d02ubf 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
d02uaf or
d02uef.
d02ubf 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:
– Real (Kind=nag_wp)
Input
-
On entry: , the lower bound of domain .
Constraint:
.
-
3:
– Real (Kind=nag_wp)
Input
-
On entry: , the upper bound of domain .
Constraint:
.
-
4:
– Integer
Input
-
On entry: the order, , of the derivative to evaluate.
Constraint:
.
-
5:
– Real (Kind=nag_wp) array
Input
-
On entry: the Chebyshev coefficients,
, for .
-
6:
– Real (Kind=nag_wp) array
Output
-
On exit: the derivatives
, for , of the Chebyshev series, .
-
7:
– Integer
Input/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).
If on entry
or
, explanatory error messages are output on the current error message unit (as defined by
x04aaf).
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 routine. Please also consult the
Users' Note for your implementation for any additional implementation-specific information.