`scipy.optimize._lsq.common:solve_lsq_trust_region`

source: /scipy/optimize/_lsq/common.py :57

Signature

   def     solve_lsq_trust_region (    n    ,    m    ,    uf    ,    s    ,    V    ,    Delta    ,    initial_alpha    =  None   ,    rtol    =  0.01   ,    max_iter    =  10     )

Summary

Solve a trust-region problem arising in least-squares minimization.

Extended Summary

This function implements a method described by J. J. More ^[1] and used in MINPACK, but it relies on a single SVD of Jacobian instead of series of Cholesky decompositions. Before running this function, compute: U, s, VT = svd(J, full_matrices=False).

Parameters

n : int: Number of variables.
m : int: Number of residuals.
uf : ndarray: Computed as U.T.dot(f).
s : ndarray: Singular values of J.
V : ndarray: Transpose of VT.
Delta : float: Radius of a trust region.
initial_alpha : float, optional: Initial guess for alpha, which might be available from a previous iteration. If None, determined automatically.
rtol : float, optional: Stopping tolerance for the root-finding procedure. Namely, the solution p will satisfy abs(norm(p) - Delta) < rtol * Delta.
max_iter : int, optional: Maximum allowed number of iterations for the root-finding procedure.

Returns

p : ndarray, shape (n,): Found solution of a trust-region problem.
alpha : float: Positive value such that (J.T*J + alpha*I)*p = -J.T*f. Sometimes called Levenberg-Marquardt parameter.
n_iter : int: Number of iterations made by root-finding procedure. Zero means that Gauss-Newton step was selected as the solution.

Aliases

scipy.optimize._lsq.common.solve_lsq_trust_region