KCB February 2016
### Fitting boxcar (rectangle) function in R

I am trying to fit a boxcar / rectangle function to a dataset in R. I am using nls and a custom function describing a unit pulse of varying width. Here is what I have so far:

```
# Defines the unit pulse function
# The left side of the pulse is at x0, the right at x1
pulse <- function(x, x0, x1) {
if (x >= x0 & x <= x1) {
return (1)
} else {
return (0)
}
}
xdata <- 1:30
ydata <- c(sample(-1:1, 10, replace = TRUE), sample(10:15, 10, replace = TRUE), sample(-1:1, 10, replace = TRUE))
plot(xdata, ydata)
df <- data.frame(xdata, ydata)
fitfit <- nls(ydata ~ I(A * pulse(xdata, L, R) + B), df, start = list(L = 0, R = 1, B = 0, A = 10))
```

I am having trouble understanding the error I get:

Error in qr(.swts * attr(rhs, "gradient")) : dims [product 4] do not match the length of object [30] In addition: Warning messages: 1: In if (x >= x0 & x <= x1) { : the condition has length > 1 and only the first element will be used 2: In if (x >= x0 & x <= x1) { : the condition has length > 1 and only the first element will be used 3: In if (x >= x0 & x <= x1) { : the condition has length > 1 and only the first element will be used 4: In if (x >= x0 & x <= x1) { : the condition has length > 1 and only the first element will be used 5: In if (x >= x0 & x <= x1) { : the condition has length > 1 and only the first element will be used 6: In if (x >= x0 & x <= x1) { : the condition has length > 1 and only the first element will be used 7: In .swts * attr(rhs, "gradient") : longer object length is not a multiple of shorter object length

HubertL February 2016

your pulse function doesn't return a vector, try this one:

```
pulse <- function(x, x0, x1) {
ifelse (x >= x0 & x <= x1,1,0)
}
```

G. Grothendieck February 2016

Non-smooth functions can cause problems. Try brute force over the two boundaries of the pulse and optimization over the linear parameters. Note that below we have added a `set.seed`

to make `ydata`

reproducible.

```
library(nls2)
set.seed(123)
xdata <- 1:30
ydata <- c(sample(-1:1, 10, replace = TRUE), sample(10:15, 10, replace = TRUE),
sample(-1:1, 10, replace = TRUE))
df <- data.frame(xdata, ydata)
pulse <- function(x, x0, x1) (x >= x0 & x <= x1) + 0
st <- subset(expand.grid(L = xdata, R = xdata), L < R)
nls2(ydata ~ cbind(pulse(xdata, L, R), 1), df, start = st, alg = "plinear-brute")
```

giving some error messages which you can ignore and finally this output where `.lin1`

and `.lin2`

correspond to `A`

and `B`

in the question:

```
Nonlinear regression model
model: ydata ~ cbind(pulse(xdata, L, R), 1)
data: df
L R .lin1 .lin2
11.0 20.0 12.4 0.2
residual sum-of-squares: 49.6
Number of iterations to convergence: 435
Achieved convergence tolerance: NA
```

Asked in February 2016

Viewed 3,355 times

Voted 12

Answered 2 times

Viewed 3,355 times

Voted 12

Answered 2 times