Data commit

Task/Numerical-integration/Lambdatalk/numerical-integration.lambdatalk

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+1) FUNCTIONS
+
+{def left_rect {lambda {:f :x :h} {:f :x}}}
+-> left_rect
+
+{def mid_rect {lambda {:f :x :h} {:f {+ :x {/ :h 2}}}}}
+-> mid_rect
+
+{def right_rect {lambda {:f :x :h} {:f {+ :x :h}}}}
+-> right_rect
+
+{def trapezium {lambda {:f :x :h} {/ {+ {:f :x} {:f {+ :x :h}}} 2}}}
+-> trapezium
+
+{def simpson
+ {lambda {:f :x :h}
+  {/ {+ {:f :x} {* 4 {:f {+ :x {/ :h 2}}}} {:f {+ :x :h}}} 6}}}
+-> simpson
+
+{def cube {lambda {:x} {* :x :x :x}}}
+-> cube
+
+{def reciprocal {lambda {:x} {/ 1 :x}}}
+-> reciprocal
+
+{def identity {lambda {:x} :x}}
+-> identity
+
+{def integrate
+ {lambda {:f :a :b :steps :meth}
+  {let { {:f :f} {:a :a} {:steps :steps} {:meth :meth}
+         {:h {/ {- :b :a} :steps}}
+       } {* :h {+ {S.map {{lambda {:meth :f :a :h :i}
+                                  {:meth :f {+ :a {* :i :h}} :h}
+                                 } :meth :f :a :h}
+                         {S.serie 1 :steps}} }}}}}
+-> integrate
+
+{def methods left_rect mid_rect right_rect trapezium simpson}
+-> methods
+
+2) TESTS
+
+We apply the following template
+
+{b ∫*function* from *a* to *b* steps *steps*}
+{table
+ {tr {td exact value:} {td *value*}}  // the awaited value
+ {S.map {lambda {:m}
+          {tr {td :m}
+              {td {integrate *function* *a* *b* *steps* :m}} }}
+        {methods}} }
+
+to the given *functions* from *a* to *b* with *steps*
+and we get:
+
+∫x3 from 0 to 100 steps 100         (computed in 13ms)
+exact value: 	0.25                  // 1/4
+left_rect 	0.25502500000000006
+mid_rect 	0.26013825000000007
+right_rect 	0.26532800000000006
+trapezium 	0.2601765
+simpson 	0.260151
+
+∫1/x from 1 to 100 steps 1000       (computed in 94ms)
+exact value: 	4.605170185988092     // log(100)
+left_rect 	4.55698105751468
+mid_rect 	4.511421425235764
+right_rect 	4.467888185754358
+trapezium 	4.512434621634517
+simpson 	4.511759157368674
+
+∫x from 0 to 5000 steps 5000000     (computed in ... 560000m)
+exact value: 	12500000              // 5000*5000/2
+left_rect 	12500002.5
+mid_rect 	12500005
+right_rect 	12500007.5
+trapezium 	12500005
+simpson 	12500005
+
+∫x from 0 to 6000 steps 6000      (computed in 420ms) too impatient for 6000000, sorry
+exact value: 	18000000            // 6000*6000/2
+left_rect 	18003000
+mid_rect 	18006000
+right_rect 	18009000
+trapezium 	18006000
+simpson 	18006000