The Jacobian section allows you to control which methods for computing Jacobians the software uses.
Analytic Jacobians can only be used for specific Problem Definition Files. Currently the supported formats are cutest and NIST. The only option is:
default- use the analytic derivative provided by a supported format.
[JACOBIAN] analytic: default
Calculates the Jacobian using the numerical Jacobian in
SciPy, this uses
scipy.optimize._numdiff.approx_derivative. The supported
2-point- use the first order accuracy forward or backward difference.
3-point- use central difference in interior points and the second order accuracy forward or backward difference near the boundary.
cs- use a complex-step finite difference scheme. This assumes that the user function is real-valued and can be analytically continued to the complex plane. Otherwise, produces bogus results.
[JACOBIAN] scipy: 2-point
Solver Default Jacobian (
This uses the approximation of the Jacobian that is used by default in the minimizer, and will vary between solvers. If the minimizer requires the user to pass a Jacobian, a warning will be printed to the screen and the SciPy (scipy) 2-point approximation will be used. The only option is:
default- use the default derivative approximation provided by the software.
[JACOBIAN] default: default
Calculates the Jacobian using the python package
We allow the user to change the method used, but other options
(e.g, the step size generator and the order of the approximation) are set the defaults.
The supported options are:
central- central differencing. Almost as accurate as complex, but with no restriction on the type of function.
forward- forward differencing.
backward- backward differencing.
complex- based on the complex-step derivative method of Lyness and Moler. Usually the most accurate, provided the function is analytic.
multicomplex- extends complex method using multicomplex numbers. (see, e.g., Lantoine, Russell, Dargent (2012)).
numdifftools is available under a 3-clause BSD Licence.
[JACOBIAN] numdifftools: central