/// <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="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));
}