naginterfaces.library.sparse.direct_​real_​gen_​diag

naginterfaces.library.sparse.direct_real_gen_diag(icolzp, a, iprm, il, lval, iu, uval)

direct_real_gen_diag computes the reciprocal pivot growth factor of an $LU$ factorization of a real sparse matrix in compressed column (Harwell–Boeing) format.

For full information please refer to the NAG Library document for f11mm

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/f11/f11mmf.html

Parameters

icolzpint, array-like, shape $(n+1)$

The new column index array of sparse matrix $A$. See the F11 Introduction.

afloat, array-like, shape $\left(\text{asize}\right)$

The array of nonzero values in the sparse matrix $A$.

iprmint, array-like, shape $(7\times n)$

The column permutation which defines $P_c$, the row permutation which defines $P_r$, plus associated data structures as computed by direct_real_gen_lu().

ilint, array-like, shape $(:)$

Records the sparsity pattern of matrix $L$ as computed by direct_real_gen_lu().

lvalfloat, array-like, shape $(:)$

Records the nonzero values of matrix $L$ and some nonzero values of matrix $U$ as computed by direct_real_gen_lu().

iuint, array-like, shape $(:)$

Records the sparsity pattern of matrix $U$ as computed by direct_real_gen_lu().

uvalfloat, array-like, shape $(:)$

Records some nonzero values of matrix $U$ as computed by direct_real_gen_lu().

Returns

rpgfloat

The reciprocal pivot growth factor ${\text{max}}_j\left({\Vert A_j\Vert }_{\infty }/{\Vert U_j\Vert }_{\infty }\right)$. If the reciprocal pivot growth factor is much less than $1$, the stability of the $LU$ factorization may be poor.

Raises

NagValueError

(errno $1$)

On entry, $n=⟨value⟩$.

Constraint: $n\ge 0$.

(errno $2$)

Incorrect column permutations in array $iprm$.

Notes

direct_real_gen_diag computes the reciprocal pivot growth factor ${\text{max}}_j\left({\Vert A_j\Vert }_{\infty }/{\Vert U_j\Vert }_{\infty }\right)$ from the columns $A_j$ and $U_j$ of an $LU$ factorization of the matrix $A$, $P_{r}A{P}_c=LU$ where $P_r$ is a row permutation matrix, $P_c$ is a column permutation matrix, $L$ is unit lower triangular and $U$ is upper triangular as computed by direct_real_gen_lu().