#!/usr/bin/env python3
"""
Utilities for analytic description of parameter-dependent model attributes.
This module provides classes and helper functions useful for least-squares
regression and general handling of model functions.
"""
from itertools import chain, combinations
import logging
import numpy as np
import os
import re
from scipy import optimize
from .utils import is_numeric, param_to_ndarray
logger = logging.getLogger(__name__)
def powerset(iterable):
"""
Return powerset of `iterable` elements.
Example: `powerset([1, 2])` -> `[(), (1), (2), (1, 2)]`
"""
s = list(iterable)
return chain.from_iterable(combinations(s, r) for r in range(len(s) + 1))
def gplearn_to_function(function_str: str):
"""
Convert gplearn-style function string to Python function.
Takes a function string like "mul(add(X0, X1), X2)" and returns
a Python function implementing the specified behaviour,
e.g. "lambda x, y, z: (x + y) * z".
Supported functions:
add -- x + y
sub -- x - y
mul -- x * y
div -- x / y if |y| > 0.001, otherwise 1
sqrt -- sqrt(|x|)
log -- log(|x|) if |x| > 0.001, otherwise 0
inv -- 1 / x if |x| > 0.001, otherwise 0
"""
eval_globals = {
"add": lambda x, y: x + y,
"sub": lambda x, y: x - y,
"mul": lambda x, y: x * y,
"div": lambda x, y: np.divide(x, y) if np.abs(y) > 0.001 else 1.0,
"sqrt": lambda x: np.sqrt(np.abs(x)),
"log": lambda x: np.log(np.abs(x)) if np.abs(x) > 0.001 else 0.0,
"inv": lambda x: 1.0 / x if np.abs(x) > 0.001 else 0.0,
}
last_arg_index = 0
for i in range(0, 100):
if function_str.find("X{:d}".format(i)) >= 0:
last_arg_index = i
arg_list = []
for i in range(0, last_arg_index + 1):
arg_list.append("X{:d}".format(i))
eval_str = "lambda {}, *whatever: {}".format(",".join(arg_list), function_str)
logger.debug(eval_str)
return eval(eval_str, eval_globals)
class ParamFunction:
"""
A one-dimensional model function, ready for least squares optimization and similar.
Supports validity checks (e.g. if it is undefined for x <= 0) and an
error measure.
"""
def __init__(self, param_function, validation_function, num_vars, repr_str=None):
"""
Create function object suitable for regression analysis.
This documentation assumes that 1-dimensional functions
(-> single float as model input) are used. However, n-dimensional
functions (-> list of float as model input) are also supported.
:param param_function: regression function (reg_param, model_param) -> float.
reg_param is a list of regression variable values,
model_param is the model input value (float).
Example: `lambda rp, mp: rp[0] + rp[1] * mp`
:param validation_function: function used to check whether param_function
is defined for a given model_param. Signature:
model_param -> bool
Example: `lambda mp: mp > 0`
:param num_vars: How many regression variables are used by this function,
i.e., the length of param_function's reg_param argument.
"""
self._param_function = param_function
self._validation_function = validation_function
self._num_variables = num_vars
self.repr_str = repr_str
def __repr__(self) -> str:
if self.repr_str:
return f"ParamFunction<{self.repr_str}>"
return f"ParamFunction<{self._param_function}, {self.validation_function}, {self._num_variables}>"
def is_valid(self, arg: float) -> bool:
"""
Check whether the regression function is defined for the given argument.
:param arg: argument (e.g. model parameter) to check for
:returns: True iff the function is defined for `arg`
"""
return self._validation_function(arg)
def eval(self, param: list, arg: float) -> float:
"""
Evaluate regression function.
:param param: regression variable values (list of float)
:param arg: model input (float)
:returns: regression function output (float)
"""
return self._param_function(param, arg)
def error_function(self, P: list, X: float, y: float) -> float:
"""
Calculate model error.
:param P: regression variables as returned by optimization (list of float)
:param X: model input (float)
:param y: expected model output / ground truth for model input (float)
:returns: Deviation between model output and ground truth (float)
"""
return self._param_function(P, X) - y
class NormalizationFunction:
"""
Wrapper for parameter normalization functions used in YAML PTA/DFA models.
"""
def __init__(self, function_str: str):
"""
Create a new normalization function from `function_str`.
:param function_str: Function string. Must use the single argument
`param` and return a float.
"""
self._function_str = function_str
self._function = eval("lambda param: " + function_str)
def eval(self, param_value: float) -> float:
"""
Evaluate the normalization function and return its output.
:param param_value: Parameter value
"""
return self._function(param_value)
class ModelFunction:
always_predictable = False
has_eval_arr = False
"""
Encapsulates the behaviour of a single model attribute, e.g. TX power or write duration.
The behaviour may be constant or depend on a number of factors. Modelfunction is a virtual base class,
individuel decendents describe actual behaviour.
