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### linear approximation
linapprox <- function(xyin, xout)
{
x <- sort(unique(c(0, xyin[, 1])))
y <- as.vector(tapply(c(0, xyin[, 2]), c(0, xyin[, 1]), max))
n <- length(x)
xmax <- max(xout)
if (max(x) < xmax) {
x <- c(x, xmax)
y <- c(y, y[n-1] + (xmax - x[n-1])/(x[n] - x[n-1]) * (y[n] - y[n-1]))
}
approx(x, y, xout)$y
}
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