simulations

pfi.utils.simulations

Simulation utilities for benchmark dynamical systems.

g_rate(x1, x2, gr)

Compute the cell growth rate used in the toggle-switch simulator.

Parameters:

• x1 (ndarray of shape (n_samples,)) –

  First coordinate of the state.

• x2 (ndarray of shape (n_samples,)) –

  Second coordinate of the state.

• gr (float) –

  Growth-rate scale.

Returns:

• rate ( ndarray of shape (n_samples,) ) –

  Growth rate for each sample.

simulate_ornstein_uhlenbeck(Om, D, m0, S0, nsamples, ndim, Dt, K, dt=0.006)

Simulate snapshots from a linear Ornstein-Uhlenbeck process.

Parameters:

• Om (ndarray of shape (ndim, ndim)) –

  Drift matrix.

• D (ndarray of shape (ndim, ndim)) –

  Diffusion matrix.

• m0 (ndarray of shape (ndim,)) –

  Mean of the initial Gaussian distribution.

• S0 (float) –

  Isotropic variance factor for the initial covariance S0 * I.

• nsamples (int) –

  Number of particles sampled at each snapshot time.

• ndim (int) –

  State dimension.

• Dt (float) –

  Snapshot interval in simulation time.

• K (int) –

  Number of snapshots.

• dt (float, default: 0.006 ) –

  Euler-Maruyama integration step.

Returns:

• samples ( list of length K ) –

  samples[k] is an ndarray of shape (nsamples, ndim).

• tt ( ndarray of shape (K,) ) –

  Snapshot times.

simulate_toggle_switch(model_params, vol, gr, nsamples, ndim, Dt, K, dt=0.01)

Simulate snapshots from stochastic toggle-switch dynamics.

Parameters:

• model_params (array-like of shape (7,)) –

  Toggle-switch parameters [a1, a2, b1, b2, k1, k2, n].

• vol (float) –

  System volume scaling the stochastic term.

• gr (float) –

  Growth-rate scale. Growth is active only when gr > 0.

• nsamples (int) –

  Number of particles sampled at the initial time.

• ndim (int) –

  State dimension.

• Dt (float) –

  Snapshot interval in simulation time.

• K (int) –

  Number of snapshots.

• dt (float, default: 0.01 ) –

  Euler-Maruyama integration step.

Returns:

• samples_full ( list of length K ) –

  samples_full[k] is an ndarray of shape (n_k, ndim), where n_k can increase across snapshots when growth is active.

• tt ( ndarray of shape (K,) ) –

  Snapshot times.

toggle_switch(x, model_params)

Evaluate the deterministic toggle-switch production term.

Parameters:

• x (ndarray of shape (n_samples, 2)) –

  State values, where each row is [x1, x2].

• model_params (array-like of shape (7,)) –

  Model parameters [a1, a2, b1, b2, k1, k2, n].

Returns:

• f ( ndarray of shape (n_samples, 2) ) –

  Deterministic production term for each sample.