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, or may be complex. If iflag is returned as nonzero then f01eff will terminate the computation, with .
2: – IntegerInput
On entry: , the number of function values required.
3: – Real (Kind=nag_wp) arrayInput
On entry: the points at which the function is to be evaluated.
4: – Real (Kind=nag_wp) arrayOutput
On exit: the function values.
should return the value , for .
5: – Integer arrayUser Workspace
6: – Real (Kind=nag_wp) arrayUser Workspace
f is called with the arguments iuser and ruser as supplied to f01eff. 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 f01eff 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 f01eff. If your code inadvertently does return any NaNs or infinities, f01eff is likely to produce unexpected results.
6: – Integer arrayUser Workspace
7: – Real (Kind=nag_wp) arrayUser Workspace
iuser and ruser are not used by f01eff, but are passed directly to f and may be used to pass information to this routine.
8: – IntegerOutput
On exit: , unless you have set iflag nonzero inside f, in which case iflag will be the value you set and ifail will be set to .
9: – 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:
The computation of the spectral factorization failed to converge.
The value of ifail gives the number of off-diagonal elements of an intermediate tridiagonal form that did not converge to zero (see f08faf).
On entry, .
Constraint: or .
On entry, .
An internal error occurred when computing the spectral factorization. Please contact NAG.
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.
Provided that can be computed accurately then the computed matrix function will be close to the exact matrix function. See Section 10.2 of Higham (2008) for details and further discussion.
8Parallelism and Performance
Background information to multithreading can be found in the Multithreading documentation.
f01eff is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.
f01eff 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.
The integer allocatable memory required is n, and the real allocatable memory required is approximately , where nb is the block size required by f08faf.
The cost of the algorithm is plus the cost of evaluating . If is the th computed eigenvalue of , then the user-supplied subroutine f will be asked to evaluate the function at , .