public IMapackMatrix Solve(IMapackMatrix rhs)
{
if (rhs.Rows != L.Rows)
{
throw new ArgumentException("Matrix dimensions do not match.");
}
if (!isSymmetric)
{
throw new InvalidOperationException("Matrix is not symmetric.");
}
if (!isPositiveDefinite)
{
throw new InvalidOperationException("Matrix is not positive definite.");
}
int dimension = L.Rows;
int count = rhs.Columns;
IMapackMatrix B = (IMapackMatrix)rhs.Clone();
double[][] l = L.Array;
// Solve L*Y = B;
for (int k = 0; k < L.Rows; k++)
{
for (int i = k + 1; i < dimension; i++)
{
for (int j = 0; j < count; j++)
{
B[i, j] -= B[k, j] * l[i][k];
}
}
for (int j = 0; j < count; j++)
{
B[k, j] /= l[k][k];
}
}
// Solve L'*X = Y;
for (int k = dimension - 1; k >= 0; k--)
{
for (int j = 0; j < count; j++)
{
B[k, j] /= l[k][k];
}
for (int i = 0; i < k; i++)
{
for (int j = 0; j < count; j++)
{
B[i, j] -= B[k, j] * l[k][i];
}
}
}
return B;
}
public IMapackMatrix Solve(IMapackMatrix rhs)
{
if (rhs.Rows != QR.Rows) throw new ArgumentException("Matrix row dimensions must agree.");
if (!IsFullRank) throw new InvalidOperationException("Matrix is rank deficient.");
// Copy right hand side
int count = rhs.Columns;
IMapackMatrix X = rhs.Clone();
int m = QR.Rows;
int n = QR.Columns;
double[][] qr = QR.Array;
// Compute Y = transpose(Q)*B
for (int k = 0; k < n; k++)
{
for (int j = 0; j < count; j++)
{
double s = 0.0;
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 < 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);
}