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

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

direct_real_gen_diag computes the reciprocal pivot growth factor of an 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://www.nag.com/numeric/nl/nagdoc_28.7/flhtml/f11/f11mmf.html

Parameters
icolzpint, array-like, shape

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

afloat, array-like, shape

The array of nonzero values in the sparse matrix .

iprmint, array-like, shape

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

ilint, array-like, shape

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

lvalfloat, array-like, shape

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

iuint, array-like, shape

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

uvalfloat, array-like, shape

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

Returns
rpgfloat

The reciprocal pivot growth factor . If the reciprocal pivot growth factor is much less than , the stability of the factorization may be poor.

Raises
NagValueError
(errno )

On entry, .

Constraint: .

(errno )

Incorrect column permutations in array .

Notes

direct_real_gen_diag computes the reciprocal pivot growth factor from the columns and of an factorization of the matrix , where is a row permutation matrix, is a column permutation matrix, is unit lower triangular and is upper triangular as computed by direct_real_gen_lu().