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Task/Numerical-integration/11l/numerical-integration.11l

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+F left_rect((Float -> Float) f, Float x, Float h) -> Float
+   R f(x)
+
+F mid_rect((Float -> Float) f, Float x, Float h) -> Float
+   R f(x + h / 2)
+
+F right_rect((Float -> Float) f, Float x, Float h) -> Float
+   R f(x + h)
+
+F trapezium((Float -> Float) f, Float x, Float h) -> Float
+   R (f(x) + f(x + h)) / 2.0
+
+F simpson((Float -> Float) f, Float x, Float h) -> Float
+   R (f(x) + 4 * f(x + h / 2) + f(x + h)) / 6.0
+
+F cube(Float x) -> Float
+   R x * x * x
+
+F reciprocal(Float x) -> Float
+   R 1 / x
+
+F identity(Float x) -> Float
+   R x
+
+F integrate(f, a, b, steps, meth)
+   V h = (b - a) / steps
+   V ival = h * sum((0 .< steps).map(i -> @meth(@f, @a + i * @h, @h)))
+   R ival
+
+L(a, b, steps, func, func_name) [(0.0, 1.0, 100, cube, ‘cube’),
+                                 (1.0, 100.0, 1000, reciprocal, ‘reciprocal’),
+                                 (0.0, 5000.0, 5'000'000, identity, ‘identity’),
+                                 (0.0, 6000.0, 6'000'000, identity, ‘identity’)]
+   L(rule, rule_name) [(left_rect,  ‘left_rect’),
+                        (mid_rect,   ‘mid_rect’),
+                      (right_rect, ‘right_rect’),
+                       (trapezium,  ‘trapezium’),
+                         (simpson,    ‘simpson’)]
+      print("#. integrated using #.\n  from #. to #. (#. steps) = #.".format(
+            func_name, rule_name, a, b, steps, integrate(func, a, b, steps, rule)))