The database compute API resolves named blocks and their dependencies for a scenario. Standalone calc_* functions are listed in Calculations. To request blocks from a database:

db.resolve("Xa")
db.resolve_many(["u", "s", "Xc"])
db.calc_all(["fc", "pc"])
db.Xa
db.wcc

Use mario.CoreModel.available_matrices to list the block names accepted by the current table, and mario.CoreModel.get_block_spec to inspect their semantic axes.

For SUT databases, the built-in split and quadrant blocks include U, u, S, s, Xa, Xc, Va, Vc, Ea, Ec, Ya, Yc, wcc, wca, wac, waa, fa, fc, ma, mc, pa and pc. The canonical commodity production vector name is Xc; Cx is not a built-in MARIO matrix name.

Use and supply coefficients#

The native use and supply calculations have dedicated block pages:

In particular, u divides each use-flow column by activity production. s follows the database technology assumption:

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

The native SUT calculation reference also links production vectors, Leontief/Ghosh quadrants, direct-output coefficients and price vectors.

Core equations#

IOT results follow the equations in Calculations. For SUT, u maps activity production to commodity inputs and s maps commodity demand to activity production. The technology assumption determines the construction of s; see Supply and Use Tables. Once those coefficients are available, the four Leontief quadrants are:

\[\begin{split}\begin{aligned} w_{cc} &= (I-us)^{-1}, & w_{ca} &= w_{cc}u, \\ w_{aa} &= (I-su)^{-1}, & w_{ac} &= w_{aa}s. \end{aligned}\end{split}\]

The total environmental multipliers include direct coefficients on both sides:

\[f_a = (e_a+e_cu)w_{aa}, \qquad f_c = (e_as+e_c)w_{cc}.\]

The value-added multipliers ma and mc use the same equations with \(v_a\) and \(v_c\) in place of \(e_a\) and \(e_c\). The price vectors sum all factor rows:

\[p_a = m_a^{\mathsf{T}}\mathbf{1}, \qquad p_c = m_c^{\mathsf{T}}\mathbf{1}.\]

The solve path evaluates the same multipliers through transposed linear systems. For example:

\[(I-us)^{\mathsf{T}} f_c^{\mathsf{T}} = (e_as+e_c)^{\mathsf{T}}.\]

This avoids constructing wcc when it is not otherwise needed. Runtime settings and already materialized blocks determine the selected path; db.explain("fc") describes the current dependency plan. An already stored result is returned directly, so that plan does not reconstruct how it was originally calculated.

Block catalog#

The reference table below reuses the authoritative nomenclature matrix catalog and therefore covers both IOT and SUT built-ins, along with their table format, mode and default axes.

For an introduction with block diagrams, see IOT structure and SUT structure. Sets and indices explains the sets and aliases. * marks extension axes that can carry additional levels via matrix_layouts; ** marks the assumption-dependent definition of s.

