homology¶

Usage

use homology;

var hypergraph = new AdjListHyperGraph(4, 3, new unmanaged Cyclic(startIdx = 0))¶

var _vtxSubsetSet = new set(string)¶

iter processVtxSubset(vtxSubset)¶

proc doProcessVertices(verticesSet)¶

Generate the permutation

var setContent = AppendExpr.Call08¶

Verify the set by printing

var _sz = 0¶

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¶

var numKCells: int¶

var D = {1..numKCells}¶

var A: [D] string¶

proc init(_N: int)¶

proc findCellIndex(s: string)¶

var numBins = kCellMap.size-1¶

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

var kCellKeys = AppendExpr.Call08¶

record Comparator¶

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

var absComparator: Comparator¶

class Matrix¶

Start of the construction of boundary matrices.

var N: int¶

var M: int¶

var matrix: [1..N, 1..M] int¶

proc init(_N: int, _M: int)¶

var K = kCellMap.size-1¶

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

var i: int = 1¶

var vs = new set(string)¶

iter processVtxSubset2(vtxSubset)¶

proc doProcessVertices2(verticesSet)¶

Generate the permutation

proc printBoundaryMap(boundaryMap)¶

proc printmatrix(M)¶

proc IdentityMatrix(n)¶

class Matrix2D¶

var N: int¶

var M: int¶

var _arr: [1..N, 1..M] int¶

proc init(row: int, col: int)¶

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

proc swap_rows(i, j, M)¶

proc swap_columns(i, j, M)¶

proc add_to_row(M, i, j, ri = 1, rj = 1, mod = 2)¶

proc add_to_column(M, i, j, ci = 1, cj = 1, mod = 2)¶

proc matmultmod2(M, N, mod = 2)¶

proc matmultmod3(M, N, mod = 2)¶

proc matmultmod(M, N, mod = 2)¶

type listType = unmanaged nilable Matrix2Dlisttrue¶

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

proc calculateRank(M)¶

proc smithNormalForm(b)¶

var computedMatrices = smithNormalForm(boundaryMaps(1).matrix)¶

var computedMatrices2 = smithNormalForm(boundaryMaps(2).matrix)¶

var L1 = computedMatrices(1)¶

var R1 = computedMatrices(2)¶

var S1 = computedMatrices(3)¶

var L1invF = computedMatrices(4)¶

var R1invF = computedMatrices(5)¶

var L2 = computedMatrices2(1)¶

var R2 = computedMatrices2(2)¶

var S2 = computedMatrices2(3)¶

var L2invF = computedMatrices2(4)¶

var R2invF = computedMatrices2(5)¶

var rank1 = calculateRank(S1)¶

var rank2 = calculateRank(S2)¶

var nullity1 = AppendExpr.Call08-rank1¶

var betti1 = AppendExpr.Call08-rank1-rank2¶

var cokernel2_dim = AppendExpr.Call08-rank2¶

var nr1 = AppendExpr.Call08-rank1¶

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

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

var nr2 = AppendExpr.Call08-rank2¶

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

var LKernel = new unmanaged nilable Matrix2Dlisttrue¶

var _L2 = new unmanaged AppendExpr.Call08Matrix2DAppendExpr.Call08¶

var _ker1 = new unmanaged AppendExpr.Call08Matrix2DAppendExpr.Call08¶

var result = matmulreduce(LKernel)¶

var slc = AppendExpr.Call08-rank2¶

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

var L2invKernel = new unmanaged nilable Matrix2Dlisttrue¶

var _L2inv = new unmanaged AppendExpr.Call08Matrix2Dnr2¶

var _proj = new unmanaged AppendExpr.Call08Matrix2DAppendExpr.Call08¶

var proj2 = matmulreduce(L2invKernel)¶

proc reducedRowEchelonForm(b)¶