Source code for pybamm.parameters.parameter_values

#
# Parameter values for a simulation
#
import numpy as np
import pybamm
import numbers
from pprint import pformat
from collections import defaultdict


[docs] class ParameterValues: """ The parameter values for a simulation. Note that this class does not inherit directly from the python dictionary class as this causes issues with saving and loading simulations. Parameters ---------- values : dict or string Explicit set of parameters, or reference to an inbuilt parameter set If string and matches one of the inbuilt parameter sets, returns that parameter set. Examples -------- >>> values = {"some parameter": 1, "another parameter": 2} >>> param = pybamm.ParameterValues(values) >>> param["some parameter"] 1 >>> param = pybamm.ParameterValues("Marquis2019") >>> param["Reference temperature [K]"] 298.15 """ def __init__(self, values, chemistry=None): if chemistry is not None: raise ValueError( "The 'chemistry' keyword argument has been deprecated. " "Call `ParameterValues` with a dictionary dictionary of " "parameter values, or the name of a parameter set (string), " "as the single argument, e.g. `ParameterValues('Chen2020')`.", ) # add physical constants as default values self._dict_items = pybamm.FuzzyDict( { "Ideal gas constant [J.K-1.mol-1]": pybamm.constants.R.value, "Faraday constant [C.mol-1]": pybamm.constants.F.value, "Boltzmann constant [J.K-1]": pybamm.constants.k_b.value, "Electron charge [C]": pybamm.constants.q_e.value, } ) if isinstance(values, (dict, ParameterValues)): # remove the "chemistry" key if it exists values.pop("chemistry", None) self.update(values, check_already_exists=False) else: # Check if values is a named parameter set if isinstance(values, str) and values in pybamm.parameter_sets.keys(): values = pybamm.parameter_sets[values] values.pop("chemistry", None) self.update(values, check_already_exists=False) else: raise ValueError("Invalid Parameter Value") # Initialise empty _processed_symbols dict (for caching) self._processed_symbols = {} # save citations if "citations" in self._dict_items: for citation in self._dict_items["citations"]: pybamm.citations.register(citation)
[docs] @staticmethod def create_from_bpx(filename, target_soc=1): """ Parameters ---------- filename: str The filename of the bpx file target_soc : float, optional Target state of charge. Must be between 0 and 1. Default is 1. Returns ------- ParameterValues A parameter values object with the parameters in the bpx file """ if target_soc < 0 or target_soc > 1: raise ValueError("Target SOC should be between 0 and 1") from bpx import parse_bpx_file, get_electrode_concentrations from bpx.schema import ElectrodeBlended, ElectrodeBlendedSPM from .bpx import _bpx_to_param_dict # parse bpx bpx = parse_bpx_file(filename) pybamm_dict = _bpx_to_param_dict(bpx) if "Open-circuit voltage at 0% SOC [V]" not in pybamm_dict: pybamm_dict["Open-circuit voltage at 0% SOC [V]"] = pybamm_dict[ "Lower voltage cut-off [V]" ] pybamm_dict["Open-circuit voltage at 100% SOC [V]"] = pybamm_dict[ "Upper voltage cut-off [V]" ] # probably should put a warning here to indicate we are going # ahead with the low voltage limit. # get initial concentrations based on SOC # Note: we cannot set SOC for blended electrodes, # see https://github.com/pybamm-team/PyBaMM/issues/2682 bpx_neg = bpx.parameterisation.negative_electrode bpx_pos = bpx.parameterisation.positive_electrode if isinstance(bpx_neg, (ElectrodeBlended, ElectrodeBlendedSPM)) or isinstance( bpx_pos, (ElectrodeBlended, ElectrodeBlendedSPM) ): pybamm.logger.warning( "Initial concentrations cannot be set using stoichiometry limits for " "blend electrodes. Please set the initial concentrations manually." ) else: c_n_init, c_p_init = get_electrode_concentrations(target_soc, bpx) pybamm_dict["Initial concentration in negative electrode [mol.m-3]"] = ( c_n_init ) pybamm_dict["Initial concentration in positive electrode [mol.m-3]"] = ( c_p_init ) return pybamm.ParameterValues(pybamm_dict)
def __getitem__(self, key): try: return self._dict_items[key] except KeyError as err: if ( "Exchange-current density for lithium metal electrode [A.m-2]" in err.args[0] and "Exchange-current density for plating [A.m-2]" in self._dict_items ): raise KeyError( "'Exchange-current density for plating [A.m-2]' has been renamed " "to 'Exchange-current density for lithium metal electrode [A.m-2]' " "when referring to the reaction at the surface of a lithium metal " "electrode. This is to avoid confusion with the exchange-current " "density for the lithium plating reaction in a porous negative " "electrode. To avoid this error, change your parameter file to use " "the new name." ) from err else: raise err
