pttools.bubble.integrate

Functions

pttools.bubble.integrate.add_df_dtau(name, cs2_fun)

Add a new differential equation to the cache based on the given sound speed function.

Parameters:

  • name (str) – the name of the function

  • cs2_fun (Callable[[float | float64 | ndarray, float | float64 | ndarray], float | float64 | ndarray] | CPUDispatcher) – function, which gives the speed of sound squared \(c_s^2\).

Returns:

Return type:

(float64, float64*, float64*, float64*) -> none*

pttools.bubble.integrate.fluid_integrate_param(v0, w0, xi0, phase=-1., t_end=const.T_END_DEFAULT, n_xi=const.N_XI_DEFAULT, df_dtau_ptr=DF_DTAU_BAG_PTR, method='odeint')

Integrates parametric fluid equations in df_dtau from an initial condition. Positive t_end integrates along curves from \((v,w) = (0,c_{s,0})\) to \((1,1)\). Negative t_end integrates towards \((0,c_s{s,0})\).

Parameters:

  • v0 (float) – \(v_0\)

  • w0 (float) – \(w_0\)

  • xi0 (float) – \(\xi_0\)

  • phase (float) – phase \(\phi\)

  • t_end (float) – \(t_\text{end}\)

  • n_xi (int) – number of \(\xi\) points

  • df_dtau_ptr ((float64, float64*, float64*, float64*) -> none*) – pointer to the differential equation function

  • method (str) – differential equation solver to be used

Returns:

\(v, w, \xi, t\)

Return type:

Tuple[ndarray, ndarray, ndarray, ndarray]

pttools.bubble.integrate.fluid_integrate_param_numba(t, y0, data, df_dtau_ptr)

Integrate a differential equation using NumbaLSODA.

Parameters:

  • t (ndarray) – time

  • y0 (ndarray) – starting point

  • data (ndarray) – constants

  • df_dtau_ptr ((float64, float64*, float64*, float64*) -> none*) – pointer to the differential equation function

Returns:

\(v, w, \xi\), success status

pttools.bubble.integrate.fluid_integrate_param_odeint(t, y0, data, df_dtau_ptr)

Integrate a differential equation using scipy.integrate.odeint().

Parameters:

  • t (ndarray) – time

  • y0 (ndarray) – starting point

  • df_dtau_ptr ((float64, float64*, float64*, float64*) -> none*) – pointer to the differential equation function, which is already in the cache

  • data (ndarray)

Returns:

\(v, w, \xi\), success status

pttools.bubble.integrate.fluid_integrate_param_solve_ivp(t, y0, data, df_dtau_ptr, method)

Integrate a differential equation using scipy.integrate.solve_ivp().

Parameters:

  • t (ndarray) – time

  • y0 (ndarray) – starting point

  • df_dtau_ptr ((float64, float64*, float64*, float64*) -> none*) – pointer to the differential equation function, which is already in the cache

  • method (str) – name of the integrator to be used. See the scipy.integrate.solve_ivp() documentation.

  • data (ndarray)

pttools.bubble.integrate.gen_df_dtau(cs2_fun)

Generate a function for the differentials of fluid variables \((v, w, \xi)\) in parametric form. The parametrised differential equation is as in Hindmarsh et al., 2019 eq. B.14-16:

  • \(\frac{dv}{dt} = 2v c_s^2 (1-v^2) (1 - \xi v)\)

  • \(\frac{dw}{dt} = \frac{w}{1-v^2} \frac{\xi - v}{1 - \xi v} (\frac{1}{c_s^2}+1) \frac{dv}{dt}\)

  • \(\frac{d\xi}{dt} = \xi \left( (\xi - v)^2 - c_s^2 (1 - \xi v)^2 \right)\)

Parameters:

cs2_fun (Callable[[float | float64 | ndarray, float | float64 | ndarray], float | float64 | ndarray] | CPUDispatcher) – function, which gives the speed of sound squared \(c_s^2\).

Returns:

function for the differential equation

Return type:

Callable[[float, ndarray, ndarray, ndarray | None], None] | CFunc

pttools.bubble.integrate.precompile()

Attributes

pttools.bubble.integrate.differentials = <pttools.speedup.differential.DifferentialCache object>

Cache for the differential equations. New differential equations have to be added here before usage so that they can be found by scipy.integrate.odeint() and scipy.integrate.solve_ivp().

pttools.bubble.integrate.DF_DTAU_BAG_PTR = 137771129938192

Pointer to the differential equation of the bag model