db.s

For the standalone function, see mario.calc_s().

Calculate activity-by-commodity supply coefficients using the database technology assumption.

\[\begin{split}s=\begin{cases} S\operatorname{diag}(X_c)^{-1} & \text{IT},\\ \left(S^{\mathsf{T}}\operatorname{diag}(X_a)^{-1}\right)^{-1} & \text{PT}. \end{cases}\end{split}\]

Inputs#

S: supply flows, with activity rows and commodity columns.

For IT, Xc is indexed like S.columns. For PT, Xa is indexed like S.index; the intermediate product-mix matrix is c.

Result#

Activity nodes on rows and commodity nodes on columns. Under IT, s is the market-share matrix. Under PT, it is the inverse of c.

Calculation details#

db.tech_assumption selects IT (industry-based) or PT (product-based). PT requires square c; its inverse swaps the commodity and activity axes. If c is singular, the current inverse builder falls back to the Moore-Penrose pseudoinverse. Under IT, zero commodity production gives a zero coefficient column.

See Supply and Use Tables for assumption switching and the fallback to IT when importing a non-square SUT.

Example#

import mario

db = mario.load_test("SUT", tech_assumption="IT")
result = db.resolve("s")
# Dotted access requests the same block:
result = db.s

Use resolve for scenario selection and recomputation options. Existing targets are reused. The other SUT equations are listed in Resolvable Matrices and Blocks.