mario.calc_f_from_z(
e,
z,
*,
method: str | None = None,
solver: str | None = None,
strategy: str | None = None,
)#

Calculate the f total (direct+indirect) environmental transaction coefficients matrix.

\[(I-z)^{\mathsf{T}}f^{\mathsf{T}} = e^{\mathsf{T}}\]

This is the direct path for f. Under method="solve", MARIO solves the transposed system without materializing the w Leontief inverse matrix.

Parameters:

  • e (pandas.DataFrame) – e environmental transaction coefficients matrix.

  • z (pandas.DataFrame) – z intersectoral transaction coefficients matrix.

  • method (str, optional) – Optional runtime compute method override. Accepted values are "auto", "inverse" and "solve".

  • solver (str, optional) – Optional linear solver backend used when the solve path is selected.

  • strategy (str, optional) – Optional sparse linear strategy used when the solve path is selected.

Returns:

f total (direct+indirect) environmental transaction coefficients matrix.

Return type:

pandas.DataFrame

Notes

The returned matrix is \(f=e(I-z)^{-1}\). The solve operates on its transpose and returns the original account-by-node orientation.