nlinfit not accurately modeling data

Hi! I am probably doing something stupid, but I have a bell-shaped function I want to model as an inverse of the sum of exponentials (of the form 1/(exp((x+a1)/a2)+exp((x+a3)/a4))+a5).

Here is what I have;

input=[-45:5:30]';

output=[.95;1.05;1.3;1.85;1.55;.95;.6;.5;.4;.35;.3;.275;.25;.225;.2;.175]';

mdl = @(a,x)((1/(exp((x+a(1))/a(2))+exp((x+a(3))/a(4))))+a(5))

a0=[97;-30;-18;15;.5];

and then

fitted=nlinfit(input, output, mdl, a0);

but the values I get back are terrible, and don't match the data at all, even when I change the starting values in a0. What am I doing wrong?

[the cyclist]

I can't look at this right now, but try the following plots:

figure

hold on

plot(input,output,'b.-')

plot(input,mdl(a0,input),'r.-')

Is that about what you expect your initial guess to look like? I see you get a lot of warnings out of nlinfit, too, although I haven't looked at why.

[Nick Schmandt]

The starting values I used were values from another bell-curve double exponential fit, but I must doing something wrong, because if I just type in mdl(a0, input), all the output values are zero except for the last one...

[Nick Schmandt]

and thank you very much!

Answer 1

[Tom Lane]

In your model function you have "1/<stuff>" where you almost certainly intended element-by-element division, "1./<stuff>". You'll also want to remove the transpose from the definition of output.

[Nick Schmandt]

Thank you! That fixed it, the starting values were just off so much that it wasn't working.