Data commit

Task/Numerical-integration/Swift/numerical-integration.swift

@@ -0,0 +1,105 @@
+public enum IntegrationType : CaseIterable {
+  case rectangularLeft
+  case rectangularRight
+  case rectangularMidpoint
+  case trapezium
+  case simpson
+}
+
+public func integrate(
+  from: Double,
+  to: Double,
+  n: Int,
+  using: IntegrationType = .simpson,
+  f: (Double) -> Double
+) -> Double {
+  let integrationFunc: (Double, Double, Int, (Double) -> Double) -> Double
+
+  switch using {
+  case .rectangularLeft:
+    integrationFunc = integrateRectL
+  case .rectangularRight:
+    integrationFunc = integrateRectR
+  case .rectangularMidpoint:
+    integrationFunc = integrateRectMid
+  case .trapezium:
+    integrationFunc = integrateTrapezium
+  case .simpson:
+    integrationFunc = integrateSimpson
+  }
+
+  return integrationFunc(from, to, n, f)
+}
+
+private func integrateRectL(from: Double, to: Double, n: Int, f: (Double) -> Double) -> Double {
+  let h = (to - from) / Double(n)
+  var x = from
+  var sum = 0.0
+
+  while x <= to - h {
+    sum += f(x)
+    x += h
+  }
+
+  return h * sum
+}
+
+private func integrateRectR(from: Double, to: Double, n: Int, f: (Double) -> Double) -> Double {
+  let h = (to - from) / Double(n)
+  var x = from
+  var sum = 0.0
+
+  while x <= to - h {
+    sum += f(x + h)
+    x += h
+  }
+
+  return h * sum
+}
+
+private func integrateRectMid(from: Double, to: Double, n: Int, f: (Double) -> Double) -> Double {
+  let h = (to - from) / Double(n)
+  var x = from
+  var sum = 0.0
+
+  while x <= to - h {
+    sum += f(x + h / 2.0)
+    x += h
+  }
+
+  return h * sum
+}
+
+private func integrateTrapezium(from: Double, to: Double, n: Int, f: (Double) -> Double) -> Double {
+  let h = (to - from) / Double(n)
+  var sum = f(from) + f(to)
+
+  for i in 1..<n {
+    sum += 2 * f(from + Double(i) * h)
+  }
+
+  return h * sum / 2
+}
+
+private func integrateSimpson(from: Double, to: Double, n: Int, f: (Double) -> Double) -> Double {
+  let h = (to - from) / Double(n)
+  var sum1 = 0.0
+  var sum2 = 0.0
+
+  for i in 0..<n {
+    sum1 += f(from + h * Double(i) + h / 2.0)
+  }
+
+  for i in 1..<n {
+    sum2 += f(from + h * Double(i))
+  }
+
+  return h / 6.0 * (f(from) + f(to) + 4.0 * sum1 + 2.0 * sum2)
+}
+
+let types = IntegrationType.allCases
+
+print("f(x) = x^3:", types.map({ integrate(from: 0, to: 1, n: 100, using: $0, f: { pow($0, 3) }) }))
+print("f(x) = 1 / x:", types.map({ integrate(from: 1, to: 100, n: 1000, using: $0, f: { 1 / $0 }) }))
+print("f(x) = x, 0 -> 5_000:", types.map({ integrate(from: 0, to: 5_000, n: 5_000_000, using: $0, f: { $0 }) }))
+print("f(x) = x, 0 -> 6_000:", types.map({ integrate(from: 0, to: 6_000, n: 6_000_000, using: $0, f: { $0 }) }))