get_trend_windows: Consensus ADMM for overlapping windows
In halleybrantley/detrendr: Quantile Trend Filtering

consensus ADMM Uses ADMM to smooth overlapping windows

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get_trend_windows(y, tau, lambda, k, window_size, overlap, max_iter,
  rho = 1, update = 10, use_gurobi = TRUE, eps_abs = 0.05,
  eps_rel = 0.001, scale = TRUE)

`y`	observed data
`tau`	quantile levels at which to evaluate trend
`lambda`	smoothing penalty parameter
`k`	order of differencing
`window_size`	size of windows to use
`overlap`	integer length of overlap between windows
`max_iter`	Maximum number of iterations
`rho`	parameter for ADMM
`update`	number of iterations at which to print residuals
`use_gurobi`	TRUE if gurobi solver is installed and should be used
`eps_abs`	absolute threshold for stopping criteria
`eps_rel`	relative threshold for stopping criteria
`scale`	(TRUE/FALSE) scale response before estimating trend

require(Matrix)
n <- 100
x <- seq(1, n, 1)
y <- sin(x*2*pi/n) + rnorm(n, 0, .4)
lambda <- 10
k <- 3
y_n <- length(y)
overlap <- 20
window_size <- round((y_n+overlap)/2)
tau <- c(0.05, .2)
max_iter <- 20
trend <- get_trend_windows(y, tau, lambda, k, window_size, overlap, max_iter)
plot(trend[,1]~x, type="l")