Note
Click here to download the full example code
7.15. Forecasting¶
On this example we present a full forecasting workflow for the Sioux Falls example model.
## Imports
from uuid import uuid4
from tempfile import gettempdir
from os.path import join
from aequilibrae.utils.create_example import create_example
import logging
import sys
We create the example project inside our temp folder
fldr = join(gettempdir(), uuid4().hex)
project = create_example(fldr)
logger = project.logger
# We the project open, we can tell the logger to direct all messages to the terminal as well
stdout_handler = logging.StreamHandler(sys.stdout)
formatter = logging.Formatter("%(asctime)s;%(levelname)s ; %(message)s")
stdout_handler.setFormatter(formatter)
logger.addHandler(stdout_handler)
## Traffic assignment with skimming
from aequilibrae.paths import TrafficAssignment, TrafficClass
# we build all graphs
project.network.build_graphs()
# We get warnings that several fields in the project are filled with NaNs. Which is true, but we won't use those fields
/home/runner/work/aequilibrae/aequilibrae/aequilibrae/paths/graph.py:354: FutureWarning: In a future version, `df.iloc[:, i] = newvals` will attempt to set the values inplace instead of always setting a new array. To retain the old behavior, use either `df[df.columns[i]] = newvals` or, if columns are non-unique, `df.isetitem(i, newvals)`
df.loc[:, "id"] = np.arange(df.shape[0])
2022-11-29 07:35:45,471;WARNING ; Field(s) name, lanes has(ve) at least one NaN value. Check your computations
/home/runner/work/aequilibrae/aequilibrae/aequilibrae/paths/graph.py:371: FutureWarning: In a future version, `df.iloc[:, i] = newvals` will attempt to set the values inplace instead of always setting a new array. To retain the old behavior, use either `df[df.columns[i]] = newvals` or, if columns are non-unique, `df.isetitem(i, newvals)`
df.loc[:, "direction"] = df.direction.values.astype(np.int8)
/home/runner/work/aequilibrae/aequilibrae/aequilibrae/paths/graph.py:354: FutureWarning: In a future version, `df.iloc[:, i] = newvals` will attempt to set the values inplace instead of always setting a new array. To retain the old behavior, use either `df[df.columns[i]] = newvals` or, if columns are non-unique, `df.isetitem(i, newvals)`
df.loc[:, "id"] = np.arange(df.shape[0])
/home/runner/work/aequilibrae/aequilibrae/aequilibrae/paths/graph.py:371: FutureWarning: In a future version, `df.iloc[:, i] = newvals` will attempt to set the values inplace instead of always setting a new array. To retain the old behavior, use either `df[df.columns[i]] = newvals` or, if columns are non-unique, `df.isetitem(i, newvals)`
df.loc[:, "direction"] = df.direction.values.astype(np.int8)
/home/runner/work/aequilibrae/aequilibrae/aequilibrae/paths/graph.py:354: FutureWarning: In a future version, `df.iloc[:, i] = newvals` will attempt to set the values inplace instead of always setting a new array. To retain the old behavior, use either `df[df.columns[i]] = newvals` or, if columns are non-unique, `df.isetitem(i, newvals)`
df.loc[:, "id"] = np.arange(df.shape[0])
2022-11-29 07:35:45,508;WARNING ; Field(s) name, lanes has(ve) at least one NaN value. Check your computations
/home/runner/work/aequilibrae/aequilibrae/aequilibrae/paths/graph.py:371: FutureWarning: In a future version, `df.iloc[:, i] = newvals` will attempt to set the values inplace instead of always setting a new array. To retain the old behavior, use either `df[df.columns[i]] = newvals` or, if columns are non-unique, `df.isetitem(i, newvals)`
df.loc[:, "direction"] = df.direction.values.astype(np.int8)
/home/runner/work/aequilibrae/aequilibrae/aequilibrae/paths/graph.py:354: FutureWarning: In a future version, `df.iloc[:, i] = newvals` will attempt to set the values inplace instead of always setting a new array. To retain the old behavior, use either `df[df.columns[i]] = newvals` or, if columns are non-unique, `df.isetitem(i, newvals)`
