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utils

species_concentration 

species_concentration(
    concentration, log_beta, stoichiometry, full=False
)

Calculate the species concentrations through the mass action law.

\[ S_{i} = \beta_i \prod_{j=1}^{N_c} C_j^{p_{ij}} \]

With \(S_i\) being the concentration of the species \(i\), \(\beta_i\) the equilibrium constant of the species \(i\), \(C_j\) the concentration of the component \(j\), and \(p_{ij}\) the stoichiometric coefficient of the component \(j\) in the species \(i\).

Parameters:

Name Type Description Default
concentration ndarray

The concentration array of shape (n, c+p), where n is the number of points c is the number of components and p is the number of solid species.

 required
log_beta ndarray

The logarithm of the equilibrium constants with shape (n, s), where s is the number of solid species.

 required
stoichiometry ndarray

The stoichiometry matrix with shape (n, s), where s is the number of soluble species.

 required
full bool

If True, return the concentrations of all species including the original concentrations. If False, return only the concentrations of the new species.

 False

Returns:

Type Description
ndarray

The calculated species concentrations.
Source code in src/libeq/utils.py 
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def species_concentration(
    concentration,
    log_beta,
    stoichiometry,
    full=False,
):
    r"""
    Calculate the species concentrations through the mass action law.

    $$
    S_{i} = \beta_i \prod_{j=1}^{N_c} C_j^{p_{ij}}
    $$

    With $S_i$ being the concentration of the species $i$, $\beta_i$ the equilibrium constant of the species $i$,
    $C_j$ the concentration of the component $j$, and $p_{ij}$ the stoichiometric coefficient of the component $j$ in the species $i$.

    Parameters
    ----------
    concentration : numpy.ndarray
        The concentration array of shape (n, c+p), where n is the number of points c is the number of components and p is the number of solid species.
    log_beta : numpy.ndarray
        The logarithm of the equilibrium constants with shape (n, s), where s is the number of solid species.
    stoichiometry : numpy.ndarray
        The stoichiometry matrix with shape (n, s), where s is the number of soluble species.
    full : bool, optional
        If True, return the concentrations of all species including the original concentrations.
        If False, return only the concentrations of the new species.

    Returns
    -------
    numpy.ndarray
        The calculated species concentrations.

    """
    nc = stoichiometry.shape[0]
    _c = np.log10(concentration[:, :nc])

    cext = 10 ** (log_beta + _c @ stoichiometry)

    if full:
        p = np.concatenate((concentration, cext), axis=1)
    else:
        p = cext

    return p