/// <summary>
/// Adds the specified sparse rows regarding defined multipliers.
/// </summary>
/// <param name="a1">The a1.</param>
/// <param name="a2">The a2.</param>
/// <param name="a1Coef">The a1 coef.</param>
/// <param name="a2Coef">The a2 coef.</param>
/// <returns> a1 * a1Coef + a2 * a2Coef</returns>
public static SparseRow Add(SparseRow a1, SparseRow a2, double a1Coef, double a2Coef)
{
var buf = new SparseRow(a2.Size + a1.Size);
//based on https://stackoverflow.com/a/12993675/1106889
//result = a1 * a1Coef + a2 * a2Coef;
var c1 = 0;
var c2 = 0;
var i1s = a1.Indexes;
var v1s = a1.Values;
var l1 = a1.Size;
var i2s = a2.Indexes;
var v2s = a2.Values;
var l2 = a2.Size;
while (c1 < l1 && c2 < l2)
{
var i1 = i1s[c1];
var i2 = i2s[c2];
var v1 = v1s[c1];
var v2 = v2s[c2];
if (i1 > i2)
{
buf.Add(i2 /*or i1*/, v2 * a2Coef);
c2++;
}
else if (i1 < i2)
{
buf.Add(i1, v1 * a1Coef);
c1++;
}
else
{//common
var newValue = v1 * a1Coef + v2 * a2Coef;
buf.Add(i1, newValue);
c1++;
c2++;
}
}
return(buf);
}
public static SparseRow From(int[] columns, double[] values)
{
Array.Sort(columns, values);
Array.Sort(columns);
var buf = new SparseRow();
buf.Columns = new List <int>(columns);
buf.Values = new List <double>(values);
buf.NextMember = new List <int>(Enumerable.Range(0, columns.Length).Select(i => i + 1));
buf.NextMember[buf.NextMember.Count - 1] = -1;
buf.Head = 0;
return(buf);
}
/// <summary>
/// Adds the addition into the target
/// </summary>
/// <param name="target"></param>
/// <param name="addition"></param>
/// <param name="factor"></param>
public static void Add(SparseRow target, SparseRow addition, double factor)
{
var it = target.Head;
var ia = addition.Head;
while (true)
{
var c1 = target.Columns[it];
var c2 = addition.Columns[ia];
while (c2 < c1)
{
}
it = target.NextMember[it];
}
throw new NotImplementedException();
}
public CCS CalculateRref(CCS a)
{
var sys = SparseEqSystem.Generate((CSparse.Double.CompressedColumnStorage)a);
var dns = a.ToDenseMatrix();
sys.RowsPool = new SortedSet <SparseRow>();
var eqs = sys.Equations;
for (var i = 0; i < sys.Equations.Length; i++)
{
sys.Equations[i].Tag = i;
}
var lastColIndex = a.ColumnCount - 1;
//should have n columns with one nonzero
//var colPivotHistory = new HashSet<int>();
//var rowPivotHistory = new HashSet<int>();
var dependentRows = new bool[sys.RowCount];// HashSet<int>();
var leadingMember = new bool[sys.RowCount];
//var pivotedYet = new bool[a.RowCount];
for (var i = 0; i < sys.Equations.Length; i++)
{
foreach (var tuple in sys.Equations[i].EnumerateIndexed())
{
if (sys.ColumnNonzeros[tuple.Item1] == 1)
{
leadingMember[i] = true;
}
}
}
var maxItter = Math.Max(a.ColumnCount, a.RowCount);
var itter = 0;
while (itter++ < maxItter)
{
//find count
var oneNnzCols = sys.ColumnNonzeros.Count(i => i == 1);
var eqNeeded = Math.Min(a.ColumnCount - 1, a.RowCount - dependentRows.Count(i => i == true));
if (oneNnzCols == eqNeeded)
{
break;
}
//select pivot
