On exit: iflag should either be unchanged from its entry value of zero, or may be set nonzero to indicate that there is a problem in evaluating the function ; for instance may not be defined. If iflag is returned as nonzero then f01kcf will terminate the computation, with .
3: – IntegerInput
On entry: , the number of function or derivative values required.
4: – Complex (Kind=nag_wp) arrayInput
On entry: the points at which the function is to be evaluated.
5: – Complex (Kind=nag_wp) arrayOutput
On exit: the function or derivative values.
should return the value , for .
6: – Integer arrayUser Workspace
7: – Real (Kind=nag_wp) arrayUser Workspace
f is called with the arguments iuser and ruser as supplied to f01kcf. You should use the arrays iuser and ruser to supply information to f.
f must either be a module subprogram USEd by, or declared as EXTERNAL in, the (sub)program from which f01kcf is called. Arguments denoted as Input must not be changed by this procedure.
Note:f should not return floating-point NaN (Not a Number) or infinity values, since these are not handled by f01kcf. If your code inadvertently does return any NaNs or infinities, f01kcf is likely to produce unexpected results.
5: – Integer arrayUser Workspace
6: – Real (Kind=nag_wp) arrayUser Workspace
iuser and ruser are not used by f01kcf, but are passed directly to f and may be used to pass information to this routine.
7: – IntegerOutput
On exit: , unless iflag has been set nonzero inside f, in which case iflag will be the value set and ifail will be set to .
8: – Real (Kind=nag_wp)Output
On exit: an estimate of the absolute condition number of at .
9: – Real (Kind=nag_wp)Output
On exit: the -norm of .
10: – Real (Kind=nag_wp)Output
On exit: the -norm of .
11: – IntegerInput/Output
On entry: ifail must be set to , or to set behaviour on detection of an error; these values have no effect when no error is detected.
A value of causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of means that an error message is printed while a value of means that it is not.
If halting is not appropriate, the value or is recommended. If message printing is undesirable, then the value is recommended. Otherwise, the value is recommended. When the value or is used it is essential to test the value of ifail on exit.
On exit: unless the routine detects an error or a warning has been flagged (see Section 6).
6Error Indicators and Warnings
If on entry or , explanatory error messages are output on the current error message unit (as defined by x04aaf).
Errors or warnings detected by the routine:
An internal error occurred when estimating the norm of the Fréchet derivative of at . Please contact NAG.
An internal error occurred when evaluating the matrix function . You can investigate further by calling f01fmf with the matrix and the function .
An unexpected error has been triggered by this routine. Please
See Section 7 in the Introduction to the NAG Library FL Interface for further information.
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library FL Interface for further information.
Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.
f01kcf uses the norm estimation routine f04zdf to estimate a quantity , where and . For further details on the accuracy of norm estimation, see the documentation for f04zdf.
8Parallelism and Performance
f01kcf is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library. In these implementations, this routine may make calls to the user-supplied functions from within an OpenMP parallel region. Thus OpenMP directives within the user functions can only be used if you are compiling the user-supplied function and linking the executable in accordance with the instructions in the Users' Note for your implementation. The user workspace arrays iuser and ruser are classified as OpenMP shared memory and use of iuser and ruser has to take account of this in order to preserve thread safety whenever information is written back to either of these arrays. If at all possible, it is recommended that these arrays are only used to supply read-only data to the user functions when a multithreaded implementation is being used.
f01kcf 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.
Approximately of complex allocatable memory is required by the routine, in addition to the memory used by the underlying matrix function routine f01fmf.
f01kcf returns the matrix function . This is computed using f01fmf. If only is required, without an estimate of the condition number, then it is far more efficient to use f01fmf directly.