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

Calculate the m total (direct+indirect) value added coefficients matrix.

\[(I-z)^{\mathsf{T}}m^{\mathsf{T}} = v^{\mathsf{T}}\]

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

Parameters:

  • v (pandas.DataFrame) – v value added 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:

m total (direct+indirect) value added coefficients matrix.

Return type:

pandas.DataFrame

Notes

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