# Computes sum of distances between consecutive samples in a multivariate time-series. Computes the sum of distances between consecutive samples in a multivariate time-series. Required to compute the measure of dissimilarity `psi` (Birks and Gordon 1985). Distances can be computed through the methods "manhattan", "euclidean", "chi", and "hellinger", and are implemented in the function `distance`. ```r autoSum( sequences = NULL, least.cost.path = NULL, time.column = NULL, grouping.column = NULL, exclude.columns = NULL, method = "manhattan", parallel.execution = TRUE ) ``` ## Arguments - `sequences`: dataframe with one or several multivariate time-series identified by a grouping column. - `least.cost.path`: a list usually resulting from either `leastCostPath` or `leastCostPathNoBlocks`. - `time.column`: character string, name of the column with time/depth/rank data. The data in this column is not modified. - `grouping.column`: character string, name of the column in `sequences` to be used to identify separates sequences within the file. This argument is ignored if `sequence.A` and `sequence.B` are provided. - `exclude.columns`: character string or character vector with column names in `sequences`, or `squence.A` and `sequence.B` to be excluded from the analysis. - `method`: character string naming a distance metric. Valid entries are: "manhattan", "euclidean", "chi", and "hellinger". Invalid entries will throw an error. - `parallel.execution`: boolean, if `TRUE` (default), execution is parallelized, and serialized if `FALSE`. ## Returns A list with slots named according `grouping.column` if there are several sequences in `sequences` or a number if there is only one sequence. ## Details Distances are computed as: * `manhattan`: `d \<- sum(abs(x - y))` * `euclidean`: `d \<- sqrt(sum((x - y)^2))` * `chi`: `xy \<- x + y y. \<- y / sum(y) x. \<- x / sum(x) d \<- sqrt(sum(((x. -y.)^2) / (xy / sum(xy))))` * `hellinger`: `d \<- sqrt(1/2 * sum(sqrt(x) - sqrt(y))^2)` Note that zeroes are replaced by 0.00001 whem `method` equals "chi" or "hellinger". ## Examples ```r #loading data data(sequenceA) data(sequenceB) #preparing datasets AB.sequences <- prepareSequences( sequence.A = sequenceA, sequence.A.name = "A", sequence.B = sequenceB, sequence.B.name = "B", merge.mode = "complete", if.empty.cases = "zero", transformation = "hellinger" ) #computing distance matrix AB.distance.matrix <- distanceMatrix( sequences = AB.sequences, grouping.column = "id", method = "manhattan", parallel.execution = FALSE ) #computing least cost matrix AB.least.cost.matrix <- leastCostMatrix( distance.matrix = AB.distance.matrix, diagonal = FALSE, parallel.execution = FALSE ) AB.least.cost.path <- leastCostPath( distance.matrix = AB.distance.matrix, least.cost.matrix = AB.least.cost.matrix, parallel.execution = FALSE ) #autosum AB.autosum <- autoSum( sequences = AB.sequences, least.cost.path = AB.least.cost.path, grouping.column = "id", parallel.execution = FALSE ) AB.autosum ``` ## See Also `distance` ## Author(s) Blas Benito * Birks, H.J.B. and Gordon, A.D. (1985) Numerical Methods in Quaternary Pollen Analysis. Academic Press.

autoSum function