[R] nls singular gradient matrix with an integrand

[Jeff Newmiller]

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Sent from my phone. Please excuse my brevity.

On July 15, 2015 7:26:59 AM PDT, "Laura Teresa Corredor Bohórquez" <ltcorredorb at gmail.com> wrote:
>Hi. I am trying to make a nls fit for a little bit complicated
>expression that
>includes two integrals (please find enclosed the equations).
>
>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 am enclosing the data too (file.csv).
>
>And 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.
>______________________________________________
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