The routine may be called by the names f07fff, nagf_lapacklin_dpoequ or its LAPACK name dpoequ.
f07fff computes 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
1: – IntegerInput
On entry: , the order of the matrix .
2: – Real (Kind=nag_wp) arrayInput
Note: the second dimension of the array a
must be at least
On entry: the matrix whose scaling factors are to be computed. Only the diagonal elements of the array a are referenced.
3: – IntegerInput
On entry: the first dimension of the array a as declared in the (sub)program from which f07fff is called.
4: – Real (Kind=nag_wp) arrayOutput
On exit: if , s contains the diagonal elements of the scaling matrix .
5: – Real (Kind=nag_wp)Output
On exit: if , scond contains the ratio of the smallest value of s to the largest value of s. If and amax is neither too large nor too small, it is not worth scaling by .
6: – Real (Kind=nag_wp)Output
On exit: . If amax is very close to overflow or underflow, the matrix should be scaled.
7: – IntegerOutput
On exit: unless the routine detects an error (see Section 6).
6Error Indicators and Warnings
If , argument had an illegal value. An explanatory message is output, and execution of the program is terminated.
The th diagonal element of is not positive
(and hence cannot be positive definite).
The computed scale factors will be close to the exact scale factors.