44 lines
1.3 KiB
Scala
44 lines
1.3 KiB
Scala
|
import java.lang.Math._
|
|||
|
|
|
|||
|
|
class Approx(val ν: Double, val σ: Double = 0.0) {
|
|||
|
|
def this(a: Approx) = this(a.ν, a.σ)
|
|||
|
|
def this(n: Number) = this(n.doubleValue(), 0.0)
|
|||
|
|
|
|||
|
|
override def toString = s"$ν ±$σ"
|
|||
|
|
|
|||
|
|
def +(a: Approx) = Approx(ν + a.ν, sqrt(σ * σ + a.σ * a.σ))
|
|||
|
|
def +(d: Double) = Approx(ν + d, σ)
|
|||
|
|
def -(a: Approx) = Approx(ν - a.ν, sqrt(σ * σ + a.σ * a.σ))
|
|||
|
|
def -(d: Double) = Approx(ν - d, σ)
|
|||
|
|
|
|||
|
|
def *(a: Approx) = {
|
|||
|
|
val v = ν * a.ν
|
|||
|
|
Approx(v, sqrt(v * v * σ * σ / (ν * ν) + a.σ * a.σ / (a.ν * a.ν)))
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
def *(d: Double) = Approx(ν * d, abs(d * σ))
|
|||
|
|
|
|||
|
|
def /(a: Approx) = {
|
|||
|
|
val t = ν / a.ν
|
|||
|
|
Approx(t, sqrt(t * t * σ * σ / (ν * ν) + a.σ * a.σ / (a.ν * a.ν)))
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
def /(d: Double) = Approx(ν / d, abs(d * σ))
|
|||
|
|
|
|||
|
|
def ^(d: Double) = {
|
|||
|
|
val t = pow(ν, d)
|
|||
|
|
Approx(t, abs(t * d * σ / ν))
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
object Approx { def apply(ν: Double, σ: Double = 0.0) = new Approx(ν, σ) }
|
|||
|
|
|
|||
|
|
object NumericError extends App {
|
|||
|
|
def √(a: Approx) = a^0.5
|
|||
|
|
val x1 = Approx(100.0, 1.1)
|
|||
|
|
val x2 = Approx(50.0, 1.2)
|
|||
|
|
val y1 = Approx(200.0, 2.2)
|
|||
|
|
val y2 = Approx(100.0, 2.3)
|
|||
|
|
println(√(((x1 - x2)^2.0) + ((y1 - y2)^2.0))) // => 111.80339887498948 ±2.938366893361004
|
|||
|
|
}
|