[docs] def get(self, key, default=None): """Return item corresponding to key if it exists, otherwise return default""" try: return self._dict_items[key] except KeyError: return default
def __setitem__(self, key, value): """Call the update functionality when doing a setitem""" self.update({key: value}) def __delitem__(self, key): del self._dict_items[key] def __repr__(self): return pformat(self._dict_items, width=1) def __eq__(self, other): return self._dict_items == other._dict_items
[docs] def keys(self): """Get the keys of the dictionary""" return self._dict_items.keys()
[docs] def values(self): """Get the values of the dictionary""" return self._dict_items.values()
[docs] def items(self): """Get the items of the dictionary""" return self._dict_items.items()
def pop(self, *args, **kwargs): self._dict_items.pop(*args, **kwargs)
[docs] def copy(self): """Returns a copy of the parameter values. Makes sure to copy the internal dictionary.""" new_copy = ParameterValues(self._dict_items.copy()) return new_copy
[docs] def search(self, key, print_values=True): """ Search dictionary for keys containing 'key'. See :meth:`pybamm.FuzzyDict.search()`. """ return self._dict_items.search(key, print_values)
[docs] def update(self, values, check_conflict=False, check_already_exists=True, path=""): """ Update parameter dictionary, while also performing some basic checks. Parameters ---------- values : dict Dictionary of parameter values to update parameter dictionary with check_conflict : bool, optional Whether to check that a parameter in `values` has not already been defined in the parameter class when updating it, and if so that its value does not change. This is set to True during initialisation, when parameters are combined from different sources, and is False by default otherwise check_already_exists : bool, optional Whether to check that a parameter in `values` already exists when trying to update it. This is to avoid cases where an intended change in the parameters is ignored due a typo in the parameter name, and is True by default but can be manually overridden. path : string, optional Path from which to load functions """ # check if values is not a dictionary if not isinstance(values, dict): values = values._dict_items # check parameter values self.check_parameter_values(values) # update for name, value in values.items(): # check for conflicts if ( check_conflict is True and name in self.keys() and not (self[name] == float(value) or self[name] == value) ): raise ValueError( f"parameter '{name}' already defined with value '{self[name]}'" ) # check parameter already exists (for updating parameters) if check_already_exists is True: try: self._dict_items[name] except KeyError as err: raise KeyError( f"Cannot update parameter '{name}' as it does not " + f"have a default value. ({err.args[0]}). If you are " + "sure you want to update this parameter, use " + "param.update({{name: value}}, check_already_exists=False)" ) from err # if no conflicts, update if isinstance(value, str): if ( value.startswith("[function]") or value.startswith("[current data]") or value.startswith("[data]") or value.startswith("[2D data]") ): raise ValueError( "Specifying parameters via [function], [current data], [data] " "or [2D data] is no longer supported. For functions, pass in a " "python function object. For data, pass in a python function " "that returns a pybamm Interpolant object. " "See https://tinyurl.com/merv43ss for an example with both." ) elif value == "[input]": self._dict_items[name] = pybamm.InputParameter(name) # Anything else should be a converted to a float else: self._dict_items[name] = float(value) elif isinstance(value, tuple) and isinstance(value[1], np.ndarray): # If data is provided as a 2-column array (1D data), # convert to two arrays for compatibility with 2D data # see #1805 func_name, data = value data = ([data[:, 0]], data[:, 1]) self._dict_items[name] = (func_name, data) else: self._dict_items[name] = value # reset processed symbols self._processed_symbols = {}
