ARIOPsiModel#

class ARIOPsiModel(pym_mrio, *, order_type='alt', alpha_base=1.0, alpha_max=1.25, alpha_tau=365, rebuild_tau=60, main_inv_dur=90, monetary_factor=1000000, temporal_units_by_step=1, iotable_year_to_temporal_unit_factor=365, infinite_inventories_sect=None, inventory_dict=None, productive_capital_vector=None, productive_capital_to_VA_dict=None, psi_param=0.8, inventory_restoration_tau=60)[source]#

Bases: ARIOBaseModel

Methods

`__init__`(pym_mrio, *[, order_type, ...])	An ARIO model with some additional features.
`calc_inventory_constraints`(production)	Compute inventory constraints (with psi parameter, for the non psi version, see `calc_inventory_constraints()`)
`calc_matrix_stock_gap`(matrix_stock_goal)	Computes and returns inputs stock gap matrix
`calc_orders`()	Computes and sets the orders (intermediate demand) for the next step.
`calc_overproduction`()	Computes and updates the overproduction vector.
`calc_production`(current_temporal_unit)	Computes and updates actual production.
`distribute_production`([...])	Production distribution module
`rebuild_prod_house_event`(ev_id)
`rebuild_prod_indus_event`(ev_id)
`update_prod_delta`()
`write_index`(index_file)	Write the indexes of the different dataframes of the model in a json file.

