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In this example we fit a piecewise linear function to example data.

Please see here for a discussion of the methodology.

library("RcppDynProg") set.seed(2018) g <- 100 d <- data.frame( x = 0.05*(1:(3*g))) # ordered in x d$y_ideal <- sin((0.3*d$x)^2) d$y_observed <- d$y_ideal + 0.25*rnorm(length(d$y_ideal)) # plot plot(d$x, d$y_observed, xlab = "x", ylab = "y", main = "raw data\ncircles: observed values, dashed line: unobserved true values") lines(d$x, d$y_ideal, type = "l", lty = "dashed") x_cuts <- solve_for_partition(d$x, d$y_observed, penalty = 1) print(x_cuts) d$estimate <- approx(x_cuts$x, x_cuts$pred, xout = d$x, method = "linear", rule = 2)$y d$group <- as.character(findInterval(d$x, x_cuts[x_cuts$what=="left", "x"]))

print(sum((d$y_observed - d$y_ideal)^2))

print(sum((d$estimate - d$y_ideal)^2))

print(sum((d$estimate - d$y_observed)^2))

# plot plot(d$x, d$y_observed, xlab = "x", ylab = "y", main = "RcppDynProg piecewise linear estimate\ndots: observed values, segments: estimated shape") points(d$x, d$y_ideal, type = "l", lty = "dashed") cmap <- c("#a6cee3", "#1f78b4", "#b2df8a", "#33a02c", "#fb9a99", "#e31a1c", "#fdbf6f", "#ff7f00", "#cab2d6", "#6a3d9a", "#ffff99", "#b15928") names(cmap) <- as.character(seq_len(length(cmap))) points(d$x, d$y_observed, col = cmap[d$group], pch=19) groups <- sort(unique(d$group)) for(gi in groups) { di <- d[d$group==gi, , drop = FALSE] lines(di$x, di$estimate, col = cmap[di$group[[1]]], lwd=2) }

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