Data commit

Task/Numerical-integration/R/numerical-integration.r

@@ -0,0 +1,32 @@
+integ <- function(f, a, b, n, u, v) {
+  h <- (b - a) / n
+  s <- 0
+  for (i in seq(0, n - 1)) {
+    s <- s + sum(v * f(a + i * h + u * h))
+  }
+  s * h
+}
+
+test <- function(f, a, b, n) {
+  c(rect.left = integ(f, a, b, n, 0, 1),
+    rect.right = integ(f, a, b, n, 1, 1),
+    rect.mid = integ(f, a, b, n, 0.5, 1),
+    trapezoidal = integ(f, a, b, n, c(0, 1), c(0.5, 0.5)),
+    simpson = integ(f, a, b, n, c(0, 0.5, 1), c(1, 4, 1) / 6))
+}
+
+test(\(x) x^3, 0, 1, 100)
+#  rect.left  rect.right    rect.mid trapezoidal     simpson
+#  0.2450250   0.2550250   0.2499875   0.2500250   0.2500000
+
+test(\(x) 1 / x, 1, 100, 1000)
+#  rect.left  rect.right    rect.mid trapezoidal     simpson
+#   4.654991    4.556981    4.604763    4.605986    4.605170
+
+test(\(x) x, 0, 5000, 5e6)
+#  rect.left  rect.right    rect.mid trapezoidal     simpson
+#   12499998    12500003    12500000    12500000    12500000
+
+test(\(x) x, 0, 6000, 6e6)
+#  rect.left  rect.right    rect.mid trapezoidal     simpson
+#    1.8e+07     1.8e+07     1.8e+07     1.8e+07     1.8e+07