refactor function code into separate file to solve circular import

5 files changed, 292 insertions, 260 deletions

diff --git a/bin/analyze-archive.py b/bin/analyze-archive.py
index 821c413..c46ffc9 100755
--- a/bin/analyze-archive.py
+++ b/bin/analyze-archive.py
@@ -1,6 +1,7 @@
 #!/usr/bin/env python3
 
 import getopt
+import json
 import plotter
 import re
 import sys
@@ -92,12 +93,14 @@ if __name__ == '__main__':
     function_override = {}
     show_models = []
     show_quality = []
+    hwmodel = None
+    energymodel_export_file = None
 
     try:
         optspec = (
             'plot-unparam= plot-param= show-models= show-quality= '
             'ignored-trace-indexes= discard-outliers= function-override= '
-            'with-safe-functions'
+            'with-safe-functions hwmodel= export-energymodel='
         )
         raw_opts, args = getopt.getopt(sys.argv[1:], "", optspec.split(' '))
 
@@ -127,6 +130,10 @@ if __name__ == '__main__':
             if 'with-safe-functions' in opts:
                 safe_functions_enabled = True
 
+            if 'hwmodel' in opts:
+                with open(opts['hwmodel'], 'r') as f:
+                    hwmodel = json.load(f)
+
     except getopt.GetoptError as err:
         print(err)
         sys.exit(2)
@@ -137,7 +144,8 @@ if __name__ == '__main__':
     model = EnergyModel(preprocessed_data,
         ignore_trace_indexes = ignored_trace_indexes,
         discard_outliers = discard_outliers,
-        function_override = function_override)
+        function_override = function_override,
+        hwmodel = hwmodel)
 
 
     if 'plot-unparam' in opts:
@@ -208,4 +216,13 @@ if __name__ == '__main__':
                 function = None
             plotter.plot_param(model, state_or_trans, attribute, model.param_index(param_name), extra_function=function)
 
+    if 'export-energymodel' in opts:
+        if not hwmodel:
+            print('[E] --export-energymodel requires --hwmodel to be set')
+            sys.exit(1)
+        json_model = model.to_json()
+        with open(opts['export-energymodel'], 'w') as f:
+            json.dump(json_model, f, indent = 2, sort_keys = True)
+
+
     sys.exit(0)
diff --git a/lib/automata.py b/lib/automata.py
index 5e80ad6..e59c1ed 100755
--- a/lib/automata.py
+++ b/lib/automata.py
@@ -1,4 +1,4 @@
-from dfatool import AnalyticFunction
+from functions import AnalyticFunction
 
 def _parse_function(input_function):
     if type('input_function') == 'str':
diff --git a/lib/dfatool.py b/lib/dfatool.py
index 896dc12..0b2260d 100755
--- a/lib/dfatool.py
+++ b/lib/dfatool.py
@@ -1,7 +1,6 @@
 #!/usr/bin/env python3
 
 import csv
-from itertools import chain, combinations
 import io
 import json
 import numpy as np
@@ -13,6 +12,9 @@ import struct
 import sys
 import tarfile
 from multiprocessing import Pool
+from automata import PTA
+from functions import analytic
+from utils import is_numeric
 
 arg_support_enabled = True
 
@@ -20,15 +22,6 @@ def running_mean(x, N):
     cumsum = np.cumsum(np.insert(x, 0, 0))
     return (cumsum[N:] - cumsum[:-N]) / N
 
-def is_numeric(n):
-    if n == None:
-        return False
-    try:
-        int(n)
-        return True
-    except ValueError:
-        return False
-
 def soft_cast_int(n):
     if n == None or n == '':
         return None
@@ -145,10 +138,6 @@ def regression_measures(predicted, actual):
 
     return measures
 
-def powerset(iterable):
-    s = list(iterable)
-    return chain.from_iterable(combinations(s, r) for r in range(len(s)+1))
-
 class Keysight:
 
     def __init__(self):
@@ -448,248 +437,6 @@ def _param_slice_eq(a, b, index):
         return True
     return False
 
-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 = None
-
-    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 self._regression_args == None:
-            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)
 
 def _try_fits_parallel(arg):
     return {
@@ -837,7 +584,7 @@ def _corr_by_param(by_name, state_or_trans, key, param_index):
 
 class EnergyModel:
 
-    def __init__(self, preprocessed_data, ignore_trace_indexes = None, discard_outliers = None, function_override = {}, verbose = True, use_corrcoef = False):
+    def __init__(self, preprocessed_data, ignore_trace_indexes = None, discard_outliers = None, function_override = {}, verbose = True, use_corrcoef = False, hwmodel = None):
         self.traces = preprocessed_data
         self.by_name = {}
         self.by_param = {}
@@ -851,6 +598,7 @@ class EnergyModel:
         self._use_corrcoef = use_corrcoef
         self.function_override = function_override
         self.verbose = verbose
+        self.hwmodel = hwmodel
         if discard_outliers != None:
             self._compute_outlier_stats(ignore_trace_indexes, discard_outliers)
         for run in self.traces:
@@ -1158,6 +906,11 @@ class EnergyModel:
 
         return model_getter, info_getter
 
+    def to_json(self):
+        _, param_info = self.get_fitted()
+        pta = PTA.from_json(self.hwmodel)
+        pta.update(param_info)
+        return pta.to_json()
 
     def states(self):
         return sorted(list(filter(lambda k: self.by_name[k]['isa'] == 'state', self.by_name.keys())))
diff --git a/lib/functions.py b/lib/functions.py
new file mode 100644
index 0000000..fd9063f
--- /dev/null
+++ b/lib/functions.py
@@ -0,0 +1,254 @@
+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)
diff --git a/lib/utils.py b/lib/utils.py
new file mode 100644
index 0000000..405d148
--- /dev/null
+++ b/lib/utils.py
@@ -0,0 +1,8 @@
+def is_numeric(n):
+    if n == None:
+        return False
+    try:
+        int(n)
+        return True
+    except ValueError:
+        return False