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from itertools import chain, combinations
import numpy as np
import re
from scipy import optimize
from utils import is_numeric
arg_support_enabled = True
def powerset(iterable):
s = list(iterable)
return chain.from_iterable(combinations(s, r) for r in range(len(s)+1))
class ParamFunction:
def __init__(self, param_function, validation_function, num_vars):
self._param_function = param_function
self._validation_function = validation_function
self._num_variables = num_vars
def is_valid(self, arg):
return self._validation_function(arg)
def eval(self, param, args):
return self._param_function(param, args)
def error_function(self, P, X, y):
return self._param_function(P, X) - y
class AnalyticFunction:
def __init__(self, function_str, parameters, num_args, verbose = True, regression_args = None):
self._parameter_names = parameters
self._num_args = num_args
self._model_str = function_str
rawfunction = function_str
self._dependson = [False] * (len(parameters) + num_args)
self.fit_success = False
self.verbose = verbose
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._regression_args = regression_args.copy()
self._fit_success = True
elif type(function_str) == str:
self._regression_args = list(np.ones((num_vars)))
else:
self._regression_args = []
def get_fit_data(self, by_param, state_or_tran, model_attribute):
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 key[0] == state_or_tran and len(key[1]) == dimension:
valid = True
num_total += 1
for i in range(dimension):
if self._dependson[i] and not is_numeric(key[1][i]):
valid = False
if valid:
num_valid += 1
Y.extend(val[model_attribute])
for i in range(dimension):
if self._dependson[i]:
X[i].extend([float(key[1][i])] * len(val[model_attribute]))
else:
X[i].extend([np.nan] * len(val[model_attribute]))
elif key[0] == state_or_tran and len(key[1]) != dimension:
vprint(self.verbose, '[W] Invalid parameter key length while gathering fit data for {}/{}. is {}, want {}.'.format(state_or_tran, model_attribute, len(key[1]), dimension))
X = np.array(X)
Y = np.array(Y)
return X, Y, num_valid, num_total
def fit(self, by_param, state_or_tran, model_attribute):
X, Y, num_valid, num_total = self.get_fit_data(by_param, state_or_tran, model_attribute)
if num_valid > 2:
error_function = lambda P, X, y: self._function(P, X) - y
try:
res = optimize.least_squares(error_function, self._regression_args, args=(X, Y), xtol=2e-15)
except ValueError as err:
vprint(self.verbose, '[W] Fit failed for {}/{}: {} (function: {})'.format(state_or_tran, model_attribute, err, self._model_str))
return
if res.status > 0:
self._regression_args = res.x
self.fit_success = True
else:
vprint(self.verbose, '[W] Fit failed for {}/{}: {} (function: {})'.format(state_or_tran, model_attribute, res.message, self._model_str))
else:
vprint(self.verbose, '[W] Insufficient amount of valid parameter keys, cannot fit {}/{}'.format(state_or_tran, model_attribute))
def is_predictable(self, param_list):
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, arg_list = []):
if len(self._regression_args) == 0:
return self._function(param_list, arg_list)
return self._function(self._regression_args, param_list)
class analytic:
_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.)
_safe_inv = np.vectorize(lambda x: 1 / x if np.abs(x) > 0.001 else 1.)
_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.,
'safe_inv' : lambda x: 1 / x if np.abs(x) > 0.001 else 1.,
'safe_sqrt': lambda x: np.sqrt(np.abs(x)),
}
def functions(safe_functions_enabled = False):
functions = {
'linear' : ParamFunction(
lambda reg_param, model_param: reg_param[0] + reg_param[1] * model_param,
lambda model_param: True,
2
),
'logarithmic' : ParamFunction(
lambda reg_param, model_param: reg_param[0] + reg_param[1] * np.log(model_param),
lambda model_param: model_param > 0,
2
),
'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
),
'exponential' : ParamFunction(
lambda reg_param, model_param: reg_param[0] + reg_param[1] * np.exp(model_param),
lambda model_param: model_param <= 64,
2
),
#'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
),
'inverse' : ParamFunction(
lambda reg_param, model_param: reg_param[0] + reg_param[1] / model_param,
lambda model_param: model_param != 0,
2
),
'sqrt' : ParamFunction(
lambda reg_param, model_param: reg_param[0] + reg_param[1] * np.sqrt(model_param),
lambda model_param: model_param >= 0,
2
),
'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:
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
)
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
)
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
)
return functions
def _fmap(reference_type, reference_name, function_type):
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)
def function_powerset(function_descriptions, parameter_names, num_args):
buf = '0'
arg_idx = 0
for combination in powerset(function_descriptions.items()):
buf += ' + regression_arg({:d})'.format(arg_idx)
arg_idx += 1
for function_item in combination:
if arg_support_enabled and 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(buf, parameter_names, num_args)
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