diff function

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 $k$th 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)]. methods

## S4 method for signature 'Expression'
diff(x, lag = 1, differences = 1, ...)

Arguments

• x: An Expression .
• lag: An integer indicating which lag to use.
• differences: An integer indicating the order of the difference.
• ...: (Optional) Addition axis argument, specifying the dimension across which to apply the function: 1 indicates rows, 2 indicates columns, and NA indicates rows and columns. The default is axis = 1.

Returns

An Expression representing the kth order difference.

Examples

## 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()