Common attributes:
:param value: median data value
:type value: float
:param value_error: static model value error
:type value_error: dict, optional
:param function_error: model error
:type value_error: dict, optional
"""
def __init__(self, value):
# a model always has a static (median/mean) value. For StaticFunction, it's the only data point.
# For more complex models, it's usede both as fallback in case the model cannot predict the current
# parameter combination, and for use cases requiring static models
self.value = value
# A ModelFunction may track its own accuracy, both of the static value and of the eval() method.
# However, it does not specify how the accuracy was calculated (e.g. which data was used and whether cross-validation was performed)
self.value_error = None
self.function_error = None
def is_predictable(self, param_list):
raise NotImplementedError
def eval(self, param_list):
raise NotImplementedError
def eval_arr(self, params):
raise NotImplementedError
def get_complexity_score(self):
raise NotImplementedError
def eval_mae(self, param_list):
"""Return model Mean Absolute Error (MAE) for `param_list`."""
if self.is_predictable(param_list):
return self.function_error["mae"]
return self.value_error["mae"]
def webconf_function_map(self):
return list()
def to_json(self, **kwargs):
"""Convert model to JSON."""
ret = {
"value": self.value,
"valueError": self.value_error,
"functionError": self.function_error,
}
return ret
@classmethod
def from_json(cls, data):
"""
Create ModelFunction instance from JSON.
Delegates to StaticFunction, SplitFunction, etc. as appropriate.
"""
if data["type"] == "static":
mf = StaticFunction.from_json(data)
elif data["type"] == "split":
mf = SplitFunction.from_json(data)
elif data["type"] == "analytic":
mf = AnalyticFunction.from_json(data)
else:
raise ValueError("Unknown ModelFunction type: " + data["type"])
if "valueError" in data:
mf.value_error = data["valueError"]
if "functionError" in data:
mf.function_error = data["functionError"]
return mf
@classmethod
def from_json_maybe(cls, json_wrapped: dict, attribute: str):
# Legacy Code for PTA / tests. Do not use.
if type(json_wrapped) is dict and attribute in json_wrapped:
# benchmark data obtained before 2021-03-04 uses {"attr": {"static": 0}}
# benchmark data obtained after 2021-03-04 uses {"attr": {"type": "static", "value": 0}} or {"attr": None}
# from_json expects the latter.
if json_wrapped[attribute] is None:
return None
if (
"static" in json_wrapped[attribute]
and "type" not in json_wrapped[attribute]
):
json_wrapped[attribute]["type"] = "static"
json_wrapped[attribute]["value"] = json_wrapped[attribute]["static"]
json_wrapped[attribute].pop("static")
return cls.from_json(json_wrapped[attribute])
return StaticFunction(0)
class StaticFunction(ModelFunction):
always_predictable = True
has_eval_arr = True
def is_predictable(self, param_list=None):
"""
Return whether the model function can be evaluated on the given parameter values.
For a StaticFunction, this is always the case (i.e., this function always returns true).
"""
return True
def eval(self, param_list=None):
"""
Evaluate model function with specified param/arg values.
Far a Staticfunction, this is just the static value
"""
return self.value
def eval_arr(self, params):
return [self.value for p in params]
def get_complexity_score(self):
return 1
def to_json(self, **kwargs):
ret = super().to_json(**kwargs)
ret.update({"type": "static", "value": self.value})
return ret
def to_dot(self, pydot, graph, feature_names, parent=None):
graph.add_node(
pydot.Node(str(id(self)), label=f"{self.value:.2f}", shape="rectangle")
)
@classmethod
def from_json(cls, data):
assert data["type"] == "static"
return cls(data["value"])
def __repr__(self):
return f"StaticFunction({self.value})"
class SplitFunction(ModelFunction):
def __init__(self, value, param_index, child):
super().__init__(value)
self.param_index = param_index
self.child = child
def is_predictable(self, param_list):
"""
Return whether the model function can be evaluated on the given parameter values.
The first value corresponds to the lexically first model parameter, etc.
All parameters must be set, not just the ones this function depends on.
Returns False iff a parameter the function depends on is not numeric
(e.g. None).