Attributes

`entire_demand`	Returns the entire demand matrix, including intermediate demand (orders), final demand, and possible rebuilding demand.
`entire_demand_tot`	Returns the entire demand matrix, including intermediate demand (orders), final demand, and possible rebuilding demand.
`final_demand`	Returns the entire intermediate demand matrix (orders)
`final_demand_tot`	Returns the total final demand addressed to each industry
`intermediate_demand`	Returns the entire intermediate demand matrix (orders)
`intermediate_demand_tot`	Returns the total intermediate demand addressed to each industry
`inventory_constraints_act`	Computes and returns inventory constraints for "actual production" (see `calc_inventory_constraints()`)
`inventory_constraints_opt`	Computes and returns inventory constraints for "optimal production" (see `calc_inventory_constraints()`)
`prod_cap_delta_arbitrary`	Return the possible "arbitrary" production capacity lost vector if it was set.
`prod_cap_delta_productive_capital`	Return the possible production capacity lost due to capital destroyed vector if it was set.
`prod_cap_delta_tot`	Computes and return total current production delta.
`production_cap`	Compute and update production capacity.
`production_opt`	Computes and returns "optimal production" \(\iox^{textrm{Opt}}\), as the per industry minimum between total demand and production capacity.
`productive_capital_lost`	Returns current stock of destroyed capital
`rebuild_demand`	Returns the entire intermediate demand matrix (orders)
`rebuild_demand_house`	Returns household rebuilding demand matrix.
`rebuild_demand_house_tot`	Returns total household rebuilding demand vector.
`rebuild_demand_indus`	Returns industrial rebuilding demand matrix.
`rebuild_demand_indus_tot`	Returns total industrial rebuilding demand vector.
`rebuild_demand_tot`	Returns the total rebuild demand addressed to each industry
`rebuild_prod`
`rebuild_prod_house`
`rebuild_prod_indus`
`rebuild_prod_tot`
`psi`	float: Value of the psi parameter.
`restoration_tau`	numpy.ndarray of int: Array of size \(n\) setting for each inputs its characteristic restoration time \(\tau_{\textrm{INV}}\) in `n_temporal_units_by_step`.
`n_temporal_units_by_step`	int, default 1: The number of temporal_units between each step.
`iotable_year_to_temporal_unit_factor`	int, default 365: The (inverse of the) factor by which MRIO data should be multiplied in order to get "per temporal unit value", assuming IO data is yearly.
`rebuild_tau`	int: Rebuilding characteristic time \(\tau_{\textrm{REBUILD}}\) (see Model description).
`overprod_max`	float: Maximum factor of overproduction \(\alpha^{\textrm{max}}\) (default should be 1.25).
`overprod_tau`	float: Characteristic time of overproduction \(\tau_{\alpha}\) in `n_temporal_units_by_step` (default should be 365 days).
`overprod_base`	float: Base value of overproduction factor \(\alpha^{b}\) (Default to 1.0).
`Z_0`	numpy.ndarray of float: 2-dim square matrix array \(\ioz\) of size \((n \times m, n \times m)\) representing the daily intermediate (transaction) matrix (see Initial state).
`Z_C`	numpy.ndarray of float: 2-dim matrix array \(\ioz^{\sectorsset}\) of size \((n, n \times m)\) representing the intermediate (transaction) matrix aggregated by inputs (see here).
`Z_distrib`	numpy.ndarray of float: math:ioz normalised by \(\ioz^{\sectorsset}\), i.e. representing for each input the share of the total ordered transiting from an industry to another (see here).
`Y_C`	numpy.ndarray of float: 2-dim matrix array \(\ioy^{\sectorsset}\) of size \((n, m \times \text{number of final demand categories})\) representing the final demand matrix aggregated by inputs (see here).
`Y_distrib`	numpy.ndarray of float: math:ioy normalised by \(\ioy^{\sectorsset}\), i.e. representing for each input the share of the total ordered transiting from an industry to final demand (see here).
`Y_0`	numpy.ndarray of float: 2-dim array \(\ioy\) of size \((n \times m, m \times \text{number of final demand categories})\) representing the daily final demand matrix.
`X_0`	numpy.ndarray of float: Array \(\iox(0)\) of size \(n \times m\) representing the initial daily gross production.
`gva_df`	pandas.DataFrame: Dataframe of the total GDP of each region of the model
`VA_0`	numpy.ndarray of float: Array \(\iov\) of size \(n \times m\) representing the total value added for each sectors.
`tech_mat`	numpy.ndarray of float: 2-dim array \(\ioa\) of size \((n \times m, n \times m)\) representing the technical coefficients matrix.
`productive_capital`	numpy.ndarray of float: Array of size \(n imes m\) representing the estimated stock of capital of each industry.
`threshold_not_input`	numpy.ndarray of float: 2-dim square matrix array of size \((n , n \times m)\) representing the threshold under which an input is not considered being an input (0.00001).
`overprod`	numpy.ndarray of float: Array of size \(n \times m\) representing the overproduction coefficients vector \(\mathbf{\alpha}(t)\).
`inputs_stock`	numpy.ndarray of float: 2-dim square matrix array \(\ioinv\) of size \((n \times m, n \times m)\) representing the stock of inputs (see Initial state).
`production`	numpy.ndarray of float: Array \(\iox(t)\) of size \(n \times m\) representing the current gross production.
`in_shortage`	Boolean stating if at least one industry is in shortage (i.e.) if at least one of its inputs inventory is low enough to reduce production.
`had_shortage`	Boolean stating if at least one industry was in shortage at some point.
`final_demand_not_met`	numpy.ndarray of float: Array of size \(n \times m\) representing the final demand that could not be met at current step for each industry.

psi#: float: Value of the psi parameter. (see Model description).

restoration_tau#: numpy.ndarray of int: Array of size \(n\) setting for each inputs its characteristic restoration time \(\tau_{\textrm{INV}}\) in n_temporal_units_by_step. (see Model description).

property inventory_constraints_opt#: Computes and returns inventory constraints for “optimal production” (see calc_inventory_constraints())

calc_orders()#

Computes and sets the orders (intermediate demand) for the next step.

See Order module

Raises:

RuntimeError: If negative orders are found, which shouldn’t happen.

calc_overproduction()#

Computes and updates the overproduction vector.

