- naginterfaces.library.lapacklin.zpoequ(n, a)¶
zpoequcomputes a diagonal scaling matrix intended to equilibrate a complex Hermitian positive definite matrix and reduce its condition number.
For full information please refer to the NAG Library document for f07ft
, the order of the matrix .
- acomplex, array-like, shape
The matrix whose scaling factors are to be computed. Only the diagonal elements of the array are referenced.
- sfloat, ndarray, shape
If no exception or warning is raised, contains the diagonal elements of the scaling matrix .
If no exception or warning is raised, contains the ratio of the smallest value of to the largest value of . If and is neither too large nor too small, it is not worth scaling by .
. If is very close to overflow or underflow, the matrix should be scaled.
- (errno )
On entry, error in parameter .
- (errno )
The th diagonal element of is not positive (and hence cannot be positive definite).
zpoequcomputes a diagonal scaling matrix chosen so that
This means that the matrix given by
has diagonal elements equal to unity. This in turn means that the condition number of , , is within a factor of the matrix of smallest possible condition number over all possible choices of diagonal scalings (see Corollary 7.6 of Higham (2002)).
Higham, N J, 2002, Accuracy and Stability of Numerical Algorithms, (2nd Edition), SIAM, Philadelphia