Source code for

# coding: utf-8
# Copyright (c) Pymatgen Development Team.
# Distributed under the terms of the MIT License

Module for reading Lobster output files. For more information
on LOBSTER see

import itertools
import os
import warnings
from collections import OrderedDict
from typing import Dict, Any, Optional, List

import numpy as np
import spglib
from import zopen
from monty.json import MSONable
from monty.serialization import loadfn

from pymatgen.core.structure import Structure
from import Incar, Kpoints, Potcar
from pymatgen.symmetry.bandstructure import HighSymmKpath

__author__ = "Janine George, Marco Esters"
__copyright__ = "Copyright 2017, The Materials Project"
__version__ = "0.2"
__maintainer__ = "Janine George, Marco Esters "
__email__ = ","
__date__ = "Dec 13, 2017"

MODULE_DIR = os.path.dirname(os.path.abspath(__file__))

[docs]class Lobsterin(dict, MSONable): """ This class can handle and generate lobsterin files Furthermore, it can also modify INCAR files for lobster, generate KPOINT files for fatband calculations in Lobster, and generate the standard primitive cells in a POSCAR file that are needed for the fatband calculations. There are also several standard lobsterin files that can be easily generated. """ # all keywords known to this class so far # reminder: lobster is not case sensitive AVAILABLEKEYWORDS = ['COHPstartEnergy', 'COHPendEnergy', 'basisSet', 'cohpGenerator', 'gaussianSmearingWidth', 'saveProjectionToFile', 'basisfunctions', 'skipdos', 'skipcohp', 'skipcoop', 'skipPopulationAnalysis', 'skipGrossPopulation', 'userecommendedbasisfunctions', 'loadProjectionFromFile', 'forceEnergyRange', 'DensityOfEnergy', 'BWDF', 'BWDFCOHP', 'skipProjection', 'createFatband', 'writeBasisFunctions', 'writeMatricesToFile', 'realspaceHamiltonian', 'realspaceOverlap', 'printPAWRealSpaceWavefunction', 'printLCAORealSpaceWavefunction', 'noFFTforVisualization', 'RMSp', 'onlyReadVasprun.xml', 'noMemoryMappedFiles', 'skipPAWOrthonormalityTest', 'doNotIgnoreExcessiveBands', 'doNotUseAbsoluteSpilling', 'skipReOrthonormalization', 'forceV1HMatrix', 'useOriginalTetrahedronMethod', 'useDecimalPlaces', 'kSpaceCOHP'] # keyword + one float can be used in file FLOATKEYWORDS = ['COHPstartEnergy', 'COHPendEnergy', 'gaussianSmearingWidth', 'useDecimalPlaces', 'COHPSteps'] # one of these keywords +endstring can be used in file STRINGKEYWORDS = ['basisSet', 'cohpGenerator', 'realspaceHamiltonian', 'realspaceOverlap', 'printPAWRealSpaceWavefunction', 'printLCAORealSpaceWavefunction', 'kSpaceCOHP'] # the keyword alone will turn on or off a function BOOLEANKEYWORDS = ['saveProjectionToFile', 'skipdos', 'skipcohp', 'skipcoop', 'loadProjectionFromFile', 'forceEnergyRange', 'DensityOfEnergy', 'BWDF', 'BWDFCOHP', 'skipPopulationAnalysis', 'skipGrossPopulation', 'userecommendedbasisfunctions', 'skipProjection', 'writeBasisFunctions', 'writeMatricesToFile', 'noFFTforVisualization', 'RMSp', 'onlyReadVasprun.xml', 'noMemoryMappedFiles', 'skipPAWOrthonormalityTest', 'doNotIgnoreExcessiveBands', 'doNotUseAbsoluteSpilling', 'skipReOrthonormalization', 'forceV1HMatrix', 'useOriginalTetrahedronMethod', 'forceEnergyRange', 'bandwiseSpilling', 'kpointwiseSpilling'] # several of these keywords + ending can be used in a lobsterin file: LISTKEYWORDS = ['basisfunctions', 'cohpbetween', 'createFatband'] def __init__(self, settingsdict: dict): """ Args: settingsdict: dict to initialize Lobsterin """ super().__init__() # check for duplicates listkey = [key.lower() for key in settingsdict.keys()] if len(listkey) != len(list(set(listkey))): raise IOError("There are duplicates for the keywords! The program will stop here.") self.update(settingsdict) def __setitem__(self, key, val): """ Add parameter-val pair to Lobsterin. Warns if parameter is not in list of valid lobsterintags. Also cleans the parameter and val by stripping leading and trailing white spaces. Similar to INCAR class. """ # due to the missing case sensitivity of lobster, the following code is neccessary found = False for key_here in self.keys(): if key.strip().lower() == key_here.lower(): new_key = key_here found = True if not found: new_key = key if new_key.lower() not in [element.lower() for element in Lobsterin.AVAILABLEKEYWORDS]: raise (ValueError("Key is currently not available")) super().__setitem__(new_key, val.strip() if isinstance(val, str) else val) def __getitem__(self, item): """ implements getitem from dict to avoid problems with cases """ found = False for key_here in self.keys(): if item.strip().lower() == key_here.lower(): new_key = key_here found = True if not found: new_key = item val = dict.__getitem__(self, new_key) return val
