def _get_interaction_predicted_values(dbf, comps, phase_name, configuration, output): mod = Model(dbf, comps, phase_name) mod.models['idmix'] = 0 # TODO: better reference state handling endpoints = endmembers_from_interaction(configuration) first_endpoint = _translate_endmember_to_array(endpoints[0], mod.ast.atoms(v.SiteFraction)) second_endpoint = _translate_endmember_to_array(endpoints[1], mod.ast.atoms(v.SiteFraction)) grid = np.linspace(0, 1, num=100) point_matrix = grid[None].T * second_endpoint + (1 - grid)[None].T * first_endpoint # TODO: Real temperature support point_matrix = point_matrix[None, None] predicted_values = calculate( dbf, comps, [phase_name], output=output, T=298.15, P=101325, points=point_matrix, model=mod)[output].values.flatten() return grid, predicted_values
def fit_formation_energy(dbf, comps, phase_name, configuration, symmetry, datasets, ridge_alpha=None, aicc_phase_penalty=None, features=None): """ Find suitable linear model parameters for the given phase. We do this by successively fitting heat capacities, entropies and enthalpies of formation, and selecting against criteria to prevent overfitting. The "best" set of parameters minimizes the error without overfitting. Parameters ---------- dbf : Database pycalphad Database. Partially complete, so we know what degrees of freedom to fix. comps : [str] Names of the relevant components. phase_name : str Name of the desired phase for which the parameters will be found. configuration : ndarray Configuration of the sublattices for the fitting procedure. symmetry : [[int]] Symmetry of the sublattice configuration. datasets : PickleableTinyDB All the datasets desired to fit to. ridge_alpha : float Value of the :math:`\\alpha` hyperparameter used in ridge regression. Defaults to 1.0e-100, which should be degenerate with ordinary least squares regression. For now, the parameter is applied to all features. aicc_feature_factors : dict Map of phase name to feature to a multiplication factor for the AICc's parameter penalty. features : dict Maps "property" to a list of features for the linear model. These will be transformed from "GM" coefficients e.g., {"CPM_FORM": (v.T*sympy.log(v.T), v.T**2, v.T**-1, v.T**3)} (Default value = None) Returns ------- dict {feature: estimated_value} """ aicc_feature_factors = aicc_phase_penalty if aicc_phase_penalty is not None else {} if interaction_test(configuration): _log.debug('ENDMEMBERS FROM INTERACTION: %s', endmembers_from_interaction(configuration)) fitting_steps = (["CPM_FORM", "CPM_MIX"], ["SM_FORM", "SM_MIX"], ["HM_FORM", "HM_MIX"]) else: # We are only fitting an endmember; no mixing data needed fitting_steps = (["CPM_FORM"], ["SM_FORM"], ["HM_FORM"]) # create the candidate models and fitting steps if features is None: features = OrderedDict([("CPM_FORM", (v.T * sympy.log(v.T), v.T**2, v.T**-1, v.T**3)), ("SM_FORM", (v.T,)), ("HM_FORM", (sympy.S.One,)), ]) # dict of {feature, [candidate_models]} candidate_models_features = build_candidate_models(configuration, features) # All possible parameter values that could be taken on. This is some legacy # code from before there were many candidate models built. For very large # sets of candidate models, this could be quite slow. # TODO: we might be able to remove this initialization for clarity, depends on fixed poritions parameters = {} for candidate_models in candidate_models_features.values(): for model in candidate_models: for coef in model: parameters[coef] = 0 # These is our previously fit partial model from previous steps # Subtract out all of these contributions (zero out reference state because these are formation properties) fixed_model = Model(dbf, comps, phase_name, parameters={'GHSER'+(c.upper()*2)[:2]: 0 for c in comps}) fixed_portions = [0] for desired_props in fitting_steps: feature_type = desired_props[0].split('_')[0] # HM_FORM -> HM aicc_factor = aicc_feature_factors.get(feature_type, 1.0) solver_qry = (where('solver').test(symmetry_filter, configuration, recursive_tuplify(symmetry) if symmetry else symmetry)) desired_data = get_prop_data(comps, phase_name, desired_props, datasets, additional_query=solver_qry) desired_data = filter_configurations(desired_data, configuration, symmetry) desired_data = filter_temperatures(desired_data) _log.trace('%s: datasets found: %s', desired_props, len(desired_data)) if len(desired_data) > 0: config_tup = tuple(map(tuplify, configuration)) calculate_dict = get_prop_samples(desired_data, config_tup) sample_condition_dicts = _get_sample_condition_dicts(calculate_dict, list(map(len, config_tup))) weights = calculate_dict['weights'] assert len(sample_condition_dicts) == len(weights) # We assume all properties in the same fitting step have the same # features (all CPM, all HM, etc., but different ref states). # data quantities are the same for each candidate model and can be computed up front data_qtys = get_data_quantities(feature_type, fixed_model, fixed_portions, desired_data, sample_condition_dicts) # build the candidate model transformation matrix and response vector (A, b in Ax=b) feature_matricies = [] data_quantities = [] for candidate_coefficients in candidate_models_features[desired_props[0]]: # Map coeffiecients in G to coefficients in the feature_type (H, S, CP) transformed_coefficients = list(map(feature_transforms[feature_type], candidate_coefficients)) if interaction_test(configuration, 3): feature_matricies.append(_build_feature_matrix(sample_condition_dicts, transformed_coefficients)) else: feature_matricies.append(_build_feature_matrix(sample_condition_dicts, transformed_coefficients)) data_quantities.append(data_qtys) # provide candidate models and get back a selected model. selected_model = select_model(zip(candidate_models_features[desired_props[0]], feature_matricies, data_quantities), ridge_alpha, weights=weights, aicc_factor=aicc_factor) selected_features, selected_values = selected_model parameters.update(zip(*(selected_features, selected_values))) # Add these parameters to be fixed for the next fitting step fixed_portion = np.array(selected_features, dtype=np.object_) fixed_portion = np.dot(fixed_portion, selected_values) fixed_portions.append(fixed_portion) return parameters
def fit_formation_energy(dbf, comps, phase_name, configuration, symmetry, datasets, ridge_alpha=1.0e-100, features=None): """ Find suitable linear model parameters for the given phase. We do this by successively fitting heat capacities, entropies and enthalpies of formation, and selecting against criteria to prevent overfitting. The "best" set of parameters minimizes the error without overfitting. Parameters ---------- dbf : Database pycalphad Database. Partially complete, so we know what degrees of freedom to fix. comps : [str] Names of the relevant components. phase_name : str Name of the desired phase for which the parameters will be found. configuration : ndarray Configuration of the sublattices for the fitting procedure. symmetry : [[int]] Symmetry of the sublattice configuration. datasets : PickleableTinyDB All the datasets desired to fit to. ridge_alpha : float Value of the $alpha$ hyperparameter used in ridge regression. Defaults to 1.0e-100, which should be degenerate with ordinary least squares regression. For now, the parameter is applied to all features. features : dict Maps "property" to a list of features for the linear model. These will be transformed from "GM" coefficients e.g., {"CPM_FORM": (v.T*sympy.log(v.T), v.T**2, v.T**-1, v.T**3)} (Default value = None) Returns ------- dict {feature: estimated_value} """ if interaction_test(configuration): logging.debug('ENDMEMBERS FROM INTERACTION: {}'.format( endmembers_from_interaction(configuration))) fitting_steps = (["CPM_FORM", "CPM_MIX"], ["SM_FORM", "SM_MIX"], ["HM_FORM", "HM_MIX"]) else: # We are only fitting an endmember; no mixing data needed fitting_steps = (["CPM_FORM"], ["SM_FORM"], ["HM_FORM"]) # create the candidate models and fitting steps if features is None: features = OrderedDict([("CPM_FORM", (v.T * sympy.log(v.T), v.T**2, v.T**-1, v.T**3)), ("SM_FORM", (v.T, )), ("HM_FORM", (sympy.S.One, ))]) # dict of {feature, [candidate_models]} candidate_models_features = build_candidate_models(configuration, features) # All possible parameter values that could be taken on. This is some legacy # code from before there were many candidate models built. For very large # sets of candidate models, this could be quite slow. # TODO: we might be able to remove this initialization for clarity, depends on fixed poritions parameters = {} for candidate_models in candidate_models_features.values(): for model in candidate_models: for coef in model: parameters[coef] = 0 # These is our previously fit partial model from previous steps # Subtract out all of these contributions (zero out reference state because these are formation properties) fixed_model = Model( dbf, comps, phase_name, parameters={'GHSER' + (c.upper() * 2)[:2]: 0 for c in comps}) fixed_model.models['idmix'] = 0 fixed_portions = [0] moles_per_formula_unit = sympy.S(0) YS = sympy.Symbol('YS') # site fraction symbol that we will reuse Z = sympy.Symbol('Z') # site fraction symbol that we will reuse subl_idx = 0 for num_sites, const in zip(dbf.phases[phase_name].sublattices, dbf.phases[phase_name].constituents): if v.Species('VA') in const: moles_per_formula_unit += num_sites * ( 1 - v.SiteFraction(phase_name, subl_idx, v.Species('VA'))) else: moles_per_formula_unit += num_sites subl_idx += 1 for desired_props in fitting_steps: desired_data = get_data(comps, phase_name, configuration, symmetry, datasets, desired_props) logging.debug('{}: datasets found: {}'.format(desired_props, len(desired_data))) if len(desired_data) > 0: # We assume all properties in the same fitting step have the same features (all CPM, all HM, etc.) (but different ref states) all_samples = get_samples(desired_data) site_fractions = [ build_sitefractions( phase_name, ds['solver']['sublattice_configurations'], ds['solver'].get( 'sublattice_occupancies', np.ones(( len(ds['solver']['sublattice_configurations']), len(ds['solver']['sublattice_configurations'][0])), dtype=np.float))) for ds in desired_data for _ in ds['conditions']['T'] ] # Flatten list site_fractions = list(itertools.chain(*site_fractions)) # build the candidate model transformation matrix and response vector (A, b in Ax=b) feature_matricies = [] data_quantities = [] for candidate_model in candidate_models_features[desired_props[0]]: if interaction_test(configuration, 3): feature_matricies.append( build_ternary_feature_matrix(desired_props[0], candidate_model, desired_data)) else: feature_matricies.append( _build_feature_matrix(desired_props[0], candidate_model, desired_data)) data_qtys = np.concatenate(shift_reference_state( desired_data, feature_transforms[desired_props[0]], fixed_model), axis=-1) # Remove existing partial model contributions from the data data_qtys = data_qtys - feature_transforms[desired_props[0]]( fixed_model.ast) # Subtract out high-order (in T) parameters we've already fit data_qtys = data_qtys - feature_transforms[desired_props[0]]( sum(fixed_portions)) / moles_per_formula_unit # if any site fractions show up in our data_qtys that aren't in this datasets site fractions, set them to zero. for sf, i, (_, (sf_product, inter_product)) in zip(site_fractions, data_qtys, all_samples): missing_variables = sympy.S( i * moles_per_formula_unit).atoms( v.SiteFraction) - set(sf.keys()) sf.update({x: 0. for x in missing_variables}) # The equations we have just have the site fractions as YS # and interaction products as Z, so take the product of all # the site fractions that we see in our data qtys sf.update({YS: sf_product, Z: inter_product}) # moles_per_formula_unit factor is here because our data is stored per-atom # but all of our fits are per-formula-unit data_qtys = [ sympy.S(i * moles_per_formula_unit).xreplace(sf).xreplace({ v.T: ixx[0] }).evalf() for i, sf, ixx in zip(data_qtys, site_fractions, all_samples) ] data_qtys = np.asarray(data_qtys, dtype=np.float) data_quantities.append(data_qtys) # provide candidate models and get back a selected model. selected_model = select_model( zip(candidate_models_features[desired_props[0]], feature_matricies, data_quantities), ridge_alpha) selected_features, selected_values = selected_model parameters.update(zip(*(selected_features, selected_values))) # Add these parameters to be fixed for the next fitting step fixed_portion = np.array(selected_features, dtype=np.object) fixed_portion = np.dot(fixed_portion, selected_values) fixed_portions.append(fixed_portion) return parameters
def _compare_data_to_parameters(dbf, comps, phase_name, desired_data, mod, configuration, x, y, ax=None): """ Return one set of plotted Axes with data compared to calculated parameters Parameters ---------- dbf : Database pycalphad thermodynamic database containing the relevant parameters. comps : list Names of components to consider in the calculation. phase_name : str Name of the considered phase phase desired_data : mod : Model A pycalphad Model. The Model may or may not have the reference state zeroed out for formation properties. configuration : x : str Model property to plot on the x-axis e.g. 'T', 'HM_MIX', 'SM_FORM' y : str Model property to plot on the y-axis e.g. 'T', 'HM_MIX', 'SM_FORM' ax : matplotlib.Axes Default axes used if not specified. Returns ------- matplotlib.Axes """ species = unpack_components(dbf, comps) # phase constituents are Species objects, so we need to be doing intersections with those phase_constituents = dbf.phases[phase_name].constituents # phase constituents must be filtered to only active: constituents = [[sp.name for sp in sorted(subl_constituents.intersection(species))] for subl_constituents in phase_constituents] subl_dof = list(map(len, constituents)) calculate_dict = get_prop_samples(desired_data, constituents) sample_condition_dicts = _get_sample_condition_dicts(calculate_dict, subl_dof) endpoints = endmembers_from_interaction(configuration) interacting_subls = [c for c in recursive_tuplify(configuration) if isinstance(c, tuple)] disordered_config = False if (len(set(interacting_subls)) == 1) and (len(interacting_subls[0]) == 2): # This configuration describes all sublattices with the same two elements interacting # In general this is a high-dimensional space; just plot the diagonal to see the disordered mixing endpoints = [endpoints[0], endpoints[-1]] disordered_config = True if not ax: ax = plt.subplot() bar_chart = False bar_labels = [] bar_data = [] if y.endswith('_FORM'): # We were passed a Model object with zeroed out reference states yattr = y[:-5] else: yattr = y if len(endpoints) == 1: # This is an endmember so we can just compute T-dependent stuff Ts = calculate_dict['T'] temperatures = np.asarray(Ts if len(Ts) > 0 else 298.15) if temperatures.min() != temperatures.max(): temperatures = np.linspace(temperatures.min(), temperatures.max(), num=100) else: # We only have one temperature: let's do a bar chart instead bar_chart = True temperatures = temperatures.min() endmember = _translate_endmember_to_array(endpoints[0], mod.ast.atoms(v.SiteFraction))[None, None] predicted_quantities = calculate(dbf, comps, [phase_name], output=yattr, T=temperatures, P=101325, points=endmember, model=mod, mode='numpy') if y == 'HM' and x == 'T': # Shift enthalpy data so that value at minimum T is zero predicted_quantities[yattr] -= predicted_quantities[yattr].sel(T=temperatures[0]).values.flatten() response_data = predicted_quantities[yattr].values.flatten() if not bar_chart: extra_kwargs = {} if len(response_data) < 10: extra_kwargs['markersize'] = 20 extra_kwargs['marker'] = '.' extra_kwargs['linestyle'] = 'none' extra_kwargs['clip_on'] = False ax.plot(temperatures, response_data, label='This work', color='k', **extra_kwargs) ax.set_xlabel(plot_mapping.get(x, x)) ax.set_ylabel(plot_mapping.get(y, y)) else: bar_labels.append('This work') bar_data.append(response_data[0]) elif len(endpoints) == 2: # Binary interaction parameter first_endpoint = _translate_endmember_to_array(endpoints[0], mod.ast.atoms(v.SiteFraction)) second_endpoint = _translate_endmember_to_array(endpoints[1], mod.ast.atoms(v.SiteFraction)) point_matrix = np.linspace(0, 1, num=100)[None].T * second_endpoint + \ (1 - np.linspace(0, 1, num=100))[None].T * first_endpoint # TODO: Real temperature support point_matrix = point_matrix[None, None] predicted_quantities = calculate(dbf, comps, [phase_name], output=yattr, T=300, P=101325, points=point_matrix, model=mod, mode='numpy') response_data = predicted_quantities[yattr].values.flatten() if not bar_chart: extra_kwargs = {} if len(response_data) < 10: extra_kwargs['markersize'] = 20 extra_kwargs['marker'] = '.' extra_kwargs['linestyle'] = 'none' extra_kwargs['clip_on'] = False ax.plot(np.linspace(0, 1, num=100), response_data, label='This work', color='k', **extra_kwargs) ax.set_xlim((0, 1)) ax.set_xlabel(str(':'.join(endpoints[0])) + ' to ' + str(':'.join(endpoints[1]))) ax.set_ylabel(plot_mapping.get(y, y)) else: bar_labels.append('This work') bar_data.append(response_data[0]) else: raise NotImplementedError('No support for plotting configuration {}'.format(configuration)) bib_reference_keys = sorted({entry.get('reference', '') for entry in desired_data}) symbol_map = bib_marker_map(bib_reference_keys) for data in desired_data: indep_var_data = None response_data = np.zeros_like(data['values'], dtype=np.float_) if x == 'T' or x == 'P': indep_var_data = np.array(data['conditions'][x], dtype=np.float_).flatten() elif x == 'Z': if disordered_config: # Take the second element of the first interacting sublattice as the coordinate # Because it's disordered all sublattices should be equivalent # TODO: Fix this to filter because we need to guarantee the plot points are disordered occ = data['solver']['sublattice_occupancies'] subl_idx = np.nonzero([isinstance(c, (list, tuple)) for c in occ[0]])[0] if len(subl_idx) > 1: subl_idx = int(subl_idx[0]) else: subl_idx = int(subl_idx) indep_var_data = [c[subl_idx][1] for c in occ] else: interactions = np.array([cond_dict[Symbol('YS')] for cond_dict in sample_condition_dicts]) indep_var_data = 1 - (interactions+1)/2 if y.endswith('_MIX') and data['output'].endswith('_FORM'): # All the _FORM data we have still has the lattice stability contribution # Need to zero it out to shift formation data to mixing mod_latticeonly = Model(dbf, comps, phase_name, parameters={'GHSER'+c.upper(): 0 for c in comps}) mod_latticeonly.models = {key: value for key, value in mod_latticeonly.models.items() if key == 'ref'} temps = data['conditions'].get('T', 300) pressures = data['conditions'].get('P', 101325) points = build_sitefractions(phase_name, data['solver']['sublattice_configurations'], data['solver']['sublattice_occupancies']) for point_idx in range(len(points)): missing_variables = mod_latticeonly.ast.atoms(v.SiteFraction) - set(points[point_idx].keys()) # Set unoccupied values to zero points[point_idx].update({key: 0 for key in missing_variables}) # Change entry to a sorted array of site fractions points[point_idx] = list(OrderedDict(sorted(points[point_idx].items(), key=str)).values()) points = np.array(points, dtype=np.float_) # TODO: Real temperature support points = points[None, None] stability = calculate(dbf, comps, [phase_name], output=data['output'][:-5], T=temps, P=pressures, points=points, model=mod_latticeonly, mode='numpy') response_data -= stability[data['output'][:-5]].values.squeeze() response_data += np.array(data['values'], dtype=np.float_) response_data = response_data.flatten() if not bar_chart: extra_kwargs = {} extra_kwargs['markersize'] = 8 extra_kwargs['linestyle'] = 'none' extra_kwargs['clip_on'] = False ref = data.get('reference', '') mark = symbol_map[ref]['markers'] ax.plot(indep_var_data, response_data, label=symbol_map[ref]['formatted'], marker=mark['marker'], fillstyle=mark['fillstyle'], **extra_kwargs) else: bar_labels.append(data.get('reference', None)) bar_data.append(response_data[0]) if bar_chart: ax.barh(0.02 * np.arange(len(bar_data)), bar_data, color='k', height=0.01) endmember_title = ' to '.join([':'.join(i) for i in endpoints]) ax.get_figure().suptitle('{} (T = {} K)'.format(endmember_title, temperatures), fontsize=20) ax.set_yticks(0.02 * np.arange(len(bar_data))) ax.set_yticklabels(bar_labels, fontsize=20) # This bar chart is rotated 90 degrees, so "y" is now x ax.set_xlabel(plot_mapping.get(y, y)) else: ax.set_frame_on(False) leg = ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) # legend outside leg.get_frame().set_edgecolor('black') return ax
def plot_endmember(dbf, comps, phase_name, configuration, output, datasets=None, symmetry=None, x='T', ax=None, plot_kwargs=None, dataplot_kwargs=None) -> plt.Axes: """ Return one set of plotted Axes with data compared to calculated parameters Parameters ---------- dbf : Database pycalphad thermodynamic database containing the relevant parameters. comps : Sequence[str] Names of components to consider in the calculation. phase_name : str Name of the considered phase phase configuration : Tuple[Tuple[str]] ESPEI-style configuration output : str Model property to plot on the y-axis e.g. ``'HM_MIX'``, or ``'SM_MIX'``. Must be a ``'_MIX'`` property. datasets : tinydb.TinyDB symmetry : list List of lists containing indices of symmetric sublattices e.g. [[0, 1], [2, 3]] ax : plt.Axes Default axes used if not specified. plot_kwargs : Optional[Dict[str, Any]] Keyword arguments to ``ax.plot`` for the predicted data. dataplot_kwargs : Optional[Dict[str, Any]] Keyword arguments to ``ax.plot`` the observed data. Returns ------- plt.Axes """ if output.endswith('_MIX'): raise ValueError("`plot_interaction` only supports HM, HM_FORM, SM, SM_FORM or CPM, CPM_FORM outputs.") if x not in ('T',): raise ValueError(f'`x` passed to `plot_endmember` must be "T" got {x}') if not plot_kwargs: plot_kwargs = {} if not dataplot_kwargs: dataplot_kwargs = {} if not ax: ax = plt.subplot() if datasets is not None: solver_qry = (tinydb.where('solver').test(symmetry_filter, configuration, recursive_tuplify(symmetry) if symmetry else symmetry)) desired_data = get_prop_data(comps, phase_name, output, datasets, additional_query=solver_qry) desired_data = filter_configurations(desired_data, configuration, symmetry) desired_data = filter_temperatures(desired_data) else: desired_data = [] # Plot predicted values from the database endpoints = endmembers_from_interaction(configuration) if len(endpoints) != 1: raise ValueError(f"The configuration passed to `plot_endmember` must be an endmebmer configuration. Got {configuration}") if output.endswith('_FORM'): # TODO: better reference state handling mod = Model(dbf, comps, phase_name, parameters={'GHSER'+(c.upper()*2)[:2]: 0 for c in comps}) prop = output[:-5] else: mod = Model(dbf, comps, phase_name) prop = output endmember = _translate_endmember_to_array(endpoints[0], mod.ast.atoms(v.SiteFraction))[None, None] # Set up the domain of the calculation species = unpack_components(dbf, comps) # phase constituents are Species objects, so we need to be doing intersections with those phase_constituents = dbf.phases[phase_name].constituents # phase constituents must be filtered to only active constituents = [[sp.name for sp in sorted(subl_constituents.intersection(species))] for subl_constituents in