df.loc[:, "id"] = np.arange(df.shape[0])
/home/runner/work/aequilibrae/aequilibrae/aequilibrae/paths/graph.py:371: FutureWarning: In a future version, `df.iloc[:, i] = newvals` will attempt to set the values inplace instead of always setting a new array. To retain the old behavior, use either `df[df.columns[i]] = newvals` or, if columns are non-unique, `df.isetitem(i, newvals)`
df.loc[:, "direction"] = df.direction.values.astype(np.int8)
/home/runner/work/aequilibrae/aequilibrae/aequilibrae/paths/graph.py:354: FutureWarning: In a future version, `df.iloc[:, i] = newvals` will attempt to set the values inplace instead of always setting a new array. To retain the old behavior, use either `df[df.columns[i]] = newvals` or, if columns are non-unique, `df.isetitem(i, newvals)`
df.loc[:, "id"] = np.arange(df.shape[0])
2022-11-29 07:35:45,544;WARNING ; Field(s) name, lanes has(ve) at least one NaN value. Check your computations
/home/runner/work/aequilibrae/aequilibrae/aequilibrae/paths/graph.py:371: FutureWarning: In a future version, `df.iloc[:, i] = newvals` will attempt to set the values inplace instead of always setting a new array. To retain the old behavior, use either `df[df.columns[i]] = newvals` or, if columns are non-unique, `df.isetitem(i, newvals)`
df.loc[:, "direction"] = df.direction.values.astype(np.int8)
/home/runner/work/aequilibrae/aequilibrae/aequilibrae/paths/graph.py:354: FutureWarning: In a future version, `df.iloc[:, i] = newvals` will attempt to set the values inplace instead of always setting a new array. To retain the old behavior, use either `df[df.columns[i]] = newvals` or, if columns are non-unique, `df.isetitem(i, newvals)`
df.loc[:, "id"] = np.arange(df.shape[0])
2022-11-29 07:35:45,581;WARNING ; Field(s) name, lanes has(ve) at least one NaN value. Check your computations
/home/runner/work/aequilibrae/aequilibrae/aequilibrae/paths/graph.py:371: FutureWarning: In a future version, `df.iloc[:, i] = newvals` will attempt to set the values inplace instead of always setting a new array. To retain the old behavior, use either `df[df.columns[i]] = newvals` or, if columns are non-unique, `df.isetitem(i, newvals)`
df.loc[:, "direction"] = df.direction.values.astype(np.int8)
/home/runner/work/aequilibrae/aequilibrae/aequilibrae/paths/graph.py:354: FutureWarning: In a future version, `df.iloc[:, i] = newvals` will attempt to set the values inplace instead of always setting a new array. To retain the old behavior, use either `df[df.columns[i]] = newvals` or, if columns are non-unique, `df.isetitem(i, newvals)`
df.loc[:, "id"] = np.arange(df.shape[0])
/home/runner/work/aequilibrae/aequilibrae/aequilibrae/paths/graph.py:371: FutureWarning: In a future version, `df.iloc[:, i] = newvals` will attempt to set the values inplace instead of always setting a new array. To retain the old behavior, use either `df[df.columns[i]] = newvals` or, if columns are non-unique, `df.isetitem(i, newvals)`
df.loc[:, "direction"] = df.direction.values.astype(np.int8)
/home/runner/work/aequilibrae/aequilibrae/aequilibrae/paths/graph.py:354: FutureWarning: In a future version, `df.iloc[:, i] = newvals` will attempt to set the values inplace instead of always setting a new array. To retain the old behavior, use either `df[df.columns[i]] = newvals` or, if columns are non-unique, `df.isetitem(i, newvals)`
df.loc[:, "id"] = np.arange(df.shape[0])
2022-11-29 07:35:45,617;WARNING ; Field(s) name, lanes has(ve) at least one NaN value. Check your computations
/home/runner/work/aequilibrae/aequilibrae/aequilibrae/paths/graph.py:371: FutureWarning: In a future version, `df.iloc[:, i] = newvals` will attempt to set the values inplace instead of always setting a new array. To retain the old behavior, use either `df[df.columns[i]] = newvals` or, if columns are non-unique, `df.isetitem(i, newvals)`
