public static int QRPTDecomp(PZMath_matrix A, PZMath_vector tau, PZMath_permutation p, out int signum, PZMath_vector norm)
{
int M = A.RowCount;
int N = A.ColumnCount;
signum = 0;
if (tau.Size != System.Math.Min(M, N))
{
PZMath_errno.ERROR("size of tau must be MIN(M,N)", PZMath_errno.PZMath_EBADLEN);
}
else if (p.Size != N)
{
PZMath_errno.ERROR("permutation size must be N", PZMath_errno.PZMath_EBADLEN);
}
else if (norm.Size != N)
{
PZMath_errno.ERROR("norm size must be N", PZMath_errno.PZMath_EBADLEN);
}
else
{
int i;
signum = 1;
p.Init(); /* set to identity */
/* Compute column norms and store in workspace */
for (i = 0; i < N; i++)
{
PZMath_vector c = A.Column(i);
double x = PZMath_blas.Dnrm2(c);
norm[i] = x;
}
for (i = 0; i < System.Math.Min(M, N); i++)
{
/* Bring the column of largest norm into the pivot position */
double max_norm = norm[i];
int j;
int kmax = i;
for (j = i + 1; j < N; j++)
{
double x = norm[j];
if (x > max_norm)
{
max_norm = x;
kmax = j;
}
}
if (kmax != i)
{
A.SwapColumns(i, kmax);
p.Swap(i, kmax);
norm.Swap(i, kmax);
signum = - signum;
}
/* Compute the Householder transformation to reduce the j-th
column of the matrix to a multiple of the j-th unit vector */
{
PZMath_vector c_full = A.Column(i);
PZMath_vector c = c_full.SubVector(i, M - i);
double tau_i = HouseholderTransform(c);
tau[i] = tau_i;
/* Apply the transformation to the remaining columns */
if (i + 1 < N)
{
PZMath_matrix m = A.Submatrix(i, i + 1, M - i, N - (i + 1));
HouseholderHM (tau_i, c, m);
}
}
/* Update the norms of the remaining columns too */
if (i + 1 < M)
{
for (j = i + 1; j < N; j++)
{
double x = norm[j];
if (x > 0.0)
{
double y = 0;
double temp= A[i, j] / x;
if (System.Math.Abs(temp) >= 1)
y = 0.0;
else
y = x * System.Math.Sqrt(1 - temp * temp);
/* recompute norm to prevent loss of accuracy */
if (System.Math.Abs(y / x) < System.Math.Sqrt(20.0) * PZMath_machine.PZMath_SQRT_DBL_EPSILON)
{
PZMath_vector c_full = A.Column(j);
PZMath_vector c = c_full.SubVector(i + 1, M - (i + 1));
y = PZMath_blas.Dnrm2(c);
}
norm[j] = y;
}
}
}
}
}
return PZMath_errno.PZMath_SUCCESS;
}
// These functions factorize the square matrix A into the LU decomposition PA = LU.
// On output the diagonal and upper triangular part of the input matrix A contain the matrix U.
// The lower triangular part of the input matrix (excluding the diagonal) contains L.
// The diagonal elements of L are unity, and are not stored.
// The permutation matrix P is encoded in the permutation p.
// The j-th column of the matrix P is given by the k-th column of the identity matrix,
// where k = p_j the j-th element of the permutation vector.
// The sign of the permutation is given by signum.
// It has the value (-1)^n, where n is the number of interchanges in the permutation.
// The algorithm used in the decomposition is Gaussian Elimination with partial pivoting
// (Golub & Van Loan, Matrix Computations, Algorithm 3.4.1).
public static int LUDecomp(PZMath_matrix A, PZMath_permutation p, out int signum)
{
if (A.ColumnCount != A.RowCount)
{
PZMath_errno.ERROR("PZMath_linalg::LUDecomp(), LU decomposition requires square matrix", PZMath_errno.PZMath_ENOTSQR);
signum = 1;
return PZMath_errno.PZMath_ENOTSQR;
}
else if (p.Size != A.ColumnCount)
{
PZMath_errno.ERROR("PZMath_linalg::LUDecomp(), permutation length must match matrix size", PZMath_errno.PZMath_EBADLEN);
signum = 1;
return PZMath_errno.PZMath_EBADLEN;
}
else
{
int N = A.ColumnCount;
int i, j, k;
signum = 1;
p.Init();
for (j = 0; j < N - 1; j++)
{
/* Find maximum in the j-th column */
double ajj;
double max = System.Math.Abs(A[j, j]);
int i_pivot = j;
for (i = j + 1; i < N; i++)
{
double aij = System.Math.Abs(A[i, j]);
if (aij > max)
{
max = aij;
i_pivot = i;
}
}
if (i_pivot != j)
{
A.SwapRows(j, i_pivot);
p.Swap(j, i_pivot);
signum = -(signum);
}
ajj = A[j, j];
if (ajj != 0.0)
{
for (i = j + 1; i < N; i++)
{
double aij = A[i, j] / ajj;
A[i, j] = aij;
for (k = j + 1; k < N; k++)
{
double aik = A[i, k];
double ajk = A[j, k];
A[i, k] = aik - aij * ajk;
}
}
}
}
return PZMath_errno.PZMath_SUCCESS;
}
}