tasks a-s

Task/Numerical-integration/J/numerical-integration-1.j

@@ -0,0 +1,11 @@
+integrate=: adverb define
+  'a b steps'=. 3{.y,128
+  size=. (b - a)%steps
+  size * +/ u |: 2 ]\ a + size * i.>:steps
+)
+
+rectangle=: adverb def 'u -: +/ y'
+
+trapezium=: adverb def '-: +/ u y'
+
+simpson  =: adverb def '6 %~ +/ 1 1 4 * u y, -:+/y'

Task/Numerical-integration/J/numerical-integration-2.j

@@ -0,0 +1,28 @@
+   Ir=: rectangle integrate
+   It=: trapezium integrate
+   Is=: simpson integrate
+
+   ^&3 Ir 0 1 100
+0.249987
+   ^&3 It 0 1 100
+0.250025
+   ^&3 Is 0 1 100
+0.25
+   % Ir 1 100 1000
+4.60476
+   % It 1 100 1000
+4.60599
+   % Is 1 100 1000
+4.60517
+   ] Ir 0 5000 5e6
+1.25e7
+   ] It 0 5000 5e6
+1.25e7
+   ] Is 0 5000 5e6
+1.25e7
+   ] Ir 0 6000 6e6
+1.8e7
+   ] It 0 6000 6e6
+1.8e7
+   ] Is 0 6000 6e6
+1.8e7

Task/Numerical-integration/J/numerical-integration-3.j

@@ -0,0 +1,6 @@
+   *: rectangle integrate 0 1p1 10
+10.3095869962
+   *: trapezium integrate 0 1p1 10
+10.3871026879
+   *: simpson integrate 0 1p1 10
+10.3354255601

Task/Numerical-integration/J/numerical-integration-4.j

@@ -0,0 +1,7 @@
+   sin=: 1&o.
+   sin rectangle integrate 0 1p1 10
+2.00824840791
+   sin trapezium integrate 0 1p1 10
+1.98352353751
+   sin simpson integrate 0 1p1 10
+2.00000678444

Task/Numerical-integration/J/numerical-integration-5.j

@@ -0,0 +1,4 @@
+   0 p.. 0 0 1
+0 0 0 0.333333333333
+   0 p.. 0 0 1x        NB. or using rationals
+0 0 0 1r3

Task/Numerical-integration/J/numerical-integration-6.j

@@ -0,0 +1,2 @@
+   0 0 1 (0&p..@[ -~/@:p. ]) 0 1p1
+10.3354255601

Task/Numerical-integration/J/numerical-integration-7.j

@@ -0,0 +1,2 @@
+   *:d._1]1p1
+10.3354