Source code for gala.potential.potential.util

""" Utilities for Potential classes """

# Standard library
from functools import wraps

# Third-party
import numpy as np

# Project
from ..common import PotentialParameter
from .core import PotentialBase

__all__ = ['from_equation']


[docs]def from_equation(expr, vars, pars, name=None, hessian=False): r""" Create a potential class from an expression for the potential. .. note:: This utility requires having `Sympy <http://www.sympy.org/>`_ installed. .. warning:: These potentials are *not* pickle-able and cannot be written out to YAML files (using `~gala.potential.PotentialBase.save()`) Parameters ---------- expr : :class:`sympy.core.expr.Expr`, str Either a ``Sympy`` expression, or a string that can be converted to a ``Sympy`` expression. vars : iterable An iterable of variable names in the expression. pars : iterable An iterable of parameter names in the expression. name : str (optional) The name of the potential class returned. hessian : bool (optional) Generate a function to compute the Hessian. Returns ------- CustomPotential : `~gala.potential.PotentialBase` A potential class that represents the input equation. To instantiate the potential, use just like a normal class with parameters. Examples -------- Here we'll create a potential class for the harmonic oscillator potential, :math:`\Phi(x) = \frac{1}{2}\,k\,x^2`:: >>> Potential = from_equation("1/2*k*x**2", vars="x", pars="k", ... name='HarmonicOscillator') >>> p1 = Potential(k=1.) >>> p1 <HarmonicOscillatorPotential: k=1.00 (dimensionless)> The potential class (and object) is a fully-fledged subclass of `~gala.potential.PotentialBase` and therefore has many useful methods. For example, to integrate an orbit:: >>> from gala.potential import Hamiltonian >>> H = Hamiltonian(p1) >>> orbit = H.integrate_orbit([1., 0], dt=0.01, n_steps=1000) """ try: import sympy from sympy.utilities.lambdify import lambdify except ImportError: raise ImportError("sympy is required to use 'from_equation()' " "potential class creation.") # convert all input to Sympy objects expr = sympy.sympify(expr) vars = [sympy.sympify(v) for v in vars] var_names = [v.name for v in vars] pars = [sympy.sympify(p) for p in pars] par_names = [p.name for p in pars] ndim = len(vars) # Energy / value energyfunc = lambdify(vars + pars, expr, dummify=False, modules='numpy') # Gradient gradfuncs = [] for var in vars: gradfuncs.append(lambdify(vars + pars, sympy.diff(expr, var), dummify=False, modules='numpy')) parameters = {} for _name in par_names: parameters[_name] = PotentialParameter(_name, physical_type='dimensionless') class CustomPotential(PotentialBase, parameters=parameters): ndim = len(vars) def _energy(self, w, t=0.): kw = self.parameters.copy() for k, v in kw.items(): kw[k] = v.value for i, name in enumerate(var_names): kw[name] = w[:, i] return np.array(energyfunc(**kw)) def _gradient(self, w, t=0.): kw = self.parameters.copy() for k, v in kw.items(): kw[k] = v.value for i, name in enumerate(var_names): kw[name] = w[:, i] grad = np.vstack([f(**kw)[np.newaxis] for f in gradfuncs]) return grad.T if name is not None: # name = _classnamify(name) if "potential" not in name.lower(): name = name + "Potential" CustomPotential.__name__ = str(name) # Hessian if hessian: hessfuncs = [] for var1 in vars: for var2 in vars: hessfuncs.append(lambdify(vars + pars, sympy.diff(expr, var1, var2), dummify=False, modules='numpy')) def _hessian(self, w, t): kw = self.parameters.copy() for k, v in kw.items(): kw[k] = v.value for i, name in enumerate(var_names): kw[name] = w[:, i] # expand = [np.newaxis] * w[i].ndim # This ain't pretty, bub arrs = [] for f in hessfuncs: hess_arr = np.array(f(**kw)) if hess_arr.shape != w[:, i].shape: hess_arr = np.tile(hess_arr, reps=w[:, i].shape) arrs.append(hess_arr) hess = np.vstack(arrs) return hess.reshape((ndim, ndim, len(w[:, i]))) CustomPotential._hessian = _hessian CustomPotential.save = None return CustomPotential
def format_doc(*args, **kwargs): """ Replaces the docstring of the decorated object and then formats it. Modeled after astropy.utils.decorators.format_doc """ def set_docstring(obj): # None means: use the objects __doc__ doc = obj.__doc__ # Delete documentation in this case so we don't end up with # awkwardly self-inserted docs. obj.__doc__ = None # If the original has a not-empty docstring append it to the format # kwargs. kwargs['__doc__'] = obj.__doc__ or '' obj.__doc__ = doc.format(*args, **kwargs) return obj return set_docstring class SympyWrapper: @classmethod def as_decorator(cls, func=None, **kwargs): self = cls(**kwargs) if func is not None and not kwargs: return self(func) else: return self def __init__(self, func=None, var=None, include_G=True): if var is None: _var = 'x, y, z' else: _var = var self.var = _var self.include_G = include_G def __call__(self, wrapped_function): @wraps(wrapped_function) def wrapper(cls, *func_args, **func_kwargs): try: import sympy as sy # noqa except ImportError: raise ImportError("Converting to a latex expression requires " "the sympy package to be installed") _var = sy.symbols(self.var, seq=True) _var = {v.name: v for v in _var} if cls._parameters: par = sy.symbols(' '.join(cls._parameters.keys()), seq=True) par = {v.name: v for v in par} else: par = {} if self.include_G: par['G'] = sy.symbols('G') return wrapped_function(cls, _var, par) return wrapper sympy_wrap = SympyWrapper.as_decorator