1: $n$ – Integer Input: On entry: $n$ , where the number of grid points is $n + 1$ . This is also the largest order of Chebyshev polynomial in the Chebyshev series to be computed.

Constraint: $n > 0$ and n is even.
2: $a$ – double Input: On entry: $a$ , the lower bound of domain $[a, b]$ .

Constraint: $a < b$ .
3: $b$ – double Input: On entry: $b$ , the upper bound of domain $[a, b]$ .

Constraint: $b > a$ .
4: $q$ – Integer Input: On entry: the order, $q$ , of the derivative to evaluate.

Constraint: $0 \leq q \leq 4$ .
5: $c [n + 1]$ – const double Input: On entry: the Chebyshev coefficients, $c_{i}$ , for $i = 1, 2, \dots, n + 1$ .
6: $f [n + 1]$ – double Output: On exit: the derivatives $S^{(q)} x_{i}$ , for $i = 1, 2, \dots, n + 1$ , of the Chebyshev series, $S$ .
7: $fail$ – NagError * Input/Output: The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error 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 $⟨ value ⟩$ had an illegal value.
NE_INT: On entry, $n = ⟨ value ⟩$ .
Constraint: $n > 0$ .

On entry, $n = ⟨ value ⟩$ .
Constraint: n is even.

On entry, $q = ⟨ value ⟩$ .
Constraint: $0 \leq q \leq 4$ .
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_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_REAL_2: On entry, $a = ⟨ value ⟩$ and $b = ⟨ value ⟩$ .
Constraint: $a < b$ .

7 Accuracy

Evaluations of DFT to obtain function or derivative values should be an order

n

multiple of machine precision assuming full accuracy to machine precision in the given Chebyshev series representation.

8 Parallelism and Performance

d02ubc is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.

d02ubc 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 function. Please also consult the Users' Note for your implementation for any additional implementation-specific information.