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

naginterfaces.library.sparse.direct_real_gen_cond(norm, n, il, lval, iu, uval, anorm)[source]

direct_real_gen_cond computes an estimate of the reciprocal of the condition number of a sparse matrix given an factorization of the matrix computed by direct_real_gen_lu().

For full information please refer to the NAG Library document for f11mg

https://www.nag.com/numeric/nl/nagdoc_28.7/flhtml/f11/f11mgf.html

Parameters
normstr, length 1

Indicates whether or is to be estimated.

or

is estimated.

is estimated.

nint

, the order of the matrix .

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().

anormfloat

If or , the -norm of the matrix .

If , the -norm of the matrix .

may be computed by calling direct_real_gen_norm() with the same value for the argument .

Returns
rcondfloat

An estimate of the reciprocal of the condition number of . is set to zero if exact singularity is detected or the estimate underflows. If is less than machine precision, is singular to working precision.

Raises
NagValueError
(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: , or .

Notes

direct_real_gen_cond estimates the condition number of a real sparse matrix , in either the -norm or the -norm:

Note that .

Because the condition number is infinite if is singular, the function actually returns an estimate of the reciprocal of the condition number.

The function should be preceded by a call to direct_real_gen_norm() to compute or , and a call to direct_real_gen_lu() to compute the factorization of . The function then estimates or and computes the reciprocal of the condition number.