Amos D E (1983) Algorithm 610: A portable FORTRAN subroutine for derivatives of the psi function ACM Trans. Math. Software9 494–502
1: – Real (Kind=nag_wp)Input
On entry: the argument of the function.
2: – IntegerInput
On entry: the index of the first member of the sequence of functions.
3: – IntegerInput
On entry: the number of members required in the sequence
, for .
4: – Real (Kind=nag_wp) arrayOutput
On exit: the first elements of ans contain the required values
, for .
5: – 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:
On entry, .
On entry, .
On entry, .
Computation abandoned due to the likelihood of underflow.
Computation abandoned due to the likelihood of overflow.
There is not enough internal workspace to continue computation. m is probably too large.
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.
All constants in s14adf are given to approximately digits of precision. Calling the number of digits of precision in the floating-point arithmetic being used , then clearly the maximum number of correct digits in the results obtained is limited by . Empirical tests of s14adf, taking values of in the range , and in the range , have shown that the maximum relative error is a loss of approximately two decimal places of precision. Tests with , i.e., testing the function , have shown somewhat better accuracy, except at points close to the zero of , , where only absolute accuracy can be obtained.
8Parallelism and Performance
Background information to multithreading can be found in the Multithreading documentation.
s14adf is not threaded in any implementation.
The time taken for a call of s14adf is approximately proportional to , plus a constant. In general, it is much cheaper to call s14adf with greater than to evaluate the function , for , rather than to make separate calls of s14adf.
This example reads values of the argument from a file, evaluates the function at each value of and prints the results.