The function may be called by the names: s22cac or nag_specfun_mathieu_ang_periodic_real.
s22cac calculates an approximation to and/or , or and/or , where and are respectively the even and odd parity real-valued periodic angular Mathieu functions, for an array of values of , and for integer order value , where for even parity, and for odd parity. The function also returns values of for these periodic Mathieu functions, this is known as the characteristic value or eigenvalue.
On entry: , the order number of the Mathieu function to be computed.
if (even Mathieu function), ;
if (odd Mathieu function), .
2: – doubleInput
On entry: , the Mathieu function parameter.
3: – IntegerInput
On entry: specifies whether to compute even or odd Mathieu function.
Compute even Mathieu function, .
Compute odd Mathieu function, .
4: – IntegerInput
On entry: specifies whether the Mathieu function or its derivative is required.
Compute Mathieu function values.
Compute derivative values of Mathieu function.
Compute both Mathieu function and derivative values.
Compute neither Mathieu functions nor derivative values, returns only a (the characteristic value).
, , or .
5: – IntegerInput
On entry: , the number of values to compute.
6: – const doubleInput
On entry: the values of at which to compute Mathieu function or derivative values.
7: – doubleOutput
On exit: if or , the Mathieu function values or . If or , f is not used.
8: – doubleOutput
On exit: if or , the Mathieu function derivative values or . If or , f_deriv is not used.
9: – double *Output
On exit: , the characteristic value for the Mathieu function.
10: – NagError *Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).
6Error Indicators and Warnings
Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
On entry, argument had an illegal value.
On entry, . Constraint: , , or .
On entry, .
On entry, . Constraint: or .
On entry, and . Constraint: if , or if , .
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.
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.
8Parallelism and Performance
s22cac is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.
s22cac 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.
This example calculates the first four even and odd function and derivative values at for .