///<Sumary>Least squares solution of A*X = B</Sumary>
///<param name="B">A Matrix with as many rows as A and any number of columns.</param>
///<returns> X that minimizes the two norm of Q*R*X-B.</returns>
public Matrix3d Solve(Matrix3d B)
{
if (B.RowLength() != m)
{
throw new ArgumentException("Matrix row dimensions must agree.");
}
if (!IsFullRank())
{
throw new Exception("Matrix is rank deficient.");
}
// Copy right hand side
int nx = B.ColumnLength();
double[,] X = B.ToArray();
// Compute Y = transpose(Q)*B
for (int k = 0; k < n; k++)
{
for (int j = 0; j < nx; j++)
{
double s = 0.0f;
for (int i = k; i < m; i++)
{
s += QR[i, k] * X[i, j];
}
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 < nx; j++)
{
X[k, j] /= Rdiag[k];
}
for (int i = 0; i < k; i++)
{
for (int j = 0; j < nx; j++)
{
X[i, j] -= X[k, j] * QR[i, k];
}
}
}
Matrix3d mat = new Matrix3d();
mat = mat.FromDoubleArray(X);
return(mat.GetMatrix(0, n - 1, 0, nx - 1));
}
/** Solve A*X = B
* @param B A Matrix with as many rows as A and any number of columns.
* @return X so that L*U*X = B(piv,:)
* @exception System.ArgumentException Matrix row dimensions must agree.
* @exception System.Exception Matrix is singular.
*/
public Matrix3d solve(Matrix3d B)
{
if (B.RowLength() != m)
{
throw new ArgumentException("Matrix row dimensions must agree.");
}
if (!this.IsNonsingular())
{
throw new Exception("Matrix is singular.");
}
// Copy right hand side with pivoting
int nx = B.ColumnLength();
Matrix3d Xmat = B.GetMatrix(piv, 0, nx - 1);
double[,] X = Xmat.ToArray();
// 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(Xmat);
}
