Source code for zfit.core.sample

#  Copyright (c) 2020 zfit

from typing import Callable, Union, Iterable, List, Optional, Tuple

import tensorflow as tf

import zfit
from zfit import z

ztf = z
from zfit.core.interfaces import ZfitPDF
from zfit.util import ztyping
from zfit.util.exception import WorkInProgressError
from .. import settings
from ..util.container import convert_to_container
from .space import Space
from ..settings import ztypes, run


[docs]class UniformSampleAndWeights: def __call__(self, n_to_produce: Union[int, tf.Tensor], limits: Space, dtype): rnd_samples = [] thresholds_unscaled_list = [] weights = tf.broadcast_to(ztf.constant(1., shape=(1,)), shape=(n_to_produce,)) n_produced = tf.constant(0) for i, space in enumerate(limits): lower, upper = space.rect_limits # TODO: remove new space if i == len(limits) - 1: n_partial_to_produce = n_to_produce - n_produced # to prevent roundoff errors, shortcut for 1 space else: if isinstance(space, EventSpace): frac = 1. # TODO(Mayou36): remove hack for Eventspace else: tot_area = limits.rect_area() frac = (space.rect_area() / tot_area)[0] n_partial_to_produce = tf.cast( ztf.to_real(n_to_produce) * ztf.to_real(frac), dtype=tf.int32) # TODO(Mayou36): split right! sample_drawn = tf.random.uniform(shape=(n_partial_to_produce, limits.n_obs + 1), # + 1 dim for the function value dtype=ztypes.float) rnd_sample = sample_drawn[:, :-1] * (upper - lower) + lower # -1: all except func value thresholds_unscaled = sample_drawn[:, -1] # if not multiple_limits: # return rnd_sample, thresholds_unscaled rnd_samples.append(rnd_sample) thresholds_unscaled_list.append(thresholds_unscaled) n_produced += n_partial_to_produce rnd_sample = tf.concat(rnd_samples, axis=0) thresholds_unscaled = tf.concat(thresholds_unscaled_list, axis=0) n_drawn = n_to_produce return rnd_sample, thresholds_unscaled, weights, weights, n_drawn
[docs]class EventSpace(Space): """EXPERIMENTAL SPACE CLASS!""" def __init__(self, obs: ztyping.ObsTypeInput, limits: ztyping.LimitsTypeInput, factory=None, dtype=ztypes.float, name: Optional[str] = "Space"): if limits is None: raise ValueError("Limits cannot be None for EventSpaces (currently)") self._limits_tensor = None self.dtype = dtype self._factory = factory super().__init__(obs, limits, name) @property def factory(self): return self._factory @property def is_generator(self): return self.factory is not None @property def limits(self) -> ztyping.LimitsTypeReturn: limits = super().limits limits_tensor = self._limits_tensor if limits_tensor is not None: lower, upper = limits new_bounds = [[], []] for i, old_bounds in enumerate(lower, upper): for bound in old_bounds: if self.is_generator: new_bound = tuple(lim(limits_tensor) for lim in bound) else: new_bound = tuple(lim() for lim in bound) new_bounds[i].append(new_bound) new_bounds[i] = tuple(new_bounds[i]) limits = tuple(new_bounds) return limits
[docs] def create_limits(self, n): if self._factory is not None: self._limits_tensor = self._factory(n)
[docs] def iter_areas(self, rel: bool = False) -> Tuple[float, ...]: if not rel: raise RuntimeError("Currently, only rel with one limits is implemented in EventSpace") return (1.,) # TODO: remove HACK, use tensors? raise RuntimeError("Cannot be called with an event space.")
[docs] def add(self, other: ztyping.SpaceOrSpacesTypeInput): raise RuntimeError("Cannot be called with an event space.")
[docs] def combine(self, other: ztyping.SpaceOrSpacesTypeInput): raise RuntimeError("Cannot be called with an event space.")
