public virtual double Determinant()
{
if (Lu.RowCount() != Lu.ColumnCount())
{
throw new ArgumentException("Matrix must be square.");
}
double d = PivotSign;
for (int j = 0; j < Lu.ColumnCount(); j++)
{
d *= Lu[j, j];
}
return(d);
}
/// <summary>Solve A*X = B</summary>
/// <param name="B">
/// A Matrix with as many rows as A and any number of columns.
/// </param>
/// <returns>
/// X so that L*U*X = B(piv,:)
/// </returns>
/// <exception cref="System.ArgumentException">
/// Matrix row dimensions must agree.
/// </exception>
/// <exception cref="System.SystemException">
/// Matrix is singular.
/// </exception>
public virtual double[,] Solve(double[,] B)
{
if (B.RowCount() != Lu.RowCount())
{
throw new ArgumentException("Matrix row dimensions must agree.");
}
if (!IsNonSingular)
{
throw new SystemException("Matrix is singular.");
}
int n = Lu.ColumnCount();
// Copy right hand side with pivoting
int nx = B.ColumnCount();
double[,] X = B.Submatrix(Pivot, 0, nx - 1);
// Solve L*Y = B(piv,:)
for (int k = 0; k < n; k++)
{
for (int i = k + 1; i < n; i++)
{
for (int j = 0; j < nx; j++)
{
X[i, j] -= X[k, j] * Lu[i, k];
}
}
}
// Solve U*X = Y;
for (int k = n - 1; k >= 0; k--)
{
for (int j = 0; j < nx; j++)
{
X[k, j] /= Lu[k, k];
}
for (int i = 0; i < k; i++)
{
for (int j = 0; j < nx; j++)
{
X[i, j] -= X[k, j] * Lu[i, k];
}
}
}
return(X);
}