Data commit

Task/Cumulative-standard-deviation/R/cumulative-standard-deviation-1.r

@@ -0,0 +1,15 @@
+cumsd <- function(x) {
+  n <- seq_along(x)
+  sqrt(cumsum(x^2) / n - (cumsum(x) / n)^2)
+}
+
+set.seed(12345L)
+x <- rnorm(10)
+
+cumsd(x)
+# [1] 0.0000000 0.3380816 0.8752973 1.1783628 1.2345538 1.3757142 1.2867220 1.2229056 1.1665168 1.1096814
+
+# Compare to the naive implementation, i.e. compute sd on each sublist:
+Vectorize(function(k) sd(x[1:k]) * sqrt((k - 1) / k))(seq_along(x))
+# [1]        NA 0.3380816 0.8752973 1.1783628 1.2345538 1.3757142 1.2867220 1.2229056 1.1665168 1.1096814
+# Note that the first is NA because sd is unbiased formula, hence there is a division by n-1, which is 0 for n=1.

Task/Cumulative-standard-deviation/R/cumulative-standard-deviation-2.r

@@ -0,0 +1,16 @@
+accumsd <- function() {
+  n <- 0
+  m <- 0
+  s <- 0
+
+  function(x) {
+    n <<- n + 1
+    m <<- m + x
+    s <<- s + x * x
+    sqrt(s / n - (m / n)^2)
+  }
+}
+
+f <- accumsd()
+sapply(x, f)
+# [1] 0.0000000 0.3380816 0.8752973 1.1783628 1.2345538 1.3757142 1.2867220 1.2229056 1.1665168 1.1096814