Running IPF with NumPy array

In this example, we show how to use aequilibrae.distribution.ipf_core, a high-performance alternative for all those who want to (re)balance values within a matrix making direct use of growth factors. ipf_core was built to suit countless applications rather than being limited to trip distribution.

We demonstrate the usage of ipf_core with a 4x4 matrix with 64-bit data, which is indeed very small. Additionally, a more comprehensive discussion of the algorithm’s performance with a 32-bit or 64-bit seed matrices is provided in IPF Performance.

The data used in this example comes from Table 5.6 in Ortúzar & Willumsen (2011).

References

• IPF Performance

See also

Several functions, methods, classes and modules are used in this example:

• aequilibrae.distribution.ipf_core()

# Imports
import numpy as np

from aequilibrae.distribution.ipf_core import ipf_core

matrix = np.array([[5, 50, 100, 200], [50, 5, 100, 300], [50, 100, 5, 100], [100, 200, 250, 20]], dtype="float64")
future_prod = np.array([400, 460, 400, 702], dtype="float64")
future_attr = np.array([260, 400, 500, 802], dtype="float64")

Given our use of default parameter values in the other application of IPF, we should set tolerance value to obtain the same result.

num_iter, gap = ipf_core(matrix, future_prod, future_attr, tolerance=0.0001)

Let’s print our updated matrix

matrix

array([[  5.19523253,  43.60117896,  97.1907419 , 254.02026689],
       [ 44.70942645,   3.75225496,  83.64095928, 327.90930057],
       [ 76.67583276, 128.70094592,   7.17213428, 187.45277887],
       [133.41950826, 223.94562016, 311.99616454,  32.61765367]])

Notice that the matrix value was updated, and results are the same as in Running IPF without an AequilibraE model - and this is no coincidence. Under the hood, when we call aequilibrae.distribution.Ipf, we are actually calling the ipf_core method.