"""
param_value = param_list[self.param_index]
if param_value in self.child:
return self.child[param_value].is_predictable(param_list)
return all(
map(lambda child: child.is_predictable(param_list), self.child.values())
)
def eval(self, param_list):
param_value = param_list[self.param_index]
if param_value in self.child:
return self.child[param_value].eval(param_list)
return np.mean(
list(map(lambda child: child.eval(param_list), self.child.values()))
)
def webconf_function_map(self):
ret = list()
for child in self.child.values():
ret.extend(child.webconf_function_map())
return ret
def to_json(self, **kwargs):
ret = super().to_json(**kwargs)
with_param_name = kwargs.get("with_param_name", False)
param_names = kwargs.get("param_names", list())
update = {
"type": "split",
"paramIndex": self.param_index,
"child": dict([[k, v.to_json(**kwargs)] for k, v in self.child.items()]),
}
if with_param_name and param_names:
update["paramName"] = param_names[self.param_index]
ret.update(update)
return ret
def get_number_of_nodes(self):
ret = 1
for v in self.child.values():
if type(v) is SplitFunction:
ret += v.get_number_of_nodes()
else:
ret += 1
return ret
def get_max_depth(self):
ret = [0]
for v in self.child.values():
if type(v) is SplitFunction:
ret.append(v.get_max_depth())
return 1 + max(ret)
def get_number_of_leaves(self):
ret = 0
for v in self.child.values():
if type(v) is SplitFunction:
ret += v.get_number_of_leaves()
else:
ret += 1
return ret
def get_complexity_score(self):
if not self.child:
return 1
ret = 1
for v in self.child.values():
ret += v.get_complexity_score()
return ret
def to_dot(self, pydot, graph, feature_names, parent=None):
try:
label = feature_names[self.param_index]
except IndexError:
label = f"param{self.param_index}"
graph.add_node(pydot.Node(str(id(self)), label=label))
for key, child in self.child.items():
child.to_dot(pydot, graph, feature_names, str(id(self)))
graph.add_edge(pydot.Edge(str(id(self)), str(id(child)), label=key))
@classmethod
def from_json(cls, data):
assert data["type"] == "split"
self = cls(data["value"], data["paramIndex"], dict())
for k, v in data["child"].items():
self.child[k] = ModelFunction.from_json(v)
return self
def __repr__(self):
return f"SplitFunction<{self.value}, param_index={self.param_index}>"
class SubstateFunction(ModelFunction):
def __init__(self, value, sequence_by_count, count_model, sub_model):
super().__init__(value)
self.sequence_by_count = sequence_by_count
self.count_model = count_model
self.sub_model = sub_model
# only used by analyze-archive model quality evaluation. Not serialized.
self.static_duration = None
def is_predictable(self, param_list):
substate_count = round(self.count_model.eval(param_list))
return substate_count in self.sequence_by_count
def eval(self, param_list, duration=None):
substate_count = round(self.count_model.eval(param_list))
cumulative_energy = 0
total_duration = 0
substate_model, _ = self.sub_model.get_fitted()
substate_sequence = self.sequence_by_count[substate_count]
for i, sub_name in enumerate(substate_sequence):
sub_duration = substate_model(sub_name, "duration", param=param_list)
sub_power = substate_model(sub_name, "power", param=param_list)
if i == substate_count - 1:
if duration is not None:
sub_duration = duration - total_duration
elif self.static_duration is not None:
sub_duration = self.static_duration - total_duration
cumulative_energy += sub_power * sub_duration
total_duration += sub_duration
return cumulative_energy / total_duration
def to_json(self, **kwargs):
ret = super().to_json(**kwargs)
ret.update(
{
"type": "substate",
"sequence": self.sequence_by_count,
"countModel": self.count_model.to_json(**kwargs),
"subModel": self.sub_model.to_json(**kwargs),
}
)
return ret
@classmethod
def from_json(cls, data):
assert data["type"] == "substate"
raise NotImplementedError
def __repr__(self):
return "SubstateFunction"
class SKLearnRegressionFunction(ModelFunction):
always_predictable = True
has_eval_arr = True
def __init__(self, value, regressor, categorial_to_index, ignore_index):
super().__init__(value)
self.regressor = regressor
self.categorial_to_index = categorial_to_index
self.ignore_index = ignore_index
def is_predictable(self, param_list=None):
"""
Return whether the model function can be evaluated on the given parameter values.
For a StaticFunction, this is always the case (i.e., this function always returns true).
"""
return True
def eval(self, param_list=None):
"""
Evaluate model function with specified param/arg values.
Far a Staticfunction, this is just the static value
"""
if param_list is None:
return self.value
actual_param_list = list()
for i, param in enumerate(param_list):
if not self.ignore_index[i]:
if i in self.categorial_to_index:
try:
actual_param_list.append(self.categorial_to_index[i][param])
except KeyError:
# param was not part of training data. substitute an unused scalar.
# Note that all param values which were not part of training data map to the same scalar this way.
# This should be harmless.
actual_param_list.append(
max(self.categorial_to_index[i].values()) + 1
)
else:
actual_param_list.append(int(param))
predictions = self.regressor.predict(np.array([actual_param_list]))
if predictions.shape == (1,):
return predictions[0]
return predictions
def eval_arr(self, params):
actual_params = list()
for param_tuple in params:
actual_param_list = list()
for i, param in enumerate(param_tuple):
if not self.ignore_index[i]:
if i in self.categorial_to_index:
try:
actual_param_list.append(self.categorial_to_index[i][param])
except KeyError:
