BrianWeinstein

circ = 1; rad = circ/(2 \[Pi]); nRunners = 5;
rList[t_] := {1 t, 2 t, 4 t, 8 t, 9.6 t, 21 t, 31 t, 33 t}[[1 ;; nRunners]]

dist[d\[Theta]_, circ_] := 
  N[circ/2 (TriangleWave[(d\[Theta] - \[Pi]/2)/(2 \[Pi])] + 1)/2]
minDist[runnerList_, circ_] :=
 Table[
  runner = runnerList[[i]];
  other = DeleteCases[runnerList, runner];
  Min[dist[Abs[runner - other], circ]],

BrianWeinstein

ic[x_, y_] := 1 E^(-350 ((x - 1/5)^2 + ( y - 1/3)^2))

solnDir =
 NDSolve[
  {D[u[x, y, t], {t, 2}] == D[u[x, y, t], {x, 2}] + D[u[x, y, t], {y, 2}],
   u[x, y, 0] == ic[x, y],
   (D[u[x, y, t], t] /. t -> 0) == 0,
   u[0, y, t] == ic[0, y],
   u[1, y, t] == ic[1, y],
   u[x, 0, t] == ic[x, 0],

BrianWeinstein

# tm::removeSparseTerms attempts to remove sparse terms via slicing a sparse matrix.
# The slicing operation tries to convert the sparse matrix to a dense matrix, but this
# fails if the dense matrix has more than ((2^31) - 1) entries [i.e., if (nrow * ncol) > ((2^31) - 1)]
# 
# The error message is 
# In nr * nc : NAs produced by integer overflow
# 
# Instead of using tm::removeSparseTerms, the following function subsets the sparse matrix directly
# and avoids converting the sparse matrix to a dense one.

BrianWeinstein

bootstrap_ci <- function(data, sample_size_pct = 0.50, samples = 100, conf_level = 0.95){
    # Computes a bootstrapped confidence interval
    # INPUT: 
    #    data: a numeric vector
    #    sample_size_pct: the percentage of the input data to be used in each bootsrapped sample
    #    samples: the number of samples
    #    conf_level: the desired confidence level
    # OUTPUT:
    #    a bootstrapped conf_level confidence interval
    

BrianWeinstein

is_outlier <- function(x) {
    # Computes a bootstrapped confidence interval
    # INPUT: 
    #    x: a numeric vector
    # OUTPUT:
    #    a boolean vector, indicating if each value in x is an outlier
    
    return(x < quantile(x, 0.25) - 1.5 * IQR(x) | x > quantile(x, 0.75) + 1.5 * IQR(x))
}