The list rejects almost all attachments.
You could dput the data and put it in your posting.
You may also want to try a Marquardt solver. In R from my nlmrt or
compiled in Kate Mullen's minpack.lm. They are slightly different in
flavour and the call is a bit different from nls.
JN
On 15-07-16 08:21 AM, Laura Teresa Corredor Bohórquez wrote:
> -------The las post rejected two files I had attached, so I modified
> it.---------------
>
>
> Hi. I am trying to make a nls fit for a little bit complicated expression that
> includes two integrals with two of the fit parameters in their upper limits.
>
> I got the error "Error in nlsModel(formula, mf, start, wts) :
> singular gradient
> matrix at initial parameter estimates". First of all, I have searched
> already in the previous answers, but didn´t help. The parameters
> initialization
> seems to be ok, I have tried to change the parameters but no one works. If
> my function has just one integral everything works very nicely, but when
> adding
> a second integral term just got the error. I don´t believe the function is
> over-parametrized, as I have performed other fits with much more parameters
> and they worked. I did try to enclose the data but the attachment was
> rejected.
>
> The minimal example is the following:
>
> # read the data from a csv file
> dados = read.csv("file.csv", header=FALSE, stringsAsFactors=FALSE)
> x = 0*(1:97)
> y = 0*(1:97)
> for(i in 1:97){
> x[i] = dados[i,1]
> y[i] = dados[i,2]
> }
> integrand <- function(X) {
> return(X^4/(2*sinh(X/2))^2)
> }
> fitting = function(T1, T2, N, D, x){
> int1 = integrate(integrand, lower=0, upper = T1)$value
> int2 = integrate(integrand, lower=0, upper = T2)$value
> return(N*(D/x)^2*(exp(D/x)/(1+exp(D/x))^2
> )+(448.956*(x/T1)^3*int1)+(299.304*(x/T2)^3*int2))
> }
> fit = nls(y ~ fitting(T1, T2, N, D, x),
> start=list(T1=400,T2=200,N=0.01,D=2))
>
> ------>For reference, the fit that worked is the following:
>
> # read the data from a csv file
> dados = read.csv("file.csv", header=FALSE, stringsAsFactors=FALSE)
> x = 0*(1:97)
> y = 0*(1:97)
> for(i in 1:97){
> x[i] = dados[i,1]
> y[i] = dados[i,2]
> }
> integrand <- function(X) {
> return(X^4/(2*sinh(X/2))^2)
> }
> fitting = function(T1, N, D, x){
> int = integrate(integrand, lower=0, upper = T1)$value
> return(N*(D/x)^2*(exp(D/x)/(1+exp(D/x))^2 )+(748.26)*(x/T1)^3*int)
> }
> fit = nls(y ~ fitting(T1 , N, D, x), start=list(T1=400,N=0.01,D=2))
>
>
> I cannot figure out what happen. I need to perform this fit for three
> integral components, but even for two I have this problem. I appreciate so
> much your help. Thank you.
>
> [[alternative HTML version deleted]]
>
> ______________________________________________
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> and provide commented, minimal, self-contained, reproducible code.
>
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