df.loc[:, "direction"] = df.direction.values.astype(np.int8)
/home/runner/work/aequilibrae/aequilibrae/aequilibrae/paths/graph.py:354: FutureWarning: In a future version, `df.iloc[:, i] = newvals` will attempt to set the values inplace instead of always setting a new array. To retain the old behavior, use either `df[df.columns[i]] = newvals` or, if columns are non-unique, `df.isetitem(i, newvals)`
df.loc[:, "id"] = np.arange(df.shape[0])
2022-11-29 07:35:45,654;WARNING ; Field(s) name, lanes has(ve) at least one NaN value. Check your computations
/home/runner/work/aequilibrae/aequilibrae/aequilibrae/paths/graph.py:371: FutureWarning: In a future version, `df.iloc[:, i] = newvals` will attempt to set the values inplace instead of always setting a new array. To retain the old behavior, use either `df[df.columns[i]] = newvals` or, if columns are non-unique, `df.isetitem(i, newvals)`
df.loc[:, "direction"] = df.direction.values.astype(np.int8)
# we grab the graph for cars
graph = project.network.graphs["c"]
# let's say we want to minimize free_flow_time
graph.set_graph("free_flow_time")
# And will skim time and distance while we are at it
graph.set_skimming(["free_flow_time", "distance"])
# And we will allow paths to be compute going through other centroids/centroid connectors
# required for the Sioux Falls network, as all nodes are centroids
graph.set_blocked_centroid_flows(False)
/home/runner/work/aequilibrae/aequilibrae/aequilibrae/paths/graph.py:445: FutureWarning: The default value of numeric_only in DataFrameGroupBy.sum is deprecated. In a future version, numeric_only will default to False. Either specify numeric_only or select only columns which should be valid for the function.
df = self.__graph_groupby.sum()[[cost_field]].reset_index()
2022-11-29 07:35:45,682;WARNING ; Cost field with wrong type. Converting to float64
/home/runner/work/aequilibrae/aequilibrae/aequilibrae/paths/graph.py:479: FutureWarning: The default value of numeric_only in DataFrameGroupBy.sum is deprecated. In a future version, numeric_only will default to False. Either specify numeric_only or select only columns which should be valid for the function.
df = self.__graph_groupby.sum()[skim_fields].reset_index()
# We get the demand matrix directly from the project record
# so let's inspect what we have in the project
proj_matrices = project.matrices
proj_matrices.list()
# Let's get it in this better way
demand = proj_matrices.get_matrix("demand_omx")
demand.computational_view(["matrix"])
assig = TrafficAssignment()
# Creates the assignment class
assigclass = TrafficClass(name="car", graph=graph, matrix=demand)
# The first thing to do is to add at list of traffic classes to be assigned
assig.add_class(assigclass)
# We set these parameters only after adding one class to the assignment
assig.set_vdf("BPR") # This is not case-sensitive # Then we set the volume delay function
assig.set_vdf_parameters({"alpha": "b", "beta": "power"}) # And its parameters
assig.set_capacity_field("capacity") # The capacity and free flow travel times as they exist in the graph
assig.set_time_field("free_flow_time")
# And the algorithm we want to use to assign
assig.set_algorithm("bfw")
# since I haven't checked the parameters file, let's make sure convergence criteria is good
assig.max_iter = 1000
assig.rgap_target = 0.001
assig.execute() # we then execute the assignment
/home/runner/work/aequilibrae/aequilibrae/aequilibrae/paths/graph.py:445: FutureWarning: The default value of numeric_only in DataFrameGroupBy.sum is deprecated. In a future version, numeric_only will default to False. Either specify numeric_only or select only columns which should be valid for the function.
