# Optimal Transport Cost Calculate the optimal transport cost. ```r ## S3 method for class 'numeric' transport_cost(x, y, wx, wy, p = 1, sorted = FALSE, threshold = 1e-15, ...) transport_cost(x, ...) ## S3 method for class 'otgridtransport' transport_cost(x, threshold = 1e-15, ...) ## S3 method for class 'otgrid' transport_cost(x, ...) ## S3 method for class 'data.frame' transport_cost(x, costm, ...) ``` ## Arguments - `x`: a vector of points; a data frame with columns `from`, `to` and `mass` specifying the optimal transport plan; an object of class `"otgridtransport"` or `"otgrid"`, in the latter case `...` must be the arguments of `pivot_measure`. - `y`: second vector of points. - `wx`: weight vector of the first vector of points. - `wy`: weight vector of the second vector of points. - `p`: the power $\geq 1$ of the cost function. - `sorted`: logical value indicating whether or not `a` and `b` are sorted. - `threshold`: small value that indicates when a value is considered to be zero. - `...`: further arguments (for `pivot_measure` if `x` is an object of class `"otgrid"`). - `costm`: cost matrix of the transport ## Returns the optimal transport cost or, in case of two-dimensional case, an object of class `"otgridtransport"` with element `cost` that contains it. ## Details In case of two-dimensional grids, the pivot measure is used to calculate the optimal transport cost. For one-dimensional optimal transport, the cost function is given by $c(x, y) = | x - y |^p$. In this case, the north-west-corner algorithm is used. ## Examples ```r ## one-dimensional example set.seed(1) a <- 1:5 wa <- rep(1/5, 5) b <- 1:6 wb <- runif(6) wb <- wb / sum(wb) transport_cost(a, b, wa, wb, p = 1) ## two-dimensional example x <- otgrid(cbind(0:1, 1:0)) y <- otgrid(cbind(1:0, 0:1)) # first calculate pivot manually pm <- pivot_measure(x, y) pm <- transport_cost(pm) print(pm$cost) # or just pm2 <- transport_cost(x, y) print(pm2$cost) # or from transport plan and cost matrix costm <- transport_costmat(pm) tp <- transport_df(pm) print(transport_cost(tp$df, costm)) ``` ## See Also pivot measure `pivot_measure`

transport_cost function