@staticmethod def _calculate_areas(limits) -> Tuple[float]: # TODO: return the area as a tensor? return (1.,) def __hash__(self): return id(self)
@z.function(wraps='sample') def accept_reject_sample(prob: Callable, n: int, limits: Space, sample_and_weights_factory: Callable = UniformSampleAndWeights, dtype=ztypes.float, prob_max: Union[None, int] = None, efficiency_estimation: float = 1.0) -> tf.Tensor: """Accept reject sample from a probability distribution. Args: prob (function): A function taking x a Tensor as an argument and returning the probability (or anything that is proportional to the probability). n (int): Number of samples to produce limits (:py:class:`~zfit.Space`): The limits to sample from sample_and_weights_factory (Callable): An (immutable!) factory function that returns the following function: A function that returns the sample to insert into `prob` and the weights (probability density) of each sample together with the random thresholds. The API looks as follows: - Parameters: - n_to_produce (int, tf.Tensor): The number of events to produce (not exactly). - limits (Space): the limits in which the samples will be. - dtype (dtype): DType of the output. - Return: A tuple of length 5: - proposed sample (tf.Tensor with shape=(n_to_produce, n_obs)): The new (proposed) sample whose values are inside `limits`. - thresholds_unscaled (tf.Tensor with shape=(n_to_produce,): Uniformly distributed random values **between 0 and 1**. - weights (tf.Tensor with shape=(n_to_produce)): (Proportional to the) probability for each sample of the distribution it was drawn from. - weights_max (int, tf.Tensor, None): The maximum of the weights (if known). This is what the probability maximum will be scaled with, so it should be rather lower than the maximum if the peaks do not exactly coincide. Otherwise return None (which will **assume** that the peaks coincide). - n_produced: the number of events produced. Can deviate from the requested number. dtype (): prob_max (Union[None, int]): The maximum of the model function for the given limits. If None is given, it will be automatically, safely estimated (by a 10% increase in computation time (constant weak scaling)). efficiency_estimation (float): estimation of the initial sampling efficiency. Returns: tf.Tensor: """ multiple_limits = len(limits) > 1 sample_and_weights = sample_and_weights_factory() n = tf.cast(n, dtype=tf.int32) if run.numeric_checks: tf.debugging.assert_non_negative(n) # whether we may produce more then n, we normally do (except for EventSpace which is not a generator) # we cannot cut inside the while loop as soon as we have produced enough because we may sample from # multiple limits and therefore need to randomly remove events, otherwise we are biased because the # drawn samples are ordered in the different dynamic_array_shape = True # for fixed limits in EventSpace we need to know which indices have been successfully sampled. Therefore this # can be None (if not needed) or a boolean tensor with the size `n` initial_is_sampled = tf.constant("EMPTY") if (isinstance(limits, EventSpace) and not limits.is_generator) or limits.n_events > 1: dynamic_array_shape = False if run.numeric_checks: tf.debugging.assert_equal(limits.n_events, n) initial_is_sampled = tf.fill(value=False, dims=(n,)) efficiency_estimation = 1.0 # generate exactly n inital_n_produced = tf.constant(0, dtype=tf.int32) initial_n_drawn = tf.constant(0, dtype=tf.int32) sample = tf.TensorArray(dtype=dtype, size=n, dynamic_size=dynamic_array_shape, clear_after_read=True, # we read only once at end to tensor element_shape=(limits.n_obs,)) @z.function(wraps='tensor') def not_enough_produced(n, sample, n_produced, n_total_drawn, eff, is_sampled, weights_scaling): return tf.greater(n, n_produced) @z.function(wraps='tensor') def sample_body(n, sample, n_produced=0, n_total_drawn=0, eff=1.0, is_sampled=None, weights_scaling=0.): eff = tf.reduce_max(input_tensor=[eff, ztf.to_real(1e-6)]) n_to_produce = n - n_produced if isinstance(limits, EventSpace): # EXPERIMENTAL(Mayou36): added to test EventSpace limits.create_limits(n=n) do_print = settings.get_verbosity() > 5 if do_print: tf.print("Number of samples to produce:", n_to_produce, " with