.. default-domain:: chpl

.. module:: homology

homology
========
**Usage**

.. code-block:: chapel

   use homology;

.. data:: var hypergraph = new AdjListHyperGraph(4, 3, new unmanaged Cyclic(startIdx = 0))

.. data:: var _vtxSubsetSet = new set(string)

.. iterfunction:: iter processVtxSubset(vtxSubset)

.. function:: proc doProcessVertices(verticesSet)

   Generate the permutation 

.. data:: var setContent = AppendExpr.Call08

   Verify the set by printing

.. data:: var _sz = 0

.. data:: var kCellMap = new intmapstringlisttrue

   bin k-cells, with key as the length of the list and value is a list with all the k-cells

.. class:: kCellsArray

   .. attribute:: var numKCells: int

   .. attribute:: var D = {1..numKCells}

   .. attribute:: var A: [D] string

   .. method:: proc init(_N: int)

   .. method:: proc findCellIndex(s: string)

.. data:: var numBins = kCellMap.size-1

.. data:: var kCellsArrayMap: [0..numBins] owned nilable kCellsArray

.. data:: var kCellKeys = AppendExpr.Call08

.. record:: Comparator

.. method:: proc Comparator.compare(a: string, b: string): int

.. data:: var absComparator: Comparator

.. class:: Matrix

   Start of the construction of boundary matrices.


   .. attribute:: var N: int

   .. attribute:: var M: int

   .. attribute:: var matrix: [1..N, 1..M] int

   .. method:: proc init(_N: int, _M: int)

.. data:: var K = kCellMap.size-1

.. data:: var boundaryMaps: [1..K] owned nilable Matrix

.. data:: var i: int = 1

.. data:: var vs = new set(string)

.. iterfunction:: iter processVtxSubset2(vtxSubset)

.. function:: proc doProcessVertices2(verticesSet)

   Generate the permutation 

.. function:: proc printBoundaryMap(boundaryMap)

.. function:: proc printmatrix(M)

.. function:: proc IdentityMatrix(n)

.. class:: Matrix2D

   .. attribute:: var N: int

   .. attribute:: var M: int

   .. attribute:: var _arr: [1..N, 1..M] int

   .. method:: proc init(row: int, col: int)

.. function:: proc _get_next_pivot(M, s1, in s2: int = 0)

.. function:: proc swap_rows(i, j, M)

.. function:: proc swap_columns(i, j, M)

.. function:: proc add_to_row(M, i, j, ri = 1, rj = 1, mod = 2)

.. function:: proc add_to_column(M, i, j, ci = 1, cj = 1, mod = 2)

.. function:: proc matmultmod2(M, N, mod = 2)

.. function:: proc matmultmod3(M, N, mod = 2)

.. function:: proc matmultmod(M, N, mod = 2)

.. type:: type listType = unmanaged nilable Matrix2Dlisttrue

.. function:: proc matmulreduce(arr: listType, reverse = false, mod = 2)

.. function:: proc calculateRank(M)

.. function:: proc smithNormalForm(b)

.. data:: var computedMatrices = smithNormalForm(boundaryMaps(1).matrix)

.. data:: var computedMatrices2 = smithNormalForm(boundaryMaps(2).matrix)

.. data:: var L1 = computedMatrices(1)

.. data:: var R1 = computedMatrices(2)

.. data:: var S1 = computedMatrices(3)

.. data:: var L1invF = computedMatrices(4)

.. data:: var R1invF = computedMatrices(5)

.. data:: var L2 = computedMatrices2(1)

.. data:: var R2 = computedMatrices2(2)

.. data:: var S2 = computedMatrices2(3)

.. data:: var L2invF = computedMatrices2(4)

.. data:: var R2invF = computedMatrices2(5)

.. data:: var rank1 = calculateRank(S1)

.. data:: var rank2 = calculateRank(S2)

.. data:: var nullity1 = AppendExpr.Call08-rank1

.. data:: var betti1 = AppendExpr.Call08-rank1-rank2

.. data:: var cokernel2_dim = AppendExpr.Call08-rank2

.. data:: var nr1 = AppendExpr.Call08-rank1

.. data:: var ker1: [1..AppendExpr.Call08, 1..nr1] int = ..R1rank1+1..

.. data:: var im2: [1..AppendExpr.Call08, 1..rank2] int = ..L2invF1..rank2

.. data:: var nr2 = AppendExpr.Call08-rank2

.. data:: var cokernel2: [1..AppendExpr.Call08, 1..nr2] int = ..L2invFrank2+1..

.. data:: var LKernel = new unmanaged nilable Matrix2Dlisttrue

.. data:: var _L2 = new unmanaged AppendExpr.Call08Matrix2DAppendExpr.Call08

.. data:: var _ker1 = new unmanaged AppendExpr.Call08Matrix2DAppendExpr.Call08

.. data:: var result = matmulreduce(LKernel)

.. data:: var slc = AppendExpr.Call08-rank2

.. data:: var proj: [1..slc, 1..AppendExpr.Call08] int = rank2+1..result..

.. data:: var L2invKernel = new unmanaged nilable Matrix2Dlisttrue

.. data:: var _L2inv = new unmanaged AppendExpr.Call08Matrix2Dnr2

.. data:: var _proj = new unmanaged AppendExpr.Call08Matrix2DAppendExpr.Call08

.. data:: var proj2 = matmulreduce(L2invKernel)

.. function:: proc reducedRowEchelonForm(b)