[docs] def set_initial_stoichiometry_half_cell( self, initial_value, param=None, known_value="cyclable lithium capacity", inplace=True, options=None, inputs=None, ): """ Set the initial stoichiometry of the working electrode, based on the initial SOC or voltage """ param = param or pybamm.LithiumIonParameters(options) x = pybamm.lithium_ion.get_initial_stoichiometry_half_cell( initial_value, self, param=param, known_value=known_value, options=options, inputs=inputs, ) if inplace: parameter_values = self else: parameter_values = self.copy() c_max = self.evaluate(param.p.prim.c_max) parameter_values.update( { "Initial concentration in {} electrode [mol.m-3]".format( options["working electrode"] ): x * c_max } ) return parameter_values
[docs] def set_initial_stoichiometries( self, initial_value, param=None, known_value="cyclable lithium capacity", inplace=True, options=None, inputs=None, tol=1e-6, ): """ Set the initial stoichiometry of each electrode, based on the initial SOC or voltage """ param = param or pybamm.LithiumIonParameters(options) x, y = pybamm.lithium_ion.get_initial_stoichiometries( initial_value, self, param=param, known_value=known_value, options=options, tol=tol, inputs=inputs, ) if inplace: parameter_values = self else: parameter_values = self.copy() c_n_max = self.evaluate(param.n.prim.c_max) c_p_max = self.evaluate(param.p.prim.c_max) parameter_values.update( { "Initial concentration in negative electrode [mol.m-3]": x * c_n_max, "Initial concentration in positive electrode [mol.m-3]": y * c_p_max, } ) return parameter_values
[docs] def set_initial_ocps( self, initial_value, param=None, known_value="cyclable lithium capacity", inplace=True, options=None, ): """ Set the initial OCP of each electrode, based on the initial SOC or voltage """ param = param or pybamm.LithiumIonParameters(options) Un, Up = pybamm.lithium_ion.get_initial_ocps( initial_value, self, param=param, known_value=known_value, options=options ) if inplace: parameter_values = self else: parameter_values = self.copy() parameter_values.update( { "Initial voltage in negative electrode [V]": Un, "Initial voltage in positive electrode [V]": Up, } ) return parameter_values
def check_parameter_values(self, values): for param in values: if "propotional term" in param: raise ValueError( f"The parameter '{param}' has been renamed to " "'... proportional term [s-1]', and its value should now be divided" "by 3600 to get the same results as before." ) # specific check for renamed parameter "1 + dlnf/dlnc" if "1 + dlnf/dlnc" in param: raise ValueError( f"parameter '{param}' has been renamed to " "'Thermodynamic factor'" )
[docs] def process_model(self, unprocessed_model, inplace=True): """Assign parameter values to a model. Currently inplace, could be changed to return a new model. Parameters ---------- unprocessed_model : :class:`pybamm.BaseModel` Model to assign parameter values for inplace: bool, optional If True, replace the parameters in the model in place. Otherwise, return a new model with parameter values set. Default is True. Raises ------ :class:`pybamm.ModelError` If an empty model is passed (`model.rhs = {}` and `model.algebraic = {}` and `model.variables = {}`) """ pybamm.logger.info(f"Start setting parameters for {unprocessed_model.name}") # set up inplace vs not inplace if inplace: # any changes to unprocessed_model attributes will change model attributes # since they point to the same object model = unprocessed_model else: # create a copy of the model model = unprocessed_model.new_copy() if ( len(unprocessed_model.rhs) == 0 and len(unprocessed_model.algebraic) == 0 and len(unprocessed_model.variables) == 0 ): raise pybamm.ModelError("Cannot process parameters for empty model") new_rhs = {} for variable, equation in unprocessed_model.rhs.items(): pybamm.logger.verbose(f"Processing parameters for {variable!r} (rhs)") new_variable = self.process_symbol(variable) new_rhs[new_variable] = self.process_symbol(equation) model.rhs = new_rhs new_algebraic = {} for variable, equation in unprocessed_model.algebraic.items(): pybamm.logger.verbose(f"Processing parameters for {variable!r} (algebraic)") new_variable = self.process_symbol(variable) new_algebraic[new_variable] = self.process_symbol(equation) model.algebraic = new_algebraic new_initial_conditions = {} for variable, equation in unprocessed_model.initial_conditions.items(): pybamm.logger.verbose( f"Processing parameters for {variable!r} (initial conditions)" ) new_variable = self.process_symbol(variable) new_initial_conditions[new_variable] = self.process_symbol(equation) model.initial_conditions = new_initial_conditions model.boundary_conditions = self.process_boundary_conditions(unprocessed_model) new_variables = {} for variable, equation in unprocessed_model.variables.items(): pybamm.logger.verbose(f"Processing