pm_fftpack::getFactorFFT Interface Reference

Generate and return the factorization vector factor of the specified input sequence length and the corresponding vector of trigonometric coefficients coef.
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Detailed Description

Generate and return the factorization vector factor of the specified input sequence length and the corresponding vector of trigonometric coefficients coef.

The factorization and the trigonometric coefficient vectors are required for computing the Forward or Reverse FFT.
Note that the computed factoring is not necessarily a complete prime factoring of the length of the input data sequence.
This is because some of target algorithms corresponding to some higher factors are more efficient than the composition of the lower factors.
For example, the corresponding algorithms to the composite factors 4 and 6 are faster than combining the corresponding algorithms for 2*2 and 2*3.

Parameters

[in]	data	: The input contiguous vector of either, type complex of kind any supported by the processor (e.g., CK, CK32, CK64, or CK128), or type real of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128), or containing the data sequence whose Forward or Reverse FFT is to computed. Only the length and the type of input vector is used within the algorithm.
[out]	coef	: The output contiguous vector of the same type, kind, and size as the input data sequence vector, containing the trigonometric look up table required for Forward or Reverse FFT of the specified data sequence. (optional. If missing, the trigonometric coefficients will not be computed.)
[in]	attr	: The input scalar of type allocatable_type signifying the allocatable status of the input coef vector. If present, the input coef will be reallocated to size(data). (optional. It can be present only if the input argument coef has the allocatable attribute.)

Returns

factor : The output allocatable array of shape (:) of type integer of default kind IK, containing the factorization of the length of the data sequence whose Forward or Reverse FFT is to be computed.
By definition, the condition product(factor) == size(data) holds.

Possible calling interfaces ⛓

use pm_fftpack, only: getFactorFFT
integer(IK), allocatable :: factor(:)
 
factor = getFactorFFT(data(1:lenData))
factor = getFactorFFT(data(1:lenData), coef(1:lenData))
factor = getFactorFFT(data(1:lenData), coef(:), attr)

Warning

The condition size(data) > 1 must hold for the corresponding arguments.
The condition size(data) == size(coef) must hold for the corresponding arguments.
These conditions are verified only if the library is built with the preprocessor macro CHECK_ENABLED=1.

The pure procedure(s) documented herein become impure when the ParaMonte library is compiled with preprocessor macro CHECK_ENABLED=1.
By default, these procedures are pure in release build and impure in debug and testing builds. The procedures under this generic interface are always impure when the output argument coef is present.

Remarks

While the contents of the input data sequence is not used within the algorithm, its presence and requirement is to minimize user-mistakes.

See also

getFFTF
getFFTI
getFFTR
setFFTF
setFFTI
setFFTR

Example usage ⛓

program example
 
    use pm_kind, only: SK, IK, LK
    use pm_io, only: display_type
    use pm_fftpack, only: getfactorFFT
    use pm_arrayFill, only: getFilled
    use pm_err, only: setAsserted
 
    implicit none
 
    integer(IK), allocatable :: factor(:)
 
    type(display_type) :: disp
    disp = display_type(file = "main.out.F90")
 
    block
        use pm_kind, only: TKG => CKS
        complex(TKG), allocatable :: coef(:)
        call disp%skip()
        call disp%show("allocate(coef(13))")
                        allocate(coef(13))
        call disp%show("factor = getfactorFFT(getFilled((0._TKG, 0._TKG), size(coef, 1, IK)), coef)")
                        factor = getfactorFFT(getFilled((0._TKG, 0._TKG), size(coef, 1, IK)), coef)
        call disp%show("factor")
        call disp%show( factor )
        call disp%show("coef")
        call disp%show( coef )
        call disp%show("call setAsserted(product([factor]) == size(coef, 1, IK))")
                        call setAsserted(product([factor]) == size(coef, 1, IK))
        call disp%skip()
    end block
 
