# [R] fitting cosine curve

J C Nash profjcnash at gmail.com
Wed Jun 21 14:17:47 CEST 2017

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

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)
,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)
,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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>
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