Source code for pycalphad.core.lower_convex_hull

"""
The lower_convex_hull module handles geometric calculations associated with
equilibrium calculation.
"""
from __future__ import print_function
from pycalphad.core.cartesian import cartesian
from pycalphad.core.constants import MIN_SITE_FRACTION
from .hyperplane import hyperplane
import numpy as np
import itertools


[docs]def lower_convex_hull(global_grid, state_variables, result_array): """ Find the simplices on the lower convex hull satisfying the specified conditions in the result array. Parameters ---------- global_grid : Dataset A sample of the energy surface of the system. state_variables : list A list of the state variables (e.g., P, T) used in this calculation. result_array : Dataset This object will be modified! Coordinates correspond to conditions axes. Returns ------- None. Results are written to result_array. Notes ----- This routine will not check if any simplex is degenerate. Degenerate simplices will manifest with duplicate or NaN indices. Examples -------- None yet. """ indep_conds = sorted([str(sv) for sv in state_variables]) comp_conds = sorted([x for x in sorted(result_array.coords.keys()) if x.startswith('X_')]) comp_conds_indices = sorted([idx for idx, x in enumerate(sorted(result_array.coords['component'])) if 'X_'+x in comp_conds]) comp_conds_indices = np.array(comp_conds_indices, dtype=np.uint64) pot_conds = sorted([x for x in sorted(result_array.coords.keys()) if x.startswith('MU_')]) pot_conds_indices = sorted([idx for idx, x in enumerate(sorted(result_array.coords['component'])) if 'MU_'+x in pot_conds]) pot_conds_indices = np.array(pot_conds_indices, dtype=np.uint64) if len(set(pot_conds_indices) & set(comp_conds_indices)) > 0: raise ValueError('Cannot specify component chemical potential and amount simultaneously') if len(comp_conds) > 0: cart_values = cartesian([result_array.coords[cond] for cond in comp_conds]) else: cart_values = np.atleast_2d(1.) # TODO: Handle W(comp) as well as X(comp) here comp_values = np.zeros(cart_values.shape[:-1] + (len(result_array.coords['component']),)) for idx in range(comp_values.shape[-1]): if idx in comp_conds_indices: comp_values[..., idx] = cart_values[..., np.where(comp_conds_indices == idx)[0][0]] elif idx in pot_conds_indices: # Composition value not used comp_values[..., idx] = 0 else: # Dependent component (composition value not used) comp_values[..., idx] = 0 # Prevent compositions near an edge from going negative comp_values[np.nonzero(comp_values < MIN_SITE_FRACTION)] = MIN_SITE_FRACTION*10 if len(pot_conds) > 0: cart_pot_values = cartesian([result_array.coords[cond] for cond in pot_conds]) #result_array['Phase'] = force_indep_align(result_array.Phase) # factored out via profiling result_array_GM_values = result_array.GM result_array_GM_dims = result_array.data_vars['GM'][0] result_array_points_values = result_array.points result_array_MU_values = result_array.MU result_array_NP_values = result_array.NP result_array_X_values = result_array.X result_array_Y_values = result_array.Y result_array_Phase_values = result_array.Phase global_grid_GM_values = global_grid.GM global_grid_X_values = global_grid.X global_grid_Y_values = global_grid.Y global_grid_Phase_values = global_grid.Phase num_comps = len(result_array.coords['component']) it = np.nditer(result_array_GM_values, flags=['multi_index']) comp_coord_shape = tuple(len(result_array.coords[cond]) for cond in comp_conds) pot_coord_shape = tuple(len(result_array.coords[cond]) for cond in pot_conds) while not it.finished: indep_idx = tuple(idx for idx, key in zip(it.multi_index, result_array_GM_dims) if key in indep_conds) if len(comp_conds) > 0: comp_idx = np.ravel_multi_index(tuple(idx for idx, key in zip(it.multi_index, result_array_GM_dims) if key in comp_conds), comp_coord_shape) idx_comp_values = comp_values[comp_idx, :] else: idx_comp_values = np.atleast_1d(1.) if len(pot_conds) > 0: pot_idx = np.ravel_multi_index(tuple(idx for idx, key in zip(it.multi_index, result_array_GM_dims) if key in pot_conds), pot_coord_shape) idx_pot_values = np.array(cart_pot_values[pot_idx, :]) idx_global_grid_X_values = global_grid_X_values[indep_idx] idx_global_grid_GM_values = global_grid_GM_values[indep_idx] idx_result_array_MU_values = result_array_MU_values[it.multi_index] idx_result_array_MU_values[:] = 0 for idx in range(len(pot_conds_indices)): idx_result_array_MU_values[pot_conds_indices[idx]] = idx_pot_values[idx] idx_result_array_NP_values = result_array_NP_values[it.multi_index] idx_result_array_points_values = result_array_points_values[it.multi_index] result_array_GM_values[it.multi_index] = \ hyperplane(idx_global_grid_X_values, idx_global_grid_GM_values, idx_comp_values, idx_result_array_MU_values, float(global_grid.coords['N'][0]), pot_conds_indices, comp_conds_indices, idx_result_array_NP_values, idx_result_array_points_values) # Copy phase values out points = result_array_points_values[it.multi_index] result_array_Phase_values[it.multi_index][:num_comps] = global_grid_Phase_values[indep_idx].take(points, axis=0)[:num_comps] result_array_X_values[it.multi_index][:num_comps] = global_grid_X_values[indep_idx].take(points, axis=0)[:num_comps] result_array_Y_values[it.multi_index][:num_comps] = global_grid_Y_values[indep_idx].take(points, axis=0)[:num_comps] # Special case: Sometimes fictitious points slip into the result if '_FAKE_' in result_array_Phase_values[it.multi_index]: new_energy = 0. molesum = 0. for idx in range(len(result_array_Phase_values[it.multi_index])): midx = it.multi_index + (idx,) if result_array_Phase_values[midx] == '_FAKE_': result_array_Phase_values[midx] = '' result_array_X_values[midx] = np.nan result_array_Y_values[midx] = np.nan idx_result_array_NP_values[idx] = np.nan else: new_energy += idx_result_array_NP_values[idx] * global_grid.GM[np.index_exp[indep_idx + (points[idx],)]] molesum += idx_result_array_NP_values[idx] result_array_GM_values[it.multi_index] = new_energy / molesum it.iternext() result_array.remove('points') return result_array