Initial data commit

Task/Numerical-integration/Lua/numerical-integration.lua

@@ -0,0 +1,73 @@
+function leftRect( f, a, b, n )
+    local h = (b - a) / n
+    local x = a
+    local sum = 0
+
+    for i = 1, 100 do
+        sum = sum + a + f(x)
+        x = x + h
+    end
+
+    return sum * h
+end
+
+function rightRect( f, a, b, n )
+    local h = (b - a) / n
+    local x = b
+    local sum = 0
+
+    for i = 1, 100 do
+        sum = sum + a + f(x)
+        x = x - h
+    end
+
+    return sum * h
+end
+
+function midRect( f, a, b, n )
+    local h = (b - a) / n
+    local x = a + h/2
+    local sum = 0
+
+    for i = 1, 100 do
+        sum = sum + a + f(x)
+        x = x + h
+    end
+
+    return sum * h
+end
+
+function trapezium( f, a, b, n )
+    local h = (b - a) / n
+    local x = a
+    local sum = 0
+
+    for i = 1, 100 do
+        sum = sum + f(x)*2
+        x = x + h
+    end
+
+    return (b - a) * sum / (2 * n)
+end
+
+function simpson( f, a, b, n )
+    local h = (b - a) / n
+    local sum1 = f(a + h/2)
+    local sum2 = 0
+
+    for i = 1, n-1 do
+        sum1 = sum1 + f(a + h * i + h/2)
+        sum2 = sum2 + f(a + h * i)
+    end
+
+    return (h/6) * (f(a) + f(b) + 4*sum1 + 2*sum2)
+end
+
+
+int_methods = { leftRect, rightRect, midRect, trapezium, simpson }
+for i = 1, 5 do
+    print( int_methods[i]( function(x) return x^3 end, 0, 1, 100 ) )
+    print( int_methods[i]( function(x) return 1/x end, 1, 100, 1000 ) )
+    print( int_methods[i]( function(x) return x end, 0, 5000, 5000000 ) )
+    print( int_methods[i]( function(x) return x end, 0, 6000, 6000000 ) )
+end