Description Format Details Source Examples
The Lanczos1
data frame has 24 rows and 2 columns of generated
data.
This data frame contains the following columns:
A numeric vector of generated responses.
A numeric vector of generated input values
These data are taken from an example discussed in
Lanczos (1956). The data were generated to 14-digits
of accuracy using
f(x) = 0.0951*exp(-x) + 0.8607*exp(-3*x) + 1.5576*exp(-5*x)
.
Lanczos, C. (1956). Applied Analysis. Englewood Cliffs, NJ: Prentice Hall, pp. 272-280.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 | Try <- function(expr) if (!inherits(val <- try(expr), "try-error")) val
plot(y ~ x, data = Lanczos1)
## plot on log scale to see the apparent number of exponential terms
plot(y ~ x, data = Lanczos1, log = "y")
## data are an exact fit so the convergence criterion fails
Try(fm1 <- nls(y ~ b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x),
data = Lanczos1, trace = TRUE,
start = c(b1 = 1.2, b2 = 0.3, b3 = 5.6, b4 = 5.5,
b5 = 6.5, b6 = 7.6)))
Try(fm1a <- nls(y ~ b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x),
data = Lanczos1, trace = TRUE, alg = "port",
start = c(b1 = 1.2, b2 = 0.3, b3 = 5.6,
b4 = 5.5, b5 = 6.5, b6 = 7.6)))
## data are an exact fit so the convergence criterion fails
Try(fm2 <- nls(y ~ b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x),
data = Lanczos1, trace = TRUE,
start = c(b1 = 0.5, b2 = 0.7, b3 = 3.6, b4 = 4.2,
b5 = 4, b6 = 6.3)))
Try(fm2a <- nls(y ~ b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x),
data = Lanczos1, trace = TRUE, alg = "port",
start = c(b1 = 0.5, b2 = 0.7, b3 = 3.6,
b4 = 4.2, b5 = 4, b6 = 6.3)))
## data are an exact fit so the convergence criterion fails
Try(fm3 <- nls(y ~ exp(outer(x,-c(b2, b4, b6))),
data = Lanczos1, trace = TRUE, algorithm = "plinear",
start = c(b2 = 0.3, b4 = 5.5, b6 = 7.6)))
## data are an exact fit so the convergence criterion fails
Try(fm4 <- nls(y ~ exp(outer(x,-c(b2, b4, b6))),
data = Lanczos1, trace = TRUE, algorithm = "plinear",
start = c(b2 = 0.7, b4 = 4.2, b6 = 6.3)))
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