approx_derivative

cuqi.utilities.approx_derivative(func, wrt, direction=None, epsilon=1.4901161193847656e-08)

Approximates the derivative of callable (possibly vector-valued) function func evaluated at point wrt. If direction is provided, the direction-Jacobian product will be computed and returned, otherwise, the Jacobian matrix (or the gradient in case of a scalar function func) will be returned. The approximation is done using forward differences.

Parameters:

• func (function handler) – A vector-valued function of the form func(x).

• wrt (ndarray) – The point at which the derivative to be evaluated.

• direction (ndarray) – The direction used to compute direction-Jacobian product. If None, the Jacobian matrix is returned.

• epsilon (float) – The spacing in the finite difference approximation.

Returns:

The approximate Jacobian matrix.

Return type:

ndarray