seisflows.optimize.NLCG

Nonlinear conjugate gradient method for optimization

Classes

NLCG

NLCG Optimization

Functions

`check_conjugacy`(g_new, g_old)	Check for conjugacy between two vectors
`check_descent`(p_new, g_new)	Ensure that the search direction is descending

Module Contents

class seisflows.optimize.NLCG.NLCG(nlcg_max=np.inf, nlcg_thresh=np.inf, calc_beta='pollak_ribere', **kwargs)

Bases: seisflows.optimize.gradient.Gradient

NLCG Optimization

Nonlinear conjugate gradient method

Parameters

type nlcg_max:: int
param nlcg_max:: NLCG periodic restart interval, should be between 1 and infinity
type nlcg_thresh:: NLCG conjugacy restart threshold, should be between 1 and infinity
type calc_beta:: str
param calc_beta:: method to calculate the parameter ‘beta’ in the NLCG algorithm. Available: ‘pollak_ribere’, ‘fletcher_reeves’

Paths

***

__doc__ = Multiline-String

Show Value

"""
    Gradient Optimization [Optimize Base]
    -------------------------------------
    Defines foundational structure for Optimization module. Applies a
    gradient/steepest descent optimization algorithm.

    Parameters
    ----------
    :type line_search_method: str
    :param line_search_method: chosen line_search algorithm. Currently available
        are 'bracket' and 'backtrack'. See seisflows.plugins.line_search
        for all available options
    :type preconditioner: str
    :param preconditioner: algorithm for preconditioning gradients. Currently
        available: 'diagonal'. Requires `path_preconditioner` to point to a
        set of files that define the preconditioner, formatted the same as the
        input model
    :type step_count_max: int
    :param step_count_max: maximum number of trial steps to perform during
        the line search before a change in line search behavior is
        considered, or a line search is considered to have failed.
    :type step_len_init: float
    :param step_len_init: initial line search step length guess, provided
        as a fraction of current model parameters.
    :type step_len_max: float
    :param step_len_max: optional, maximum allowable step length during the line
        search. Set as a fraction of the current model parameters
    :type step_len_min: float
    :param step_len_min: optional, minimum allowable step length during the line
        search. Set as a fraction of the current model parameters

    Paths
    -----
    :type path_preconditioner: str
    :param path_preconditioner: optional path to a set of preconditioner files
        formatted the same as the input model (or output model of solver).
        Required to exist and contain files if `preconditioner`==True
    ***

Nonlinear conjugate gradient method for optimization
"""

NLCG_max

NLCG_thresh

calc_beta = 'pollak_ribere'

_NLCG_iter = 0

_calc_beta

checkpoint(): Overwrite default checkpointing to store internal L-BFGS Attributes

compute_direction()

Compute search direction using the Nonlinear Conjugate Gradient method The potential outcomes when computing direction with NLCG

First iteration of an NLCG optimization, search direction is
the inverse gradient
NLCG internal iteration ticks over the maximum allowable number of
iterations, force a restart condition, search direction is the inverse gradient
New NLCG search direction does not have conjugacy with previous
search direction, force restart, inverse gradient search direction
New NLCG search direction is not a descent direction,
force restart, inverse gradient search direction
New NLCG search direction has conjugacy and is a descent direction
and is set as the new search direction.

Return type:: seisflows.tools.specfem.Model
Returns:: search direction as a Model instance

restart(): Overwrite the Base restart class and include a restart of the NLCG

_fletcher_reeves(g_new, g_old)

One method for calculating beta in the NLCG Algorithm from Fletcher & Reeves, 1964

Parameters:

g_new (np.array) – new search direction
g_old (np.array) – old search direction

Return type:

float

Returns:

beta, the scale factor to apply to the old search direction to determine the new search direction

_pollak_ribere(g_new, g_old)

One method for calculating beta in the NLCG Algorithm from Polak & Ribiere, 1969

Parameters:

g_new (np.array) – new search direction
g_old (np.array) – old search direction

Return type:

float

Returns:

beta, the scale factor to apply to the old search direction to determine the new search direction

seisflows.optimize.NLCG.check_conjugacy(g_new, g_old)

Check for conjugacy between two vectors

Parameters:

g_new (np.array) – new search direction
g_old (np.array) – old search direction

Return type:

float

Returns:

an element that proves conjugacy

seisflows.optimize.NLCG.check_descent(p_new, g_new)

Ensure that the search direction is descending

Parameters:

p_new (np.array) – search direction
g_new (np.array) – gradient direction

Return type:

float

Returns:

the angle between search direction and gradient direction, should be negative to ensure descent