//minimum row nnz x col nnz
//select row strategy: row with minimum nnz, where nnz is nonzero count except last column (right side) and nnz > 1
var minRowNnz = int.MaxValue; // sys.RowNonzeros.Where(i => i > 1).Min();
var minRowNnzIndex = -1; // sys.RowNonzeros.FirstIndexOf(minRowNnz);
{
for (var j = 0; j < sys.RowCount; j++)
{
if (leadingMember[j])
{
continue;
}
if (dependentRows[j])
{
continue;
}
//if (sys.RowNonzeros[j] <= 1)
// continue;
if (sys.RowNonzeros[j] < minRowNnz)
{
minRowNnzIndex = j;
minRowNnz = sys.RowNonzeros[j];
}
}
}
if (minRowNnzIndex == -1)
{
throw new Exception();
}
//var minColNnz = sys.ColumnNonzeros.Where(i => i > 1).Min();
var minColNnz = int.MaxValue;// sys.ColumnNonzeros.Where(i => i > 1).Min();
var minColNnzIndex = -1;
{
for (var jj = 0; jj < sys.Equations[minRowNnzIndex].Size; jj++)
{
var j = sys.Equations[minRowNnzIndex].Indexes[jj];
//if (colPivotHistory.Contains(j))
// continue;
if (sys.ColumnNonzeros[j] <= 1)
{
continue;
}
if (sys.ColumnNonzeros[j] < minColNnz)
{
minColNnzIndex = j;
minColNnz = sys.ColumnNonzeros[j];
}
}
}
//var minColNnzIndex = sys.ColumnNonzeros.FirstIndexOf(minColNnz);
if (minColNnzIndex == -1)
{
//var t = sys.ToCcs().ToDenseMatrix();
throw new Exception();
}
var col = minColNnzIndex;
var c1 = sys.Equations.Where(i => i.ContainsIndex(col) && !leadingMember[i.Tag]);
var rw =
c1.MinBy(j => j.Size, null);
//sys.Equations[minRowNnzIndex];
if (dependentRows[sys.Equations.IndexOfReference(rw)])
{
throw new Exception();
}
Console.WriteLine("Pivot: {0},{1}", sys.Equations.IndexOfReference(rw), col);
//Console.ReadKey();
// eqs.Equations.Where(i => i.Size > 1).MinBy(new SparseRowLengthComparer());
var eliminator = rw;// sys.Equations[rw];
//eliminate all rows with pivot
for (var i = 0; i < sys.Equations.Length; i++)
{
var canditate = eqs[i];
if (canditate.ContainsIndex(col) && !ReferenceEquals(eliminator, canditate))
{
var oldOne = eqs[i];//to be removed
foreach (var enm in oldOne.EnumerateIndexed())
{
sys.ColumnNonzeros[enm.Item1]--;
}
var newOne = SparseRow.Eliminate(eliminator, oldOne, col);
if (newOne.CalcNnz(lastColIndex) == 0 && newOne.GetRightSideValue(lastColIndex) != 0)
{
throw new Exception("Inconsistent system");
}
if (newOne.CalcNnz(lastColIndex) == 0 && newOne.GetRightSideValue(lastColIndex) == 0)
{
//fully zero equation
dependentRows[i] = true;// newOne.Tag);
}
newOne.Tag = oldOne.Tag;
foreach (var enm in newOne.EnumerateIndexed())
{
sys.ColumnNonzeros[enm.Item1]++;
if (sys.ColumnNonzeros[enm.Item1] == 1)
{
leadingMember[i] = true;
}
}
if (sys.ColumnNonzeros.Contains(0))
{
Guid.NewGuid();
}
eqs[i] = newOne;
sys.RowNonzeros[i] = newOne.CalcNnz(lastColIndex);
}
}
leadingMember[sys.Equations.IndexOfReference(rw)] = true;
Console.WriteLine("elimination done for all eqs, Col[{0}] : {1} nnzs", col, sys.ColumnNonzeros[col]);
if (sys.ColumnNonzeros[col] != 1)
{
Guid.NewGuid();
}
}
SparseEqSystem newSys;// = new SparseEqSystem();
{
