betti_number

This helper function wraps <code><a href="/link/Matrix%3A%3ArankMatrix()?package=SimplicialComplex&version=0.1.0" data-mini-rdoc="SimplicialComplex::Matrix::rankMatrix()">Matrix::rankMatrix()</a></code> to safely handle empty matrices (i.e., with 0 rows or columns).

internal

Provides an implementation of simplicial complexes for
Topological Data Analysis (TDA). The package includes functions to
compute faces, boundary operators, Betti numbers, Euler characteristic,
and to construct simplicial complexes. It also implements persistent
homology, from building filtrations to computing persistence diagrams,
with the aim of helping readers understand the core concepts of
computational topology.
Methods are based on standard references in persistent homology such as
Zomorodian and Carlsson (2005) <doi:10.1007/s00454-004-1146-y> and
Chazal and Michel (2021) <doi:10.3389/frai.2021.667963>.

ChiChien Wang

SimplicialComplex

Topological Data Analysis: Simplicial Complex

betti_number function

<dl><dt>simplices</dt>
<dd>A list of simplices representing the simplicial complex.</dd>
<dt>bound_dim</dt>
<dd>The dimension of the boundary to compute the Betti number for.</dd>
<dt>tol</dt>
<dd>Optional numerical tolerance to pass to <code>rankMatrix()</code>.</dd></dl>

Arguments

This helper function wraps <code><a href='https://rdrr.io/pkg/Matrix/man/rankMatrix.html'>Matrix::rankMatrix()</a></code> to safely handle empty matrices (i.e., with 0 rows or columns).

Safely compute the rank of a sparse matrix — betti_number

<dl>

<dt>simplices</dt>
<dd>A list of simplices representing the simplicial complex.</dd>


<dt>bound_dim</dt>
<dd>The dimension of the boundary to compute the Betti number for.</dd>


<dt>tol</dt>
<dd>Optional numerical tolerance to pass to <code>rankMatrix()</code>.</dd>

</dl>

betti_number: Safely compute the rank of a sparse matrix

Description

Usage

Value

Arguments

Examples