desc.optimize.lsqtr

class desc.optimize.lsqtr(fun, x0, jac, bounds=(-inf, inf), args=(), x_scale='jac', ftol=1e-06, xtol=1e-06, gtol=1e-06, verbose=1, maxiter=None, callback=None, options=None)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

  • bounds (tuple of array-like) – Lower and upper bounds on independent variables. Defaults to no bounds. Each array must match the size of x0 or be a scalar, in the latter case a bound will be the same for all variables. Use np.inf with an appropriate sign to disable bounds on all or some variables.

  • 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. 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. 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. Optimizer terminates when max(abs(g)) < gtol. If None, the termination by this condition is disabled.

  • verbose ({0, 1, 2}, optional) –

    • 0 : work silently.

    • 1 (default) : display a termination report.

    • 2 : display progress during iterations

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

  • 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.

    • "max_nfev" : (int > 0) Maximum number of function evaluations (each iteration may take more than one function evaluation). Default is 5*maxiter+1

    • "max_dx" : (float > 0) Maximum allowed change in the norm of x from its starting point. Default np.inf.

    • "initial_trust_radius" : ("scipy", "conngould", "mix" or float > 0) Initial trust region radius. "scipy" uses the scaled norm of x0, which is the default behavior in scipy.optimize.least_squares. "conngould" uses the norm of the Cauchy point, as recommended in ch17 of [1]. "mix" uses the geometric mean of the previous two options. A float can also be passed to specify the trust radius directly. Default is "scipy".

    • "initial_trust_ratio" : (float > 0) A extra scaling factor that is applied after one of the previous heuristics to determine the initial trust radius. Default 1.

    • "max_trust_radius" : (float > 0) Maximum allowable trust region radius. Default np.inf.

    • "min_trust_radius" : (float >= 0) Minimum allowable trust region radius. Optimization is terminated if the trust region falls below this value. Default np.finfo(x0.dtype).eps.

    • "tr_increase_threshold" : (0 < float < 1) Increase the trust region radius when the ratio of actual to predicted reduction exceeds this threshold. Default 0.75.

    • "tr_decrease_threshold" : (0 < float < 1) Decrease the trust region radius when the ratio of actual to predicted reduction is less than this threshold. Default 0.25.

    • "tr_increase_ratio" : (float > 1) Factor to increase the trust region radius by when the ratio of actual to predicted reduction exceeds threshold. Default 2.

    • "tr_decrease_ratio" : (0 < float < 1) Factor to decrease the trust region radius by when the ratio of actual to predicted reduction falls below threshold. Default 0.25.

    • "tr_method" : "svd", "cho") 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 for badly scaled systems. Default "svd"

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.

References