# param was not part of training data. substitute an unused scalar.
# Note that all param values which were not part of training data map to the same scalar this way.
# This should be harmless.
actual_param_list.append(
max(self.categorial_to_index[i].values()) + 1
)
else:
actual_param_list.append(int(param))
actual_params.append(actual_param_list)
predictions = self.regressor.predict(np.array(actual_params))
return predictions
class CARTFunction(SKLearnRegressionFunction):
def get_number_of_nodes(self):
return self.regressor.tree_.node_count
def get_number_of_leaves(self):
return self.regressor.tree_.n_leaves
def get_max_depth(self):
return self.regressor.get_depth()
def get_complexity_score(self):
return self.get_number_of_nodes()
def to_json(self, feature_names=None, **kwargs):
import sklearn.tree
self.leaf_id = sklearn.tree._tree.TREE_LEAF
self.feature_names = feature_names
ret = super().to_json(**kwargs)
ret.update(self.recurse_(self.regressor.tree_, 0))
return ret
# recursive function for all nodes:
def recurse_(self, tree, node_id, depth=0):
left_child = tree.children_left[node_id]
right_child = tree.children_right[node_id]
# basic leaf with standard values
# conversion because of numpy
sub_data = {
"functionError": None,
"type": "static",
"value": float(tree.value[node_id]),
"valueError": float(tree.impurity[node_id]),
# "samples": int(tree.n_node_samples[node_id])
}
# if has childs / not a leaf:
if left_child != self.leaf_id or right_child != self.leaf_id:
# sub_data["paramName"] = "X[" + str(self.regressor.tree_.feature[left_child_id]) + "]"
# sub_data["paramIndex"] = int(self.regressor.tree_.feature[left_child_id])
sub_data["paramName"] = self.feature_names[
self.regressor.tree_.feature[node_id]
]
sub_data["paramDecisionValue"] = tree.threshold[node_id]
sub_data["type"] = "scalarSplit"
# child value
if left_child != self.leaf_id:
sub_data["left"] = self.recurse_(tree, left_child, depth=depth + 1)
if right_child != self.leaf_id:
sub_data["right"] = self.recurse_(tree, right_child, depth=depth + 1)
return sub_data
class LMTFunction(SKLearnRegressionFunction):
def get_number_of_nodes(self):
return self.regressor.node_count
def get_number_of_leaves(self):
return len(self.regressor._leaves.keys())
def get_complexity_score(self):
ret = self.get_number_of_nodes() - self.get_number_of_leaves()
for leaf in self.regressor._leaves.values():
ret += len(
list(
filter(lambda x: x > 0, leaf.model.coef_ + [leaf.model.intercept_])
)
)
return ret
def get_max_depth(self):
return max(map(len, self.regressor._leaves.keys())) + 1
class XGBoostFunction(SKLearnRegressionFunction):
def to_json(self, feature_names=None, **kwargs):
import json
tempfile = f"/tmp/xgb{os.getpid()}.json"
self.regressor.get_booster().dump_model(
tempfile, dump_format="json", with_stats=True
)
with open(tempfile, "r") as f:
data = json.load(f)
os.remove(tempfile)
if feature_names:
return list(
map(
lambda tree: self.tree_to_webconf_json(
tree, feature_names, **kwargs
),
data,
)
)
return data
def tree_to_webconf_json(self, tree, feature_names, **kwargs):
ret = dict()
if "children" in tree:
return {
"functionError": None,
"type": "scalarSplit",
"paramName": feature_names[int(tree["split"][1:])],
"paramDecisionValue": tree["split_condition"],
"value": None,
"valueError": None,
"left": self.tree_to_webconf_json(
tree["children"][0], feature_names, **kwargs
),
"right": self.tree_to_webconf_json(
tree["children"][1], feature_names, **kwargs
),
}
else:
return {
"functionError": None,
"type": "static",
"value": tree["leaf"],
"valueError": None,
}
def get_number_of_nodes(self):
return sum(map(self._get_number_of_nodes, self.to_json()))
def _get_number_of_nodes(self, data):
ret = 1
for child in data.get("children", list()):
ret += self._get_number_of_nodes(child)
return ret
def get_number_of_leaves(self):
return sum(map(self._get_number_of_leaves, self.to_json()))
def _get_number_of_leaves(self, data):
if "leaf" in data:
return 1
ret = 0
for child in data.get("children", list()):
ret += self._get_number_of_leaves(child)
return ret
def get_max_depth(self):
return max(map(self._get_max_depth, self.to_json()))
def _get_max_depth(self, data):
ret = [0]
for child in data.get("children", list()):
ret.append(self._get_max_depth(child))
return 1 + max(ret)
def get_complexity_score(self):
return self.get_number_of_nodes()
# first-order linear function (no feature interaction)
class FOLFunction(ModelFunction):
always_predictable = True
def __init__(self, value, parameters, num_args=0):
super().__init__(value)
self.parameter_names = parameters
self._num_args = num_args
self.fit_success = False
def fit(self, param_values, data, ignore_param_indexes=None):
