brainpy.analysis.SlowPointFinder

class brainpy.analysis.SlowPointFinder(f_cell, f_type=None, f_loss=None, verbose=True, args=(), inputs=None, t=None, dt=None, target_vars=None, excluded_vars=None, f_loss_batch=None, fun_inputs=None)

Find fixed/slow points by numerical optimization.

This class can help you:

• optimize to find the closest fixed points / slow points

• exclude any fixed points whose fixed point loss is above threshold

• exclude any non-unique fixed points according to a tolerance

• exclude any far-away “outlier” fixed points

Parameters

• f_cell (callable, function, DynamicalSystem) – The target of computing the recurrent units.

• f_type (str) –

  The system’s type: continuous system or discrete system.

  • ’continuous’: continuous derivative function, denotes this is a continuous system, or

  • ’discrete’: discrete update function, denotes this is a discrete system.

• verbose (bool) – Whether output the optimization progress.

• f_loss (callable) –

  The loss function. - If f_type is “discrete”, the loss function must receive three

  arguments, i.e., loss(outputs, targets, axis).

  • If f_type is “continuous”, the loss function must receive two arguments, i.e., loss(outputs, axis).

  New in version 2.2.0.

• t (float) –

  Parameter for f_cell is instance of DynamicalSystem. The time to evaluate the fixed points. Default is 0.

  New in version 2.2.0.

• dt (float) –

  Parameter for f_cell is instance of DynamicalSystem. The numerical integration step, which can be used when . The default is given by brainpy.math.get_dt().

  New in version 2.2.0.

• inputs (sequence, callable) –

  Parameter for f_cell is instance of DynamicalSystem. Same as inputs in DSRunner.

  New in version 2.2.0.

• excluded_vars (sequence, dict) –

  Parameter for f_cell is instance of DynamicalSystem. The excluded variables (can be a sequence of Variable instances). These variables will not be included for optimization of fixed points.

  New in version 2.2.0.

• target_vars (dict) –

  Parameter for f_cell is instance of DynamicalSystem. The target variables (can be a dict of Variable instances). These variables will be included for optimization of fixed points. The candidate points later provided should have same keys as in target_vars.

  New in version 2.2.0.

• f_loss_batch (callable, function) –

  Parameter for f_cell is instance of DynamicalSystem. The function to compute the loss.

  Deprecated since version 2.2.0: Has been removed. Please use f_loss to set different loss function.

• fun_inputs (callable) –

  Deprecated since version 2.3.1: Will be removed since version 2.4.0.

__init__(f_cell, f_type=None, f_loss=None, verbose=True, args=(), inputs=None, t=None, dt=None, target_vars=None, excluded_vars=None, f_loss_batch=None, fun_inputs=None)

Methods

__init__(f_cell[, f_type, f_loss, verbose, ...])
compute_jacobians(points[, stack_dict_var, ...])	Compute the Jacobian matrices at the points.
decompose_eigenvalues(matrices[, sort_by, ...])	Compute the eigenvalues of the matrices.
exclude_outliers([tolerance])	Exclude points whose closest neighbor is further than threshold.
filter_loss([tolerance])	Filter fixed points whose speed larger than a given tolerance.
find_fps_with_gd_method(candidates[, ...])	Optimize fixed points with gradient descent methods.
find_fps_with_opt_solver(candidates[, ...])	Optimize fixed points with nonlinear optimization solvers.
keep_unique([tolerance])	Filter unique fixed points by choosing a representative within tolerance.

Attributes

fixed_points	The final fixed points found.
losses	Losses of fixed points.
num_fps	rtype int
opt_losses	The optimization losses.
selected_ids	The selected ids of candidate points.