/// <summary>
/// Kopierkonstruktor
/// </summary>
/// <param name="other">Original</param>
internal MatrixEx(MatrixEx other)
{
m_cmps = new Fraction[other.Rows][];
for (int i = 0; i < other.Rows; i++)
{
m_cmps[i] = new Fraction[other.Columns];
for (int j = 0; j < other.Columns; j++)
{
m_cmps[i][j] = new Fraction(other.m_cmps[i][j]);
}
}
}
private static bool SolveFromPivot(ref MatrixEx matrix, uint row, uint col)
{
bool result = true;
//int max = 0;
//if rad_equation.Checked then max := edt_Dimension.Value else if rad_inverse.Checked then max := edt_Dimension.Value*2-1;
//Pivotelement ist Null - tausche Pivotzeile mit anderer Zeile
if (matrix[row, col].Numerator == 0)
{
bool valid = false;
//gültige Zeile ohne Null suchen
for (uint i = row + 1; i < matrix.Rows; i++)
{
if (matrix[i, col].Numerator != 0)
{
valid = true;
//Zeilenelemente tauschen
for (uint j = 0; j < /*max*/ matrix.Columns; j++)
{
Fraction h = matrix[row, j];
matrix[row, j] = matrix[i, j];
matrix[i, j] = h;
}
break;
}
}
result = valid;
}
// Erzeugen von Nullen unterhalb des Pivotelements
if (result)
{
for (uint i = row + 1; i < matrix.Rows; i++)
{
if (matrix[i, col].Numerator != 0)
{
// Zeilenmodifikator bestimmen
Fraction mul = matrix[i, col] / matrix[row, col] * -1;
for (uint j = col; j < /*col*/ matrix.Columns; j++)
{
matrix[i, j] = matrix[row, j] * mul + matrix[i, j];
}
}
}
}
// Mit nächster Spalte weitermachen
if (row + 1 < matrix.Rows - 1 && result)
{
result = SolveFromPivot(ref matrix, row + 1, col + 1);
}
return(result);
}
/// <summary>
/// Transponierte Matrix
/// </summary>
/// <returns>Transponierte Matrix</returns>
public MatrixEx Transpone()
{
MatrixEx trans = new MatrixEx(Columns, Rows);
for (int i = 0; i < Rows; i++)
{
for (int j = 0; j < Columns; j++)
{
trans.m_cmps[j][i] = m_cmps[i][j];
}
}
return(trans);
}
/// <summary>
/// Division durch Skalar
/// </summary>
/// <param name="v"></param>
/// <param name="skalar"></param>
/// <returns></returns>
public static MatrixEx operator /(MatrixEx m, Fraction skalar)
{
MatrixEx matrix = new MatrixEx(m);
for (int i = 0; i < matrix.Rows; i++)
{
for (int j = 0; j < matrix.Columns; j++)
{
matrix.m_cmps[i][j] /= skalar;
}
}
return(matrix);
}
private static bool ReverseSolveFromPivot(ref MatrixEx matrix, uint row, uint col)
{
bool result = true;
//max := 0;
//if rad_equation.Checked then max := edt_Dimension.Value else if rad_inverse.Checked then max := edt_Dimension.Value*2-1;
//Pivotelement ist nicht Eins - gesamte Zeile dividieren
if (matrix[row, col].Equals(1) == false)
{
Fraction h = new Fraction(matrix[row, col]);
for (uint j = /*max*/ matrix.Columns - 1; j >= 0; j--)
{
matrix[row, j] /= h;
if (j == 0)
{
break;
}
}
}
// Erzeugen von Nullen überhalb des Pivotelements
if (row > 0)
{
for (uint i = row - 1; ; i--)
{
// Zeilenmodifikator bestimmen
//mul := Matrix.Element[i,Col]/Matrix.Element[Row,Col]*-1;
Fraction mul = new Fraction(matrix[i, col]) / matrix[row, col] * -1;
for (uint j = matrix.Columns - 1; ; j--)
{
//Matrix.Element[i,j] := mul*Matrix.Element[Row,j]+Matrix.Element[i,j];
Fraction h = new Fraction(matrix[row, j]) * mul + matrix[i, j];
matrix[i, j] = h;
if (j == 0)
{
break;
}
}
if (i == 0)
{
break;
}
}
}
// Mit kleinerer Matrix fortsetzen
if (row > 0 && result)
{
result = ReverseSolveFromPivot(ref matrix, row - 1, col - 1);
}
return(result);
}
private static Fraction CalcDeterminant(MatrixEx matrix)
{
if (matrix.Rows != matrix.Columns)
{
//Determinante nur für quadr. Matrizen
throw new NotSupportedException("Determinant only applicable to quadratic matrices.");
}
if (matrix.Columns == 2)
{
return(matrix[0, 0] * matrix[1, 1] - matrix[1, 0] * matrix[0, 1]);
}
else
{
Fraction sum = new Fraction(0);
//Laplace'scher Entwicklungssatz
for (uint i = 0; i < matrix.Columns; i++)
{
//Matrix nach Spalte i entwickeln
MatrixEx eMat = new MatrixEx(matrix.Rows - 1, matrix.Columns - 1);
for (uint m = 1; m < matrix.Rows; m++)
{
for (uint n = 0; n < matrix.Columns; n++)
{
if (n < i)
{
eMat[m - 1, n] = new Fraction(matrix[m, n]);
}
else if (n > i)
{
eMat[m - 1, n - 1] = new Fraction(matrix[m, n]);
}
}
}
//rekursiver Aufruf
if (matrix[0, i].Numerator != 0)
{