efficiency ", eff, " with total produced ", n_produced, " and total drawn ", n_total_drawn, " with weights scaling", weights_scaling) if dynamic_array_shape: # TODO: move all this fixed numbers out into settings n_to_produce = tf.cast(ztf.to_real(n_to_produce) / eff * 1.1, dtype=tf.int32) + 10 # just to make sure # TODO: adjustable efficiency cap for memory efficiency (prevent too many samples at once produced) max_produce_cap = tf.constant(800000, dtype=tf.int32) tf.debugging.assert_positive(n_to_produce, "n_to_produce went negative, overflow?") # TODO: remove below? was there due to overflow in tf? # safe_to_produce = tf.maximum(max_produce_cap, n_to_produce) # protect against overflow, n_to_prod -> neg. n_to_produce = tf.minimum(n_to_produce, max_produce_cap) # introduce a cap to force serial new_limits = limits else: # TODO(Mayou36): add cap for n_to_produce here as well if multiple_limits: raise WorkInProgressError("Multiple limits for fixed event space not yet implemented") is_not_sampled = tf.logical_not(is_sampled) lower, upper = limits._rect_limits_tf lower = tf.boolean_mask(tensor=lower, mask=is_not_sampled) upper = tf.boolean_mask(tensor=upper, mask=is_not_sampled) new_limits = limits.with_limits(limits=(lower, upper)) draw_indices = tf.where(is_not_sampled) rnd_sample, thresholds_unscaled, weights, weights_max, n_drawn = sample_and_weights( n_to_produce=n_to_produce, limits=new_limits, dtype=dtype) n_drawn = tf.cast(n_drawn, dtype=tf.int32) if run.numeric_checks: tf.debugging.assert_non_negative(n_drawn) n_total_drawn += n_drawn probabilities = prob(rnd_sample) shape_rnd_sample = tf.shape(input=rnd_sample)[0] if run.numeric_checks: tf.debugging.assert_equal(tf.shape(input=probabilities), shape_rnd_sample) probabilities = tf.identity(probabilities) if prob_max is None or weights_max is None: # TODO(performance): estimate prob_max, after enough estimations -> fix it? # TODO(Mayou36): This control dependency is needed because otherwise the max won't be determined # correctly. A bug report on will be filled (WIP). # The behavior is very odd: if we do not force a kind of copy, the `reduce_max` returns # a value smaller by a factor of 1e-14 # UPDATE: this works now? Was it just a one-time bug? # safety margin, predicting future, improve for small samples? weights_maximum = tf.reduce_max(input_tensor=weights) weights_clipped = tf.maximum(weights, weights_maximum * 1e-5) # prob_weights_ratio = probabilities / weights prob_weights_ratio = probabilities / weights_clipped max_prob_weights_ratio = tf.reduce_max(input_tensor=prob_weights_ratio) # clipping means that we don't scale more for a certain threshold # to properly account for very small numbers, the thresholds should be scaled to match the ratio # but if a weight of a sample is very low (compared to the other weights), this would force the acceptance # of other samples to decrease strongly. We introduce a cut here, meaning that any event with an acceptance # chance of less then 1 in ratio_threshold will be underestimated. # TODO(Mayou36): make ratio_threshold a global setting # max_prob_weights_ratio_clipped = tf.minimum(max_prob_weights_ratio, # min_prob_weights_ratio * ratio_threshold) max_prob_weights_ratio_clipped = max_prob_weights_ratio weights_scaling = tf.maximum(weights_scaling, max_prob_weights_ratio_clipped * (1 + 1e-2)) else: weights_scaling = prob_max / weights_max weights_scaled = weights_scaling * weights * (1 + 1e-8) # numerical epsilon random_thresholds = thresholds_unscaled * weights_scaled if run.numeric_checks: invalid_probs_weights = tf.greater(probabilities, weights_scaled) failed_weights = tf.boolean_mask(tensor=weights_scaled, mask=invalid_probs_weights) failed_probs = tf.boolean_mask(tensor=probabilities, mask=invalid_probs_weights) # def bias_print(): # tf.print("HACK WARNING: if the following is NOT empty, your sampling _may_ be biased." # " Failed weights:", failed_weights, " failed probs", failed_probs) # tf.cond(tf.not_equal(tf.shape(input=failed_weights), [0]), bias_print, lambda: None) tf.debugging.assert_equal(tf.shape(input=failed_weights), [0]) # for weights scaled more then ratio_threshold if run.numeric_checks: tf.debugging.assert_greater_equal(x=weights_scaled, y=probabilities, message="Not