Check Gradient (Jacobian) of objective function -- what is the meaning of absolute difference (1e-6) if component of gradient is less than 1 ?

14 vues (au cours des 30 derniers jours)
I use lsqnonlin to solve my data-fitting problem and provide the Jacobian, which I verify using CheckGradients option.
As stated here, if a component of the Jacobian is less than 1, gradient check is successful if the absolute difference between the user-shipped Jacobian and Matlabs finite-difference approximation of that component is less than 1e-6.
Example: Jacobian_USER(1,1)=2e-7, Jacobian_MATLAB(1,1)=1e-7.
Here, Jacobian_USER(1,1) is clearly wrong, but Jacobian check would be successful. Is that true?
  11 commentaires
Torsten le 18 Jan 2023
Modifié(e) : Torsten le 18 Jan 2023
Why should I not be alarmed in that case?
If I know my values are so small (around 1e-7) per nature, a difference between 1e-7 and 2e-7 is significant.
The values you investigate are numerical derivatives (usually of complex functions). Already when choosing the h in approximating the derivative as (f(x+h)-f(x))/h can cause such differences.

Connectez-vous pour commenter.

Réponse acceptée

Matt J
Matt J le 18 Jan 2023
Modifié(e) : Matt J le 18 Jan 2023
If I know my values are so small (around 1e-7) per nature, a difference between 1e-7 and 2e-7 is significant.
Not necessarily. The element-wise relative error is large, but remember lsqnonlin uses the Jacobian J in matrix products of the form J*x and J.'*y to compute its updates. If the average value of abs(J(m,n)) is 1000 and the average values of abs(x(n)) or abs(y(m)) is 10, then an absolute error of 1e-7 in any entry J(m,n) would likely contribute negligibly to J*x or J.'*y.
Regardless, if you don't have full confidence in DerivativeCheck, you can implement your own finite difference computation, using for example,
and then do the comparison according to a criterion you prefer.

Plus de réponses (0)


En savoir plus sur Mathematics and Optimization dans Help Center et File Exchange

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by