df = self.__graph_groupby.sum()[[cost_field]].reset_index()
2022-11-29 07:35:46,005;WARNING ; Cost field with wrong type. Converting to float64
2022-11-29 07:35:46,005;INFO ; bfw Assignment STATS
2022-11-29 07:35:46,005;INFO ; Iteration, RelativeGap, stepsize
2022-11-29 07:35:46,010;INFO ; 1,inf,1.0
2022-11-29 07:35:46,020;INFO ; 2,0.8485503636986156,0.3649733931991619
2022-11-29 07:35:46,031;INFO ; 3,0.38139263975960314,0.22983569243524993
2022-11-29 07:35:46,040;INFO ; 4,0.19621280093105328,0.18591303407405754
2022-11-29 07:35:46,050;INFO ; 5,0.09069069564886302,0.709081525570193
2022-11-29 07:35:46,060;INFO ; 6,0.20600049841796414,0.12290139708465252
2022-11-29 07:35:46,069;INFO ; 7,0.0671057020569446,0.3863865464644097
2022-11-29 07:35:46,080;INFO ; 8,0.10307514522959232,0.10930550628245674
2022-11-29 07:35:46,090;INFO ; 9,0.042221488560558955,0.24878058909094228
2022-11-29 07:35:46,099;INFO ; 10,0.05926436280283587,0.15904812211073494
2022-11-29 07:35:46,107;INFO ; 11,0.034539501887818985,0.5180973982981508
2022-11-29 07:35:46,111;INFO ; 12,0.059426522740212366,0.101971242325629
2022-11-29 07:35:46,115;INFO ; 13,0.023239892828420625,0.1780595247621586
2022-11-29 07:35:46,119;INFO ; 14,0.01787378174233466,0.9787872892076548
2022-11-29 07:35:46,122;INFO ; 15,0.04966137112489825,0.08320656230754342
2022-11-29 07:35:46,126;INFO ; 16,0.021382882927382725,0.11517403372477297
2022-11-29 07:35:46,130;INFO ; 17,0.01314154305058098,0.1064036961470442
2022-11-29 07:35:46,133;INFO ; 18,0.009902228306191804,0.10710395852809111
2022-11-29 07:35:46,137;INFO ; 19,0.008834657124558089,0.252467895277828
2022-11-29 07:35:46,141;INFO ; 20,0.010371041656588888,0.6727839455896467
2022-11-29 07:35:46,145;INFO ; 21,0.011090096024277666,0.07468062458005388
2022-11-29 07:35:46,148;INFO ; 22,0.006512685864200749,0.12485018976276105
2022-11-29 07:35:46,152;INFO ; 23,0.00523888532832478,0.06316016036308214
2022-11-29 07:35:46,155;INFO ; 24,0.003949527733957799,0.09717892036982514
2022-11-29 07:35:46,159;INFO ; 25,0.003282221717998643,0.15775902884958926
2022-11-29 07:35:46,163;INFO ; 26,0.0057928324189390375,0.4524765555189632
2022-11-29 07:35:46,167;INFO ; 27,0.006682358714677215,0.7851865434128832
2022-11-29 07:35:46,170;INFO ; 28,0.00599261954468699,0.039098102583274626
2022-11-29 07:35:46,174;INFO ; 29,0.004031364721003652,0.04253017715977122
2022-11-29 07:35:46,178;INFO ; 30,0.00276965205224939,0.02251286694569934
2022-11-29 07:35:46,182;INFO ; 31,0.002484645375580033,0.045801689794576335
2022-11-29 07:35:46,185;INFO ; 32,0.0016385526291291498,0.034295834113305265
2022-11-29 07:35:46,189;INFO ; 33,0.0014956909894299761,0.035391999643557624
2022-11-29 07:35:46,193;INFO ; 34,0.0011355396506463338,0.053589857140533936
2022-11-29 07:35:46,197;INFO ; 35,0.0012151969842906466,0.04757129085244828
2022-11-29 07:35:46,200;INFO ; 36,0.0012393652042090905,0.06536474008117803
2022-11-29 07:35:46,204;INFO ; 37,0.0010684964499824193,0.1070395355360692
2022-11-29 07:35:46,208;INFO ; 38,0.0010899690746481111,0.09864062890245766
2022-11-29 07:35:46,211;INFO ; 39,0.0009886949061956609,0.06027624172548778
2022-11-29 07:35:46,212;INFO ; bfw Assignment finished. 39 iterations and 0.0009886949061956609 final gap
# Convergence report is easy to see
import pandas as pd
convergence_report = assig.report()
convergence_report.head()
volumes = assig.results()
volumes.head()
# We could export it to CSV or AequilibraE data, but let's put it directly into the results database
assig.save_results("base_year_assignment")
# And save the skims
assig.save_skims("base_year_assignment_skims", which_ones="all", format="omx")
2022-11-29 07:35:46,346;WARNING ; Matrix Record has been saved to the database
## Trip distribution
### Calibration
# We will calibrate synthetic gravity models using the skims for TIME that we just generated
import numpy as np
from aequilibrae.distribution import GravityCalibration
# Let's take another look at what we have in terms of matrices in the model
proj_matrices.list()
# We need the demand
demand = proj_matrices.get_matrix("demand_aem")