[docs] def diff(self, other): """ Diff function for lobsterin. Compares two lobsterin and indicates which parameters are the same. Similar to the diff in INCAR. Args: other (Lobsterin): Lobsterin object to compare to Returns: dict with differences and similarities """ similar_param = {} different_param = {} key_list_others = [element.lower() for element in other.keys()] for k1, v1 in self.items(): k1lower = k1.lower() if k1lower not in key_list_others: different_param[k1.upper()] = {"lobsterin1": v1, "lobsterin2": None} else: for key_here in other.keys(): if k1.lower() == key_here.lower(): new_key = key_here if isinstance(v1, str): if v1.strip().lower() != other[new_key].strip().lower(): different_param[k1.upper()] = {"lobsterin1": v1, "lobsterin2": other[new_key]} else: similar_param[k1.upper()] = v1 elif isinstance(v1, list): new_set1 = set([element.strip().lower() for element in v1]) new_set2 = set([element.strip().lower() for element in other[new_key]]) if new_set1 != new_set2: different_param[k1.upper()] = {"lobsterin1": v1, "lobsterin2": other[new_key]} else: if v1 != other[new_key]: different_param[k1.upper()] = {"lobsterin1": v1, "lobsterin2": other[new_key]} else: similar_param[k1.upper()] = v1 for k2, v2 in other.items(): if k2.upper() not in similar_param and k2.upper() not in different_param: for key_here in self.keys(): if k2.lower() == key_here.lower(): new_key = key_here else: new_key = k2 if new_key not in self: different_param[k2.upper()] = {"lobsterin1": None, "lobsterin2": v2} return {"Same": similar_param, "Different": different_param}
def _get_nbands(self, structure: Structure): """ get number of nbands """ if self.get("basisfunctions") is None: raise IOError("No basis functions are provided. The program cannot calculate nbands.") else: basis_functions = [] # type: List[str] for string_basis in self["basisfunctions"]: # string_basis.lstrip() string_basis_raw = string_basis.strip().split(" ") while "" in string_basis_raw: string_basis_raw.remove("") for i in range(0, int(structure.composition.element_composition[string_basis_raw[0]])): basis_functions.extend(string_basis_raw[1:]) no_basis_functions = 0 for basis in basis_functions: if "s" in basis: no_basis_functions = no_basis_functions + 1 elif "p" in basis: no_basis_functions = no_basis_functions + 3 elif "d" in basis: no_basis_functions = no_basis_functions + 5 elif "f" in basis: no_basis_functions = no_basis_functions + 7 return int(no_basis_functions)
[docs] def write_lobsterin(self, path="lobsterin", overwritedict=None): """ writes a lobsterin file Args: path (str): filename of the lobsterin file that will be written overwritedict (dict): dict that can be used to overwrite lobsterin, e.g. {"skipdos": True} """ # will overwrite previous entries # has to search first if entry is already in Lobsterindict (due to case insensitivity) if overwritedict is not None: for key, entry in overwritedict.items(): found = False for key2 in self.keys(): if key.lower() == key2.lower(): self.get[key2] = entry found = True if not found: self.get[key] = entry filename = path with open(filename, 'w') as f: for key in Lobsterin.AVAILABLEKEYWORDS: if key.lower() in [element.lower() for element in self.keys()]: if key.lower() in [element.lower() for element in Lobsterin.FLOATKEYWORDS]: f.write(key + ' ' + str(self.get(key)) + '\n') elif key.lower() in [element.lower() for element in Lobsterin.BOOLEANKEYWORDS]: # checks if entry is True or False for key_here in self.keys(): if key.lower() == key_here.lower(): new_key = key_here if self.get(new_key): f.write(key + '\n') elif key.lower() in [element.lower() for element in Lobsterin.STRINGKEYWORDS]: f.write(key + ' ' + str(self.get(key) + '\n')) elif key.lower() in [element.lower() for element in Lobsterin.LISTKEYWORDS]: for entry in self.get(key): f.write(key + ' ' + str(entry) + '\n')