categorial_to_scalar = bool(
int(os.getenv("DFATOOL_PARAM_CATEGORIAL_TO_SCALAR", "0"))
)
second_order = int(os.getenv("DFATOOL_FOL_SECOND_ORDER", "0"))
fit_parameters, categorial_to_index, ignore_index = param_to_ndarray(
param_values,
with_nan=False,
categorial_to_scalar=categorial_to_scalar,
ignore_indexes=ignore_param_indexes,
)
self.categorial_to_index = categorial_to_index
self.ignore_index = ignore_index
fit_parameters = fit_parameters.swapaxes(0, 1)
if second_order:
num_param = fit_parameters.shape[0]
rawbuf = "reg_param[0]"
num_vars = 1
for i in range(num_param):
if second_order == 2:
rawbuf += f" + reg_param[{num_vars}] * model_param[{i}]"
num_vars += 1
for j in range(i + 1, num_param):
rawbuf += f" + reg_param[{num_vars}] * model_param[{i}] * model_param[{j}]"
num_vars += 1
funbuf = "regression_arg(0)"
num_vars = 1
for j, param_name in enumerate(self.parameter_names):
if ignore_index[j]:
continue
else:
if second_order == 2:
funbuf += (
f" + regression_arg({num_vars}) * parameter({param_name})"
)
num_vars += 1
for k in range(j + 1, len(self.parameter_names)):
if ignore_index[j]:
continue
funbuf += f" + regression_arg({num_vars}) * parameter({param_name}) * parameter({self.parameter_names[k]})"
num_vars += 1
else:
num_vars = fit_parameters.shape[0] + 1
rawbuf = "reg_param[0]"
for i in range(1, num_vars):
rawbuf += f" + reg_param[{i}] * model_param[{i-1}]"
funbuf = "regression_arg(0)"
i = 1
for j, param_name in enumerate(self.parameter_names):
if ignore_index[j]:
continue
else:
funbuf += f" + regression_arg({i}) * parameter({param_name})"
i += 1
self.model_function = funbuf
self._function_str = "lambda reg_param, model_param:" + rawbuf
self._function = eval(self._function_str)
error_function = lambda P, X, y: self._function(P, X) - y
self.model_args = list(np.ones((num_vars)))
try:
res = optimize.least_squares(
error_function, self.model_args, args=(fit_parameters, data), xtol=2e-15
)
except ValueError as err:
logger.warning(f"Fit failed: {err} (function: {self.model_function})")
return
if res.status > 0:
self.model_args = res.x
self.fit_success = True
else:
logger.warning(
f"Fit failed: {res.message} (function: {self.model_function})"
)
def is_predictable(self, param_list=None):
"""
Return whether the model function can be evaluated on the given parameter values.
"""
return True
def eval(self, param_list=None):
"""
Evaluate model function with specified param/arg values.
Far a Staticfunction, this is just the static value
"""
if param_list is None:
return self.value
actual_param_list = list()
for i, param in enumerate(param_list):
if not self.ignore_index[i]:
if i in self.categorial_to_index:
try:
actual_param_list.append(self.categorial_to_index[i][param])
except KeyError:
# param was not part of training data. substitute an unused scalar.
# Note that all param values which were not part of training data map to the same scalar this way.
# This should be harmless.
actual_param_list.append(
max(self.categorial_to_index[i].values()) + 1
)
else:
actual_param_list.append(int(param))
try:
return self._function(self.model_args, actual_param_list)
except FloatingPointError as e:
logger.error(
f"{e} when predicting {self._function_str}({self.model_args}, {actual_param_list}) for {param_list}, returning static value"
)
return self.value
except TypeError as e:
logger.error(
f"{e} when predicting {self._function_str}({self.model_args}, {actual_param_list}) for {param_list}"
)
raise
def get_complexity_score(self):
return len(self.model_args)
def to_json(self, **kwargs):
ret = super().to_json(**kwargs)
ret.update(
{
"type": "analytic",
"functionStr": self.model_function,
"argCount": self._num_args,
"parameterNames": self.parameter_names,
"regressionModel": list(self.model_args),
}
)
return ret
class AnalyticFunction(ModelFunction):
"""
A multi-dimensional model function, generated from a string, which can be optimized using regression.
The function describes a single model attribute (e.g. TX duration or send(...) energy)
and how it is influenced by model parameters such as configured bit rate or
packet length.
"""
def __init__(
self,
value,
function_str,
parameters,
num_args=0,
regression_args=None,
fit_by_param=None,
):
"""
Create a new AnalyticFunction object from a function string.
:param function_str: the function.
Refer to regression variables using regression_arg(123),
to parameters using parameter(name),
and to function arguments (if any) using function_arg(123).
Example: "regression_arg(0) + regression_arg(1) * parameter(txbytes)"
:param parameters: list containing the names of all model parameters,
including those not used in function_str, sorted lexically.