Fraction det = matrix[0, i] * CalcDeterminant(eMat);
// odd(i)
if (i % 2 != 0)
{
sum -= det;
}
else
{
sum += det;
}
}
}
return(sum);
}
}
/// <summary>
/// Invertiert eine Matrix
/// </summary>
/// <param name="A">Zu intertierende Matrix</param>
/// <returns>Inverse Matrix 1/A</returns>
public static Matrix InvertMatrix(Matrix A)
{
if (A == null)
{
throw new ArgumentNullException("Matrix must not be null.");
}
if (A.Rows != A.Columns)
{
throw new NotSupportedException("Only quadratic matrices are invertable.");
}
//erweiterte Matrix erzeugen
MatrixEx enhMat = new MatrixEx(A.Rows, A.Columns * 2);
for (uint i = 0; i < A.Rows; i++)
{
for (uint j = 0; j < A.Columns; j++)
{
enhMat[i, j] = new Fraction(A[i, j]);
if (i == j)
{
enhMat[i, j + A.Columns] = new Fraction(1);
}
else
{
enhMat[i, j + A.Columns] = new Fraction(0);
}
}
}
if (SolveFromPivot(ref enhMat, 0, 0))
{
//Rang der Matrix prüfen (wenn kleiner Rows -> nicht eindeutig lösbar)
if (Rank(enhMat, A.Rows, A.Columns) != A.Rows)
{
return(null);
}
ReverseSolveFromPivot(ref enhMat, A.Rows - 1, A.Columns - 1);
}
//Ergebnis aus erw. Matrix lesen
Matrix result = new Matrix(A.Rows, A.Columns);
for (uint i = 0; i < A.Rows; i++)
{
for (uint j = 0; j < A.Columns; j++)
{
result[i, j] = enhMat[i, j + A.Columns].Value;
}
}
return(result);
}
/// <summary>
/// Subtraktion
/// </summary>
/// <param name="v1"></param>
/// <param name="v2"></param>
/// <returns></returns>
public static MatrixEx operator -(MatrixEx m1, MatrixEx m2)
{
if (m1.Columns != m2.Columns ||
m1.Rows != m2.Rows)
{
throw new ArgumentException("Dimensions of matrices do not match.");
}
MatrixEx matrix = new MatrixEx(m1);
for (int i = 0; i < matrix.Rows; i++)
{
for (int j = 0; j < matrix.Columns; j++)
{
matrix.m_cmps[i][j] -= m2.m_cmps[i][j];
}
}
return(matrix);
}
private static uint Rank(MatrixEx enhMat, uint rows, uint columns)
{
uint count = 0;
Fraction rowsum;
for (uint i = 0; i < rows; i++)
{
rowsum = new Fraction(0);
for (uint j = 0; i < columns; j++)
{
rowsum += enhMat[i, j];
}
if (rowsum.Numerator != 0)
{
count++;
}
}
return(count);
}
/// <summary>
/// Löst ein Gleichungssystem "A*x=b" und gibt den Lösungsvektor x zurück.
/// </summary>
/// <param name="A">Matrix A</param>
/// <param name="b">Vektor b</param>
/// <returns>Lösungsvektor x</returns>
public static Vector SolveEquation(Matrix A, Vector b)
{
if (A == null || b == null)
{
throw new ArgumentNullException("Parameters must not be null.");
}
if (A.Rows != b.Dimensions)
{
throw new NotSupportedException("Dimensions of matrix and vector do not match.");
}
//erweiterte Matrix erzeugen
MatrixEx enhMat = new MatrixEx(A.Rows, A.Columns + 1);
for (uint i = 0; i < A.Rows; i++)
{
for (uint j = 0; j < A.Columns; j++)
{
enhMat[i, j] = new Fraction(A[i, j]);
}
enhMat[i, A.Columns] = new Fraction(b[i]);
}
if (SolveFromPivot(ref enhMat, 0, 0))
{
//Rang der Matrix prüfen (wenn kleiner Rows -> nicht eindeutig lösbar)
if (Rank(enhMat, A.Rows, A.Columns) != A.Rows)
{
return(null);
}
ReverseSolveFromPivot(ref enhMat, A.Rows - 1, A.Columns - 1);
}
//Ergebnis aus erw. Matrix lesen
Vector result = new Vector(b.Dimensions);
for (uint i = 0; i < A.Rows; i++)
{
result[i] = enhMat[i, A.Columns].Value;
}
return(result);
}
/// <summary>
/// Multiplikation
/// </summary>
/// <param name="v1"></param>
/// <param name="v2"></param>
/// <returns></returns>
public static MatrixEx operator *(MatrixEx m1, MatrixEx m2)
{
if (m1.Columns != m2.Rows)
{
throw new ArgumentException("Inner dimensions of matrices need to match.");
}
MatrixEx matrix = new MatrixEx(m1.Rows, m2.Columns);
for (uint i = 0; i < matrix.Rows; i++)
{
for (uint j = 0; j < matrix.Columns; j++)
{
Fraction sum = new Fraction(0);
for (uint k = 0; k < m1.Columns; k++)
{
sum += m1[i, k] * m2[k, j];
}
matrix.m_cmps[i][j] = sum;
}
}
return(matrix);
}
public override bool Equals(object other)
{
if (other is MatrixEx == false)
{
return(false);
}
MatrixEx oMatrix = (MatrixEx)other;
bool equal = Columns == oMatrix.Columns;
equal &= Rows == oMatrix.Rows;
if (!equal)
{
return(false);
}
for (int i = 0; i < oMatrix.Rows; i++)
{
for (int j = 0; j < oMatrix.Columns; j++)
{
equal &= m_cmps[i][j] == oMatrix.m_cmps[i][j];
}
}
return(equal);
}