parameters for {variable!r} (variables)") new_variables[variable] = self.process_symbol(equation) model.variables = new_variables new_events = [] for event in unprocessed_model.events: pybamm.logger.verbose(f"Processing parameters for event '{event.name}''") new_events.append( pybamm.Event( event.name, self.process_symbol(event.expression), event.event_type ) ) interpolant_events = self._get_interpolant_events(model) for event in interpolant_events: pybamm.logger.verbose(f"Processing parameters for event '{event.name}''") new_events.append( pybamm.Event( event.name, self.process_symbol(event.expression), event.event_type ) ) model.events = new_events pybamm.logger.info(f"Finish setting parameters for {model.name}") return model
def _get_interpolant_events(self, model): """Add events for functions that have been defined as parameters""" # Define events to catch extrapolation. In these events the sign is # important: it should be positive inside of the range and negative # outside of it interpolants = model._find_symbols(pybamm.Interpolant) interpolant_events = [] for interpolant in interpolants: xs = interpolant.x children = interpolant.children for x, child in zip(xs, children): interpolant_events.extend( [ pybamm.Event( f"Interpolant '{interpolant.name}' lower bound", pybamm.min(child - min(x)), pybamm.EventType.INTERPOLANT_EXTRAPOLATION, ), pybamm.Event( f"Interpolant '{interpolant.name}' upper bound", pybamm.min(max(x) - child), pybamm.EventType.INTERPOLANT_EXTRAPOLATION, ), ] ) return interpolant_events
[docs] def process_boundary_conditions(self, model): """ Process boundary conditions for a model Boundary conditions are dictionaries {"left": left bc, "right": right bc} in general, but may be imposed on the tabs (or *not* on the tab) for a small number of variables, e.g. {"negative tab": neg. tab bc, "positive tab": pos. tab bc "no tab": no tab bc}. """ new_boundary_conditions = {} sides = ["left", "right", "negative tab", "positive tab", "no tab"] for variable, bcs in model.boundary_conditions.items(): processed_variable = self.process_symbol(variable) new_boundary_conditions[processed_variable] = {} for side in sides: try: bc, typ = bcs[side] pybamm.logger.verbose( f"Processing parameters for {variable!r} ({side} bc)" ) processed_bc = (self.process_symbol(bc), typ) new_boundary_conditions[processed_variable][side] = processed_bc except KeyError as err: # don't raise error if the key error comes from the side not being # found if err.args[0] in side: pass # do raise error otherwise (e.g. can't process symbol) else: raise err return new_boundary_conditions
[docs] def process_geometry(self, geometry): """ Assign parameter values to a geometry (inplace). Parameters ---------- geometry : dict Geometry specs to assign parameter values to """ def process_and_check(sym): new_sym = self.process_symbol(sym) if not isinstance(new_sym, pybamm.Scalar): raise ValueError( "Geometry parameters must be Scalars after parameter processing" ) return new_sym for domain in geometry: for spatial_variable, spatial_limits in geometry[domain].items(): # process tab information if using 1 or 2D current collectors if spatial_variable == "tabs": for tab, position_info in spatial_limits.items(): for position_size, sym in position_info.items(): geometry[domain]["tabs"][tab][position_size] = ( process_and_check(sym) ) else: for lim, sym in spatial_limits.items(): geometry[domain][spatial_variable][lim] = process_and_check(sym)
[docs] def process_symbol(self, symbol): """Walk through the symbol and replace any Parameter with a Value. If a symbol has already been processed, the stored value is returned. Parameters ---------- symbol : :class:`pybamm.Symbol` Symbol or Expression tree to set parameters for Returns ------- symbol : :class:`pybamm.Symbol` Symbol with Parameter instances replaced by Value """ try: return self._processed_symbols[symbol] except KeyError: processed_symbol = self._process_symbol(symbol) self._processed_symbols[symbol] = processed_symbol return processed_symbol
