Technical data structure to memoize the matrix computation
Technical data structure to memoize the matrix computation
the cities
the supplies of the city
the demands of the city
the transaction matrix
Stub for bonuses injection.
Stub for bonuses injection. No bonuses are modeled in this version.
information on all transactions between cities
a sequence of bonuses indexed by city index
Demand of a city from its population
Demand of a city from its population
the population the city
the demand
Decaying effect of distance on interaction
Decaying effect of distance on interaction
Factor adjusting the values of production and consumption
Factor adjusting the values of production and consumption
Stop criterion on a maximum number of state
Stop criterion on a maximum number of state
a state of the model
true if the simulation is finished
Valued balance of the cities resulting from exchanges.
Valued balance of the cities resulting from exchanges.
the cities
the network of cities
the supplies of the cities indexed by city index
the demands of the cities indexed by city index
the exchange balance of the cities indexed by city index
Create the initial state of the cities
Create the initial state of the cities
Initial state of the model
Initial state of the model
Compute the interaction potential as a gravity model.
Compute the interaction potential as a gravity model.
mass of the 1st city
mass of the 2nd city
distance between the cities
Compute the interaction potential matrix of the whole network of city.
Compute the interaction potential matrix of the whole network of city.
masses of the cities of origin
masses of the cities of destination
the interaction network
the interaction potential matrix as an adjacency matrix
Simulate from 1959 to 1989
Simulate from 1959 to 1989
The next state of the model
The next state of the model
the current state
the subsequent state
Estimate the wealth of a city from its population
Estimate the wealth of a city from its population
population of the city
the estimated wealth
Exponent of the scaling law to convert population into wealth
Exponent of the scaling law to convert population into wealth
Center the wealth distribution on the population distribution
Center the wealth distribution on the population distribution
the wealth distribution
the population distribution
the centered wealth distribution
Exponent of the scaling law between demand and population
Exponent of the scaling law between demand and population
Exponent of the scaling law between supply and population
Exponent of the scaling law between supply and population
Iterate through the states of the model
Iterate through the states of the model
Supply of a city from its population
Supply of a city from its population
the population the city
the supply
Stub for fixed costs injection.
Stub for fixed costs injection. No fixed cost are modeled in this version.
information on all transactions between cities
a sequence of fixed costs indexed by city index
Match cities according to their interaction potential and compute the transacted quantity
Match cities according to their interaction potential and compute the transacted quantity
the cities
the network of cities
the supplies of the cities indexed by city index
the demands of the cities indexed by city index
the
The updated population of a city from its updated wealth
The updated population of a city from its updated wealth
the city to update
the updated wealth
the updated population
The updated wealth of the cities as a result of economic processes:
The updated wealth of the cities as a result of economic processes:
the current state of the model
Convert a quantity of wealth into a quantity of population
Convert a quantity of wealth into a quantity of population
the stock of wealth
the matching population
Exponent of the scaling law to convert wealth into population
Exponent of the scaling law to convert wealth into population
Simple model with only core mechanisms