Limit matrix tutorial for pyanp
In this tutorial you will be shown:
- How to import the limit matrix module, where all of the ANP limit matrix related calculations are.
- How to load a matrix from an excel/csv file and how to directly input a matrix
- How to perform some of the basic limit matrix calculations
- Where to find more information on all of the limit matrix calculations available
- Reference notebooks and Excel/CSV files used in this tutorial
1. Importing the pyanp.limitmatrix module
# Pandas has DataFrames and Series, very useful things
import pandas as pd
# numpy has lots of useful things in it
import numpy as np
# lastly import our ahptree python code. If you haven't already installed the pyanp library do
# pip install pyanp
# to get it
from pyanp import limitmatrix as lm
2. Loading data from an excel / csv file
# For excel / csv file with headers or without it is the same function
matrix = lm.get_matrix("PATH_TO_YOUR_EXCEL_OR_CSV_FILE")
To create a matrix directly in python use
hierarhcyMatrix = np.array([
[0, 0, 0, 0, 0],
[0.6, 0, 0, 0, 0],
[0.4, 0, 0, 0, 0],
[0, 0.9, 0.2, 0, 0],
[0, 0.1, 0.8, 0, 0]
])
3. Some limit matrix calculations
3.1 The calculaus type limit matrix calculation
The standard limit matrix calculation used in Super Decisions
lm.calculus(matrix)
the result is:
array([[0. , 0. , 0. , 0. ],
[0. , 0. , 0. , 0. ],
[0.2857, 0.2857, 0.2857, 0.2857],
[0.7143, 0.7143, 0.7143, 0.7143]])
3.2 The hiearchy formula
We need need to calculate on the hierarchy matrix we defined above.
hierarhcyMatrix = np.array([
[0, 0, 0, 0, 0],
[0.6, 0, 0, 0, 0],
[0.4, 0, 0, 0, 0],
[0, 0.9, 0.2, 0, 0],
[0, 0.1, 0.8, 0, 0]
])
lm.hiearhcy_formula(hierarhcyMatrix)
the result is:
array([[0. , 0. , 0. , 0. , 0. ],
[0.3 , 0. , 0. , 0. , 0. ],
[0.2 , 0. , 0. , 0. , 0. ],
[0.31, 0.9 , 0.2 , 0. , 0. ],
[0.19, 0.1 , 0.8 , 0. , 0. ]])
3.3 The new hierarchy formula
To see how this calculation can be different we use a different matrix
matrix2 = np.array([
[0.5, 0.3, 0.4, 0.0, 0.0],
[0.1, 0.2, 0.2, 0.0, 0.0],
[0.1, 0.1, 0.1, 0.0, 0.0],
[0.2, 0.3, 0.1, 0.0, 0.0],
[0.1, 0.1, 0.2, 0.0, 0.0],
])
Now let’s calculate without using the extra limit
lm.limit_newhierarchy(matrix2, with_limit=False)
the result is:
array([[0.3277, 0.3277, 0.3277, 0. , 0. ],
[0.0988, 0.0988, 0.0988, 0. , 0. ],
[0.0735, 0.0735, 0.0735, 0. , 0. ],
[0.3206, 0.3206, 0.3206, 0. , 0. ],
[0.1794, 0.1794, 0.1794, 0. , 0. ]])
Next let’s do it with the extra limit
lm.limit_newhierarchy(matrix2, with_limit=False)
the result is:
array([[0.4965, 0.4965, 0.4965, 0. , 0. ],
[0.1498, 0.1498, 0.1498, 0. , 0. ],
[0.1114, 0.1114, 0.1114, 0. , 0. ],
[0.1554, 0.1554, 0.1554, 0. , 0. ],
[0.0869, 0.0869, 0.0869, 0. , 0. ]])
Lastly, let us look at the calculus type calculation:
lm.calculus(matrix2)
the result is:
array([[0.4458, 0.4458, 0.4458, 0. , 0. ],
[0.1345, 0.1345, 0.1345, 0. , 0. ],
[0.1 , 0.1 , 0.1 , 0. , 0. ],
[0.2051, 0.2051, 0.2051, 0. , 0. ],
[0.1147, 0.1147, 0.1147, 0. , 0. ]])
4. Additional limit matrix calculations
You can find all limit matrix calculations here.