pygsti.optimize.simplerlm.simplish_leastsq

pygsti.optimize.simplerlm.simplish_leastsq#

simplish_leastsq(obj_fn, jac_fn, x0, f_norm2_tol=1e-06, jac_norm_tol=1e-06, rel_ftol=1e-06, rel_xtol=1e-06, max_iter=100, num_fd_iters=0, max_dx_scale=1.0, init_munu='auto', oob_check_interval=0, oob_action='reject', oob_check_mode=0, resource_alloc=None, arrays_interface=None, serial_solve_proc_threshold=100, x_limits=None, verbosity=0, profiler=None)#

An implementation of the Levenberg-Marquardt least-squares optimization algorithm customized for use within pyGSTi.

This general purpose routine mimic to a large extent the interface used by scipy.optimize.leastsq, though it implements a newer (and more robust) version of the algorithm.

Parameters:

  • obj_fn (function) – The objective function. Must accept and return 1D numpy ndarrays of length N and M respectively. Same form as scipy.optimize.leastsq.

  • jac_fn (function) – The jacobian function (not optional!). Accepts a 1D array of length N and returns an array of shape (M,N).

  • x0 (numpy.ndarray) – Initial evaluation point.

  • f_norm2_tol (float, optional) – Tolerace for F^2 where F = `norm( sum(obj_fn(x)**2) ) is the least-squares residual. If F**2 < f_norm2_tol, then mark converged.

  • jac_norm_tol (float, optional) – Tolerance for jacobian norm, namely if infn(dot(J.T,f)) < jac_norm_tol then mark converged, where infn is the infinity-norm and f = obj_fn(x).

  • rel_ftol (float, optional) – Tolerance on the relative reduction in F^2, that is, if d(F^2)/F^2 < rel_ftol then mark converged.

  • rel_xtol (float, optional) – Tolerance on the relative value of |x|, so that if d(|x|)/|x| < rel_xtol then mark converged.

  • max_iter (int, optional) – The maximum number of (outer) iterations.

  • num_fd_iters (int optional) – Internally compute the Jacobian using a finite-difference method for the first num_fd_iters iterations. This is useful when x0 lies at a special or singular point where the analytic Jacobian is misleading.

  • max_dx_scale (float, optional) – If not None, impose a limit on the magnitude of the step, so that |dx|^2 < max_dx_scale^2 * len(dx) (so elements of dx should be, roughly, less than max_dx_scale).

  • init_munu (tuple, optional) – If not None, a (mu, nu) tuple of 2 floats giving the initial values for mu and nu.

  • oob_check_interval (int, optional) – Every oob_check_interval outer iterations, the objective function (obj_fn) is called with a second argument ‘oob_check’, set to True. In this case, obj_fn can raise a ValueError exception to indicate that it is Out Of Bounds. If oob_check_interval is 0 then this check is never performed; if 1 then it is always performed.

  • oob_action ({"reject","stop"}) – What to do when the objective function indicates (by raising a ValueError as described above). “reject” means the step is rejected but the optimization proceeds; “stop” means the optimization stops and returns as converged at the last known-in-bounds point.

  • oob_check_mode (int, optional) – An advanced option, expert use only. If 0 then the optimization is halted as soon as an attempt is made to evaluate the function out of bounds. If 1 then the optimization is halted only when a would-be accepted step is out of bounds.

  • resource_alloc (ResourceAllocation, optional) – When not None, an resource allocation object used for distributing the computation across multiple processors.

  • arrays_interface (ArraysInterface) – An object that provides an interface for creating and manipulating data arrays.

  • serial_solve_proc_threshold (int optional) – When there are fewer than this many processors, the optimizer will solve linear systems serially, using SciPy on a single processor, rather than using a parallelized Gaussian Elimination (with partial pivoting) algorithm coded in Python. Since SciPy’s implementation is more efficient, it’s not worth using the parallel version until there are many processors to spread the work among.

  • x_limits (numpy.ndarray, optional) – A (num_params, 2)-shaped array, holding on each row the (min, max) values for the corresponding parameter (element of the “x” vector). If None, then no limits are imposed.

  • verbosity (int, optional) – Amount of detail to print to stdout.

  • profiler (Profiler, optional) – A profiler object used for to track timing and memory usage.

Returns:

  • x (numpy.ndarray) – The optimal solution.

  • converged (bool) – Whether the solution converged.

  • msg (str) – A message indicating why the solution converged (or didn’t).