from_equation

gala.potential.potential.from_equation(expr, vars, pars, name=None, hessian=False)[source]

Create a potential class from an expression for the potential.

Note

This utility requires having Sympy installed.

Warning

These potentials are not pickle-able and cannot be written out to YAML files (using save())

Parameters
exprsympy.core.expr.Expr, str

Either a Sympy expression, or a string that can be converted to a Sympy expression.

varsiterable

An iterable of variable names in the expression.

parsiterable

An iterable of parameter names in the expression.

namestr (optional)

The name of the potential class returned.

hessianbool (optional)

Generate a function to compute the Hessian.

Returns
CustomPotentialPotentialBase

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, \(\Phi(x) = \frac{1}{2}\,k\,x^2\):

>>> 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 PotentialBase and therefore has many useful methods. For example, to integrate an orbit:

>>> orbit = p1.integrate_orbit([1.,0], dt=0.01, n_steps=1000)