    block
        use pm_kind, only: TKG => RKS
        real(TKG), allocatable :: coef(:)
        call disp%skip()
        call disp%show("allocate(coef(13))")
                        allocate(coef(13))
        call disp%show("factor = getfactorFFT(getFilled(0._TKG, size(coef, 1, IK)), coef)")
                        factor = getfactorFFT(getFilled(0._TKG, size(coef, 1, IK)), coef)
        call disp%show("factor")
        call disp%show( factor )
        call disp%show("coef")
        call disp%show( coef )
        call disp%show("call setAsserted(product([factor]) == size(coef, 1, IK))")
                        call setAsserted(product([factor]) == size(coef, 1, IK))
        call disp%skip()
    end block
 
    block
        use pm_kind, only: TKG => RKS
        real(TKG), allocatable :: coef(:)
        call disp%skip()
        call disp%show("allocate(coef(273))")
                        allocate(coef(273))
        call disp%show("factor = getfactorFFT(getFilled(0._TKG, size(coef, 1, IK)), coef)")
                        factor = getfactorFFT(getFilled(0._TKG, size(coef, 1, IK)), coef)
        call disp%show("factor")
        call disp%show( factor )
        call disp%show("coef")
        call disp%show( coef )
        call disp%show("call setAsserted(product([factor]) == size(coef, 1, IK))")
                        call setAsserted(product([factor]) == size(coef, 1, IK))
        call disp%skip()
    end block
 
end program example

Example Unix compile command via Intel ifort compiler ⛓

#!/usr/bin/env sh
rm main.exe
ifort -fpp -standard-semantics -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
./main.exe

Example Windows Batch compile command via Intel ifort compiler ⛓

del main.exe
set PATH=..\..\..\lib;%PATH%
ifort /fpp /standard-semantics /O3 /I:..\..\..\include main.F90 ..\..\..\lib\libparamonte*.lib /exe:main.exe
main.exe

Example Unix / MinGW compile command via GNU gfortran compiler ⛓

#!/usr/bin/env sh
rm main.exe
gfortran -cpp -ffree-line-length-none -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
./main.exe

Example output ⛓

 
allocate(coef(13))
factor = getfactorFFT(getFilled((0._TKG, 0._TKG), size(coef, 1, IK)), coef)
factor
+13
coef
(+0.885456026, +0.464723200), (+0.568064690, +0.822983861), (+0.120536566, +0.992708862), (-0.354604959, +0.935016215), (-0.748510778, +0.663122654), (-0.970941901, +0.239315450), (-0.970941782, -0.239315853), (-0.748510659, -0.663122773), (-0.354604572, -0.935016334), (+0.120536745, -0.992708862), (+0.568064928, -0.822983742), (+0.885456264, -0.464722782), (+0.885456264, -0.464722782)
call setAsserted(product([factor]) == size(coef, 1, IK))
 
 
allocate(coef(13))
factor = getfactorFFT(getFilled(0._TKG, size(coef, 1, IK)), coef)
factor
+13
coef
+0.519178530E+29, +0.308874208E-40, +0.519178293E+29, +0.308874208E-40, +0.00000000, +0.00000000, +0.574532370E-43, +0.00000000, +0.280259693E-44, +0.00000000, +0.140129846E-44, +0.00000000, +0.519850947E+29
call setAsserted(product([factor]) == size(coef, 1, IK))
 
