tasks a-s

Task/Numerical-integration/Ruby/numerical-integration.rb

@@ -0,0 +1,58 @@
+def leftrect(f, left, right)
+  f.call(left)
+end
+
+def midrect(f, left, right)
+  f.call((left+right)/2.0)
+end
+
+def rightrect(f, left, right)
+  f.call(right)
+end
+
+def trapezium(f, left, right)
+  (f.call(left) + f.call(right)) / 2.0
+end
+
+def simpson(f, left, right)
+  (f.call(left) + 4*f.call((left+right)/2.0) + f.call(right)) / 6.0
+end
+
+def integrate(f, a, b, steps, method)
+  delta = 1.0 * (b - a) / steps
+  total = 0.0
+  steps.times do |i|
+    left = a + i*delta
+    right = left + delta
+    total += delta * send(method, f, left, right)
+  end
+  total
+end
+
+def square(x)
+  x**2
+end
+
+def def_int(f, a, b)
+  l = case f.to_s
+      when /sin>/
+        lambda {|x| -Math.cos(x)}
+      when /square>/
+        lambda {|x| (x**3)/3.0}
+      end
+  l.call(b) - l.call(a)
+end
+
+a = 0
+b = Math::PI
+steps = 10
+
+for func in [method(:square), Math.method(:sin)]
+  puts "integral of #{func} from #{a} to #{b} in #{steps} steps"
+  actual = def_int(func, a, b)
+  for method in [:leftrect, :midrect, :rightrect, :trapezium, :simpson]
+    int = integrate(func, a, b, steps, method)
+    diff = (int - actual) * 100.0 / actual
+    printf "   %-10s  %s\t(%.1f%%)\n", method, int, diff
+  end
+end