See Overproduction module

distribute_production(general_distribution_scheme='proportional')#

Production distribution module

Computes rebuilding demand for each rebuildable events (applying the rebuild_tau characteristic time)
Creates/Computes total demand matrix (Intermediate + Final + Rebuild)
Assesses if total demand is greater than realized production, hence requiring rationing
Distributes production proportionally to demand.
Updates stocks matrix. (Only if np.allclose(stock_add, stock_use).all() is false)
Computes final demand not met due to rationing and write it.
Updates rebuilding demand for each event (by substracting distributed production)

Parameters:

rebuildable_events‘list[Event]’: List of rebuildable events
schemestr: Placeholder for future distribution scheme

Raises:

RuntimeError: If negative values are found in places there’s should not be any
NotImplementedError: If an attempt to run an unimplemented distribution scheme is tried

property entire_demand#: Returns the entire demand matrix, including intermediate demand (orders), final demand, and possible rebuilding demand.

property entire_demand_tot#: Returns the entire demand matrix, including intermediate demand (orders), final demand, and possible rebuilding demand.

property final_demand#: Returns the entire intermediate demand matrix (orders)

property final_demand_tot#: Returns the total final demand addressed to each industry

property intermediate_demand#: Returns the entire intermediate demand matrix (orders)

property intermediate_demand_tot#: Returns the total intermediate demand addressed to each industry

property inventory_constraints_act#: Computes and returns inventory constraints for “actual production” (see calc_inventory_constraints())

property prod_cap_delta_arbitrary#

Return the possible “arbitrary” production capacity lost vector if it was set.

Returns:

npt.NDArray: An array of same shape as math:iox, stating the amount of production
capacity lost arbitrarily (ie exogenous).

property prod_cap_delta_productive_capital#

Return the possible production capacity lost due to capital destroyed vector if it was set.

Returns:

npt.NDArray: An array of same shape as math:iox, stating the amount of production
capacity lost due to capital destroyed.

property prod_cap_delta_tot#

Computes and return total current production delta.

Returns:

npt.NDArray: The total production delta (ie share of production capacity lost) for each industry.

property production_cap#

Compute and update production capacity.

Compute and update production capacity from current total production delta and overproduction.

\[x^{Cap}_{f}(t) = \alpha_{f}(t) (1 - \Delta_{f}(t)) x_{f}(t)\]

Raises:

ValueError: Raised if any industry has negative production.

property production_opt#: Computes and returns “optimal production” \(\iox^{textrm{Opt}}\), as the per industry minimum between total demand and production capacity.

property productive_capital_lost#

Returns current stock of destroyed capital

Returns:

npt.NDArray: An array of same shape as math:iox, containing the “stock”
of capital currently destroyed for each industry.

property rebuild_demand#: Returns the entire intermediate demand matrix (orders)

property rebuild_demand_house#

Returns household rebuilding demand matrix.

Returns:

npt.NDArray: An array of same shape as math:ioy, containing the sum of all currently rebuildable final demand stock.

property rebuild_demand_house_tot#

Returns total household rebuilding demand vector.

Returns:

npt.NDArray: An array of same shape as math:iox, containing the sum of all currently rebuildable households demands.

property rebuild_demand_indus#

Returns industrial rebuilding demand matrix.

Returns:

npt.NDArray: An array of same shape as math:ioz, containing the sum of all currently rebuildable intermediate demand stock.

property rebuild_demand_indus_tot#

Returns total industrial rebuilding demand vector.

Returns:

npt.NDArray: An array of same shape as math:iox, containing the sum of all currently rebuildable intermediate demands.

property rebuild_demand_tot#: Returns the total rebuild demand addressed to each industry

property rebuild_prod#

write_index(index_file)#

Write the indexes of the different dataframes of the model in a json file.

In order to easily rebuild the dataframes from the ‘raw’ data, this method create a JSON file with all columns and indexes names, namely :

regions names
sectors names
final demand categories
number of regions, sectors and industries (regions * sectors)

Parameters:

index_filepathlib.Path: Path to the file to save the indexes.

n_temporal_units_by_step#: int, default 1: The number of temporal_units between each step. (Current version of the model was not tested with values other than 1).

iotable_year_to_temporal_unit_factor#: int, default 365: The (inverse of the) factor by which MRIO data should be multiplied in order to get “per temporal unit value”, assuming IO data is yearly.

rebuild_tau#: int: Rebuilding characteristic time \(\tau_{\textrm{REBUILD}}\) (see Model description).

overprod_max#: float: Maximum factor of overproduction \(\alpha^{\textrm{max}}\) (default should be 1.25).

overprod_tau#: float: Characteristic time of overproduction \(\tau_{\alpha}\) in n_temporal_units_by_step (default should be 365 days).

overprod_base#: float: Base value of overproduction factor \(\alpha^{b}\) (Default to 1.0).