[docs] def as_dict(self): """ :return: MSONable dict """ d = dict(self) d["@module"] = self.__class__.__module__ d["@class"] = self.__class__.__name__ return d
[docs] @classmethod def from_dict(cls, d): """ :param d: Dict representation :return: Lobsterin """ return Lobsterin({k: v for k, v in d.items() if k not in ["@module", "@class"]})
[docs] def write_INCAR(self, incar_input: str = "INCAR", incar_output: str = "INCAR.lobster", poscar_input: str = "POSCAR", isym: int = -1, further_settings: dict = None): """ Will only make the run static, insert nbands, make ISYM=-1, set LWAVE=True and write a new INCAR. You have to check for the rest. Args: incar_input (str): path to input INCAR incar_output (str): path to output INCAR poscar_input (str): path to input POSCAR isym (int): isym equal to -1 or 0 are possible. Current Lobster version only allow -1. further_settings (dict): A dict can be used to include further settings, e.g. {"ISMEAR":-5} """ # reads old incar from file, this one will be modified incar = Incar.from_file(incar_input) warnings.warn("Please check your incar_input before using it. This method only changes three settings!") if isym == -1: incar["ISYM"] = -1 elif isym == 0: incar["ISYM"] = 0 else: ValueError("isym has to be -1 or 0.") incar["NSW"] = 0 incar["LWAVE"] = True # get nbands from _get_nbands (use basis set that is inserted) incar["NBANDS"] = self._get_nbands(Structure.from_file(poscar_input)) if further_settings is not None: for key, item in further_settings.items(): incar[key] = further_settings[key] # print it to file incar.write_file(incar_output)
[docs] @staticmethod def get_basis(structure: Structure, potcar_symbols: list, address_basis_file: str = os.path.join(MODULE_DIR, "lobster_basis/BASIS_PBE_54_standard.yaml")): """ will get the basis from given potcar_symbols (e.g., ["Fe_pv","Si"] #include this in lobsterin class Args: structure (Structure): Structure object potcar_symbols: list of potcar symbols Returns: returns basis """ Potcar_names = [name for name in potcar_symbols] AtomTypes_Potcar = [name.split('_')[0] for name in Potcar_names] AtomTypes = structure.symbol_set if set(AtomTypes) != set(AtomTypes_Potcar): raise IOError("Your POSCAR does not correspond to your POTCAR!") BASIS = loadfn(address_basis_file)['BASIS'] basis_functions = [] list_forin = [] for itype, type in enumerate(Potcar_names): if type not in BASIS: raise ValueError("You have to provide the basis for" + str( type) + "manually. We don't have any information on this POTCAR.") basis_functions.append(BASIS[type].split()) tojoin = str(AtomTypes_Potcar[itype]) + " " tojoin2 = "".join(str(str(e) + " ") for e in BASIS[type].split()) list_forin.append(str(tojoin + tojoin2)) return list_forin
[docs] @staticmethod def get_all_possible_basis_functions(structure: Structure, potcar_symbols: list, address_basis_file_min: str = os.path.join(MODULE_DIR, "lobster_basis/BASIS_PBE_54_min.yaml"), address_basis_file_max: str = os.path.join(MODULE_DIR, "lobster_basis/BASIS_PBE_54_max.yaml")): """ Args: structure: Structure object potcar_symbols: list of the potcar symbols address_basis_file_min: path to file with the minium required basis by the POTCAR address_basis_file_max: path to file with the largest possible basis of the POTCAR Returns: List of dictionaries that can be used to create new Lobsterin objects in standard_calculations_from_vasp_files as dict_for_basis """ max_basis = Lobsterin.get_basis(structure=structure, potcar_symbols=potcar_symbols, address_basis_file=address_basis_file_max) min_basis = Lobsterin.get_basis(structure=structure, potcar_symbols=potcar_symbols, address_basis_file=address_basis_file_min) all_basis = get_all_possible_basis_combinations(min_basis=min_basis, max_basis=max_basis) list_basis_dict = [] for ibasis, basis in enumerate(all_basis): basis_dict = {} for iel, elba in enumerate(basis): basplit = elba.split() basis_dict[basplit[0]] = " ".join(basplit[1:]) list_basis_dict.append(basis_dict) return list_basis_dict
