Amos D E (1983) Algorithm 610: A portable FORTRAN subroutine for derivatives of the psi function ACM Trans. Math. Software9 494–502
5Arguments
1: – doubleInput
On entry: the argument of the function.
Constraint:
.
2: – IntegerInput
On entry: the index of the first member of the sequence of functions.
Constraint:
.
3: – IntegerInput
On entry: the number of members required in the sequence
, for .
Constraint:
.
4: – doubleOutput
On exit: the first elements of ans contain the required values
, for .
5: – NagError *Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).
6Error Indicators and Warnings
NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
NE_BAD_PARAM
On entry, argument had an illegal value.
NE_INT
On entry, .
Constraint: .
On entry, .
Constraint: .
NE_INTERNAL_ERROR
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.
NE_INTERNAL_WORKSPACE
There is not enough internal workspace to continue computation. m is probably too large.
NE_NO_LICENCE
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.
NE_OVERFLOW_LIKELY
Computation abandoned due to the likelihood of overflow.
NE_REAL
On entry, .
Constraint: .
NE_UNDERFLOW_LIKELY
Computation abandoned due to the likelihood of underflow.
7Accuracy
All constants in s14adc 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 s14adc, 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.
s14adc is not threaded in any implementation.
9Further Comments
The time taken for a call of s14adc is approximately proportional to , plus a constant. In general, it is much cheaper to call s14adc with greater than to evaluate the function , for , rather than to make separate calls of s14adc.
10Example
This example reads values of the argument from a file, evaluates the function at each value of and prints the results.