Z_0#: numpy.ndarray of float: 2-dim square matrix array \(\ioz\) of size \((n \times m, n \times m)\) representing the daily intermediate (transaction) matrix (see Initial state).

Z_C#: numpy.ndarray of float: 2-dim matrix array \(\ioz^{\sectorsset}\) of size \((n, n \times m)\) representing the intermediate (transaction) matrix aggregated by inputs (see here).

Z_distrib#: numpy.ndarray of float: math:ioz normalised by \(\ioz^{\sectorsset}\), i.e. representing for each input the share of the total ordered transiting from an industry to another (see here).

Y_C#: numpy.ndarray of float: 2-dim matrix array \(\ioy^{\sectorsset}\) of size \((n, m \times \text{number of final demand categories})\) representing the final demand matrix aggregated by inputs (see here).

Y_distrib#: numpy.ndarray of float: math:ioy normalised by \(\ioy^{\sectorsset}\), i.e. representing for each input the share of the total ordered transiting from an industry to final demand (see here).

Y_0#: numpy.ndarray of float: 2-dim array \(\ioy\) of size \((n \times m, m \times \text{number of final demand categories})\) representing the daily final demand matrix.

X_0#: numpy.ndarray of float: Array \(\iox(0)\) of size \(n \times m\) representing the initial daily gross production.

gva_df#: pandas.DataFrame: Dataframe of the total GDP of each region of the model

VA_0#: numpy.ndarray of float: Array \(\iov\) of size \(n \times m\) representing the total value added for each sectors.

tech_mat#: numpy.ndarray of float: 2-dim array \(\ioa\) of size \((n \times m, n \times m)\) representing the technical coefficients matrix.

productive_capital#: numpy.ndarray of float: Array of size \(n imes m\) representing the estimated stock of capital of each industry.

threshold_not_input#: numpy.ndarray of float: 2-dim square matrix array of size \((n , n \times m)\) representing the threshold under which an input is not considered being an input (0.00001).

overprod#: numpy.ndarray of float: Array of size \(n \times m\) representing the overproduction coefficients vector \(\mathbf{\alpha}(t)\).

inputs_stock#: numpy.ndarray of float: 2-dim square matrix array \(\ioinv\) of size \((n \times m, n \times m)\) representing the stock of inputs (see Initial state).

production#: numpy.ndarray of float: Array \(\iox(t)\) of size \(n \times m\) representing the current gross production.

in_shortage#: Boolean stating if at least one industry is in shortage (i.e.) if at least one of its inputs inventory is low enough to reduce production.

had_shortage#: Boolean stating if at least one industry was in shortage at some point.

final_demand_not_met#: numpy.ndarray of float: Array of size \(n \times m\) representing the final demand that could not be met at current step for each industry.

calc_production(current_temporal_unit)[source]#

Computes and updates actual production. The difference with ARIOBaseModel is in the way inventory constraints are computed. See Production module.

Parameters:

current_temporal_unitint: current step number

calc_inventory_constraints(production)[source]#

Compute inventory constraints (with psi parameter, for the non psi version, see calc_inventory_constraints())

Parameters:

productionnp.ndarray: The production vector to consider.

Returns:

np.ndarray: For each input, for each industry, the size of the inventory required to produce at production level
for the duration goal (inv_duration) times the psi parameter.

calc_matrix_stock_gap(matrix_stock_goal)[source]#

Computes and returns inputs stock gap matrix

The gap is simply the difference between the goal (given as argument) and the current stock.

Parameters:

matrix_stock_goalnpt.NDArray of float: The target inventories.

Returns:

npt.NDArray: The (only positive) gap between goal and current inventories.

Raises:

RuntimeError: If NaN are found in the result.