[docs] @staticmethod def write_POSCAR_with_standard_primitive(POSCAR_input="POSCAR", POSCAR_output="POSCAR.lobster", symprec=0.01): """ writes a POSCAR with the standard primitive cell. This is needed to arrive at the correct kpath Args: POSCAR_input (str): filename of input POSCAR POSCAR_output (str): filename of output POSCAR symprec (float): precision to find symmetry """ structure = Structure.from_file(POSCAR_input) kpath = HighSymmKpath(structure, symprec=symprec) new_structure = kpath.prim'POSCAR', filename=POSCAR_output)
[docs] @staticmethod def write_KPOINTS(POSCAR_input: str = "POSCAR", KPOINTS_output="KPOINTS.lobster", reciprocal_density: int = 100, isym: int = -1, from_grid: bool = False, input_grid: list = [5, 5, 5], line_mode: bool = True, kpoints_line_density: int = 20, symprec: float = 0.01): """ writes a KPOINT file for lobster (only ISYM=-1 and ISYM=0 are possible), grids are gamma centered Args: POSCAR_input (str): path to POSCAR KPOINTS_output (str): path to output KPOINTS reciprocal_density (int): Grid density isym (int): either -1 or 0. Current Lobster versions only allow -1. from_grid (bool): If True KPOINTS will be generated with the help of a grid given in input_grid. Otherwise, they will be generated from the reciprocal_density input_grid (list): grid to generate the KPOINTS file line_mode (bool): If True, band structure will be generated kpoints_line_density (int): density of the lines in the band structure symprec (float): precision to determine symmetry """ structure = Structure.from_file(POSCAR_input) if not from_grid: kpointgrid = Kpoints.automatic_density_by_vol(structure, reciprocal_density).kpts mesh = kpointgrid[0] else: mesh = input_grid # The following code is taken from: SpacegroupAnalyzer # we need to switch off symmetry here latt = structure.lattice.matrix positions = structure.frac_coords unique_species = [] # type: List[Any] zs = [] magmoms = [] for species, g in itertools.groupby(structure, key=lambda s: s.species): if species in unique_species: ind = unique_species.index(species) zs.extend([ind + 1] * len(tuple(g))) else: unique_species.append(species) zs.extend([len(unique_species)] * len(tuple(g))) for site in structure: if hasattr(site, 'magmom'): magmoms.append(site.magmom) elif site.is_ordered and hasattr(site.specie, 'spin'): magmoms.append(site.specie.spin) else: magmoms.append(0) # For now, we are setting magmom to zero. (Taken from INCAR class) cell = latt, positions, zs, magmoms # TODO: what about this shift? mapping, grid = spglib.get_ir_reciprocal_mesh(mesh, cell, is_shift=[0, 0, 0]) # exit() # get the kpoints for the grid if isym == -1: kpts = [] weights = [] all_labels = [] for gp in grid: kpts.append(gp.astype(float) / mesh) weights.append(float(1)) all_labels.append("") elif isym == 0: # time reversal symmetry: k and -k are equivalent kpts = [] weights = [] all_labels = [] newlist = [list(gp) for gp in list(grid)] mapping = [] for gp in newlist: minusgp = [-k for k in gp] if minusgp in newlist and minusgp not in [[0, 0, 0]]: mapping.append(newlist.index(minusgp)) else: mapping.append(newlist.index(gp)) for igp, gp in enumerate(newlist): if mapping[igp] > igp: kpts.append(np.array(gp).astype(float) / mesh) weights.append(float(2)) all_labels.append("") elif mapping[igp] == igp: kpts.append(np.array(gp).astype(float) / mesh) weights.append(float(1)) all_labels.append("") else: ValueError("Only isym=-1 and isym=0 are allowed.") # line mode if line_mode: kpath = HighSymmKpath(structure, symprec=symprec) if not np.allclose(kpath.prim.lattice.matrix, structure.lattice.matrix): raise ValueError( "You are not using the standard primitive cell. The k-path is not correct. Please generate a " "standard primitive cell first.") frac_k_points, labels = kpath.get_kpoints( line_density=kpoints_line_density, coords_are_cartesian=False) for