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Task/Numerical-integration/Nim/numerical-integration.nim

@@ -0,0 +1,45 @@
+type Function = proc(x: float): float
+type Rule = proc(f: Function; x, h: float): float
+
+proc leftRect(f: Function; x, h: float): float =
+  f(x)
+
+proc midRect(f: Function; x, h: float): float =
+  f(x + h/2.0)
+
+proc rightRect(f: Function; x, h: float): float =
+  f(x + h)
+
+proc trapezium(f: Function; x, h: float): float =
+  (f(x) + f(x+h)) / 2.0
+
+proc simpson(f: Function, x, h: float): float =
+  (f(x) + 4.0*f(x+h/2.0) + f(x+h)) / 6.0
+
+proc cube(x: float): float =
+  x * x *x
+
+proc reciprocal(x: float): float =
+  1.0 / x
+
+proc identity(x: float): float =
+  x
+
+proc integrate(f: Function; a, b: float; steps: int; meth: Rule): float =
+  let h = (b-a) / float(steps)
+  for i in 0 .. <steps:
+    result += meth(f, a+float(i)*h, h)
+  result = h * result
+
+for fName, a, b, steps, fun in items(
+   [("cube", 0, 1, 100, cube),
+    ("reciprocal", 1, 100, 1000, reciprocal),
+    ("identity", 0, 5000, 5_000_000, identity),
+    ("identity", 0, 6000, 6_000_000, identity)]):
+
+  for rName, rule in items({"leftRect": leftRect, "midRect": midRect,
+      "rightRect": rightRect, "trapezium": trapezium, "simpson": simpson}):
+
+    echo fName, " integrated using ", rName
+    echo "  from ", a, " to ", b, " (", steps, " steps) = ",
+      integrate(fun, float(a), float(b), steps, rule)