# And the skims
imped = proj_matrices.get_matrix("base_year_assignment_skims_car")
# We can check which matrix cores were created for our skims to decide which one to use
imped.names
# Where free_flow_time_final is actually the congested time for the last iteration
['distance_blended', 'distance_final', 'free_flow_time_blended', 'free_flow_time_final']
# But before using the data, let's get some impedance for the intrazonals
# Let's assume it is 75% of the closest zone
imped_core = "free_flow_time_final"
imped.computational_view([imped_core])
# If we run the code below more than once, we will be overwriting the diagonal values with non-sensical data
# so let's zero it first
np.fill_diagonal(imped.matrix_view, 0)
# We compute it with a little bit of NumPy magic
intrazonals = np.amin(imped.matrix_view, where=imped.matrix_view > 0, initial=imped.matrix_view.max(), axis=1)
intrazonals *= 0.75
# Then we fill in the impedance matrix
np.fill_diagonal(imped.matrix_view, intrazonals)
# Since we are working with an OMX file, we cannot overwrite a matrix on disk
# So we give a new name to save it
imped.save(names=["final_time_with_intrazonals"])
# This also updates these new matrices as those being used for computation
# As one can verify below
imped.view_names
['final_time_with_intrazonals']
# We set the matrices for being used in computation
demand.computational_view(["matrix"])
for function in ["power", "expo"]:
gc = GravityCalibration(matrix=demand, impedance=imped, function=function, nan_as_zero=True)
gc.calibrate()
model = gc.model
# we save the model
model.save(join(fldr, f"{function}_model.mod"))
# We can save the result of applying the model as well
# we can also save the calibration report
with open(join(fldr, f"{function}_convergence.log"), "w") as otp:
for r in gc.report:
otp.write(r + "\n")
## Forecast
# * We create a set of * 'future' * vectors using some random growth factors
# * We apply the model for inverse power, as the TFLD seems to be a better fit for the actual one
from aequilibrae.distribution import Ipf, GravityApplication, SyntheticGravityModel
from aequilibrae.matrix import AequilibraeData
import numpy as np
# We compute the vectors from our matrix
origins = np.sum(demand.matrix_view, axis=1)
destinations = np.sum(demand.matrix_view, axis=0)
args = {
"file_path": join(fldr, "synthetic_future_vector.aed"),
"entries": demand.zones,
"field_names": ["origins", "destinations"],
"data_types": [np.float64, np.float64],
"memory_mode": False,
}
vectors = AequilibraeData()
vectors.create_empty(**args)
vectors.index[:] = demand.index[:]
# Then grow them with some random growth between 0 and 10% - Plus balance them
vectors.origins[:] = origins * (1 + np.random.rand(vectors.entries) / 10)
vectors.destinations[:] = destinations * (1 + np.random.rand(vectors.entries) / 10)
vectors.destinations *= vectors.origins.sum() / vectors.destinations.sum()
# Impedance
imped = proj_matrices.get_matrix("base_year_assignment_skims_car")
imped.computational_view(["final_time_with_intrazonals"])
# If we wanted the main diagonal to not be considered...
# np.fill_diagonal(imped.matrix_view, np.nan)
for function in ["power", "expo"]:
model = SyntheticGravityModel()
model.load(join(fldr, f"{function}_model.mod"))
outmatrix = join(proj_matrices.fldr, f"demand_{function}_model.aem")
apply = GravityApplication()
args = {
"impedance": imped,
"rows": vectors,
"row_field": "origins",
"model": model,
"columns": vectors,
"column_field": "destinations",
"nan_as_zero": True,
}
gravity = GravityApplication(**args)
gravity.apply()
# We get the output matrix and save it to OMX too,
gravity.save_to_project(name=f"demand_{function}_modeled", file_name=f"demand_{function}_modeled.omx")
2022-11-29 07:35:47,329;WARNING ; Matrix Record has been saved to the database
2022-11-29 07:35:47,552;WARNING ; Matrix Record has been saved to the database
# We update the matrices table/records and verify that the new matrices are indeed there
proj_matrices.update_database()
proj_matrices.list()