phase_constituents] calculate_dict = get_prop_samples(desired_data, constituents) potential_values = np.asarray(calculate_dict[x] if len(calculate_dict[x]) > 0 else 298.15) potential_grid = np.linspace(max(potential_values.min()-1, 0), potential_values.max()+1, num=100) predicted_values = calculate(dbf, comps, [phase_name], output=prop, T=potential_grid, P=101325, points=endmember, model=mod)[prop].values.flatten() ax.plot(potential_grid, predicted_values, **plot_kwargs) # Plot observed values # TODO: model exclusions handling bib_reference_keys = sorted({entry.get('reference', '') for entry in desired_data}) symbol_map = bib_marker_map(bib_reference_keys) for data in desired_data: indep_var_data = None response_data = np.zeros_like(data['values'], dtype=np.float_) indep_var_data = np.array(data['conditions'][x], dtype=np.float_).flatten() response_data += np.array(data['values'], dtype=np.float_) response_data = response_data.flatten() ref = data.get('reference', '') dataplot_kwargs.setdefault('markersize', 8) dataplot_kwargs.setdefault('linestyle', 'none') dataplot_kwargs.setdefault('clip_on', False) # Cannot use setdefault because it won't overwrite previous iterations dataplot_kwargs['label'] = symbol_map[ref]['formatted'] dataplot_kwargs['marker'] = symbol_map[ref]['markers']['marker'] dataplot_kwargs['fillstyle'] = symbol_map[ref]['markers']['fillstyle'] ax.plot(indep_var_data, response_data, **dataplot_kwargs) ax.set_xlabel(plot_mapping.get(x, x)) ax.set_ylabel(plot_mapping.get(output, output)) leg = ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) # legend outside leg.get_frame().set_edgecolor('black') return ax
def plot_interaction(dbf, comps, phase_name, configuration, output, datasets=None, symmetry=None, ax=None, plot_kwargs=None, dataplot_kwargs=None) -> plt.Axes: """ Return one set of plotted Axes with data compared to calculated parameters Parameters ---------- dbf : Database pycalphad thermodynamic database containing the relevant parameters. comps : Sequence[str] Names of components to consider in the calculation. phase_name : str Name of the considered phase phase configuration : Tuple[Tuple[str]] ESPEI-style configuration output : str Model property to plot on the y-axis e.g. ``'HM_MIX'``, or ``'SM_MIX'``. Must be a ``'_MIX'`` property. datasets : tinydb.TinyDB symmetry : list List of lists containing indices of symmetric sublattices e.g. [[0, 1], [2, 3]] ax : plt.Axes Default axes used if not specified. plot_kwargs : Optional[Dict[str, Any]] Keyword arguments to ``ax.plot`` for the predicted data. dataplot_kwargs : Optional[Dict[str, Any]] Keyword arguments to ``ax.plot`` the observed data. Returns ------- plt.Axes """ if not output.endswith('_MIX'): raise ValueError("`plot_interaction` only supports HM_MIX, SM_MIX, or CPM_MIX outputs.") if not plot_kwargs: plot_kwargs = {} if not dataplot_kwargs: dataplot_kwargs = {} if not ax: ax = plt.subplot() # Plot predicted values from the database grid, predicted_values = _get_interaction_predicted_values(dbf, comps, phase_name, configuration, output) plot_kwargs.setdefault('label', 'This work') plot_kwargs.setdefault('color', 'k') ax.plot(grid, predicted_values, **plot_kwargs) # Plot the observed values from the datasets # TODO: model exclusions handling # TODO: better reference state handling mod_srf = Model(dbf, comps, phase_name, parameters={'GHSER'+c.upper(): 0 for c in comps}) mod_srf.models = {'ref': mod_srf.models['ref']} # _MIX assumption prop = output.split('_MIX')[0] desired_props = (f"{prop}_MIX", f"{prop}_FORM") if datasets is not None: solver_qry = (tinydb.where('solver').test(symmetry_filter, configuration, recursive_tuplify(symmetry) if symmetry else symmetry)) desired_data = get_prop_data(comps, phase_name, desired_props, datasets, additional_query=solver_qry) desired_data = filter_configurations(desired_data, configuration, symmetry) desired_data = filter_temperatures(desired_data) else: desired_data = [] species = unpack_components(dbf, comps) # phase constituents are Species objects, so we need to be doing intersections with those phase_constituents = dbf.phases[phase_name].constituents # phase constituents must be filtered to only active constituents = [[sp.name for sp in sorted(subl_constituents.intersection(species))] for subl_constituents in phase_constituents] subl_dof = list(map(len, constituents)) calculate_dict = get_prop_samples(desired_data, constituents) sample_condition_dicts = _get_sample_condition_dicts(calculate_dict, subl_dof) interacting_subls = [c for c in recursive_tuplify(configuration) if isinstance(c, tuple)] if (len(set(interacting_subls)) == 1) and (len(interacting_subls[0]) == 2): # This configuration describes all sublattices with the same two elements interacting # In general this is a high-dimensional space; just plot the diagonal to see the disordered mixing endpoints = endmembers_from_interaction(configuration) endpoints = [endpoints[0], endpoints[-1]] disordered_config = True else: disordered_config = False bib_reference_keys = sorted({entry.get('reference', '') for entry in desired_data}) symbol_map = bib_marker_map(bib_reference_keys) for data in desired_data: indep_var_data = None response_data = np.zeros_like(data['values'], dtype=np.float_) if disordered_config: # Take the second element of the first interacting sublattice as the coordinate # Because it's disordered all sublattices should be equivalent # TODO: Fix this to filter because we need to guarantee the plot points are disordered occ = data['solver']['sublattice_occupancies'] subl_idx = np.nonzero([isinstance(c, (list, tuple)) for c in occ[0]])[0] if len(subl_idx) > 1: subl_idx = int(subl_idx[0]) else: subl_idx = int(subl_idx) indep_var_data = [c[subl_idx][1] for c in occ] else: interactions = np.array([cond_dict[Symbol('YS')] for cond_dict in sample_condition_dicts]) indep_var_data = 1 - (interactions+1)/2 if data['output'].endswith('_FORM'): # All the _FORM data we have still has the lattice stability contribution # Need to zero it out to shift formation data to mixing temps = data['conditions'].get('T', 298.15) pressures = data['conditions'].get('P', 101325) points = build_sitefractions(phase_name, data['solver']['sublattice_configurations'], data['solver']['sublattice_occupancies']) for point_idx in range(len(points)): missing_variables = mod_srf.ast.atoms(v.SiteFraction) - set(points[point_idx].keys()) # Set unoccupied values to zero points[point_idx].update({key: 0 for key in missing_variables}) # Change entry to a sorted array of site fractions points[point_idx] = list(OrderedDict(sorted(points[point_idx].items(), key=str)).values()) points = np.array(points, dtype=np.float_) # TODO: Real temperature support points = points[None, None] stability = calculate(dbf, comps, [phase_name], output=data['output'][:-5], T=temps, P=pressures, points=points, model=mod_srf) response_data -= stability[data['output'][:-5]].values.squeeze() response_data += np.array(data['values'], dtype=np.float_) response_data = response_data.flatten() ref = data.get('reference', '') dataplot_kwargs.setdefault('markersize', 8) dataplot_kwargs.setdefault('linestyle', 'none') dataplot_kwargs.setdefault('clip_on', False) # Cannot use setdefault because it won't overwrite previous iterations dataplot_kwargs['label'] = symbol_map[ref]['formatted'] dataplot_kwargs['marker'] = symbol_map[ref]['markers']['marker'] dataplot_kwargs['fillstyle'] = symbol_map[ref]['markers']['fillstyle'] ax.plot(indep_var_data, response_data, **dataplot_kwargs) ax.set_xlim((0, 1)) ax.set_xlabel(str(':'.join(endpoints[0])) + ' to ' + str(':'.join(endpoints[1]))) ax.set_ylabel(plot_mapping.get(output, output)) leg = ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) # legend outside leg.get_frame().set_edgecolor('black') return ax