naginterfaces.library.lapacklin.dpbcon¶
- naginterfaces.library.lapacklin.dpbcon(uplo, kd, ab, anorm)[source]¶
dpbcon
estimates the condition number of a real symmetric positive definite band matrix , where has been factorized bydpbtrf()
.For full information please refer to the NAG Library document for f07hg
https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/f07/f07hgf.html
- Parameters
- uplostr, length 1
Specifies how has been factorized.
, where is upper triangular.
, where is lower triangular.
- kdint
, the number of superdiagonals or subdiagonals of the matrix .
- abfloat, array-like, shape
The Cholesky factor of , as returned by
dpbtrf()
.- anormfloat
The -norm of the original matrix , which may be computed by calling
blas.dlansb
with its argument . must be computed either before callingdpbtrf()
or else from a copy of the original matrix .
- 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, error in parameter .
Constraint: or .
- (errno )
On entry, error in parameter .
Constraint: .
- (errno )
On entry, error in parameter .
Constraint: .
- (errno )
On entry, error in parameter .
Constraint: .
- Notes
dpbcon
estimates the condition number (in the -norm) of a real symmetric positive definite band matrix :Since is symmetric, .
Because is infinite if is singular, the function actually returns an estimate of the reciprocal of .
The function should be preceded by a call to
blas.dlansb
to compute and a call todpbtrf()
to compute the Cholesky factorization of . The function then uses Higham’s implementation of Hager’s method (see Higham (1988)) to estimate .
- References
Higham, N J, 1988, FORTRAN codes for estimating the one-norm of a real or complex matrix, with applications to condition estimation, ACM Trans. Math. Software (14), 381–396