naginterfaces.library.lapacklin.zgtcon¶
- naginterfaces.library.lapacklin.zgtcon(norm, dl, d, du, du2, ipiv, anorm)[source]¶
zgtcon
estimates the reciprocal condition number of a complex tridiagonal matrix , using the factorization returned byzgttrf()
.For full information please refer to the NAG Library document for f07cu
https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/f07/f07cuf.html
- Parameters
- normstr, length 1
Specifies the norm to be used to estimate .
or
Estimate .
Estimate .
- dlcomplex, array-like, shape
Must contain the multipliers that define the matrix of the factorization of .
- dcomplex, array-like, shape
Must contain the diagonal elements of the upper triangular matrix from the factorization of .
- ducomplex, array-like, shape
Must contain the elements of the first superdiagonal of .
- du2complex, array-like, shape
Must contain the elements of the second superdiagonal of .
- ipivint, array-like, shape
Must contain the pivot indices that define the permutation matrix . At the th step, row of the matrix was interchanged with row , and must always be either or , indicating that a row interchange was not performed.
- anormfloat
If or , the -norm of the original matrix .
If , the -norm of the original matrix .
may be computed by calling
blas.zlangt
with the same value for the argument .must be computed either before calling
zgttrf()
or else from a copy of the original matrix .
- Returns
- rcondfloat
Contains an estimate of the reciprocal condition number.
- Raises
- NagValueError
- (errno )
On entry, error in parameter .
Constraint: , or .
- (errno )
On entry, error in parameter .
Constraint: .
- (errno )
On entry, error in parameter .
Constraint: .
- Notes
zgtcon
should be preceded by a call tozgttrf()
, which uses Gaussian elimination with partial pivoting and row interchanges to factorize the matrix aswhere is a permutation matrix, is unit lower triangular with at most one nonzero subdiagonal element in each column, and is an upper triangular band matrix, with two superdiagonals.
zgtcon
then utilizes the factorization to estimate either or , from which the estimate of the reciprocal of the condition number of , is computed as eitheror
is returned, rather than , since when is singular is infinite.
Note that .
- References
Higham, N J, 2002, Accuracy and Stability of Numerical Algorithms, (2nd Edition), SIAM, Philadelphia