Sorting is mandatory, as parameter indexes (and not names) are used internally.
:param num_args: number of local function arguments, if any. Set to 0 if
the model attribute does not belong to a function or if function
arguments are not included in the model.
:param regression_args: Initial regression variable values,
both for function usage and least squares optimization.
If unset, defaults to [1, 1, 1, ...]
"""
super().__init__(value)
self._parameter_names = parameters
self._num_args = num_args
self.model_function = function_str
rawfunction = function_str
self._dependson = [False] * (len(parameters) + num_args)
self.fit_success = False
self.fit_by_param = fit_by_param
if type(function_str) == str:
num_vars_re = re.compile(r"regression_arg\(([0-9]+)\)")
num_vars = max(map(int, num_vars_re.findall(function_str))) + 1
for i in range(len(parameters)):
if rawfunction.find("parameter({})".format(parameters[i])) >= 0:
self._dependson[i] = True
rawfunction = rawfunction.replace(
"parameter({})".format(parameters[i]),
"model_param[{:d}]".format(i),
)
for i in range(0, num_args):
if rawfunction.find("function_arg({:d})".format(i)) >= 0:
self._dependson[len(parameters) + i] = True
rawfunction = rawfunction.replace(
"function_arg({:d})".format(i),
"model_param[{:d}]".format(len(parameters) + i),
)
for i in range(num_vars):
rawfunction = rawfunction.replace(
"regression_arg({:d})".format(i), "reg_param[{:d}]".format(i)
)
self._function_str = rawfunction
self._function = eval("lambda reg_param, model_param: " + rawfunction)
else:
self._function_str = "raise ValueError"
self._function = function_str
if regression_args:
self.model_args = regression_args.copy()
self._fit_success = True
elif type(function_str) == str:
self.model_args = list(np.ones((num_vars)))
else:
self.model_args = []
def get_fit_data(self, by_param):
"""
Return training data suitable for scipy.optimize.least_squares.
:param by_param: measurement data, partitioned by parameter/arg values.
by_param[*] must be a list or 1-D NumPy array containing the ground truth.
The parameter values (dict keys) must be numeric for
all parameters this function depends on -- otherwise, the
corresponding data will be left out. Parameter values must be
ordered according to the order of parameter names used in
the ParamFunction constructor. Argument values (if any) always come after
parameters, in the order of their index in the function signature.
:return: (X, Y, num_valid, num_total):
X -- 2-D NumPy array of parameter combinations (model input).
First dimension is the parameter/argument index, the second
dimension contains its values.
Example: X[0] contains the first parameter's values.
Y -- 1-D NumPy array of training data (desired model output).
num_valid -- amount of distinct parameter values suitable for optimization
num_total -- total amount of distinct parameter values
"""
dimension = len(self._parameter_names) + self._num_args
X = [[] for i in range(dimension)]
Y = []
num_valid = 0
num_total = 0
for key, val in by_param.items():
if len(key) == dimension:
valid = True
num_total += 1
for i in range(dimension):
if self._dependson[i] and not is_numeric(key[i]):
valid = False
if valid:
num_valid += 1
Y.extend(val)
for i in range(dimension):
if self._dependson[i]:
X[i].extend([float(key[i])] * len(val))
else:
X[i].extend([np.nan] * len(val))
else:
logger.warning(
"Invalid parameter key length while gathering fit data. is {}, want {}.".format(
len(key), dimension
)
)
X = np.array(X)
Y = np.array(Y)
return X, Y, num_valid, num_total
def fit(self, by_param):
"""
Fit the function on measurements via least squares regression.
:param by_param: measurement data, partitioned by parameter/arg values
The ground truth is read from by_param[*],
which must be a list or 1-D NumPy array. Parameter values must be
ordered according to the parameter names in the constructor. If
argument values are present, they must come after parameter values
in the order of their appearance in the function signature.
"""
X, Y, num_valid, num_total = self.get_fit_data(by_param)
if num_valid > 2:
error_function = lambda P, X, y: self._function(P, X) - y
try:
res = optimize.least_squares(
error_function, self.model_args, args=(X, Y), xtol=2e-15
)
except ValueError as err:
logger.warning(f"Fit failed: {err} (function: {self.model_function})")
return
if res.status > 0:
self.model_args = res.x
self.fit_success = True
else:
logger.warning(
f"Fit failed: {res.message} (function: {self.model_function})"
)
else:
logger.warning("Insufficient amount of valid parameter keys, cannot fit")
def is_predictable(self, param_list):
"""
Return whether the model function can be evaluated on the given parameter values.
The first value corresponds to the lexically first model parameter, etc.
All parameters must be set, not just the ones this function depends on.
Returns False iff a parameter the function depends on is not numeric
(e.g. None).
