### documentation Line search and Quasi Newton minimizer added

parent ad3a7d38
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 ... ... @@ -24,50 +24,48 @@ from nifty import LineEnergy class LineSearch(Loggable, object): """Class for finding a step size. Initialize the line search procedure which can be used by a specific line search method. Its finds the step size in a specific direction in the minimization process. Attributes ---------- line_energy : LineEnergy Object LineEnergy object from which we can extract energy at a specific point. f_k_minus_1 : Field Value of the field at the k-1 iteration of the line search procedure. prefered_initial_step_size : float Initial guess for the step length. """ Class for finding a step size. """ __metaclass__ = abc.ABCMeta def __init__(self): """ Parameters ---------- f : callable f(x, *args) Objective function. fprime : callable f'(x, *args) Objective functions gradient. f_args : tuple (optional) Additional arguments passed to objective function and its derivation. """ self.line_energy = None self.f_k_minus_1 = None self.prefered_initial_step_size = None def _set_line_energy(self, energy, pk, f_k_minus_1=None): """ Set the coordinates for a new line search. """Set the coordinates for a new line search. Parameters ---------- xk : ndarray, d2o, field Starting point. pk : ndarray, d2o, field energy : Energy object Energy object from which we can calculate the energy, gradient and curvature at a specific point. pk : Field Unit vector in search direction. f_k : float (optional) Function value f(x_k). fprime_k : ndarray, d2o, field (optional) Function value fprime(xk). f_k_minus_1 : float *optional* Value of the field at the k-1 iteration of the line search procedure. """ self.line_energy = LineEnergy(position=0., energy=energy, ... ...
 ... ... @@ -26,6 +26,54 @@ from .line_searching import LineSearchStrongWolfe class QuasiNewtonMinimizer(Loggable, object): """A Class used by other minimization methods to find local minimum. Quasi-Newton methods are used to find local minima or maxima of a function by approximating the Jacobian or Hessian matrix at every iteration. The class performs general steps(gets the gradient, descend direction, step size and checks the conergence) which can be used then by a specific minimization method. Parameters ---------- line_searcher : callable Function which finds the step size into the descent direction. (default: LineSearchStrongWolfe()) callback : function, *optional* Function f(energy, iteration_number) specified by the user to print iteration number and energy value at every iteration step. It accepts a function(energy) and integer(iteration_number). (default: None) convergence_tolerance : scalar Tolerance specifying convergence. (default: 1E-4) convergence_level : integer Number of times the tolerance should be undershot before exiting. (default: 3) iteration_limit : integer *optional* Maximum number of iterations performed. (default: None) Attributes ---------- convergence_tolerance : float Tolerance specifying convergence. convergence_level : float Number of times the tolerance should be undershot before exiting. iteration_limit : integer Maximum number of iterations performed. line_searcher : callable Function which finds the step size into the descent direction callback : function Function f(energy, iteration_number) specified by the user to print iteration number and energy value at every iteration step. It accepts a function(energy) and integer(iteration_number). Raises ------ StopIteration Raised if *callback function does not match the specified form. """ __metaclass__ = abc.ABCMeta def __init__(self, line_searcher=LineSearchStrongWolfe(), callback=None, ... ... @@ -43,33 +91,34 @@ class QuasiNewtonMinimizer(Loggable, object): self.callback = callback def __call__(self, energy): """ Runs the steepest descent minimization. Parameters ---------- x0 : field Starting guess for the minimization. alpha : scalar, *optional* Starting step width to be multiplied with normalized gradient (default: 1). tol : scalar, *optional* Tolerance specifying convergence; measured by maximal change in `x` (default: 1E-4). clevel : integer, *optional* Number of times the tolerance should be undershot before exiting (default: 8). self.iteration_limit : integer, *optional* Maximum number of iterations performed (default: 100,000). Returns ------- x : field Latest `x` of the minimization. convergence : integer Latest convergence level indicating whether the minimization has converged or not. """Runs the minimization on the provided Energy class. Accepts the NIFTY Energy class which describes our system and it runs the minimization to find the minimum/maximum of the system. Parameters ---------- energy : Energy object Energy object provided by the user from which we can calculate the energy, gradient and curvature at a specific point. Returns ------- x : field Latest `energy` of the minimization. convergence : integer Latest convergence level indicating whether the minimization has converged or not. Note ---- It stops the minimization if: *callback function does not match the specified form. *a perfectly flat point is reached. *according to line-search the minimum is found. *target convergence level is reached. *iteration limit is reached. """ convergence = 0 ... ...
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