seisflows.plugins.line_search.bracket
A bracketing line search (a.k.a direct line search) attempts to find an appropriate step length by identifying two points between which the minimum misfit lies. Contains some functionality for saving line search history to disk so that a line search may be resumed in the case of a failure/reset.
https://en.wikipedia.org/wiki/Line_search
Note
Line search is called on by the optimization procedure and should not really have any agency (i.e. it should not be able to iterate its own step count etc., this should be completely left to the optimization algorithm to keep everything in one place)
Classes
[line_search.bracket] The bracketing line search identifies two points |
Functions
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Checks if minimum has been bracketed |
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Checks if step length is reasonably close to quadratic estimate |
Module Contents
- class seisflows.plugins.line_search.bracket.Bracket(step_count_max, path=None)
[line_search.bracket] The bracketing line search identifies two points between which the minimum misfit lies between.
- Parameters:
step_count_max (int) – maximum number of step counts before changing line search behavior. set by PAR.STEP_COUNT_MAX
- step_count_max
- func_vals = []
- step_lens = []
- gtg = []
- gtp = []
- step_count = 0
- iteridx = []
- __str__()
Simply print out all attributes, used for debugging mainly
- property update_count
Independently keeps track of how many model updates we have made
- check()
Make sure internal parameters are consistent with expectations. This is always expected to pass if the User/workflow uses the main functions to manipulate the line search. But occasionally some manual intervention is required, so the check function makes sure things are okay.
- initialize_line_search(func_val, gtg, gtp)
Input the initial values of a line search, corresponding to the initial model for this given iteration. Step length is assumed to be 0, because step length is calculated relative to the initial model.
Note
This is a one-time permanent change to the search history, but can be rolled back manually by the User with _restart_line_search (to start over from before initialize_line_search
- Parameters:
func_val (float) – value of the objective function evaluation
step_len (float) – length of step for the trial model (alpha)
gtg (float) – dot product of gradient with itself
gtp (float) – dot product of gradient with search direction
- update_search_history(func_val, step_len)
After a misfit evaluation for a trial model, line search needs to know how large the step (alpha) was, and the corresponding objective function misfit evaluation value.
Note
This is a one-time permanent change to the search history, but can be rolled back manually by the User with _revert_line_search, to undo the update performed here
- Parameters:
func_val (float) – value of the objective function evaluation
step_len (float) – length of step for the trial model (alpha)
- clear_search_history()
Clears internal line search history after an optimization restart. This is the ‘nuclear’ option, because it gets rid of ALL saved information about misfit evaluations from the previous iterations, i.e., this is like starting from scratch.
- _restart_line_search()
Iff a line search has been initialized and something goes awry, it is often preferable to restart the line search. To do this, we roll back the number of steps we have taken during the line search, and undo variable changes that took place in ‘initialize_search’.
Note
In order to proceed with workflow after running this function you will need to restart the workflow from initialize_line_search
- _revert_search_history()
Occasionally a line search will break mid-search but the User doesn’t want to restart_line_search, but rather just roll back to the previous step count. This function steps back the search history by a number by one step. Call it multiple times to step back multiple steps Raises an error if there are no more steps to revert.
- get_search_history()
Get the step lengths and misfit function evaluations for the current line search. Sort the list by the step lengths to get a coherent list, as e.g., in a bracketing line search the actual order of the list does not match the magnitude of step lengths taken.
Note
In the original SeisFlows the values of the search history were non-intuitive and difficult to understand at a glance. The original values are copied here as they relate to the mathematical formulations and so are still important:
i = self.step_count k = len(self.step_lens) x = np.array(self.step_lens[k - i - 1:k]) f = np.array(self.func_vals[k - i - 1:k]) j = count_zeros(self.step_lens) - 1 # update count
- Return type:
(np.array, np.array, np.array)
- Returns:
(step lengths of current line search, misfits of current line search, step count associated with given step length and misfit)
- calculate_step_length()
Determines step length (alpha) and search status (status) using a bracketing line search. Evaluates Wolfe conditions to determine if a step length is acceptable.
- Return type:
tuple (float, str)
- Returns:
(alpha==calculated step length, status==how to treat the next step count evaluation)
- seisflows.plugins.line_search.bracket._check_bracket(step_lens, func_vals)
Checks if minimum has been bracketed
Looks at the minimum of the misfit values calculated through eval func to see if the misfit has been reduced w.r.t the initial misfit
- Parameters:
step_lens (numpy.array) – an array of the step lengths taken during iteration
func_vals (numpy.array) – array of misfit values from eval func function
- Return type:
bool
- Returns:
status of function as a bool
- seisflows.plugins.line_search.bracket._good_enough(step_lens, func_vals, thresh=np.log10(1.2))
Checks if step length is reasonably close to quadratic estimate
- Parameters:
step_lens (np.array) – an array of the step lengths taken during iteration
func_vals (np.array) – array of misfit values from eval func function
thresh (numpy.float64) – threshold value for comparison against quadratic estimate
- Return type:
bool
- Returns:
status of function as a bool