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# Introduction

As was expected, the `runderiv()` function has been both useful and deficient. Useful because it offers a good replacement for `smooth.spline()` calculations of derivatives for things like N^2. And deficient because it only calculated derivatives, not values!

Both an extension and a renaming were called for. The result is `runlm()`.

# Tests

Below are the examples from its manpage, with the results.

Case 1

 `1` ```library(oce) ```
```## Loading required package: methods
 ```1 2 3 4 5 6 7 8``` ```x <- 1:100 y <- 1 + x/100 + sin(x/5) yn <- y + rnorm(100, sd = 0.1) L <- 4 calc <- runlm(x, y, L = L, deriv = 0) plot(x, y, type = "l", lwd = 7, col = "gray") points(x, yn, pch = 20, col = "blue") lines(x, calc, lwd = 2, col = "red") ``` Case 2

 ```1 2 3 4 5 6 7 8 9``` ```data(ctd) plot(ctd, which = "N2") rho <- swRho(ctd) z <- swZ(ctd) zz <- seq(min(z), max(z), 0.1) N2 <- -9.8/mean(rho) * runlm(z, rho, zz, deriv = 1) lines(N2, -zz, col = "red") legend("bottomright", lwd = 2, bg = "white", col = c("black", "red"), legend = c("swN2()", "using runlm()")) ``` 1. The fit in Case 1 is almost spookily good.

2. The N^2 results suggest including this as a method for `swN2()`, perhaps the default method, but that’s for another day.