Lagged and Iterated Differences
The lagged and iterated differences of a vector.
If x is length n, this function returns a length n-k vector of the kth order difference between the lagged terms.
diff(x) returns the vector of differences between adjacent elements in the vector, i.e. [x[2] - x[1], x[3] - x[2], ...].
diff(x,1,2) is the second-order differences vector, equivalently diff(diff(x)). diff(x,1,0) returns the vector x unchanged.
diff(x,2) returns the vector of differences [x[3] - x[1], x[4] - x[2], ...], equivalent to x[(1+lag):n] - x[1:(n-lag)].
## S4 method for signature 'Expression' diff(x, lag = 1, differences = 1, ...)
x |
An Expression. |
lag |
An integer indicating which lag to use. |
differences |
An integer indicating the order of the difference. |
... |
(Optional) Addition |
An Expression representing the kth order difference.
## Problem data m <- 101 L <- 2 h <- L/(m-1) ## Form objective and constraints x <- Variable(m) y <- Variable(m) obj <- sum(y) constr <- list(x[1] == 0, y[1] == 1, x[m] == 1, y[m] == 1, diff(x)^2 + diff(y)^2 <= h^2) ## Solve the catenary problem prob <- Problem(Minimize(obj), constr) result <- solve(prob) ## Plot and compare with ideal catenary xs <- result$getValue(x) ys <- result$getValue(y) plot(c(0, 1), c(0, 1), type = 'n', xlab = "x", ylab = "y") lines(xs, ys, col = "blue", lwd = 2) grid()
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