title: R nls to fit custom gompertz curve
body: <p>I'm trying to fit my data to a user defined Gompertz equation.  However, I received an error as follows:  </p>
  
  <p>Error in nls(Eq, data = GPdata, start = list(K = 1), algorithm = "default",  : 
    singular gradient</p>
  
  <p>I know this probably means my starting value is not good enough for convergence, but is there any way around this other than guessing?  I also tried using the nls2 function (brute force), expanding a huge vector of possible K values to try but received the same error.</p>
  
  <p>Here is my code, including sample data.</p>
  
  <pre><code>t = c(0, 2.4, 4, 5.9, 8.3, 10.2, 12, 14.5, 16.1, 17.8, 19, 21.1, 23, 24.7, 26.4, 28.3,
      30.4, 32.3, 34.2, 36)
  Cells = c(14619994708, 18945074477, 19999450160, 23461507263, 22803949639, 19400861775,
          19806214226, 17390826226, 17390826226, 18186961935, 14066488593,
          13285017004, 11058253613, 8085853098, 9168523935, 8435042020, 
          8560592341, 7734294268, 7720887693, 7503367578)
  
  GPdata = data.frame(t, Cells)
  
  Ninf = (1 * 10 ^ 6) * (1 / 0.001)
  Eq &lt;- Cells ~ exp(log(Ninf) * (1 - exp(-K * t)))
  Gompstart = nls(Eq, data = GPdata, start = list(K = 1), 
          algorithm = "default", trace = TRUE)
  </code></pre>
  
  <p>Any help or suggestions would be greatly appreciated.</p>
  
  <p>Thanks!</p>