def _process_symbol(self, symbol): """See :meth:`ParameterValues.process_symbol()`.""" if isinstance(symbol, pybamm.Parameter): value = self[symbol.name] if isinstance(value, numbers.Number): # Check not NaN (parameter in csv file but no value given) if np.isnan(value): raise ValueError(f"Parameter '{symbol.name}' not found") # Scalar inherits name return pybamm.Scalar(value, name=symbol.name) elif isinstance(value, pybamm.Symbol): new_value = self.process_symbol(value) new_value.copy_domains(symbol) return new_value else: raise TypeError(f"Cannot process parameter '{value}'") elif isinstance(symbol, pybamm.FunctionParameter): function_name = self[symbol.name] if isinstance( function_name, (numbers.Number, pybamm.Interpolant, pybamm.InputParameter), ) or ( isinstance(function_name, pybamm.Symbol) and function_name.size_for_testing == 1 ): # no need to process children, they will only be used for shape new_children = symbol.children else: # process children new_children = [] for child in symbol.children: if symbol.diff_variable is not None and any( x == symbol.diff_variable for x in child.pre_order() ): # Wrap with NotConstant to avoid simplification, # which would stop symbolic diff from working properly new_child = pybamm.NotConstant(child) new_children.append(self.process_symbol(new_child)) else: new_children.append(self.process_symbol(child)) # Create Function or Interpolant or Scalar object if isinstance(function_name, tuple): if len(function_name) == 2: # CSV or JSON parsed data # to create an Interpolant name, data = function_name if len(data[0]) == 1: input_data = data[0][0], data[1] else: input_data = data # For parameters provided as data we use a cubic interpolant # Note: the cubic interpolant can be differentiated function = pybamm.Interpolant( input_data[0], input_data[-1], new_children, name=name, ) else: # pragma: no cover raise ValueError( f"Invalid function name length: {len(function_name)}" ) elif isinstance(function_name, numbers.Number): # Check not NaN (parameter in csv file but no value given) if np.isnan(function_name): raise ValueError( f"Parameter '{symbol.name}' (possibly a function) not found" ) # If the "function" is provided is actually a scalar, return a Scalar # object instead of throwing an error. function = pybamm.Scalar(function_name, name=symbol.name) elif callable(function_name): # otherwise evaluate the function to create a new PyBaMM object function = function_name(*new_children) elif isinstance( function_name, (pybamm.Interpolant, pybamm.InputParameter) ) or ( isinstance(function_name, pybamm.Symbol) and function_name.size_for_testing == 1 ): function = function_name else: raise TypeError( f"Parameter provided for '{symbol.name}' " + "is of the wrong type (should either be scalar-like or callable)" ) # Differentiate if necessary if symbol.diff_variable is None: # Use ones_like so that we get the right shapes function_out = function * pybamm.ones_like(*new_children) else: # return differentiated function new_diff_variable = self.process_symbol(symbol.diff_variable) function_out = function.diff(new_diff_variable) # Process again just to be sure return self.process_symbol(function_out) elif isinstance(symbol, pybamm.BinaryOperator): # process children new_left = self.process_symbol(symbol.left) new_right = self.process_symbol(symbol.right) # make new symbol, ensure domain remains the same new_symbol = symbol._binary_new_copy(new_left, new_right) new_symbol.copy_domains(symbol) return new_symbol # Unary operators elif isinstance(symbol, pybamm.UnaryOperator): new_child = self.process_symbol(symbol.child) new_symbol = symbol._unary_new_copy(new_child) # ensure domain remains the same new_symbol.copy_domains(symbol) # x_average can sometimes create a new symbol with electrode thickness # parameters, so we process again to make sure these parameters are set if isinstance(symbol, pybamm.XAverage) and not isinstance( new_symbol, pybamm.XAverage ): new_symbol = self.process_symbol(new_symbol) # f_a_dist in the size average needs to be processed if isinstance(new_symbol, pybamm.SizeAverage): new_symbol.f_a_dist = self.process_symbol(new_symbol.f_a_dist) # position in evaluate at needs to be processed, and should be a Scalar if isinstance(new_symbol, pybamm.EvaluateAt): new_symbol_position = self.process_symbol(new_symbol.position) if not isinstance(new_symbol_position, pybamm.Scalar): raise ValueError( "'position' in 'EvaluateAt' must evaluate to a scalar" ) else: new_symbol.position = new_symbol_position return new_symbol # Functions elif isinstance(symbol, pybamm.Function): new_children = [self.process_symbol(child) for child in symbol.children] return symbol._function_new_copy(new_children) # Concatenations elif isinstance(symbol, pybamm.Concatenation): new_children = [self.process_symbol(child) for child in symbol.children] return symbol._concatenation_new_copy(new_children) # Variables: update scale elif isinstance(symbol, pybamm.Variable): new_symbol = symbol.create_copy() new_symbol._scale = self.process_symbol(symbol.scale) reference = self.process_symbol(symbol.reference) if isinstance(reference, pybamm.Vector): # address numpy 1.25 deprecation warning: array should have ndim=0 # before conversion reference = pybamm.Scalar((reference.evaluate()).item()) new_symbol._reference = reference new_symbol.bounds = tuple([self.process_symbol(b) for b in symbol.bounds]) return new_symbol elif isinstance(symbol, numbers.Number): return pybamm.Scalar(symbol) else: # Backup option: return the object return symbol