////////start final check
var tol = 1e-9;
var dependentEquationCount = sys.Equations.Count(i => i.CalcNnz(lastColIndex) == 0 && i.GetRightSideValue(lastColIndex).FEquals(0, tol));
var incosistentEquationCount = sys.Equations.Count(i => i.CalcNnz(lastColIndex) == 0 && !i.GetRightSideValue(lastColIndex).FEquals(0, tol));
var NnzMemberInCol = new int[sys.ColumnCount - 1];
foreach (var eq in sys.Equations)
{
foreach (var idx in eq.EnumerateIndexed())
{
if (idx.Item1 != lastColIndex)
{
if (!idx.Item2.FEquals(0, tol))
{
NnzMemberInCol[idx.Item1]++;
}
}
}
}
var leadingMembers = NnzMemberInCol.Count(i => i == 1);
if (leadingMembers != Math.Min(sys.ColumnCount - 1, sys.RowCount - dependentEquationCount))
{
throw new Exception();
}
if (incosistentEquationCount != 0)
{
throw new Exception();
}
var allExceptDependentEqs = sys.Equations.Where(i => !(i.CalcNnz(lastColIndex) == 0 && i.GetRightSideValue(lastColIndex).FEquals(0, tol))).ToArray();
newSys = SparseEqSystem.Generate(allExceptDependentEqs, a.ColumnCount);
}
return(newSys.ToCcs());
}
/// <summary>
/// Eliminates the specified index of <see cref="eliminated"/> row by adding appropriated multiply of <see cref="eliminator"/> to it.
/// </summary>
/// <param name="eliminator">The eliminator row.</param>
/// <param name="eliminated">The eliminated row.</param>
/// <param name="eliminateIndex">The index of eliminated member.</param>
/// <returns>Eliminated version of <see cref="eliminated"/></returns>
public static SparseRow Eliminate(SparseRow eliminator, SparseRow eliminated, int eliminateIndex, double epsilon = 0)
{
var buf = new SparseRow(eliminated.Size + eliminator.Size);
//based on https://stackoverflow.com/a/12993675/1106889
//result = eliminator * coef + eliminated
double coef;
{
var t1 = Array.BinarySearch(eliminator.Indexes, 0, eliminator.Size, eliminateIndex);
var t2 = Array.BinarySearch(eliminated.Indexes, 0, eliminated.Size, eliminateIndex);
if (t1 < 0 || t2 < 0)
{
throw new Exception();
}
coef = -eliminated.Values[t2] / eliminator.Values[t1];
}
var c1 = 0;
var c2 = 0;
var i1s = eliminator.Indexes;
var v1s = eliminator.Values;
var l1 = eliminator.Size;
var i2s = eliminated.Indexes;
var v2s = eliminated.Values;
var l2 = eliminated.Size;
while (c1 < l1 && c2 < l2)
{
var i1 = i1s[c1];
var i2 = i2s[c2];
var v1 = v1s[c1];
var v2 = v2s[c2];
if (i1 > i2)
{
buf.Add(i2 /*or i1*/, v2);
c2++;
}
else if (i1 < i2)
{
buf.Add(i1, v1 * coef);
c1++;
}
else
{//common
if (i1 != i2)
{
throw new Exception();
}
var newValue = v1 * coef + v2;
if (i1 == eliminateIndex || Math.Abs(newValue) < epsilon)
{
//this is eliminated item, newValue should be zero and nothing to add
if (Math.Abs(newValue) > 1e-6)
{
throw new Exception("wrong result");
}
}
else
{
buf.Add(i1, newValue);
}
c1++;
c2++;
}
}
//tail
{
for (; c1 < l1; c1++)
{
var i1 = i1s[c1];
var v1 = v1s[c1];
buf.Add(i1, v1 * coef);
}
for (; c2 < l2; c2++)
{
var i2 = i2s[c2];
var v2 = v2s[c2];
buf.Add(i2, v2);
}
}
return(buf);
}