IEnumerable <Tuple <Vector, Vector> > Combine(Matrix M1, Matrix M2)
{
Debug.Assert(M1.CountLines == M2.CountLines);
for (int i = 0; i < M1.CountLines; i++)
{
yield return(new Tuple <Vector, Vector>(M1.Line(i), M2.Line(i)));
}
}
/// <summary>
/// Matrix wird in Dreiecksform gebracht
/// </summary>
/// <param name="countColsToNormalize">Anzahl der zu normalisierenden Spalen</param>
/// <returns></returns>
public Matrix Dreieck(int countColsToNormalize)
{
Matrix M = new Matrix(this);
for (int col = 0; col < countColsToNormalize; col++)
{
// Zeile mit Koeff != 0 in der zu normalisierenden Spalte suchen
int line;
for (line = 0; line < M.CountLines; line++)
{
if ((col == 0 || M[line, col - 1] == 0) && M[line, col] != 0)
{
break;
}
}
if (line < M.CountLines)
{
Vector normLine = M.Line(line) * (1.0 / M[line, col]);
normLine[col] = 1.0;
// Alle restlichen Zeilen in der Matrix umformen, so daß in der Spalte nur eine 1 stehen bleibt
for (int line2 = 0; line2 < M.CountLines; line2++)
{
for (int col2 = 0; col2 < M.Dimensions; col2++)
{
if (line == line2)
{
M[line2, col2] = normLine[col2];
}
else
{
M[line2, col2] -= normLine[col2] * M[line2, col2];
}
}
}
}
}
return(M);
}
/// <summary>
/// Invertierung nach Austauschverfahren (Pivot)
/// y = M x -> x = MInv y
/// </summary>
/// <param name="Minv"></param>
/// <returns></returns>
public bool Invert(out Matrix Minv)
{
Minv = new Matrix(this);
int[] ixX = IndexGenerator(Dimensions).ToArray();
bool[] Xchanged = BoolFieldGenerator(false, Dimensions).ToArray();
int[] ixY = IndexGenerator(CountLines).ToArray();
bool[] Ychanged = BoolFieldGenerator(false, Dimensions).ToArray();
int pivotC = 0, pivotL = 0;
try
{
// Tauschen aller x gegen alle y
for (pivotC = 0; pivotC < Math.Min(this.Dimensions, this.CountLines); pivotC++)
{
// Suchen in aktueller Spalte nach einem Koeff für eine Zeile, deren y noch nicht getauscht wurde
pivotL = ColAsTriple(Minv, pivotC, Ychanged).Where(line => line.Item2 != 0 && !line.Item3).First().Item1;
// x und y tauschen. Tausch protokollieren
int tausch = ixX[pivotC];
ixX[pivotC] = ixY[pivotL];
ixY[pivotL] = tausch;
Xchanged[pivotC] = Ychanged[pivotL] = true;
// Inversion in Hilfsmatrix durchführen
Matrix M2 = new Matrix(Minv);
double p = Minv[pivotC, pivotL];
M2.SetLine(pivotL, Minv.Line(pivotL) * (-1 / p));
M2.SetColumn(pivotC, Minv.Column(pivotC) * (1 / p));
M2[pivotL, pivotC] = 1 / p;
for (int line = 0; line < Dimensions; line++)
{
if (line != pivotL)
{
for (int col = 0; col < Dimensions; col++)
{
if (col != pivotC)
{
M2[line, col] = Minv[line, col] + -Minv[line, pivotC] * Minv[pivotL, col] / p;
}
}
}
}
// Hilfsmatrix zur neuen gültigen erklären
Minv = M2;
}
// Umsortieren der Zeilen
Matrix M3 = new Matrix(Minv.CountLines, Minv.Dimensions);
for (int line = 0; line < CountLines; line++)
{
M3.SetLine(ixY[line], Minv.Line(line));
}
Matrix M4 = new Matrix(Minv.CountLines, Minv.Dimensions);
for (int col = 0; col < Dimensions; col++)
{
M4.SetColumn(ixX[col], M3.Column(col));
}
Minv = M4;
}
catch (Exception)
{
return(false);
}
// Reihenfolge wiederherstellen
return(true);
}
