desc.optimize.lsqtr

class desc.optimize.lsqtr(fun, x0, jac, args=(), x_scale=1, ftol=1e-06, xtol=1e-06, gtol=1e-06, verbose=1, maxiter=None, tr_method='svd', callback=None, options={})[source]

Solve a least squares problem using a (quasi)-Newton trust region method.

Parameters:

  • fun (callable) – objective to be minimized. Should have a signature like fun(x,*args)-> 1d array

  • x0 (array-like) – initial guess

  • jac (callable:) – function to compute Jacobian matrix of fun

  • args (tuple) – additional arguments passed to fun, grad, and jac

  • x_scale (array_like or 'jac', optional) – Characteristic scale of each variable. Setting x_scale is equivalent to reformulating the problem in scaled variables xs = x / x_scale. An alternative view is that the size of a trust region along jth dimension is proportional to x_scale[j]. Improved convergence may be achieved by setting x_scale such that a step of a given size along any of the scaled variables has a similar effect on the cost function. If set to 'jac', the scale is iteratively updated using the inverse norms of the columns of the Jacobian matrix.

  • ftol (float or None, optional) – Tolerance for termination by the change of the cost function. Default is 1e-8. The optimization process is stopped when dF < ftol * F, and there was an adequate agreement between a local quadratic model and the true model in the last step. If None, the termination by this condition is disabled.

  • xtol (float or None, optional) – Tolerance for termination by the change of the independent variables. Default is 1e-8. Optimization is stopped when norm(dx) < xtol * (xtol + norm(x)). If None, the termination by this condition is disabled.

  • gtol (float or None, optional) – Absolute tolerance for termination by the norm of the gradient. Default is 1e-8. Optimizer teriminates when norm(g) < gtol, where If None, the termination by this condition is disabled.

  • verbose ({0, 1, 2}, optional) –

    • 0 (default) : work silently.

    • 1 : display a termination report.

    • 2 : display progress during iterations

  • maxiter (int, optional) – maximum number of iterations. Defaults to size(x)*100

  • tr_method ({'cho', 'svd'}) – method to use for solving the trust region subproblem. ‘cho’ uses a sequence of cholesky factorizations (generally 2-3), while ‘svd’ uses one singular value decomposition. ‘cho’ is generally faster for large systems, especially on GPU, but may be less accurate in some cases.

  • callback (callable, optional) –

    Called after each iteration. Should be a callable with the signature:

    callback(xk, *args) -> bool

    where xk is the current parameter vector. and args are the same arguments passed to fun and jac. If callback returns True the algorithm execution is terminated.

  • options (dict, optional) – dictionary of optional keyword arguments to override default solver settings. See the code for more details.

Returns:

res (OptimizeResult) – The optimization result represented as a OptimizeResult object. Important attributes are: x the solution array, success a Boolean flag indicating if the optimizer exited successfully and message which describes the cause of the termination. See OptimizeResult for a description of other attributes.