/// <summary>
/// Inverts the specified matrix.
/// </summary>
/// <param name="matrix">The matrix.</param>
/// <exception cref="System.ArgumentNullException">The matrix is null.</exception>
/// <exception cref="System.ArgumentException">The matrix is not square.</exception>
public static Matrix Invert(Matrix matrix)
{
if (matrix == null)
{
throw new ArgumentNullException("matrix", "The matrix is null.");
}
LUDecomposition luDecomposition = new LUDecomposition(matrix);
luDecomposition.Compute();
Matrix inverse = new Matrix(matrix.NumberOfColumns, matrix.NumberOfRows);
for (int i = 0; i < matrix.NumberOfRows; ++i)
{
Vector b = new Vector(matrix.NumberOfColumns, 0);
b[i] = 1; // identity vector
Vector y = SolveEquation(luDecomposition, b);
for (int j = 0; j < inverse.NumberOfRows; ++j)
{
inverse[j, i] = y[j];
}
}
return(inverse);
}
/// <summary>
/// Computes the determinant of the specified matrix.
/// </summary>
/// <param name="matrix">The matrix.</param>
/// <returns>The determinant of the specified matrix.</returns>
/// <exception cref="System.ArgumentNullException">The matrix is null.</exception>
/// <exception cref="System.ArgumentException">The matrix is not square.</exception>
public static Double ComputeDeterminant(Matrix matrix)
{
LUDecomposition luDecomposition = new LUDecomposition(matrix);
luDecomposition.Compute();
return(luDecomposition.Determinant);
}
/// <summary>
/// Decomposes the specified matrix.
/// </summary>
/// <param name="matrix">The matrix.</param>
/// <returns></returns>
/// <exception cref="System.ArgumentNullException">The matrix is null.</exception>
/// <exception cref="System.ArgumentException">The matrix is not square.</exception>
public static Matrix Decompose(Matrix matrix)
{
LUDecomposition luDecomposition = new LUDecomposition(matrix);
luDecomposition.Compute();
return(luDecomposition.LU);
}
/// <summary>
/// Decomposes the specified matrix.
/// </summary>
/// <param name="matrix">The matrix to decompose.</param>
/// <param name="l">The L (lower triangular) matrix.</param>
/// <param name="u">The U (upper triangular) matrix.</param>
/// <exception cref="System.ArgumentNullException">The matrix is null.</exception>
/// <exception cref="System.ArgumentException">The matrix is not square.</exception>
public static void Decompose(Matrix matrix, out Matrix l, out Matrix u)
{
LUDecomposition luDecomposition = new LUDecomposition(matrix);
luDecomposition.Compute();
l = luDecomposition.L;
u = luDecomposition.U;
}
/// <summary>
/// Solves a linear equation system.
/// </summary>
/// <param name="luDecomposition">The LU decomposition.</param>
/// <param name="b">The vector.</param>
/// <returns>The vector containing the unknown variables of the equation.</returns>
private static Vector SolveEquation(LUDecomposition luDecomposition, Vector b)
{
Vector pb = new Vector(b.Size);
// P*b
for (int i = 0; i < b.Size; ++i)
{
double s = 0;
for (int j = 0; j < luDecomposition.P.NumberOfColumns; ++j)
{
s += luDecomposition.P[i, j] * b[j];
}
pb[i] = s;
}
// L*y = P*b with forward substitution
Vector y = new Vector(pb.Size);
for (int i = 0; i < luDecomposition.L.NumberOfRows; ++i)
{
y[i] = pb[i];
for (int j = 0; j < i; ++j)
{
y[i] -= luDecomposition.L[i, j] * y[j];
}
y[i] /= luDecomposition.L[i, i] == 0 ? 1 : luDecomposition.L[i, i];
}
// U*x = y with back substitution
Vector x = new Vector(y.Size);
for (int i = x.Size - 1; i >= 0; --i)
{
x[i] = y[i];
for (int j = i + 1; j < luDecomposition.U.NumberOfRows; ++j)
{
x[i] -= luDecomposition.U[i, j] * x[j];
}
x[i] /= (luDecomposition.U[i, i] == 0 ? 1 : luDecomposition.U[i, i]);
}
return(x);
}
/// <summary>
/// Solves a linear equation system.
/// </summary>
/// <param name="a">The left side of the equation represented by a matrix.</param>
/// <param name="b">The right side of the equation represented by a vector.</param>
/// <returns>The vector containing the unknown variables of the equation.</returns>
/// <exception cref="System.ArgumentNullException">
/// The matrix is null.
/// or
/// The vector is null.
/// </exception>
/// <exception cref="System.ArgumentException">
/// The matrix is not square.
/// or
/// The size of the matrix does not match the size of the vector.
/// </exception>
public static Vector SolveEquation(Matrix a, Vector b)
{
if (a == null)
{
throw new ArgumentNullException("a", "The matrix is null.");
}
if (b == null)
{
throw new ArgumentNullException("b", "The vector is null.");
}
if (!a.IsSquare)
{
throw new ArgumentException("The matrix is not square.", "a");
}
if (a.NumberOfRows != b.Size)
{
throw new ArgumentException("The size of the matrix does not match the size of the vector.", "b");
}
LUDecomposition luDecomposition = new LUDecomposition(a);
luDecomposition.Compute();
return(SolveEquation(luDecomposition, b));
}
/// <summary>
/// Computes the determinant of the matrix.
/// </summary>
/// <param name="matrix">The matrix.</param>
/// <returns>The determinant of the matrix.</returns>
/// <exception cref="System.ArgumentNullException">The matrix is null.</exception>
public static Double ComputeDeterminant(this Matrix matrix)
{
return(LUDecomposition.ComputeDeterminant(matrix));
}
/// <summary>
/// Inverts the specified matrix.
/// </summary>
/// <param name="matrix">The matrix.</param>
/// <returns>The inverse matrix.</returns>
public static Matrix Invert(this Matrix matrix)
{
return(LUDecomposition.Invert(matrix));
}
