Re: integration + Levenberg-Marquardt (Numerical Recipes)
- From: Torsten Hennig <Torsten.Hennig@xxxxxxxxxxxxxx>
- Date: Wed, 02 Apr 2008 03:53:23 EDT
Hello,
I am having problems getting my fitting function >derivatives correct
for the Levenburg-Marquardt fitting routine.
I have a differential in the following format:
dAB/dt = ka*A(Bo-AB) - kd*AB
additional:
A is constant
I'm fitting ka,Bo and kd
I am getting the integrated format of the formula via >numerical
integration (this is a test equation, they will get more >difficult).
The integration is correct when I test the resulting >data but I don't
know how to properly get parameter derivatives for the >fitting
function.
How do I generate the parameter derivatives (dyda in the >LM fitting
function) without the integrated form of the formula (i >only have it
numerically).
Thank you for any hints.
Jamie
Hi,
to get the dy/dp, you simultanously have to solve
the differential equation(s)
d/dt (dy/dp_i) = df/dp_i + df/dy * dy/dp_i
if the differential equation itself is given by
dy/dt = f(t,p,y(t,p)).
Here, the p_i are your unknown parameters.
This follows by differentiating the equation
dy/dt = f(t,p,y(t,p))
with respect to p_i and then interchanging the order
of differentiation on the left-hand side.
Most codes approximate the derivatives dy/dp by finite
differences.
Best wishes
Torsten.
.
- References:
- Prev by Date: www.thenikeshoes.net wholesale gucci dior chanel sneakers sunglasses cheap lacoste t-shirts
- Next by Date: Getting Band Matrix of Sparse Block Matrix
- Previous by thread: integration + Levenberg-Marquardt (Numerical Recipes)
- Next by thread: Re: integration + Levenberg-Marquardt (Numerical Recipes)
- Index(es):
Relevant Pages
|