k in range(len(frac_k_points)): kpts.append(frac_k_points[k]) weights.append(0.0) all_labels.append(labels[k]) if isym == -1: comment = ( "ISYM=-1, grid: " + str(mesh) if not line_mode else "ISYM=-1, grid: " + str(mesh) + " plus kpoint path") elif isym == 0: comment = ( "ISYM=0, grid: " + str(mesh) if not line_mode else "ISYM=0, grid: " + str(mesh) + " plus kpoint path") KpointObject = Kpoints(comment=comment, style=Kpoints.supported_modes.Reciprocal, num_kpts=len(kpts), kpts=kpts, kpts_weights=weights, labels=all_labels) KpointObject.write_file(filename=KPOINTS_output)
[docs] @classmethod def from_file(cls, lobsterin: str): """ Args: lobsterin (str): path to lobsterin Returns: Lobsterin object """ with zopen(lobsterin, 'rt') as f: data ="\n") if len(data) == 0: raise IOError("lobsterin file contains no data.") Lobsterindict = {} # type: Dict for datum in data: # will remove all commments to avoid complications raw_datum = datum.split('!')[0] raw_datum = raw_datum.split('//')[0] raw_datum = raw_datum.split('#')[0] raw_datum = raw_datum.split(' ') while "" in raw_datum: raw_datum.remove("") if len(raw_datum) > 1: # check which type of keyword this is, handle accordingly if raw_datum[0].lower() not in [datum2.lower() for datum2 in Lobsterin.LISTKEYWORDS]: if raw_datum[0].lower() not in [datum2.lower() for datum2 in Lobsterin.FLOATKEYWORDS]: if raw_datum[0].lower() not in Lobsterindict: Lobsterindict[raw_datum[0].lower()] = " ".join(raw_datum[1:]) else: raise ValueError("Same keyword " + str(raw_datum[0].lower()) + "twice!") else: if raw_datum[0].lower() not in Lobsterindict: Lobsterindict[raw_datum[0].lower()] = float(raw_datum[1]) else: raise ValueError("Same keyword " + str(raw_datum[0].lower()) + "twice!") else: if raw_datum[0].lower() not in Lobsterindict: Lobsterindict[raw_datum[0].lower()] = [" ".join(raw_datum[1:])] else: Lobsterindict[raw_datum[0].lower()].append(" ".join(raw_datum[1:])) elif len(raw_datum) > 0: Lobsterindict[raw_datum[0].lower()] = True return cls(Lobsterindict)
@staticmethod def _get_potcar_symbols(POTCAR_input: str) -> list: """ will return the name of the species in the POTCAR Args: POTCAR_input(str): string to potcar file Returns: list of the names of the species in string format """ potcar = Potcar.from_file(POTCAR_input) for pot in potcar: if pot.potential_type != "PAW": raise IOError("Lobster only works with PAW! Use different POTCARs") if potcar.functional != "PBE": raise IOError("We only have BASIS options for PBE so far") Potcar_names = [name["symbol"] for name in potcar.spec] return Potcar_names
[docs] @classmethod def standard_calculations_from_vasp_files(cls, POSCAR_input: str = "POSCAR", INCAR_input: str = "INCAR", POTCAR_input: Optional[str] = None, dict_for_basis: Optional[dict] = None, option: str = 'standard'): """ will generate Lobsterin with standard settings Args: POSCAR_input(str): path to POSCAR INCAR_input(str): path to INCAR POTCAR_input (str): path to POTCAR dict_for_basis (dict): can be provided: it should look the following: dict_for_basis={"Fe":'3p 3d 4s 4f', "C": '2s 2p'} and will overwrite all settings from POTCAR_input option (str): 'standard' will start a normal lobster run where COHPs, COOPs, DOS, CHARGE etc. will be calculated 'standard_from_projection' will start a normal lobster run from a projection 'standard_with_fatband' will do a fatband calculation, run over all orbitals 'onlyprojection' will only do a projection 'onlydos' will only calculate a projected dos 'onlycohp' will only calculate cohp 'onlycoop' will only calculate coop 'onlycohpcoop' will only calculate cohp and coop Returns: Lobsterin Object with standard settings """ warnings.warn( "Always check and test the provided basis functions. The spilling of your Lobster calculation might help") # warn that fatband calc cannot be done with tetrahedron method at the moment if option not in ['standard', 'standard_from_projection', 'standard_with_fatband', 'onlyprojection', 'onlydos', 'onlycohp', 'onlycoop', 'onlycohpcoop']: raise ValueError("The option