SimuBlocks: Generate simulated data
In AMIAS: Alternating Minimization Induced Active Set Algorithms

Description Usage Arguments Details Value Author(s) References Examples

Generate data for simulations.

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SimuBlocks(n, sigma = 0.1, seed = NA)
SimuWave(n, sigma = 0.1, seed = NA)
SimuDoppler(n, sigma = 0.1, seed = NA)

`n`	The number of observations.
`sigma`	A positive value to specify the standard deviation of the Gaussian noise.
`seed`	a single value to specify the seed used for generating data. See `set.seed` for details.

Let x = i/n, i=1,…,n. Assume that y_x follows an underlying trend y0_x with additive noise ε_x, i.e.,

y_x = y0_x + ε_x,

where y0_x is a smooth curve representing relatively long-term movements and ε_x is often assumed to follow i.i.d. N(0, σ^2).

A list with the following components:

`y`	The simulated data of length n.
`x`	The locations of `y`, of length n.
`y0`	The true signal of length n.
`tau`	Locations of the true knots.
`SetA`	Indexs of the true knots.

Canhong Wen, Xueqin Wang, Shijie Quan, Zelin Hong and Aijun Zhang.

Maintainer: Canhong Wen <wench@ustc.edu.cn>

Wen, C., Zhu, J., Wang, X., and Zhang, A. (2019) L0 trend filtering, technique report.

  ##------ Piecewise constant trend filtering example in Wen et al.(2018).-----
  set.seed(1)
  data <- SimuBlocks(2048)
  fit <- samias(data$y, kmax = 15)           # With default input argument
  plot(fit, type="coef", main = "Blocks")    # Plot the optimal estimate
  lines(data$x, data$y0, type="s")           # Add the true signal for reference
  plot(fit, type= "vpath", main = "Blocks")  # Plot the solution path