def atomic_ordering_energy(self, dbe): """ Return the atomic ordering contribution in symbolic form. Description follows Servant and Ansara, Calphad, 2001. """ phase = dbe.phases[self.phase_name] ordered_phase_name = phase.model_hints.get('ordered_phase', None) disordered_phase_name = phase.model_hints.get('disordered_phase', None) if phase.name != ordered_phase_name: return S.Zero disordered_model = self.__class__(dbe, sorted(self.components), disordered_phase_name) constituents = [sorted(set(c).intersection(self.components)) \ for c in dbe.phases[ordered_phase_name].constituents] # Fix variable names variable_rename_dict = {} disordered_sitefracs = [x for x in disordered_model.energy.free_symbols if isinstance(x, v.SiteFraction)] for atom in disordered_sitefracs: # Replace disordered phase site fractions with mole fractions of # ordered phase site fractions. # Special case: Pure vacancy sublattices all_species_in_sublattice = \ dbe.phases[disordered_phase_name].constituents[ atom.sublattice_index] if atom.species.name == 'VA' and len(all_species_in_sublattice) == 1: # Assume: Pure vacancy sublattices are always last vacancy_subl_index = \ len(dbe.phases[ordered_phase_name].constituents)-1 variable_rename_dict[atom] = \ v.SiteFraction( ordered_phase_name, vacancy_subl_index, atom.species) else: # All other cases: replace site fraction with mole fraction variable_rename_dict[atom] = \ self.mole_fraction( atom.species, ordered_phase_name, constituents, dbe.phases[ordered_phase_name].sublattices ) # Save all of the ordered energy contributions # This step is why this routine must be called _last_ in build_phase ordered_energy = Add(*list(self.models.values())) self.models.clear() # Copy the disordered energy contributions into the correct bins for name, value in disordered_model.models.items(): self.models[name] = value.xreplace(variable_rename_dict) # All magnetic parameters will be defined in the disordered model self.TC = self.curie_temperature = disordered_model.TC self.TC = self.curie_temperature = self.TC.xreplace(variable_rename_dict) molefraction_dict = {} # Construct a dictionary that replaces every site fraction with its # corresponding mole fraction in the disordered state ordered_sitefracs = [x for x in ordered_energy.free_symbols if isinstance(x, v.SiteFraction)] for sitefrac in ordered_sitefracs: all_species_in_sublattice = \ dbe.phases[ordered_phase_name].constituents[ sitefrac.sublattice_index] if sitefrac.species.name == 'VA' and len(all_species_in_sublattice) == 1: # pure-vacancy sublattices should not be replaced # this handles cases like AL,NI,VA:AL,NI,VA:VA and # ensures the VA's don't get mixed up continue molefraction_dict[sitefrac] = \ self.mole_fraction(sitefrac.species, ordered_phase_name, constituents, dbe.phases[ordered_phase_name].sublattices) return ordered_energy - ordered_energy.xreplace(molefraction_dict)
