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Normal Static LCA#

The actual LCA class (bw2calc.LCA) is more of a coordinator then an accountant, as the matrix builder is doing much of the data manipulation. The lca class only has to do the following:

Translate the functional unit into a demand array
Find the right parameter arrays, and ask matrix builder for matrices
Solve the linear system \(Ax=B\) using SuperLU or UMFpack.
Multiply the result by the LCIA CFs, if a LCIA method is present

Due to licensing conflicts, recent versions of SciPy do not include UMFpack. UMFpack is faster than SuperLU, especially for repeated calculations. Python wrappers for UMFpack must be installed separately using scikits.umfpack.

The LCA class also has some convenience functions for redoing some calculations with slight changes, e.g. for uncertainty and sensitivity analysis. See the redo()*\ and rebuild_* methods in the LCA class.

Stochastic LCA#

The various stochastic Monte Carlo LCA classes function almost the same as the static LCA, and reuse most of the code. The only change is that instead of building matrices once, random number generators from stats_arrays are instantiated directly from each parameter array. For each Monte Carlo iteration, the amount column is then overwritten with the output from the random number generator, and the system solved as normal. The code to do a new Monte Carlo iteration is quite succinct:

def next(self):
    self.rebuild_technosphere_matrix(self.tech_rng.next())
    self.rebuild_biosphere_matrix(self.bio_rng.next())
    if self.lcia:
        self.rebuild_characterization_matrix(self.cf_rng.next())

    self.lci_calculation()

    if self.lcia:
        self.lcia_calculation()
        return self.score
    else:
        return self.supply_array

This design is one of the most elegant parts of Brightway2.

Because there is a common procedure to build static and stochastic matrices, any matrix can easily support uncertainty, e.g. not just LCIA characterization factors, but also weighting, normalization, and anything else you can think of; see Defining a new Matrix - example of Weighting and Normalization matrices.