Source code for chempy.util.stoich

# -*- coding: utf-8 -*-
Utility functions related to stoichiometry.

from __future__ import (absolute_import, division, print_function)

import numpy as np
from chempy.units import unit_of, to_unitless

[docs]def get_coeff_mtx(substances, stoichs): """ Create a net stoichiometry matrix from reactions described by pairs of dictionaries. Parameters ---------- substances : sequence of keys in stoichs dict pairs stoichs : sequence of pairs of dicts Pairs of reactant and product dicts mapping substance keys to stoichiometric coefficients (integers). Returns ------- 2 dimensional array of shape (len(substances), len(stoichs)) """ A = np.zeros((len(substances), len(stoichs)), dtype=int) for ri, sb in enumerate(substances): for ci, (reac, prod) in enumerate(stoichs): A[ri, ci] = prod.get(sb, 0) - reac.get(sb, 0) return A
[docs]def decompose_yields(yields, rxns, atol=1e-10): """ Decomposes yields into mass-action reactions This function offers a way to express a reaction with non-integer stoichiometric coefficients as a linear combination of production reactions with integer coefficients. Ak = y A is (n_species x n_reactions) matrix, k is "rate coefficient", y is yields Parameters ---------- yields : OrderedDict Specie names as keys and yields as values. rxns : iterable :class:`Reaction` instances Dict keys must match those of ``yields`` each pair of dictionaries gives stoichiometry (1st is reactant, 2nd is products). atol : float Absolute tolerance for residuals. Examples -------- >>> from chempy import Reaction >>> h2a = Reaction({'H2O': 1}, {'H2': 1, 'O': 1}) >>> h2b = Reaction({'H2O': 1}, {'H2': 1, 'H2O2': 1}, inact_reac={'H2O': 1}) >>> decompose_yields({'H2': 3, 'O': 2, 'H2O2': 1}, [h2a, h2b]) array([2., 1.]) Raises ------ ValueError When atol is exceeded numpy.LinAlgError When numpy.linalg.lstsq fails to converge Returns ------- 1-dimensional array of effective rate coefficients. """ from chempy import ReactionSystem # Sanity check: rxn_keys = set.union(*(rxn.keys() for rxn in rxns)) for key in yields.keys(): if key not in rxn_keys: raise ValueError("Substance key: %s not in reactions" % key) rsys = ReactionSystem(rxns, rxn_keys) A = rsys.net_stoichs(yields.keys()) b = list(yields.values()) unit = unit_of(b[0]) x, residuals, rank, s = np.linalg.lstsq( np.asarray(A.T, dtype=np.float64), to_unitless(b, unit), rcond=2e-16*max(A.shape)) if len(residuals) > 0: if np.any(residuals > atol): raise ValueError("atol not satisfied") return x*unit