double=>Double, a:Double, b:Double)=f(b)
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def trapezoid(f:Double=>Double, a:Double, b:Double)=(f(a)+f(b))/2
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def simpson(f:Double=>Double, a:Double, b:Double)=(f(a)+4*f((a+b)/2)+f(b))/6;
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def fn1(x:Double)=x*x*x
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def fn2(x:Double)=1/x
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def fn3(x:Double)=x
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type Method = (Double=>Double, Double, Double) => Double
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def integrate(f:Double=>Double, a:Double, b:Double, steps:Double, m:Method)={
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val delta:Double=(b-a)/steps
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delta*(a until b by delta).foldLeft(0.0)((s,x) => s+m(f, x, x+delta))
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}
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def print(f:Double=>Double, a:Double, b:Double, steps:Double)={
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println("rectangular left : %f".format(integrate(f, a, b, steps, leftRect)))
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println("rectangular middle : %f".format(integrate(f, a, b, steps, midRect)))
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println("rectangular right : %f".format(integrate(f, a, b, steps, rightRect)))
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println("trapezoid : %f".format(integrate(f, a, b, steps, trapezoid)))
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println("simpson : %f".format(integrate(f, a, b, steps, simpson)))
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}
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def main(args: Array[String]): Unit = {
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print(fn1, 0, 1, 100)
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println("------")
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print(fn2, 1, 100, 1000)
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println("------")
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print(fn3, 0, 5000, 5000000)
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println("------")
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print(fn3, 0, 6000, 6000000)
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}
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}
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