fitting cosine curve

Using a more stable nonlinear modeling tool will also help, but key is to get
the periodicity right.

rsq <- function(x) {t2<-t*x;summary(lm(y~cos(t2)+sin(t2)))$r.squared}
vrsq <- Vectorize(rsq)
optimise(rsq, c(0.8,1.2)*2*pi/240,maximum=TRUE)

curve(vrsq,0.025,0.03)

y=c(16.82, 16.72, 16.63, 16.47, 16.84, 16.25, 16.15, 16.83, 17.41, 17.67,
17.62, 17.81, 17.91, 17.85, 17.70, 17.67, 17.45, 17.58, 16.99, 17.10)
t=c(7,  37,  58,  79,  96, 110, 114, 127, 146, 156, 161, 169, 176, 182,
190, 197, 209, 218, 232, 240)

lidata <- data.frame(y=y, t=t)

#I use the method to fit a curve, but it is different from the real curve,
#which can be seen in the figure.
linFit  <- lm(y ~ cos(t))
library(nlsr)
#fullFit <- nls(y ~ A*cos(omega*t+C) + B,
#start=list(A=coef(linFit)[1],B=coef(linFit)[2],C=0,omega=.4))
#omega cannot be set to 1, don't know why.
fullFit <- nlxb(y ~ A*cos(omega*t+C) + B, data=lidata,
start=list(A=coef(linFit)[1],B=coef(linFit)[2],C=0,omega=.04), trace=TRUE)
co <- coef(fullFit)
fit <- function(x, a, b, c, d) {a*cos(b*x+c)+d}
plot(x=t, y=y)
curve(fit(x, a=co['A'], b=co['omega'], c=co['C'],d=co['B']), add=TRUE
,lwd=2, col="steelblue")
jstart <- list(A=20, B=100, C=0, omega=0.01)
jfit <- nlxb(y ~ A*cos(omega*t+C) + B, data=lidata,
       start=jstart, trace=TRUE)
co <- coef(jfit)
fit <- function(x, a, b, c, d) {a*cos(b*x+c)+d}
plot(x=t, y=y)
curve(fit(x, a=co['A'], b=co['omega'], c=co['C'],d=co['B']), add=TRUE
     ,lwd=2, col="steelblue")

JN

On 2017-06-21 12:06 AM, lily li wrote:

I'm trying the different parameters, but don't know what the error is:
Error in nlsModel(formula, mf, start, wts) :
   singular gradient matrix at initial parameter estimates

Thanks for any suggestions.

On Tue, Jun 20, 2017 at 7:37 PM, Don Cohen <don-r-help at isis.cs3-inc.com>
wrote:

If you know the period and want to fit phase and amplitude, this is
equivalent to fitting a * sin + b * cos

  > >>> > I don't know how to set the approximate starting values.

I'm not sure what you meant by that, but I suspect it's related to
phase and amplitude.

  > >>> > Besides, does the method work for sine curve as well?

sin is the same as cos with a different phase
Any combination of a and b above = c * sin (theta + d) for
some value of c and d and = e * cos (theta + f) for some value
of e and f.
Also for any c,d and for any e,f there is an a,b.
the c and e are what I'm calling amplitude, the d and f are what
I'm calling phase.

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