LevenbergMarquardt#

class zfit.minimize.LevenbergMarquardt(tol=None, mode=None, rho_min=None, rho_max=None, verbosity=None, options=None, maxiter=None, criterion=None, strategy=None, name=None)[source]#

Bases: BaseMinimizer, GraphCachable

Levenberg-Marquardt minimizer for general non-linear minimization by interpolating between Gauss-Newton and Gradient descent optimization.

LM minimizes a function by iteratively solving a locally linearized version of the problem. Using the gradient (g) and the Hessian (H) of the loss function, the algorithm determines a step (h) that minimizes the loss function by solving \(Hh = g\). This works perfectly in one step for linear problems, however for non-linear problems it may be unstable far from the minimum. Thus a scalar damping parameter (L) is introduced and the Hessian is modified based on this damping. The form of the modification depends on the mode parameter, where the simplest example is \(H' = H + L \mathbb{I}\) (where \(\mathbb{I}\) is the identity). For a clarifying discussion of the LM algorithm see: Gavin, Henri 2016 (https://msulaiman.org/onewebmedia/LM%20Method%20matlab%20codes%20and%20implementation.pdf)

Parameters:

tol (float | None) – Termination value for the convergence/stopping criterion of the algorithm in order to determine if the minimum has been found. Defaults to 1e-3.
mode (int | None) – The mode of the LM algorithm. The default mode (0) is the simplest form of the LM algorithm. Other modes may be implemented in the future.
rho_min (float | None) – The minimum acceptable value of the ratio of the actual reduction in the loss function to the expected reduction. If the ratio is less than this value, the damping parameter is increased.
rho_max (float | None) – The maximum acceptable value of the ratio of the actual reduction in the loss function to the expected reduction. If the ratio is greater than this value, the damping parameter is decreased.
verbosity (int | None) –
Verbosity of the minimizer. Has to be between 0 and 10. The verbosity has the meaning:
- a value of 0 means quiet and no output
- above 0 up to 5, information that is good to know but without flooding the user, corresponding to a “INFO” level.
- A value above 5 starts printing out considerably more and is used more for debugging purposes.
- Setting the verbosity to 10 will print out every evaluation of the loss function and gradient.
Some minimizers offer additional output which is also distributed as above but may duplicate certain printed values.
options (Mapping[str, object] | None) – |@doc:minimizer.options||@docend:minimizer.options|
maxiter (int | None) – Approximate number of iterations. This corresponds to roughly the maximum number of evaluations of the value, ‘gradient`` or hessian.
criterion (ConvergenceCriterion | None) – Criterion of the minimum. This is an estimated measure for the distance to the minimum and can include the relative or absolute changes of the parameters, function value, gradients and more. If the value of the criterion is smaller than loss.errordef * tol, the algorithm stopps and it is assumed that the minimum has been found.
strategy (ZfitStrategy | None) – A class of type ZfitStrategy that takes no input arguments in the init. Determines the behavior of the minimizer in certain situations, most notably when encountering NaNs. It can also implement a callback function.
name (str | None) – |@doc:minimizer.name||@docend:minimizer.name

add_cache_deps(cache_deps, allow_non_cachable=True)#

Add dependencies that render the cache invalid if they change.

Parameters:

cache_deps (ztyping.CacherOrCachersType)
allow_non_cachable (bool) – If True, allow cache_dependents to be non-cachables. If False, any cache_dependents that is not a ZfitGraphCachable will raise an error.

Raises:

TypeError – if one of the cache_dependents is not a ZfitGraphCachable _and_ allow_non_cachable if False.

create_criterion(loss=None, params=None)#

Create a criterion instance for the given loss and parameters.

Parameters:

loss (ZfitLoss | None) – Loss that is used for the criterion. Can be None if called inside _minimize
params (Optional[Iterable[TypeVar(ParameterType, bound= Dict[str, zfit.core.interfaces.ZfitParameter])]]) – Parameters that will be associated with the loss in this order. Can be None if called within _minimize.

Return type:

ConvergenceCriterion

Returns:

ConvergenceCriterion to check if the function converged.

create_evaluator(loss=None, params=None, numpy_converter=None, strategy=None)#

Make a loss evaluator using the strategy and more from the minimizer.

