Looping functions

Functions for iterating over parameter spaces in VCA and CDMFT calculations. These include loops with predictors, the Hartree procedure, and fading between parameter sets.

Looping utilities for VCA and CDMFT calculations.

Provides functions for iterating over parameter spaces with predictors, including linear_loop(), controlled_loop(), fade(), Hartree_procedure(), and file-driven loops. These functions are added as methods of the lattice model class.

loop_from_file(self, task, file)

Performs a task ‘task’ over a set of model parameters defined in a file. The definition of each model instance must be done in the task ‘task’; it is not done by this looping function.

Parameters:

  • task – function (task) to perform

  • file (str) – name of the data file specifying the solutions, in the same tab-separated format usually used to write solutions

loop_from_table(self, task, data)

Performs a task ‘task’ over a set of model parameters defined in a table. The definition of each model instance must be done in the task ‘task’; it is not done by this looping function.

Parameters:

  • task – function (task) to perform

  • data (ndarray) – table of parameters, with named columns, as read or filtered from numpy.genfromtxt()

linear_loop(self, N, task, varia=None, params=None, predict=True)

Performs a loop with a predictor. The definition of each model instance must be done in ‘task’; it is not done by this looping function.

Parameters:

  • N – number of intervals within the loop

  • task – function called at each step of the loop

  • varia ([str]) – names of the variational parameters

  • params (dict) – dict mapping parameter names to 2-tuples of (initial, final) values

  • predict (bool) – if True, uses a linear or quadratic predictor

Returns:

None

controlled_loop(self, task, varia=None, loop_param=None, loop_range=None, control_func=None, retry=None, max_retry=4, predict=True)

Performs a controlled loop for VCA or CDMFT with a predictor. The definition of each model instance must be done and returned by ‘task’; it is not done by this looping function.

Parameters:

  • task – a function called at each step of the loop. Must return a model_instance.

  • varia ([str]) – names of the variational parameters

  • loop_param (str) – name of the parameter looped over

  • loop_range ((float, float, float)) – range of the loop (start, end, step)

  • control_func – (optional) name of the function that controls the loop (returns bool). Takes a model instance as argument

  • retry (char) – If None, stops on failure. If ‘refine’, adjusts the step (divide by 2) and retry. If ‘skip’, skip to next value.

  • max_retry (int) – Maximum number of retries of either type

  • predict (bool) – if True, uses a linear or quadratic predictor

fade(self, task, P, n)

Fades the model between two sets of parameters, in n steps

Parameters:

  • task – task to perform within the loop

  • P (dict) – dict of parameters with a tuple of values (start and finish) for each

  • n – number of steps

Returns:

None

controlled_fade(self, task, P, n, C, file='fade.tsv', tol=0.0001, method='Broyden', maxiter=32, alpha=0.0, eps_algo=0, bracket=None, delta=None, verb=False)

Fades the model between two sets of parameters, in n steps

Parameters:

  • task – task to perform within the loop

  • P (dict) – dict of parameters with a tuple of values (start and finish) for each

  • n – number of steps

  • C (dict) – dict of adjustable parameters whose average (the value of C) should stay fixed during the fade

  • file (str) – file to which the converged results are written

  • tol (float) – precision on the averages

  • method (str) – method used for solving the nonlinear constraints

  • maxiter – maximum number of iterations for solving the constraints

  • alpha (float) – parameter used in some non linear solvers (broyden)

  • eps_algo (int) – convergence accelerator parameter in fixed_point

  • bracket ((float,float)) – bracket used in some nonlinear 1D solvers

  • delta (float) – interval used to update the bracket used in some nonlinear 1D solvers

  • verb (bool) – If True, writes progress reports

Hartree_procedure(self, task, couplings, maxiter=32, iteration='fixed_point', eps_algo=0, file='hartree.tsv', SEF=False, pr=False, alpha=0.0)

Performs the Hartree approximation

Parameters:

  • task – task to perform within the loop. Must return a model_instance

  • couplings (hartree) – sequence of couplings (or single coupling), of the Hartree class

  • maxiter (int) – maximum number of iterations

  • iteration (str) – method of iteration of parameters (‘fixed_point’ or ‘broyden’)

  • eps_algo (int) – number of elements in the epsilon algorithm convergence accelerator = 2*eps_algo + 1 (0 = no acceleration)

  • file (str) – name of the file to which the converged result is written via write_summary()

  • SEF (bool) – if True, computes the Potthoff functional at the end of the procedure

  • pr (bool) – if True, prints progress of each coupling update

  • alpha (float) – if iteration=’fixed_point’, damping parameter, otherwise trial inverse Jacobian (if a float, that is (1+alpha)*unit matrix)

Returns:

model instance, converged inverse Jacobian

flexible_loop(self, task, initial_mu, final_n, initial_step, delta_n=0.005, varia=[])

Performs a controlled loop for VCA or CDMFT with a predictor. The definition of each model instance must be done and returned by ‘task’; it is not done by this looping function.

Parameters:

  • task – a function called at each step of the loop. Must return a model_instance.

  • initial_mu (float) – initial value of the chemical potential mu

  • final_n (float) – target final density at which the loop should stop

  • initial_step (float) – initial step in mu for the first iteration

  • delta_n (float) – approximate step in density to keep approximately constant across iterations

  • varia ([str]) – names of the variational parameters

Returns:

None