/// <summary>
/// Solves a set of equation systems of type <c>A * X = B</c>.
/// </summary>
/// <param name="value">Right hand side matrix with as many rows as <c>A</c> and any number of columns.</param>
/// <returns>Matrix <c>X</c> so that <c>L * U * X = B</c>.</returns>
///
public decimal[,] Solve(decimal[,] value)
{
if (value == null)
{
throw new ArgumentNullException("value");
}
if (value.GetLength(0) != rows)
{
throw new DimensionMismatchException("value", "The matrix should have the same number of rows as the decomposition.");
}
if (!Nonsingular)
{
throw new InvalidOperationException("Matrix is singular.");
}
// Copy right hand side with pivoting
int count = value.GetLength(1);
decimal[,] X = value.Submatrix(pivotVector, null);
// Solve L*Y = B(piv,:)
for (int k = 0; k < cols; k++)
{
for (int i = k + 1; i < cols; i++)
{
for (int j = 0; j < count; j++)
{
X[i, j] -= X[k, j] * lu[i, k];
}
}
}
// Solve U*X = Y;
for (int k = cols - 1; k >= 0; k--)
{
for (int j = 0; j < count; j++)
{
X[k, j] /= lu[k, k];
}
for (int i = 0; i < k; i++)
{
for (int j = 0; j < count; j++)
{
X[i, j] -= X[k, j] * lu[i, k];
}
}
}
return(X);
}
/// <summary>
/// Solves a set of equation systems of type <c>X * A = B</c>.
/// </summary>
/// <param name="value">Right hand side matrix with as many columns as <c>A</c> and any number of rows.</param>
/// <returns>Matrix <c>X</c> so that <c>X * L * U = A</c>.</returns>
///
public decimal[,] SolveTranspose(decimal[,] value)
{
if (value == null)
{
throw new ArgumentNullException("value");
}
if (value.GetLength(0) != rows)
{
throw new DimensionMismatchException("value", "The matrix should have the same number of rows as the decomposition.");
}
if (!Nonsingular)
{
throw new SingularMatrixException("Matrix is singular.");
}
// Copy right hand side with pivoting
var X = value.Submatrix(null, pivotVector);
int count = X.GetLength(1);
// Solve L*Y = B(piv,:)
for (int k = 0; k < rows; k++)
{
for (int i = k + 1; i < rows; i++)
{
for (int j = 0; j < count; j++)
{
X[j, i] -= X[j, k] * lu[i, k];
}
}
}
// Solve U*X = Y;
for (int k = rows - 1; k >= 0; k--)
{
for (int j = 0; j < count; j++)
{
X[j, k] /= lu[k, k];
}
for (int i = 0; i < k; i++)
{
for (int j = 0; j < count; j++)
{
X[j, i] -= X[j, k] * lu[i, k];
}
}
}
return(X);
}