R help - Jul 2015 - nls singular gradient matrix - fit parameters in integral's upper limits

-------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]]

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 Boh?rquez
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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