def search_error(v_str, GF_step=4, use_latex=True): global a global x g = x ** 10 + x ** 8 + x ** 5 + x ** 4 + x ** 2 + x + 1 p = x ** 4 + x + 1 string = '' degree_of_symbol_x, log_table, exp_table = get_tables_log_exp(GF_step, p, use_latex) degree_of_symbol_x_pd = pd.DataFrame(degree_of_symbol_x, columns=['Mult', 'Ans', 'Bin']) if use_latex: string += "\\noindent\n\\begin{minipage}[c]{60mm}\n\\parindent=3em" table = degree_of_symbol_x_pd.to_latex(index=False, escape=False) table = table.replace('toprule', 'hline').replace('midrule', 'hline').replace('bottomrule', 'hline') string += table string += "\n\\end{minipage}" string += "\\hfill" else: string += '\n' string += degree_of_symbol_x_pd.to_string() log_table_pd = pd.DataFrame(log_table, columns=['a', 'log(a)']) if use_latex: string += "\n\\begin{minipage}[c]{30mm}\n" table = log_table_pd.to_latex(index=False, escape=False) table = table.replace('toprule', 'hline').replace('midrule', 'hline').replace('bottomrule', 'hline') string += table string += "\n\\end{minipage}" string += "\\hfill" else: string += '\n' string += log_table_pd.to_string() exp_table_pd = pd.DataFrame(exp_table, columns=['k', r'$\alpha^k$']) if use_latex: string += "\n\\begin{minipage}[c]{30mm}\n" table = exp_table_pd.to_latex(index=False, escape=False) table = table.replace('toprule', 'hline').replace('midrule', 'hline').replace('bottomrule', 'hline') string += table string += "\n\\end{minipage}" string += "\\hfill" string += '\n' else: string += '\n' string += exp_table_pd.to_string() string += '~\\\\ \n ~\\\\ \n\n' v_vec = [int(i) for i in list(v_str)] v = Add() for i in range(len(v_vec)): v += v_vec[i] * x ** i if use_latex: string += '{tab}\n\n$v = {}${newline}\n\n'.format(latex(v), tab=r'~\\', newline=r'\\') else: string += '\n\nv = {}\n\n'.format(v) S1, ind, calc = calc_S(v_vec, 1, GF_step, degree_of_symbol_x, use_latex) if use_latex: string += '$S1 = {} = {} = {}$\n\n'.format(calc, degree_of_symbol_x[ind][2], latex(S1), GF=GF_step) else: string += 'S1 = {} = {} = {}\n'.format(calc, degree_of_symbol_x[ind][2], S1, GF=GF_step) S3, ind, calc = calc_S(v_vec, 3, GF_step, degree_of_symbol_x, use_latex) if use_latex: string += '$S3 = {} = {} = {}$\n\n'.format(calc, degree_of_symbol_x[ind][2], latex(S3), GF=GF_step) else: string += 'S3 = {} = {} = {}\n'.format(calc, degree_of_symbol_x[ind][2], S3, GF=GF_step) S5, ind, calc = calc_S(v_vec, 5, GF_step, degree_of_symbol_x, use_latex) if use_latex: string += '$S5 = {} = {} = {}$\\\\\n\n'.format(calc, degree_of_symbol_x[ind][2], latex(S5), GF=GF_step) else: string += 'S5 = {} = {} = {}\n\n'.format(calc, degree_of_symbol_x[ind][2], S5, GF=GF_step) Lambda1 = S1 success3, Lambda2, Lambda3 = get_lambda_3(S1, S3, S5, degree_of_symbol_x, GF_step) if not success3: success2, Lanbda2, Lambda3 = get_lambda_2(S1, S3, degree_of_symbol_x, GF_step) if success3: if use_latex: string += '${slash}Lambda_0 = 1$\n\n'.format(slash='\\') string += '${slash}Lambda_1 = S_1 = {}$\n\n'.format(latex(Lambda1), slash='\\') string += '${slash}Lambda_2 = (S_1^2 {slash}cdot S_3 + S_5) {slash}cdot {one} = {}$\n\n'. \ format(latex(Lambda2), slash='\\', one=r'{(S_1^3 + S_3)}^{-1}') string += '${slash}Lambda_3 = (S_1^3 + S_3) + S_1{slash}cdot{slash}Lambda_2 = {}$\\\\\n\n'. \ format(latex(Lambda3), slash='\\') else: string += 'Lambda0 = 1\n' string += 'Lambda1 = S1 = {}\n'.format(Lambda1) string += 'Lambda2 = (S1^2*S3 + S5)*(S1^3 + S3)^-1 = {}\n'.format(Lambda2) string += 'Lambda3 = (S1^3 + S3) + S1*Lambda2 = {}\n\n'.format(Lambda3) elif success2: if use_latex: string += '$\\Lambda_0 = 1$\n\n' string += '$\\Lambda_1 = S_1 = {}$\n\n'.format(latex(Lambda1)) string += '$\\Lambda_2 = (S_3 + S_1^3){one} = {}$\n\n'. \ format(latex(Lambda2), one=r'S1^{-1}') else: string += 'Lambda0 = 1\n' string += 'Lambda1 = S1 = {}\n'.format(Lambda1) string += 'Lambda2 = (S3 + S1^3)S1^-1 = {}\n\n'.format(Lambda2) else: if use_latex: string += '$\\Lambda_0 = 1$\n\n' string += '$\\Lambda_1 = S_1 = {}$\n\n'.format(latex(Lambda1)) else: string += 'Lambda0 = 1\n' string += 'Lambda1 = S1 = {}\n\n'.format(Lambda1) Lambda = Add() + 1 + Lambda1 * x + Lambda2 * (x ** 2) + Lambda3 * (x ** 3) max_count = 0 if Lambda1 != 0: max_count = 1 if Lambda2 != 0: max_count = 2 if Lambda3 != 0: max_count = 3 if use_latex: string += '\n$\\Lambda = {}$\\\\\n\n'.format(latex(Lambda)) else: string += 'Lambda = {}\n\n'.format(Lambda) Lambda_vec = np.zeros((2 ** GF_step - 1, 2), dtype=object) count = 0 stop = 0 for i in range(2 ** GF_step - 1): xreplace = Lambda.xreplace({x: a ** i}).as_poly(a, domain='GF(2)').args[0] Lambda_vec[i][0] = degree_mod(xreplace, 2 ** GF_step - 1) Lambda_vec[i][1] = sum_alpha(Lambda_vec[i][0], degree_of_symbol_x) if Lambda_vec[i][1] == 0: count += 1 if xreplace == Lambda_vec[i][0]: if use_latex: string += '$\\Lambda({}) = {} = {}$\n\n'.format(latex(a ** i), latex(Lambda_vec[i][0]), '{:>0{GF}b}'.format(Lambda_vec[i][1], GF=GF_step)) else: string += 'Lambda({}) = {} = {}\n'.format(a ** i, Lambda_vec[i][0], '{:>0{GF}b}'.format(Lambda_vec[i][1], GF=GF_step)) else: if use_latex: string += '$\\Lambda({}) = {} = {} = {}$\n\n'.format(latex(a ** i), latex(xreplace), latex(Lambda_vec[i][0]), '{:>0{GF}b}'.format(Lambda_vec[i][1], GF=GF_step)) else: string += 'Lambda({}) = {} = {} = {}\n'.format(a ** i, xreplace, Lambda_vec[i][0], '{:>0{GF}b}'.format(Lambda_vec[i][1], GF=GF_step)) if count == max_count: stop = i + 1 break ans = np.where(Lambda_vec[:stop, 1] == 0)[0] ans = [a ** int(an) for an in ans] if use_latex: string += '~\\\\\n\n' string += "\\noindent\n\\begin{minipage}[c]{40mm}\n\\parindent=3em" else: string += '\n' for i in range(len(ans)): if use_latex: string += '$x_{} = {}${end}'.format(i, latex(ans[i]), end='\n~\\\\\n' if i == (len(ans)) else '\n\n') else: string += 'x{} = {}\n'.format(i, ans[i]) if use_latex: string += "\n\\end{minipage}" string += "\\hfill" string += "\n\\begin{minipage}[c]{40mm}\n" # string += '\n\n' else: string += '\n' ans = [degree_mod(an ** (-1), 2 ** GF_step - 1) for an in ans] for i in range(len(ans)): if use_latex: string += '$x_{}^{one} = {}${end}'.format(i, latex(ans[i]), one='{-1}', end='\n~\\\\\n' if i == (len(ans)) else '\n\n') else: string += 'x{}^-1 = {}\n'.format(i, ans[i], one='{-1}') if use_latex: string += "\n\\end{minipage}" string += "\\hfill" string += "\n\\begin{minipage}[c]{40mm}\n" # string += '\n\n' else: string += '\n' ans = [0 if an == 1 else 1 if an == a else int(an.args[1]) for an in ans] for i in range(len(ans)): if use_latex: string += '$\\log(x_{}^{one}) = {}$\n\n'.format(i, ans[i], one='{-1}') else: string += 'log(x{}^-1) = {}\n'.format(i, ans[i]) if use_latex: string += "\n\\end{minipage}" string += "\\hfill" ans.sort() string += '\n~\\\\\n\nError in: {}'.format(ans) return string, ans