This Python module is the core library for the computation of Ideal Flow Network (IFN).
Ideal Flow is a steady state relative flow distribution in a strongly connected network where the flows are conserved. The IFN theory was first proposed by Kardi Teknomo in 2015. Check also: https://people.revoledu.com/kardi/research/trajectory/ifn/index.html
Ideal Flow is a new concept to analyze transportation networks or communication network.
For IFN application to traffic assignment check IFN-Transport for more details.
pip install IdealFlowNetwork
Check Also in Pypi
Latest Stable Version: 1.0.3
If you use Ideal Flow Network, you can cite this paper (Teknomo, K. (2018) Ideal Flow of Markov Chain, Discrete Mathematics, Algorithms and Applications, doi: 10.1142/S1793830918500738 ).
Here is an example BibTeX entry:
@article{doi:10.1142/S1793830918500738,
author = {Teknomo, Kardi},
title = {Ideal flow of Markov Chain},
journal = {Discrete Mathematics, Algorithms and Applications},
volume = {10},
number = {06},
pages = {1850073},
year = {2018},
doi = {10.1142/S1793830918500738},
URL = {
https://doi.org/10.1142/S1793830918500738
},
eprint = {
https://doi.org/10.1142/S1793830918500738
}}The following publications are the foundations of Ideal Flow analysis:
- Teknomo, K.(2019), Ideal Flow Network in Society 5.0 in Mahdi et al, Optimization in Large Scale Problems - Industry 4.0 and Society 5.0 Applications, Springer, p. 67-69
- Teknomo, K. and Gardon, R.W. (2019) Traffic Assignment Based on Parsimonious Data: The Ideal Flow Network, 2019 IEEE Intelligent Transportation Systems Conference (ITSC), 1393-1398.
- Teknomo, K., Gardon, R. and Saloma, C. (2019), Ideal Flow Traffic Analysis: A Case Study on a Campus Road Network, Philippine Journal of Science 148 (1): 5162.
- Teknomo, K. (2018) Ideal Flow of Markov Chain, Discrete Mathematics, Algorithms and Applications, doi: 10.1142/S1793830918500738
- Teknomo, K. and Gardon, R.W. (2017) Intersection Analysis Using the Ideal Flow Model, Proceeding of the IEEE 20th International Conference on Intelligent Transportation Systems, Oct 16-19, 2017, Yokohama, Japan
- Teknomo, K. (2017) Ideal Relative Flow Distribution on Directed Network, Proceeding of the 12th Eastern Asia Society for Transportation Studies (EASTS), Ho Chi Minh, Vietnam Sept 18-21, 2017.
- Teknomo, K. (2017) Premagic and Ideal Flow Matrices. https://arxiv.org/abs/1706.08856
- Gardon, R.W. and Teknomo, K. (2017) Analysis of the Distribution of Traffic Density Using the Ideal Flow Method and the Principle of Maximum Entropy, Proceedings of the 17th Philippine Computing Science Congress, Cebu City, March 2017
- Teknomo, K. (2015) Ideal Flow Based on Random Walk on Directed Graph, The 9th International collaboration Symposium on Information, Production and Systems (ISIPS 2015) 16-18 Nov 2015, Waseda University, KitaKyushu, Japan.
You may also cite any of the above papers if you use or improve this python library.
| Functions | Description |
|---|---|
| A = capacity2adj(C) | convert capacity matrix to adjacency matrix |
| S = capacity2stochastic(C) | convert capacity matrix into stochastic matrix |
| S = adj2stochastic(A) | convert adjacency matrix to stochastic matrix of equal outflow distribution |
| S = idealFlow2stochastic(F) | convert ideal flow matrix into Markov stochastic matrix |
| pi = steadyStateMC(S,kappa) | convert stochastic matrix into steady state Markov vector. kappa is the total of Markov vector. |
| F = idealFlow(S,pi) | return ideal flow matrix based on stochastic matrix and Markov vector |
| F = adj2idealFlow(A,kappa) | convert adjacency matrix into ideal flow matrix of equal distribution of outflow. kappa is the total flow |
| F = capacity2idealFlow(C,kappa) | convert capacity matrix into ideal flow vector, kappa is the total flow |
| sR = sumOfRow(M) | return vector sum of rows of matrix M |
| sC = sumOfCol(M) | return row vector sum of columns of matrix M |
| d = isSquare(M) | return True if M is a square matrix |
| d = isNonNegative(M) | return True of M is a non-negative matrix |
| d = isPositive(M) | return True of M is a positive matrix |
| d = isPremagic(M) | return True if M is premagic matrix |
| d = isIrreducible(M) | return True if M is irreducible matrix |
| d = isIdealFlow(M) | return True if M is an ideal flow matrix |
| h = networkEntropy(S) | return the value of network entropy |
| e = entropyRatio(S) | return network entropy ratio |
from IdealFlowNetwork import network as ifn
net=ifn.IFN()
net.name="random example network"
k=7
m=k+int(3*k/4)
C=net.randIrreducible(k,m) # k nodes, m links
A=net.capacity2adj(C)
print("A=",A,'\n')
S=net.capacity2stochastic(C)
print("S=",S,'\n')
F=net.capacity2idealFlow(C)
print("F=",F,'\n')
scaling=net.globalScaling(F,'int')
print('scaling:',scaling,'\n')
F1=net.equivalentIFN(F, scaling)
import pandas as pd
pd.options.display.float_format = '{:,.0f}'.format
print(pd.DataFrame(F1))A= [[0 1 0 0 0 1 0]
[0 0 0 1 0 0 1]
[0 0 0 1 0 1 0]
[0 0 0 0 1 0 0]
[0 0 1 0 1 0 0]
[0 0 0 0 0 0 1]
[1 0 0 0 1 0 0]]
S= [[0. 0.5 0. 0. 0. 0.5 0. ]
[0. 0. 0. 0.5 0. 0. 0.5]
[0. 0. 0. 0.5 0. 0.5 0. ]
[0. 0. 0. 0. 1. 0. 0. ]
[0. 0. 0.5 0. 0.5 0. 0. ]
[0. 0. 0. 0. 0. 0. 1. ]
[0.5 0. 0. 0. 0.5 0. 0. ]]
F= [[0. 0.03508772 0. 0. 0. 0.03508772
0. ]
[0. 0. 0. 0.01754386 0. 0.
0.01754386]
[0. 0. 0. 0.0877193 0. 0.0877193
0. ]
[0. 0. 0. 0. 0.10526316 0.
0. ]
[0. 0. 0.1754386 0. 0.1754386 0.
0. ]
[0. 0. 0. 0. 0. 0.
0.12280702]
[0.07017544 0. 0. 0. 0.07017544 0.
0. ]]
scaling: 57
0 1 2 3 4 5 6
0 0 2 0 0 0 2 0
1 0 0 0 1 0 0 1
2 0 0 0 5 0 5 0
3 0 0 0 0 6 0 0
4 0 0 10 0 10 0 0
5 0 0 0 0 0 0 7
6 4 0 0 0 4 0 0
More tutorial on Ideal Flow Network is available in Revoledu.com 
Pull requests are encouraged and always welcome. Pick an issue and help us out!
(c) 2021-2023 Kardi Teknomo