Running IPF without an AequilibraE model

In this example, we show you how to use AequilibraE’s IPF function without a model. This is a complement to the application in Forecasting.

Let’s consider that you have an OD-matrix, the future production and future attraction values.

How would your trip distribution matrix using IPF look like?

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

References

• AequilibraE Matrix

• Validation & Benchmarking

See also

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

• aequilibrae.matrix.AequilibraeMatrix()

• aequilibrae.distribution.Ipf()

# Imports
from os.path import join
from tempfile import gettempdir

import numpy as np
import pandas as pd

from aequilibrae.distribution import Ipf
from aequilibrae.matrix import AequilibraeMatrix

folder = gettempdir()

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")

num_zones = matrix.shape[0]

mtx = AequilibraeMatrix()
mtx.create_empty(file_name=join(folder, "matrix.aem"), zones=num_zones)
mtx.index[:] = np.arange(1, num_zones + 1)[:]
mtx.matrices[:, :, 0] = matrix[:]
mtx.computational_view()

args = {
    "entries": mtx.index.shape[0],
    "field_names": ["productions", "attractions"],
    "data_types": [np.float64, np.float64],
    "file_path": join(folder, "vectors.aem"),
}

vectors = pd.DataFrame({"productions": future_prod, "attractions":future_attr}, index=mtx.index)

args = {
    "matrix": mtx,
    "vectors": vectors,
    "row_field": "productions",
    "column_field": "attractions",
    "nan_as_zero": True,
}
fratar = Ipf(**args)
fratar.fit()

fratar.output.matrix_view

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]])

for line in fratar.report:
    print(line)

  #####    IPF computation    #####

Target convergence criteria: 0.0001
Maximum iterations: 5000

Rows/columns: 4
Total of seed matrix:                   1,635.0000
Total of target vectors:                1,962.0000

Iteration,   Convergence
7   ,   0.0000902085

Running time: 0.001s