The function may be called by the names: f07ffc, nag_lapacklin_dpoequ or nag_dpoequ.
f07ffc 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: – Nag_OrderTypeInput
On entry: the order argument specifies the two-dimensional storage scheme being used, i.e., row-major ordering or column-major ordering. C language defined storage is specified by . See Section 3.1.3 in the Introduction to the NAG Library CL Interface for a more detailed explanation of the use of this argument.
2: – IntegerInput
On entry: , the order of the matrix .
3: – const doubleInput
Note: the dimension, dim, of the array a
must be at least
The th element of the matrix is stored in
On entry: the matrix whose scaling factors are to be computed. Only the diagonal elements of the array a are referenced.
4: – IntegerInput
On entry: the stride separating row or column elements (depending on the value of order) in the array a.
5: – doubleOutput
On exit: if NE_NOERROR, s contains the diagonal elements of the scaling matrix .
6: – double *Output
On exit: if NE_NOERROR, 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 .
7: – double *Output
On exit: . If amax is very close to overflow or underflow, the matrix should be scaled.
8: – NagError *Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).
6Error Indicators and Warnings
Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
On entry, argument had an illegal value.
On entry, .
On entry, . Constraint: .
On entry, and .
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
The th diagonal element of is not positive
(and hence cannot be positive definite).
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.
The computed scale factors will be close to the exact scale factors.
8Parallelism and Performance
Background information to multithreading can be found in the Multithreading documentation.