The routine may be called by the names f07atf, nagf_lapacklin_zgeequ or its LAPACK name zgeequ.
f07atf computes the diagonal scaling matrices. The diagonal scaling matrices are chosen to try to make the elements of largest absolute value in each row and column of the matrix given by
have absolute value . The diagonal elements of and are restricted to lie in the safe range , where is the value returned by routine x02amf. Use of these scaling factors is not guaranteed to reduce the condition number of but works well in practice.
1: – IntegerInput
On entry: , the number of rows of the matrix .
2: – IntegerInput
On entry: , the number of columns of the matrix .
3: – Complex (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.
4: – IntegerInput
On entry: the first dimension of the array a as declared in the (sub)program from which f07atf is called.
5: – Real (Kind=nag_wp) arrayOutput
On exit: if or , r contains the row scale factors, the diagonal elements of . The elements of r will be positive.
6: – Real (Kind=nag_wp) arrayOutput
On exit: if , c contains the column scale factors, the diagonal elements of . The elements of c will be positive.
7: – Real (Kind=nag_wp)Output
On exit: if or , rowcnd contains the ratio of the smallest value of to the largest value of . If and amax is neither too large nor too small, it is not worth scaling by .
8: – Real (Kind=nag_wp)Output
On exit: if , colcnd contains the ratio of the smallest value of to the largest value of .
If , it is not worth scaling by .
9: – Real (Kind=nag_wp)Output
On exit: . If amax is very close to overflow or underflow, the matrix should be scaled.
10: – 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.
Row of is exactly zero.
Column of is exactly zero.
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.
f07atf makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.
Please consult the X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this routine. Please also consult the Users' Note for your implementation for any additional implementation-specific information.