all weights are >= probs so the sampling " "will be biased. If a custom `sample_and_weights` " "was used, make sure that either the shape of the " "custom sampler (resp. it's weights) overlap better " "or decrease the `max_weight`") # # # check disabled (below not added to deps) # assert_scaling_op = tf.assert_less(weights_scaling / min_prob_weights_ratio, z.constant(ratio_threshold), # data=[weights_scaling, min_prob_weights_ratio], # message="The ratio between the probabilities from the pdf and the" # f"probability from the sampler is higher " # f" then {ratio_threshold}. This will most probably bias the sampling. " # f"Use importance sampling or, to disable this check, do" # f"zfit.run.numeric_checks = False") # assert_op.append(assert_scaling_op) take_or_not = probabilities > random_thresholds take_or_not = take_or_not[0] if len(take_or_not.shape) == 2 else take_or_not filtered_sample = tf.boolean_mask(tensor=rnd_sample, mask=take_or_not, axis=0) n_accepted = tf.shape(input=filtered_sample)[0] n_produced_new = n_produced + n_accepted if not dynamic_array_shape: indices = tf.boolean_mask(tensor=draw_indices, mask=take_or_not) current_sampled = tf.sparse.to_dense(tf.SparseTensor(indices=indices, values=tf.broadcast_to(input=(True,), shape=(n_accepted,)), dense_shape=(tf.cast(n, dtype=tf.int64),)), default_value=False) is_sampled = tf.logical_or(is_sampled, current_sampled) indices = indices[:, 0] else: indices = tf.range(n_produced, n_produced_new) # TODO: pack into tf.function to speedup considerable the eager sampling? Is bottleneck currently sample_new = sample.scatter(indices=tf.cast(indices, dtype=tf.int32), value=filtered_sample) # efficiency (estimate) of how many samples we get eff = tf.reduce_max(input_tensor=[ztf.to_real(n_produced_new), ztf.to_real(1.)]) / tf.reduce_max( input_tensor=[ztf.to_real(n_total_drawn), ztf.to_real(1.)]) return n, sample_new, n_produced_new, n_total_drawn, eff, is_sampled, weights_scaling efficiency_estimation = ztf.to_real(efficiency_estimation) weights_scaling = ztf.constant(0.) loop_vars = ( n, sample, inital_n_produced, initial_n_drawn, efficiency_estimation, initial_is_sampled, weights_scaling) sample_array = tf.while_loop(cond=not_enough_produced, body=sample_body, # paraopt loop_vars=loop_vars, swap_memory=True, parallel_iterations=1, back_prop=False)[1] # backprop not needed here new_sample = sample_array.stack() if multiple_limits: new_sample = tf.random.shuffle(new_sample) # to make sure, randomly remove and not biased. if dynamic_array_shape: # if not dynamic we produced exact n -> no need to cut new_sample = new_sample[:n, :] # cutting away to many produced # if no failure, uncomment both for improvement of shape inference, but what if n is tensor? # with suppress(AttributeError): # if n_samples_int is not a numpy object # new_sample.set_shape((n_samples_int, n_dims)) return new_sample
[docs]def extract_extended_pdfs(pdfs: Union[Iterable[ZfitPDF], ZfitPDF]) -> List[ZfitPDF]: """Return all extended pdfs that are daughters. Args: pdfs (Iterable[pdfs]): Returns: List[pdfs]: """ from ..models.functor import BaseFunctor pdfs = convert_to_container(pdfs) indep_pdfs = [] for pdf in pdfs: if not pdf.is_extended: continue elif isinstance(pdf, BaseFunctor): if all(pdf.pdfs_extended): indep_pdfs.extend(extract_extended_pdfs(pdfs=pdf.pdfs)) elif not any(pdf.pdfs_extended): indep_pdfs.append(pdf) else: assert False, "Should not reach this point, wrong assumptions. Please report bug." else: # extended, but not a functor indep_pdfs.append(pdf) return indep_pdfs
[docs]def extended_sampling(pdfs: Union[Iterable[ZfitPDF], ZfitPDF], limits: Space) -> tf.Tensor: """Create a sample from extended pdfs by sampling poissonian using the yield. Args: pdfs (iterable[ZfitPDF]): limits (:py:class:`~zfit.Space`): Returns: Union[tf.Tensor]: """ samples = [] pdfs = convert_to_container(pdfs) pdfs = extract_extended_pdfs(pdfs) for pdf in pdfs: n = tf.random.poisson(lam=pdf.get_yield(), shape=(), dtype=ztypes.float) n = tf.cast(n, dtype=tf.int64) sample = pdf._single_hook_sample(limits=limits, n=n) # sample.set_shape((n, limits.n_obs)) samples.append(sample) samples = tf.concat(samples, axis=0) return samples