Python Add.subs方法代码示例

# 需要导入模块: from sympy import Add [as 别名]
# 或者: from sympy.Add import subs [as 别名]
    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, 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 = {}
        for atom in disordered_model.energy.atoms(v.SiteFraction):
            # 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 == "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
        for sitefrac in ordered_energy.atoms(v.SiteFraction):
            all_species_in_sublattice = dbe.phases[ordered_phase_name].constituents[sitefrac.sublattice_index]
            if sitefrac.species == "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.subs(molefraction_dict, simultaneous=True)

# 需要导入模块: from sympy import Add [as 别名]
# 或者: from sympy.Add import subs [as 别名]
def _inverse_mellin_transform(F, s, x_, strip, as_meijerg=False):
    """ A helper for the real inverse_mellin_transform function, this one here
        assumes x to be real and positive. """
    from sympy import (expand, expand_mul, hyperexpand, meijerg, And, Or,
                       arg, pi, re, factor, Heaviside, gamma, Add)
    x = _dummy('t', 'inverse-mellin-transform', F, positive=True)
    # Actually, we won't try integration at all. Instead we use the definition
    # of the Meijer G function as a fairly general inverse mellin transform.
    F = F.rewrite(gamma)
    for g in [factor(F), expand_mul(F), expand(F)]:
        if g.is_Add:
            # do all terms separately
            ress = [_inverse_mellin_transform(G, s, x, strip, as_meijerg,
                                              noconds=False) \
                    for G in g.args]
            conds = [p[1] for p in ress]
            ress = [p[0] for p in ress]
            res = Add(*ress)
            if not as_meijerg:
                res = factor(res, gens=res.atoms(Heaviside))
            return res.subs(x, x_), And(*conds)

        try:
            a, b, C, e, fac = _rewrite_gamma(g, s, strip[0], strip[1])
        except IntegralTransformError:
            continue
        G = meijerg(a, b, C/x**e)
        if as_meijerg:
            h = G
        else:
            h = hyperexpand(G)
            if h.is_Piecewise and len(h.args) == 3:
                # XXX we break modularity here!
                h = Heaviside(x - abs(C))*h.args[0].args[0] \
                  + Heaviside(abs(C) - x)*h.args[1].args[0]
        # We must ensure that the intgral along the line we want converges,
        # and return that value.
        # See [L], 5.2
        cond = [abs(arg(G.argument)) < G.delta*pi]
        # Note: we allow ">=" here, this corresponds to convergence if we let
        # limits go to oo symetrically. ">" corresponds to absolute convergence.
        cond += [And(Or(len(G.ap) != len(G.bq), 0 >= re(G.nu) + 1),
                     abs(arg(G.argument)) == G.delta*pi)]
        cond = Or(*cond)
        if cond is False:
            raise IntegralTransformError('Inverse Mellin', F, 'does not converge')
        return (h*fac).subs(x, x_), cond

    raise IntegralTransformError('Inverse Mellin', F, '')