"""
for i, param in enumerate(param_list):
if self._dependson[i] and not is_numeric(param):
return False
return True
def eval(self, param_list):
"""
Evaluate model function with specified param/arg values.
:param param_list: parameter values (list of float). First item
corresponds to lexically first parameter, etc.
:param arg_list: argument values (list of float), if arguments are used.
"""
try:
return self._function(self.model_args, param_list)
except FloatingPointError as e:
logger.error(
f"{e} when predicting {self._function_str}({param_list}), returning static value"
)
return self.value
def get_complexity_score(self):
return len(self.model_args)
def webconf_function_map(self):
js_buf = self.model_function
for i in range(len(self.model_args)):
js_buf = js_buf.replace(f"regression_arg({i})", str(self.model_args[i]))
for parameter_name in self._parameter_names:
js_buf = js_buf.replace(
f"parameter({parameter_name})", f"""param["{parameter_name}"]"""
)
for arg_num in range(self._num_args):
js_buf = js_buf.replace(f"function_arg({arg_num})", f"args[{arg_num}]")
js_buf = "(param, args) => " + js_buf.replace("np.", "Math.")
return [(f'"{self.model_function}"', js_buf)]
def to_json(self, **kwargs):
ret = super().to_json(**kwargs)
ret.update(
{
"type": "analytic",
"functionStr": self.model_function,
"argCount": self._num_args,
"parameterNames": self._parameter_names,
"regressionModel": list(self.model_args),
}
)
return ret
def to_dot(self, pydot, graph, feature_names, parent=None):
model_function = self.model_function
for i, arg in enumerate(self.model_args):
model_function = model_function.replace(
f"regression_arg({i})", f"{arg:.2f}"
)
graph.add_node(
pydot.Node(str(id(self)), label=model_function, shape="rectangle")
)
@classmethod
def from_json(cls, data):
assert data["type"] == "analytic"
return cls(
data["value"],
data["functionStr"],
data["parameterNames"],
data["argCount"],
data["regressionModel"],
)
def __repr__(self):
return f"AnalyticFunction<{self.value}, {self.model_function}>"
class analytic:
"""
Utilities for analytic description of parameter-dependent model attributes and regression analysis.
provided functions:
functions -- retrieve pre-defined set of regression function candidates
function_powerset -- combine several per-parameter functions into a single AnalyticFunction
"""
_num0_8 = np.vectorize(lambda x: 8 - bin(int(x)).count("1"))
_num0_16 = np.vectorize(lambda x: 16 - bin(int(x)).count("1"))
_num1 = np.vectorize(lambda x: bin(int(x)).count("1"))
_safe_log = np.vectorize(lambda x: np.log(np.abs(x)) if np.abs(x) > 0.001 else 1.0)
_safe_inv = np.vectorize(lambda x: 1 / x if np.abs(x) > 0.001 else 1.0)
_safe_sqrt = np.vectorize(lambda x: np.sqrt(np.abs(x)))
_function_map = {
"linear": lambda x: x,
"logarithmic": np.log,
"logarithmic1": lambda x: np.log(x + 1),
"exponential": np.exp,
"square": lambda x: x**2,
"inverse": lambda x: 1 / x,
"sqrt": lambda x: np.sqrt(np.abs(x)),
"num0_8": _num0_8,
"num0_16": _num0_16,
"num1": _num1,
"safe_log": lambda x: np.log(np.abs(x)) if np.abs(x) > 0.001 else 1.0,
"safe_inv": lambda x: 1 / x if np.abs(x) > 0.001 else 1.0,
"safe_sqrt": lambda x: np.sqrt(np.abs(x)),
}
@staticmethod
def functions(safe_functions_enabled=False):
"""
Retrieve pre-defined set of regression function candidates.
:param safe_functions_enabled: Include "safe" variants of functions with
limited argument range, e.g. a safe
inverse which returns 1 when dividing by 0.
Returns a dict of functions which are typical for energy/timing
behaviour of embedded hardware, e.g. linear, exponential or inverse
dependency on a configuration setting/runtime variable.
Each function is a ParamFunction object. In most cases, two regression
variables are expected.
