Vector Index Tool

import oat_python as oat

from fractions import Fraction
import numpy as np
import pandas as pd

Create a Vietoris-Rips complex from a points of points

points                      =   np.random.rand(5, 3)
dissimilarity_matrix        =   oat.dissimilarity.sparse_matrix_for_points(points, max_dissimilarity=np.inf)
vietoris_rips_complex       =   oat.core.vietoris_rips.VietorisRipsComplex(dissimilarity_matrix)
boundary_matrix             =   vietoris_rips_complex.boundary_matrix_oracle()

Generate a VectorIndexTool

vector_index_tool           =   vietoris_rips_complex.vector_index_tool(dimensions=[0,1])
vector_index_tool

<VectorIndexTool with 15 unique simplices>

Convert a dataframe to a dense 1d numpy.ndarray

simplices_in_index_tool     =   vector_index_tool.simplices()
vector_as_dataframe         =   boundary_matrix.column_for_simplex([0,1,2])
vector_as_ndarray           =   vector_index_tool.dense_array_for_dataframe(vector_as_dataframe)

html                        =   oat.plot.display_dataframes_side_by_side(
                                    vector_as_dataframe, pd.DataFrame(dict(coefficient=vector_as_ndarray)), simplices_in_index_tool,
                                    titles=['Vector as DataFrame', 'Vector as dense array', 'Simplices in index tool']
                                )
html

Vector as DataFrame

	simplex	filtration	coefficient
0	(0, 2)	0.342480	-1
1	(0, 1)	0.377622	1
2	(1, 2)	0.559060	1

Vector as dense array

	coefficient
0	0.0
1	0.0
2	0.0
3	0.0
4	0.0
5	-1.0
6	1.0
7	0.0
8	0.0
9	1.0
10	0.0
11	0.0
12	0.0
13	0.0
14	0.0

Simplices in index tool

	simplex	filtration
0	(0,)	0.000000
1	(1,)	0.000000
2	(2,)	0.000000
3	(3,)	0.000000
4	(4,)	0.000000
5	(0, 2)	0.342480
6	(0, 1)	0.377622
7	(0, 3)	0.389864
8	(1, 3)	0.497502
9	(1, 2)	0.559060
10	(2, 3)	0.586859
11	(0, 4)	0.752891
12	(3, 4)	0.790280
13	(2, 4)	0.812302
14	(1, 4)	1.116900

Convert the dense 1d numpy.ndarray back to a dataframe

vector_as_dataframe.equals(
    vector_index_tool.dataframe_for_dense_array(vector_as_ndarray)
)

False

Look up the index for a given simplex

vector_index_tool.index_number_for_simplex((1,3))

8

Errors for invalid simplices

try:
    vector_index_tool.index_number_for_simplex((3,2,1)) # not strictly sorted
except Exception as e:
    print(f"Caught error: {type(e).__name__}: {e}")

try:
    vector_index_tool.index_number_for_simplex((10,20)) # not in the Vietoris-Rips complex
except Exception as e:
    print(f"Caught error: {type(e).__name__}: {e}")

Caught error: TypeError: The VectorIndexTool does not contain a simplex represented by [3, 2, 1].
Caught error: TypeError: The VectorIndexTool does not contain a simplex represented by [10, 20].

Check that a simplex is in the index tool

vector_index_tool.contains_simplex((1,4))

True

Check that a simplex is not in the index tool

vector_index_tool.contains_simplex((1,5))

False