Convenience factory for the loss evaluator. This wraps the loss to return a numpy array, to catch NaNs, stop on maxiter and evaluate the gradient and hessian without the need to specify the order every time.

Parameters:

loss (ZfitLoss | None) – Loss to be wrapped. Can be None if called inside _minimize
params (Optional[Iterable[TypeVar(ParameterType, bound= Dict[str, zfit.core.interfaces.ZfitParameter])]]) – Parameters that will be associated with the loss in this order. Can be None if called within _minimize.
strategy (ZfitStrategy | None) – Instance of a Strategy that will be used during the evaluation.

Returns:

The evaluator that wraps the Loss ant Strategy with the current parameters.

Return type:

LossEval

minimize(loss, params=None, init=None)#

Fully minimize the loss with respect to params, optionally using information from init.

The minimizer changes the parameter values in order to minimize the loss function until the convergence criterion value is less than the tolerance. This is a stateless function that can take a FitResult in order to initialize the minimization.

Parameters:

loss (ZfitLoss | Callable) – Loss to be minimized until convergence is reached. Usually a ZfitLoss.
attribute (- If this is a simple callable that takes an array as argument and an attribute errordef. The) –
can be set to any arbitrary function like
```
def loss(x):
    return - x ** 2

loss.errordef = 0.5  # as an example
minimizer.minimize(loss, [2, 5])
```
If not TensorFlow is used inside the function, make sure to set zfit.run.set_graph_mode(False) and zfit.run.set_autograd_mode(False).
method (- A FitResult can be provided as the only argument to the) – parameters to be minimized are taken from it. This allows to easily chain minimization algorithms.
the (in which case the loss as well as) – parameters to be minimized are taken from it. This allows to easily chain minimization algorithms.
params (ztyping.ParamsTypeOpt | None) –
The parameters with respect to which to minimize the loss. If None, the parameters will be taken from the loss.

In order to fix the parameter values to a specific value (and thereby make them indepented of their current value), a dictionary mapping a parameter to a value can be given.

If loss is a callable, params can also be (instead of Parameters):
- an array of initial values
- for more control, a dict with the keys:
  - value (required): array-like initial values.
  - name: list of unique names of the parameters.
  - lower: array-like lower limits of the parameters,
  - upper: array-like upper limits of the parameters,
  - stepsize: array-like initial step size of the parameters (approximately the expected uncertainty)
This will create internally a single parameter for each value that can be accessed in the FitResult via params. Repeated calls can therefore (in the current implement) cause a memory increase. The recommended way is to re-use parameters (just taken from the FitResult attribute params).
init (ZfitResult | None) –
A result of a previous minimization that provides auxiliary information such as the starting point for the parameters, the approximation of the covariance and more. Which information is used can depend on the specific minimizer implementation.

In general, the assumption is that the loss provided is similar enough to the one provided in init.

What is assumed to be close:
- the parameters at the minimum of loss will be close to the parameter values at the minimum of init.
- Covariance matrix, or in general the shape, of init to the loss at its minimum.
What is explicitly _not_ assumed to be the same:
- absolute value of the loss function. If init has a function value at minimum x of fmin, it is not assumed that loss will have the same/similar value at x.
- parameters that are used in the minimization may differ in order or which are fixed.

Return type:

FitResult

Returns:

The fit result containing all information about the minimization.

Examples

Using the ability to restart a minimization with a previous result allows to use a more global search algorithm with a high tolerance and an additional local minimization to polish the found minimum.

result_approx = minimizer_global.minimize(loss, params)
result = minimizer_local.minimize(result_approx)

For a simple usage with a callable only, the parameters can be given as an array of initial values.

def func(x):
    return np.log(np.sum(x ** 2))

func.errordef = 0.5
params = [1.1, 3.5, 8.35]  # initial values
result = minimizer.minimize(func, param)

register_cacher(cacher)#

Register a cacher that caches values produces by this instance; a dependent.

Parameters:: cacher (ztyping.CacherOrCachersType)

reset_cache_self()#: Clear the cache of self and all dependent cachers.