"""
functions = {
"linear": ParamFunction(
lambda reg_param, model_param: reg_param[0]
+ reg_param[1] * model_param,
lambda model_param: True,
2,
repr_str="β₀ + β₁ * x",
),
"logarithmic": ParamFunction(
lambda reg_param, model_param: reg_param[0]
+ reg_param[1] * np.log(model_param),
lambda model_param: model_param > 0,
2,
repr_str="β₀ + β₁ * np.log(x)",
),
"logarithmic1": ParamFunction(
lambda reg_param, model_param: reg_param[0]
+ reg_param[1] * np.log(model_param + 1),
lambda model_param: model_param > -1,
2,
repr_str="β₀ + β₁ * np.log(x+1)",
),
"exponential": ParamFunction(
lambda reg_param, model_param: reg_param[0]
+ reg_param[1] * np.exp(model_param),
lambda model_param: model_param <= 64,
2,
repr_str="β₀ + β₁ * np.exp(x)",
),
#'polynomial' : lambda reg_param, model_param: reg_param[0] + reg_param[1] * model_param + reg_param[2] * model_param ** 2,
"square": ParamFunction(
lambda reg_param, model_param: reg_param[0]
+ reg_param[1] * model_param**2,
lambda model_param: True,
2,
repr_str="β₀ + β₁ * x²",
),
"inverse": ParamFunction(
lambda reg_param, model_param: reg_param[0]
+ reg_param[1] / model_param,
lambda model_param: model_param != 0,
2,
repr_str="β₀ + β₁ * 1/x",
),
"sqrt": ParamFunction(
lambda reg_param, model_param: reg_param[0]
+ reg_param[1] * np.sqrt(model_param),
lambda model_param: model_param >= 0,
2,
repr_str="β₀ + β₁ * np.sqrt(x)",
),
# "num0_8": ParamFunction(
# lambda reg_param, model_param: reg_param[0]
# + reg_param[1] * analytic._num0_8(model_param),
# lambda model_param: True,
# 2,
# ),
# "num0_16": ParamFunction(
# lambda reg_param, model_param: reg_param[0]
# + reg_param[1] * analytic._num0_16(model_param),
# lambda model_param: True,
# 2,
# ),
# "num1": ParamFunction(
# lambda reg_param, model_param: reg_param[0]
# + reg_param[1] * analytic._num1(model_param),
# lambda model_param: True,
# 2,
# ),
}
if safe_functions_enabled or bool(
int(os.getenv("DFATOOL_REGRESSION_SAFE_FUNCTIONS", "0"))
):
functions.pop("logarithmic1")
functions.pop("logarithmic")
functions["safe_log"] = ParamFunction(
lambda reg_param, model_param: reg_param[0]
+ reg_param[1] * analytic._safe_log(model_param),
lambda model_param: True,
2,
repr_str="β₀ + β₁ * safe_log(x)",
)
functions.pop("inverse")
functions["safe_inv"] = ParamFunction(
lambda reg_param, model_param: reg_param[0]
+ reg_param[1] * analytic._safe_inv(model_param),
lambda model_param: True,
2,
repr_str="β₀ + β₁ * safe(1/x)",
)
functions.pop("sqrt")
functions["safe_sqrt"] = ParamFunction(
lambda reg_param, model_param: reg_param[0]
+ reg_param[1] * analytic._safe_sqrt(model_param),
lambda model_param: True,
2,
repr_str="β₀ + β₁ * safe_sqrt(x)",
)
if bool(int(os.getenv("DFATOOL_FIT_LINEAR_ONLY", "0"))):
functions = {"linear": functions["linear"]}
return functions
@staticmethod
def _fmap(reference_type, reference_name, function_type):
"""Map arg/parameter name and best-fit function name to function text suitable for AnalyticFunction."""
ref_str = "{}({})".format(reference_type, reference_name)
if function_type == "linear":
return ref_str
if function_type == "logarithmic":
return "np.log({})".format(ref_str)
if function_type == "logarithmic1":
return "np.log({} + 1)".format(ref_str)
if function_type == "exponential":
return "np.exp({})".format(ref_str)
if function_type == "exponential":
return "np.exp({})".format(ref_str)
if function_type == "square":
return "({})**2".format(ref_str)
if function_type == "inverse":
return "1/({})".format(ref_str)
if function_type == "sqrt":
return "np.sqrt({})".format(ref_str)
return "analytic._{}({})".format(function_type, ref_str)
@staticmethod
def function_powerset(fit_results, parameter_names, num_args=0):
"""
Combine per-parameter regression results into a single multi-dimensional function.
:param fit_results: results dict. One element per parameter, each containing
a dict of the form {'best' : name of function with best fit}.
Must not include parameters which do not influence the model attribute.
Example: {'txpower' : {'best': 'exponential'}}
:param parameter_names: Parameter names, including those left
out in fit_results because they do not influence the model attribute.
Must be sorted lexically.
Example: ['bitrate', 'txpower']
:param num_args: number of local function arguments, if any. Set to 0 if
the model attribute does not belong to a function or if function
arguments are not included in the model.
Returns an AnalyticFunction instantce corresponding to the combined
function.
"""
buf = "0"
arg_idx = 0
for combination in powerset(fit_results.items()):
buf += " + regression_arg({:d})".format(arg_idx)
arg_idx += 1
for function_item in combination:
if is_numeric(function_item[0]):
buf += " * {}".format(
analytic._fmap(
"function_arg", function_item[0], function_item[1]["best"]
)
)
else:
buf += " * {}".format(
analytic._fmap(
"parameter", function_item[0], function_item[1]["best"]
)
)
return AnalyticFunction(
None, buf, parameter_names, num_args, fit_by_param=fit_results
)