is not valid!") Lobsterindict = {} # type: Dict[Any,Any] # this basis set covers most elements Lobsterindict['basisSet'] = 'pbeVaspFit2015' # energies around e-fermi Lobsterindict['COHPstartEnergy'] = -15.0 Lobsterindict['COHPendEnergy'] = 5.0 if option in ['standard', 'onlycohp', 'onlycoop', 'onlycohpcoop', 'standard_with_fatband']: # every interaction with a distance of 6.0 is checked Lobsterindict['cohpGenerator'] = "from 0.1 to 6.0 orbitalwise" # the projection is saved Lobsterindict['saveProjectionToFile'] = True if option == 'standard_from_projection': Lobsterindict['cohpGenerator'] = "from 0.1 to 6.0 orbitalwise" Lobsterindict['loadProjectionFromFile'] = True if option == 'onlycohp': Lobsterindict['skipdos'] = True Lobsterindict['skipcoop'] = True Lobsterindict['skipPopulationAnalysis'] = True Lobsterindict['skipGrossPopulation'] = True if option == 'onlycoop': Lobsterindict['skipdos'] = True Lobsterindict['skipcohp'] = True Lobsterindict['skipPopulationAnalysis'] = True Lobsterindict['skipGrossPopulation'] = True if option == 'onlycohpcoop': Lobsterindict['skipdos'] = True Lobsterindict['skipPopulationAnalysis'] = True Lobsterindict['skipGrossPopulation'] = True if option == 'onlydos': Lobsterindict['skipcohp'] = True Lobsterindict['skipcoop'] = True Lobsterindict['skipPopulationAnalysis'] = True Lobsterindict['skipGrossPopulation'] = True if option == 'onlyprojection': Lobsterindict['skipdos'] = True Lobsterindict['skipcohp'] = True Lobsterindict['skipcoop'] = True Lobsterindict['skipPopulationAnalysis'] = True Lobsterindict['skipGrossPopulation'] = True Lobsterindict['saveProjectionToFile'] = True incar = Incar.from_file(INCAR_input) if incar["ISMEAR"] == 0: Lobsterindict['gaussianSmearingWidth'] = incar["SIGMA"] if incar["ISMEAR"] != 0 and option == "standard_with_fatband": raise ValueError("ISMEAR has to be 0 for a fatband calculation with Lobster") if dict_for_basis is not None: # dict_for_basis={"Fe":'3p 3d 4s 4f', "C": '2s 2p'} # will just insert this basis and not check with poscar basis = [key + ' ' + value for key, value in dict_for_basis.items()] elif POTCAR_input is not None: # get basis from POTCAR potcar_names = Lobsterin._get_potcar_symbols(POTCAR_input=POTCAR_input) basis = Lobsterin.get_basis(structure=Structure.from_file(POSCAR_input), potcar_symbols=potcar_names) else: raise ValueError("basis cannot be generated") Lobsterindict["basisfunctions"] = basis if option == 'standard_with_fatband': Lobsterindict['createFatband'] = basis return cls(Lobsterindict)
[docs]def get_all_possible_basis_combinations(min_basis: list, max_basis: list) -> list: """ Args: min_basis: list of basis entries: e.g., ['Si 3p 3s '] max_basis: list of basis entries: e.g., ['Si 3p 3s '] Returns: all possible combinations of basis functions, e.g. [['Si 3p 3s']] """ max_basis_lists = [x.split() for x in max_basis] min_basis_lists = [x.split() for x in min_basis] # get all possible basis functions basis_dict = OrderedDict({}) # type: Dict[Any, Any] for iel, el in enumerate(max_basis_lists): basis_dict[el[0]] = {"fixed": [], "variable": [], "combinations": []} for basis in el[1:]: if basis in min_basis_lists[iel]: basis_dict[el[0]]["fixed"].append(basis) if basis not in min_basis_lists[iel]: basis_dict[el[0]]["variable"].append(basis) for L in range(0, len(basis_dict[el[0]]['variable']) + 1): for subset in itertools.combinations(basis_dict[el[0]]['variable'], L): basis_dict[el[0]]["combinations"].append(' '.join([el[0]] + basis_dict[el[0]]['fixed'] + list(subset))) list_basis = [] for el, item in basis_dict.items(): list_basis.append(item['combinations']) # get all combinations start_basis = list_basis[0] if len(list_basis) > 1: for iel, el in enumerate(list_basis[1:], 1): new_start_basis = [] for ielbasis, elbasis in enumerate(start_basis): for ielbasis2, elbasis2 in enumerate(list_basis[iel]): if type(elbasis) != list: new_start_basis.append([elbasis, elbasis2]) else: new_start_basis.append(elbasis.copy() + [elbasis2]) start_basis = new_start_basis return start_basis else: return [[basis] for basis in start_basis]