/// <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 MatrixField Solve(MatrixField value)
{
if (value == null)
{
throw new ArgumentNullException("value");
}
if (value.Rows != this.LU.Rows)
{
throw new ArgumentException("Invalid matrix dimensions.", "value");
}
if (!this.NonSingular)
{
throw new InvalidOperationException("Matrix is singular");
}
// Copy right hand side with pivoting
int count = value.Columns;
MatrixField X = value.Submatrix(pivotVector, 0, count - 1);
int rows = LU.Rows;
int columns = LU.Columns;
Field[][] lu = LU.Array;
// Solve L*Y = B(piv,:)
for (int k = 0; k < columns; k++)
{
for (int i = k + 1; i < columns; i++)
{
for (int j = 0; j < count; j++)
{
X[i, j] -= X[k, j] * lu[i][k];
}
}
}
// Solve U*X = Y;
for (int k = columns - 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>Least squares solution of <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>A matrix that minimized the two norm of <c>Q * R * X - B</c>.</returns>
/// <exception cref="T:System.ArgumentException">Matrix row dimensions must be the same.</exception>
/// <exception cref="T:System.InvalidOperationException">Matrix is rank deficient.</exception>
public MatrixField Solve(MatrixField value)
{
if (value == null)
{
throw new ArgumentNullException("value");
}
if (value.Rows != QR.Rows)
{
throw new ArgumentException("Matrix row dimensions must agree.");
}
if (!this.FullRank)
{
throw new InvalidOperationException("Matrix is rank deficient.");
}
// Copy right hand side
int count = value.Columns;
MatrixField X = value.Clone();
int m = QR.Rows;
int n = QR.Columns;
Field[][] qr = QR.Array;
// Compute Y = transpose(Q)*B
for (int k = 0; k < n; k++)
{
for (int j = 0; j < count; j++)
{
Field s = new Field(0);
for (int i = k; i < m; i++)
{
s += qr[i][k] * X[i, j];
}
s = (s - s - s) / qr[k][k];
for (int i = k; i < m; i++)
{
X[i, j] += s * qr[i][k];
}
}
}
// Solve R*X = Y;
for (int k = n - 1; k >= 0; k--)
{
for (int j = 0; j < count; j++)
{
X[k, j] /= Rdiag[k];
}
for (int i = 0; i < k; i++)
{
for (int j = 0; j < count; j++)
{
X[i, j] -= X[k, j] * qr[i][k];
}
}
}
return(X.Submatrix(0, n - 1, 0, count - 1));
}