Numerical Differentiation

pathsim.optim.numerical.num_jac(func, x, r=0.001, tol=1e-08)

Numerically computes the jacobian of the function ‘func’ by central differences.

The stepsize ‘h’ is adaptively computed as a relative perturbation ‘r’ with an absolute floor ‘tol’. The floor keeps the perturbation meaningful when components of ‘x’ are near zero, where a purely relative step would shrink below the floating point resolution of ‘func’ and the central difference would collapse to zero.

Parameters:

• func (callable) – function to compute jacobian for

• x (float, array[float]) – value for function at which the jacobian is evaluated

• r (float) – relative perturbation

• tol (float) – absolute floor for the perturbation stepsize

Returns:

jac – 2d jacobian array

Return type:

array[array[float]]

pathsim.optim.numerical.num_autojac(func)

Wraps a function object such that it computes the jacobian of the function with respect to the first argument.

This is intended to compute the jacobian ‘jac(x, u, t)’ of the right hand side function ‘func(x, u, t)’ of numerical integrators with respect to ‘x’.

Parameters:

func (callable) – function to wrap for jacobian

Returns:

wrap_func – wrapped funtion as numerical jacobian of ‘func’

Return type:

callable