WallGo.helpers.gradient

gradient(f, x, order=4, epsilon=1e-16, scale=1.0, dx=None, axis=None, args=None)

Computes the gradient of a callable function. Uses the epsilon and scale parameters to estimate the optimal value of dx, if the latter is not provided.

Parameters:

• f (function) – Function to differentiate. Should take an array as argument and return an array.

• x (array-like) – The position at which to evaluate the derivative. The size of the last axis must correspond to the number of variables on which f depends.

• order (int, optional) – The accuracy order of the scheme. Errors are of order \(\mathcal{O}({\rm d}x^{\text{order}/(\text{order}+1)})\). Can be 2 or 4. The default is 4.

• epsilon (float, optional) – Fractional accuracy at which f can be evaluated. If f is a simple function, should be close to the machine precision. Default is 1e-16.

• scale (float or array-like, optional) – Typical scale at which f(x) change by order 1. Can be an array, in which case each element corresponds to the scale of a different variable. Default is 1.

• dx (float or np.ndarray or None, optional) – The magnitude of finite differences. Can be an array, in which case each element corresponds to the dx of a different variable.If None, use epsilon and scale to estimate the optimal dx. Default is None.

• axis (list, int or None, optional) – Element of the gradient to return. If None, returns the whole gradient. Default is None.

• args (list, optional) – List of other fixed arguments passed to the function \(f\).

Returns:

res – The value of the gradient of f evaluated at x.

Return type:

float