`scipy.optimize._lsq.common:CL_scaling_vector`

source: /scipy/optimize/_lsq/common.py :467

Signature

def CL_scaling_vector ( x , g , lb , ub )

Summary

Compute Coleman-Li scaling vector and its derivatives.

Extended Summary

Components of a vector v are defined as follows

       | ub[i] - x[i], if g[i] < 0 and ub[i] < np.inf
v[i] = | x[i] - lb[i], if g[i] > 0 and lb[i] > -np.inf
       | 1,           otherwise

According to this definition v[i] >= 0 for all i. It differs from the definition in paper ^[1] (eq. (2.2)), where the absolute value of v is used. Both definitions are equivalent down the line. Derivatives of v with respect to x take value 1, -1 or 0 depending on a case.

Returns

v : ndarray with shape of x: Scaling vector.
dv : ndarray with shape of x: Derivatives of v[i] with respect to x[i], diagonal elements of v's Jacobian.

Aliases

scipy.optimize._lsq.common.CL_scaling_vector