### We now run IPF for the future vectors
args = {
"matrix": demand,
"rows": vectors,
"columns": vectors,
"column_field": "destinations",
"row_field": "origins",
"nan_as_zero": True,
}
ipf = Ipf(**args)
ipf.fit()
ipf.save_to_project(name="demand_ipfd", file_name="demand_ipfd.aem")
ipf.save_to_project(name="demand_ipfd_omx", file_name="demand_ipfd.omx")
2022-11-29 07:35:47,696;WARNING ; Matrix Record has been saved to the database
2022-11-29 07:35:47,793;WARNING ; Matrix Record has been saved to the database
<aequilibrae.project.data.matrix_record.MatrixRecord object at 0x7f7fd1a2cbb0>
proj_matrices.list()
## Future traffic assignment
from aequilibrae.paths import TrafficAssignment, TrafficClass
logger.info("\n\n\n TRAFFIC ASSIGNMENT FOR FUTURE YEAR")
2022-11-29 07:35:47,845;INFO ;
TRAFFIC ASSIGNMENT FOR FUTURE YEAR
demand = proj_matrices.get_matrix("demand_ipfd")
# let's see what is the core we ended up getting. It should be 'gravity'
demand.names
['matrix']
# Let's use the IPF matrix
demand.computational_view("matrix")
assig = TrafficAssignment()
# Creates the assignment class
assigclass = TrafficClass(name="car", graph=graph, matrix=demand)
# The first thing to do is to add at list of traffic classes to be assigned
assig.add_class(assigclass)
assig.set_vdf("BPR") # This is not case-sensitive # Then we set the volume delay function
assig.set_vdf_parameters({"alpha": "b", "beta": "power"}) # And its parameters
assig.set_capacity_field("capacity") # The capacity and free flow travel times as they exist in the graph
assig.set_time_field("free_flow_time")
# And the algorithm we want to use to assign
assig.set_algorithm("bfw")
# since I haven't checked the parameters file, let's make sure convergence criteria is good
assig.max_iter = 500
assig.rgap_target = 0.00001
assig.execute() # we then execute the assignment
/home/runner/work/aequilibrae/aequilibrae/aequilibrae/paths/graph.py:445: FutureWarning: The default value of numeric_only in DataFrameGroupBy.sum is deprecated. In a future version, numeric_only will default to False. Either specify numeric_only or select only columns which should be valid for the function.
df = self.__graph_groupby.sum()[[cost_field]].reset_index()
2022-11-29 07:35:48,161;WARNING ; Cost field with wrong type. Converting to float64
2022-11-29 07:35:48,162;INFO ; bfw Assignment STATS
2022-11-29 07:35:48,162;INFO ; Iteration, RelativeGap, stepsize
2022-11-29 07:35:48,169;INFO ; 1,inf,1.0
2022-11-29 07:35:48,180;INFO ; 2,0.8776038327947165,0.35194194800596224
2022-11-29 07:35:48,191;INFO ; 3,0.46258967612026347,0.18972760815724118
2022-11-29 07:35:48,199;INFO ; 4,0.24563915271016676,0.23462556986441843
2022-11-29 07:35:48,203;INFO ; 5,0.07289711677703088,0.9851363677496002
2022-11-29 07:35:48,208;INFO ; 6,0.2534950603426386,0.11811117417714245
2022-11-29 07:35:48,212;INFO ; 7,0.09786144704234179,0.14643197813926917
2022-11-29 07:35:48,216;INFO ; 8,0.04756352710660187,0.42838466394167934
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2022-11-29 07:35:49,173;INFO ; 205,1.133917717110072e-05,0.0011638065539680905
2022-11-29 07:35:49,177;INFO ; 206,1.1812052292740414e-05,0.0011654451276714984
2022-11-29 07:35:49,181;INFO ; 207,9.78726947556976e-06,0.0013099074935429143
2022-11-29 07:35:49,182;INFO ; bfw Assignment finished. 207 iterations and 9.78726947556976e-06 final gap
# We could export it to CSV or AequilibraE data, but let's put it directly into the results database
assig.save_results("future_year_assignment")
# And save the skims
assig.save_skims("future_year_assignment_skims", which_ones="all", format="omx")
2022-11-29 07:35:49,299;WARNING ; Matrix Record has been saved to the database
We can also plot convergence
import matplotlib.pyplot as plt
df = assig.report()
x = df.iteration.values
y = df.rgap.values
fig = plt.figure()
ax = fig.add_subplot(111)
plt.plot(x, y, "k--")
plt.yscale("log")
plt.grid(True, which="both")
plt.xlabel(r"Iterations")
plt.ylabel(r"Relative Gap")
plt.show()
Close the project
project.close()
Total running time of the script: ( 0 minutes 4.600 seconds)