SimuBlocksInv: Simulate Blocks Data

In L0TFinv: A Splicing Approach to the Inverse Problem of L0 Trend Filtering

Simulate Blocks Data

Description

This function generates data points of piecewise constant trends.

Usage

SimuBlocksInv(n, sigma, seed = NA, tau, h)

Arguments

n	Number of data points
sigma	Standard deviation of the noise added to the signal
seed	An optional seed for random number generation to make results reproducible
tau	The locations of change points in the underlying trend
h	The constant values of the length(tau)+1 segments of the underlying trend

Details

• To simplify the analysis, normalize the change point positions to a range between 0 and 1. Require that all elements of the input tau are within this range. Consequently, the change point positions in simulated data forms a subset of the set { \frac{1}{n}, \frac{2}{n}, \frac{3}{n},..., 1}.

• In fact, length(tau) change points can divide the interval into length(tau)+1 segments of constant function values. Therefore, ensure that the length of vector h is length(tau)+1.

Value

A list containing the piecewise constant simulated data and the underlying trend:

x	The set { \frac{1}{n}, \frac{2}{n}, \frac{3}{n},..., 1}
y	The piecewise constant simulated data of length n
y0	The underlying trend of length n
setA	The set of position indicators of change points in the simulated data
tau	The locations of change points in the underlying trend

Examples

tau = c(0.1, 0.3, 0.4, 0.7, 0.85)
h = c(-1, 5, 3, 0, -1, 2)
BlocksData <- SimuBlocksInv(n = 350, sigma = 0.1, seed = 50, tau = tau ,h = h)
plot(BlocksData$x, BlocksData$y, xlab="", ylab="")
lines(BlocksData$x, BlocksData$y0, col = "red")
print(BlocksData$setA)
print(BlocksData$tau)

L0TFinv documentation built on June 10, 2025, 5:14 p.m.