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Matlab tutorials on:

Complex-step derivatives

Estimate derivatives by simply passing in a complex number to your function. A single (complex) function evaluations computes both the function's value (Re) and the derivative (Im). Is it always possible to do this? I mean with a standard code form industry (Nastran, Fluent etc...)?

gradient evaluation

Comparison of Symbolic/Finite Differences/DIRECT/ADJOINT Method on a really simple mechanical system (2DOFs). Play with the code for checking Symbolic with Finite Differences. Play with $\Delta_x$ ? By the way, just add the complex step approach, not so difficult when you have access to the original code. Oh, at the end which method is exact?

BTW, How Nastran is doing for gradient computation on SOL2OO ? gradient nastran

Small exercice with Matlab Write your miniature forward-mode AD library