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

Calculate the X total production vector directly from z and Y.

\[(I-z)X = Y\mathbf{1}\]

This is the direct path for X. Under method="solve", MARIO solves the linear system (I - z) X = Y_total without materializing the w Leontief inverse matrix.

Parameters:

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

  • Y (pandas.DataFrame) – Y final demand 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:

X total production vector.

Return type:

pandas.DataFrame

Notes

The equivalent inverse expression is \(X=(I-z)^{-1}(Y\mathbf{1})\). The returned single column is named production.