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Miscellaneous#

stochastix.utils.algebraic_sigmoid #

algebraic_sigmoid(x: ndarray)

Compute an algebraic sigmoid function.

Gradient of this function decays much more slowly in the tails than the standard sigmoid function. It is defined as:

.. math:: f(x) = 0.5 + (x / (2 * \sqrt(1 + x^2)))

Parameters:

  • x (ndarray) –

    The input array.

Returns:

  • –

    The algebraic sigmoid of the input array.

stochastix.utils.entropy #

entropy(p: ndarray, base: float = 2) -> jnp.ndarray

MLE estimator for the entropy of a probability distribution.

Default calculation is in bits. No correction for finite sample size is applied.

Parameters:

  • p (ndarray) –

    The probability distribution.

  • base (float, default: 2 ) –

    The base of the logarithm. Default is 2 (bits).

Returns:

  • ndarray –

    The entropy of the probability distribution.

stochastix.utils.rate_constant_conc_to_count #

rate_constant_conc_to_count(
    rate_constant: ndarray | float,
    reaction_order: float | int | floating | integer,
    volume: float | floating,
    use_molar_units: bool = True,
    avogadro_number: float | floating | None = None,
    return_log: bool = False,
) -> jnp.ndarray

Convert a concentration-based rate constant to a count-based constant.

This converts the macroscopic (deterministic ODE) rate constant k to the mesoscopic (stochastic) propensity constant c used with molecule counts.

General relation for an m-th order reaction

c = k * (V)^(1 - m) [number-density units] c = k * (N_A * V)^(1 - m) [molar units]

Computation is performed in log10 space for numerical stability and interpretability.

Parameters:

  • rate_constant (ndarray | float) –

    Macroscopic rate constant k (in concentration units).

  • reaction_order (float | int | floating | integer) –

    Total order m of the reaction (sum of reactant stoichiometries). May be non-integer for effective kinetics.

  • volume (float | floating) –

    System volume. Liters if use_molar_units is True.

  • use_molar_units (bool, default: True ) –

    Whether k is in molar units (e.g., M^(1-m)/s).

  • avogadro_number (float | floating | None, default: None ) –

    Optional Avogadro's number override. Defaults to 6.02214076e23.

  • return_log (bool, default: False ) –

    If True, return log10(c) instead of c.

Returns:

  • ndarray –

    The propensity constant c (or its log10 if return_log is True).