// These functions compute the inverse of a matrix A from its LU decomposition (LU,p),
// storing the result in the matrix inverse.
// The inverse is computed by solving the system A x = b for each column of the identity matrix.
// It is preferable to avoid direct use of the inverse whenever possible,
// as the linear solver functions can obtain the same result more efficiently and reliably
// (consult any introductory textbook on numerical linear algebra for details).
public static int LUInvert(PZMath_matrix LU, PZMath_permutation p, PZMath_matrix inverse)
{
int i;
int n = LU.RowCount;
int status = PZMath_errno.PZMath_SUCCESS;
inverse.SetIdentity();
for (i = 0; i < n; i++)
{
PZMath_vector c = inverse.Column(i);
int status_i = LUSVX(LU, p, c);
if (status_i == PZMath_errno.PZMath_SUCCESS)
status = status_i;
}
return status;
}
public static int BidiagUnpack2(PZMath_matrix A, PZMath_vector tau_U, PZMath_vector tau_V, PZMath_matrix V)
{
int M = A.RowCount;
int N = A.ColumnCount;
int K = System.Math.Min(M, N);
if (M < N)
{
PZMath_errno.ERROR ("PZMath_linalg::BidiagUnpack2(),matrix A must have M >= N", PZMath_errno.PZMath_EBADLEN);
}
else if (tau_U.Size != K)
{
PZMath_errno.ERROR ("PZMath_linalg::BidiagUnpack2(),size of tau must be MIN(M,N)", PZMath_errno.PZMath_EBADLEN);
}
else if (tau_V.Size + 1 != K)
{
PZMath_errno.ERROR ("PZMath_linalg::BidiagUnpack2(),size of tau must be MIN(M,N) - 1", PZMath_errno.PZMath_EBADLEN);
}
else if (V.RowCount != N || V.ColumnCount != N)
{
PZMath_errno.ERROR ("PZMath_linalg::BidiagUnpack2(),size of V must be N x N", PZMath_errno.PZMath_EBADLEN);
}
else
{
int i, j;
/* Initialize V to the identity */
V.SetIdentity();
for (i = N - 1; i > 0 && (i -- > 0);)
{
/* Householder row transformation to accumulate V */
PZMath_vector r = A.Row(i);
PZMath_vector h = r.SubVector(i + 1, N - (i+1));
double ti = tau_V[i];
PZMath_matrix m = V.Submatrix(i + 1, i + 1, N-(i+1), N-(i+1));
PZMath_linalg.HouseholderHM (ti, h, m);
}
/* Copy superdiagonal into tau_v */
for (i = 0; i < N - 1; i++)
{
double Aij = A[i, i+1];
tau_V[i] = Aij;
}
/* Allow U to be unpacked into the same memory as A, copy
diagonal into tau_U */
for (j = N; j > 0 && (j -- > 0);)
{
/* Householder column transformation to accumulate U */
double tj = tau_U[j];
double Ajj = A[j, j];
PZMath_matrix m = A.Submatrix (j, j, M-j, N-j);
tau_U[j] = Ajj;
PZMath_linalg.HouseholderHM1(tj, m);
}
}
return PZMath_errno.PZMath_SUCCESS;;
}