Initial data commit

Task/Numeric-error-propagation/Scala/numeric-error-propagation.scala

@@ -0,0 +1,43 @@
+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
+}