d02ubc evaluates a function, or one of its lower order derivatives, from its Chebyshev series representation at Chebyshev Gauss–Lobatto points on
. The coefficients of the Chebyshev series representation required are usually derived from those returned by
d02uac or
d02uec.
d02ubc evaluates the Chebyshev series
or its derivative (up to fourth order) at the Chebyshev Gauss–Lobatto points on
. Here
denotes the Chebyshev polynomial of the first kind of degree
with argument
defined on
. In terms of your original variable,
say, the input values at which the function values are to be provided are
where
and
are respectively the upper and lower ends of the range of
over which the function is required.
The calculation is implemented by a forward one-dimensional discrete Fast Fourier Transform (DFT).
-
1:
– Integer
Input
-
On entry: , where the number of grid points is . This is also the largest order of Chebyshev polynomial in the Chebyshev series to be computed.
Constraint:
and
n is even.
-
2:
– double
Input
-
On entry: , the lower bound of domain .
Constraint:
.
-
3:
– double
Input
-
On entry: , the upper bound of domain .
Constraint:
.
-
4:
– Integer
Input
-
On entry: the order, , of the derivative to evaluate.
Constraint:
.
-
5:
– const double
Input
-
On entry: the Chebyshev coefficients,
, for .
-
6:
– double
Output
-
On exit: the derivatives
, for , of the Chebyshev series, .
-
7:
– NagError *
Input/Output
-
The NAG error argument (see
Section 7 in the Introduction to the NAG Library CL Interface).
Background information to multithreading can be found in the
Multithreading documentation.
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.