[docs] def evaluate(self, symbol, inputs=None): """ Process and evaluate a symbol. Parameters ---------- symbol : :class:`pybamm.Symbol` Symbol or Expression tree to evaluate Returns ------- number or array The evaluated symbol """ processed_symbol = self.process_symbol(symbol) if processed_symbol.is_constant(): return processed_symbol.evaluate() else: # In the case that the only issue is an input parameter contained in inputs, # go ahead and try and evaluate it with the inputs. If it doesn't work, raise # the value error. try: return processed_symbol.evaluate(inputs=inputs) except Exception as exc: raise ValueError( "symbol must evaluate to a constant scalar or array" ) from exc
def _ipython_key_completions_(self): return list(self._dict_items.keys())
[docs] def print_parameters(self, parameters, output_file=None): """ Return dictionary of evaluated parameters, and optionally print these evaluated parameters to an output file. Parameters ---------- parameters : class or dict containing :class:`pybamm.Parameter` objects Class or dictionary containing all the parameters to be evaluated output_file : string, optional The file to print parameters to. If None, the parameters are not printed, and this function simply acts as a test that all the parameters can be evaluated, and returns the dictionary of evaluated parameters. Returns ------- evaluated_parameters : defaultdict The evaluated parameters, for further processing if needed Notes ----- A C-rate of 1 C is the current required to fully discharge the battery in 1 hour, 2 C is current to discharge the battery in 0.5 hours, etc """ # Set list of attributes to ignore, for when we are evaluating parameters from # a class of parameters ignore = [ "__name__", "__doc__", "__package__", "__loader__", "__spec__", "__file__", "__cached__", "__builtins__", "absolute_import", "division", "print_function", "unicode_literals", "pybamm", "_options", "constants", "np", "geo", "elec", "therm", "half_cell", "x", "r", ] # If 'parameters' is a class, extract the dict if not isinstance(parameters, dict): parameters_dict = { k: v for k, v in parameters.__dict__.items() if k not in ignore } for domain in ["n", "s", "p"]: domain_param = getattr(parameters, domain) parameters_dict.update( { f"{domain}.{k}": v for k, v in domain_param.__dict__.items() if k not in ignore } ) parameters = parameters_dict evaluated_parameters = defaultdict(list) # Turn to regular dictionary for faster KeyErrors self._dict_items = dict(self._dict_items) for name, symbol in parameters.items(): if isinstance(symbol, pybamm.Symbol): try: proc_symbol = self.process_symbol(symbol) except KeyError: # skip parameters that don't have a value in that parameter set proc_symbol = None if not ( callable(proc_symbol) or proc_symbol is None or proc_symbol.has_symbol_of_classes( (pybamm.Concatenation, pybamm.Broadcast) ) ): evaluated_parameters[name] = proc_symbol.evaluate(t=0) # Turn back to FuzzyDict self._dict_items = pybamm.FuzzyDict(self._dict_items) # Print the evaluated_parameters dict to output_file if output_file: self.print_evaluated_parameters(evaluated_parameters, output_file) return evaluated_parameters
[docs] def print_evaluated_parameters(self, evaluated_parameters, output_file): """ Print a dictionary of evaluated parameters to an output file Parameters ---------- evaluated_parameters : defaultdict The evaluated parameters, for further processing if needed output_file : string, optional The file to print parameters to. If None, the parameters are not printed, and this function simply acts as a test that all the parameters can be evaluated """ # Get column width for pretty printing column_width = max(len(name) for name in evaluated_parameters.keys()) s = f"{{:>{column_width}}}" with open(output_file, "w") as file: for name, value in sorted(evaluated_parameters.items()): if 0.001 < abs(value) < 1000: file.write((s + " : {:10.4g}\n").format(name, value)) else: file.write((s + " : {:10.3E}\n").format(name, value))