pm_quadPack::setChebExpan Interface Reference

Compute and return the series expansion of the input function values via the Chebyshev polynomials of the first kind of degrees 12 and 24 using Fast Fourier Transform method. More...

Detailed Description

Compute and return the series expansion of the input function values via the Chebyshev polynomials of the first kind of degrees 12 and 24 using Fast Fourier Transform method.

The returned coefficients are such that,

\begin{eqnarray} f(x) &=& \sum_{k = 1}^{13} \ms{cheb12}(k) \times T(k-1,x) ~, \\ f(x) &=& \sum_{k = 1}^{25} \ms{cheb24}(k) \times T(k-1,x) ~, \end{eqnarray}

where \(T(n,x)\) is the Chebyshev polynomial of the first kind of degree \(n\) evaluated at proper points.

Remarks

This generic interface is meant to be primarily by and used within the Adaptive Gauss-Kronrod quadrature routines of the parent module.
There is practically no usage for this generic interface outside of the parent module.

Parameters

[in,out]	func	: The input/output vector of size 25 of type real of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128), containing the function values.
[out]	cheb12	: The output vector of the same type and kind as func, of size 13, containing the Chebyshev Coefficients of degree 12.
[out]	cheb24	: The output vector of the same type and kind as func, of size 25, containing the Chebyshev Coefficients of degree 24.

Possible calling interfaces ⛓

use pm_quadPack, only: setChebExpan
 
call setChebExpan(func, cheb12, cheb24)

Remarks

The procedures under discussion are pure.

See also

getQuadGK
getQuadErr
getQuadRomb
isFailedQuad

Test:

test_pm_quadPack

Final Remarks ⛓

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Copyright

Computational Data Science Lab

Author:

Amir Shahmoradi, Oct 16, 2009, 11:14 AM, Michigan

Definition at line 4838 of file pm_quadPack.F90.

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The documentation for this interface was generated from the following file:

• src/fortran/main/pm_quadPack.F90