Matrix Mode Table format(s) Also known as Description Row indices Column indices
Z Flows IOT T Intersectoral transaction flows matrix Region, Sector Region, Sector
z Coefficients IOT A Intersectoral transaction coefficients matrix Region, Sector Region, Sector
w Coefficients IOT L Leontief inverse matrix Region, Sector Region, Sector
Y Flows IOT F Final demand matrix Region, Sector Region, Consumption category
X Flows IOT x, q Total production vector Region, Sector -
V Flows IOT F Value added transaction flows matrix Factor of production* Region, Sector
v Coefficients IOT f, B, S Value added coefficients matrix Factor of production* Region, Sector
VY Flows All S_Y, F_hh, F_y Value added transaction matrix for final demand Factor of production* Region, Consumption category
E Flows IOT F, D_pba, terr Environmental transaction flows matrix Satellite account* Region, Sector
e Coefficients IOT f, B, S Environmental transaction coefficients matrix Satellite account* Region, Sector
EY Flows All S_Y, F_hh, F_y Environmental transaction flows matrix for final demand Satellite account* Region, Consumption category
M Flows IOT Total (direct+indirect) value added transaction matrix Factor of production* Region, Sector
m Coefficients IOT Total (direct+indirect) value added coefficients matrix Factor of production* Region, Sector
m_ex Coefficients IOT Total (direct+indirect) value added coefficients matrix, exploded by origin region and sector Factor of production, Region, Sector Region, Sector
F Flows IOT D_cba, con Total (direct+indirect) environmental transaction flows matrix Satellite account* Region, Sector
f Coefficients IOT M Total (direct+indirect) environmental coefficients matrix Satellite account* Region, Sector
f_ex Coefficients IOT Total (direct+indirect) environmental coefficients matrix, exploded by origin region and sector Satellite account, Region, Sector Region, Sector
p Coefficients IOT Price index vector Region, Sector -
p_ex Coefficients IOT Price index, exploded by origin region and sector Factor of production, Region, Sector Region, Sector
U Flows SUT T Use transaction flows matrix Region, Commodity Region, Activity
u Coefficients SUT A Use transaction coefficients matrix Region, Commodity Region, Activity
S Flows SUT V, M, T Make transaction flows matrix Region, Activity Region, Commodity
s Coefficients SUT A Make transaction coefficients matrix - Market share or inverted product-mix matrix** Region, Activity Region, Commodity
c Coefficients SUT Product-mix matrix Region, Commodity Region, Activity
wcc Coefficients SUT w Leontief inverse matrix, commodity-by-commodity coefficients Region, Commodity Region, Commodity
wca Coefficients SUT w Leontief inverse matrix, commodity-by-activity coefficients Region, Commodity Region, Activity
wac Coefficients SUT w Leontief inverse matrix, activity-by-commodity coefficients Region, Activity Region, Commodity
waa Coefficients SUT w Leontief inverse matrix, activity-by-activity coefficients Region, Activity Region, Activity
Yc Flows SUT F Final demand of commodities matrix Region, Commodity Region, Consumption category
Ya Flows SUT F Final demand of activities matrix Region, Activity Region, Consumption category
Xc Flows SUT Q Total demand (or production) of commodities vector Region, Commodity -
Xa Flows SUT X Total demand (or production) of activities vector Region, Activity -
Vc Flows SUT Value added transaction flows by commodity matrix Factor of production* Region, Commodity
Va Flows SUT Value added transaction flows by activity matrix Factor of production* Region, Activity
vc Coefficients SUT Value added transaction coefficients by commodity matrix Factor of production* Region, Commodity
va Coefficients SUT Value added transaction coefficients by activity matrix Factor of production* Region, Activity
Ec Flows SUT Environmental transaction flows by commodity matrix Satellite account* Region, Commodity
Ea Flows SUT Environmental transaction flows by activity matrix Satellite account* Region, Activity
ec Coefficients SUT Environmental transaction coefficients by commodity matrix Satellite account* Region, Commodity
ea Coefficients SUT Environmental transaction coefficients by activity matrix Satellite account* Region, Activity
Mc Flows SUT Total (direct+indirect) value added transaction by commodity matrix Factor of production* Region, Commodity
Ma Flows SUT Total (direct+indirect) value added transaction by activity matrix Factor of production* Region, Activity
mc Coefficients SUT Total (direct+indirect) value added coefficients by commodity matrix Factor of production* Region, Commodity
ma Coefficients SUT Total (direct+indirect) value added coefficients by activity matrix Factor of production* Region, Activity
mc_ex Coefficients IOT Total (direct+indirect) value added coefficients by commodity matrix, exploded by origin region and activity Factor of production, Region, Activity Region, Commodity
ma_ex Coefficients IOT Total (direct+indirect) value added coefficients by activity matrix, exploded by origin region and activity Factor of production, Region, Activity Region, Activity
Fc Flows SUT Total (direct+indirect) environmental transaction flows by commodity matrix Satellite account* Region, Commodity
Fa Flows SUT Total (direct+indirect) environmental transaction flows by actvity matrix Satellite account* Region, Activity
fc Coefficients SUT Total (direct+indirect) environmental coefficients by commodity matrix Satellite account* Region, Commodity
fa Coefficients SUT Total (direct+indirect) environmental coefficients by activity matrix Satellite account* Region, Activity
fc_ex Coefficients IOT Total (direct+indirect) environmental coefficients by commodity matrix, exploded by origin region and activity Satellite account, Region, Activity Region, Commodity
fa_ex Coefficients IOT Total (direct+indirect) environmental coefficients by activity matrix, exploded by origin region and activity Satellite account, Region, Activity Region, Activity
pc Coefficients SUT Price index vector by commodity Region, Commodity -
pa Coefficients SUT Price index vector by activity Region, Activity -
pc_ex Coefficients IOT Price indices by commodity, exploded by origin region and activity Factor of production, Region, Activity Region, Commodity
pa_ex Coefficients IOT Price indices by activity, exploded by origin region and activity Factor of production, Region, Activity Region, Activity
g Coefficients IOT G Ghosh coefficients matrix Region, Sector Region, Sector
b Coefficients IOT B Intersectoral transaction direct-output coefficients matrix Region, Sector Region, Sector

Detailed block reference#

These pages describe database access to the native SUT blocks and link to the corresponding standalone calc_* functions.