 
allocate(coef(273))
factor = getfactorFFT(getFilled(0._TKG, size(coef, 1, IK)), coef)
factor
+3, +7, +13
coef
+0.999735177, +0.230132993E-1, +0.998940766, +0.460144095E-1, +0.997617245, +0.689911395E-1, +0.995765328, +0.919313431E-1, +0.993385971, +0.114822842, +0.990480423, +0.137653515, +0.987050235, +0.160411283, +0.983097255, +0.183084086, +0.978623509, +0.205659911, +0.973631442, +0.228126809, +0.968123615, +0.250472844, +0.962103009, +0.272686213, +0.955572784, +0.294755191, +0.948536456, +0.316668004, +0.940997660, +0.338413090, +0.932960451, +0.359978914, +0.924429059, +0.381354064, +0.915408015, +0.402527243, +0.905902088, +0.423487186, +0.895916343, +0.444222867, +0.885456026, +0.464723200, +0.874526680, +0.484977365, +0.863134146, +0.504974663, +0.851284444, +0.524704456, +0.838983774, +0.544156432, +0.826238751, +0.563320100, +0.813056111, +0.582185388, +0.799442768, +0.600742280, +0.785405993, +0.618981004, +0.770953119, +0.636891842, +0.756092012, +0.654465377, +0.740830362, +0.671692193, +0.725176275, +0.688563228, +0.709138155, +0.705069542, +0.692724347, +0.721202493, +0.675943613, +0.736953318, +0.658804893, +0.752313852, +0.641317189, +0.767275870, +0.623489797, +0.781831503, +0.605332136, +0.795973003, +0.586853862, +0.809692919, +0.568064690, +0.822983861, +0.548974693, +0.835838974, +0.529593885, +0.848251283, +0.509932518, +0.860214412, +0.00000000, +0.998940766, +0.460144095E-1, +0.995765328, +0.919313431E-1, +0.990480423, +0.137653515, +0.983097255, +0.183084086, +0.973631442, +0.228126809, +0.962103009, +0.272686213, +0.948536456, +0.316668004, +0.932960451, +0.359978914, +0.915408015, +0.402527243, +0.895916343, +0.444222867, +0.874526680, +0.484977365, +0.851284444, +0.524704456, +0.826238751, +0.563320100, +0.799442768, +0.600742280, +0.770953119, +0.636891842, +0.740830362, +0.671692193, +0.709138155, +0.705069542, +0.675943613, +0.736953318, +0.641317189, +0.767275870, +0.605332136, +0.795973003, +0.568064690, +0.822983861, +0.529593885, +0.848251283, +0.490001172, +0.871721745, +0.449370414, +0.893345535, +0.407787591, +0.913076818, +0.365340978, +0.930873752, +0.322120428, +0.946698725, +0.278217465, +0.960518122, +0.233725116, +0.972302735, +0.188737512, +0.982027590, +0.143350199, +0.989672005, +0.976592079E-1, +0.995219886, +0.517613292E-1, +0.998659492, +0.575379934E-2, +0.999983430, -0.402660407E-1, +0.999189019, -0.862004608E-1, +0.996277809, -0.131952271, +0.991256058, -0.177424535, +0.984134436, -0.222520947, +0.974927902, -0.267146081, +0.963656068, -0.311205149, +0.950342774, -0.354604959, +0.935016215, -0.397253543, +0.917708874, -0.439060569, +0.898457468, -0.479937583, +0.877302647, +0.00000000, +0.997617245, +0.689911395E-1, +0.990480423, +0.137653515, +0.978623509, +0.205659896, +0.962103009, +0.272686213, +0.940997660, +0.338413060, +0.915408015, +0.402527243, +0.00000000, +0.990480423, +0.137653515, +0.962103009, +0.272686213, +0.915408015, +0.402527243, +0.851284444, +0.524704456, +0.770953178, +0.636891842, +0.675943673, +0.736953318, +0.00000000, +0.978623509, +0.205659911, +0.915408015, +0.402527243, +0.813056111, +0.582185388, +0.675943613, +0.736953318, +0.509932518, +0.860214412, +0.322120428, +0.946698725, +0.00000000, +0.962103009, +0.272686213, +0.851284444, +0.524704456, +0.675943673, +0.736953318, +0.449370414, +0.893345535, +0.188737631, +0.982027531, -0.862003416E-1, +0.996277809, +0.00000000, +0.940997660, +0.338413090, +0.770953119, +0.636891842, +0.509932518, +0.860214412, +0.188737512, +0.982027590, -0.154729441, +0.987956882, -0.479937583, +0.877302647, +0.00000000, +0.915408015, +0.402527243, +0.675943613, +0.736953318, +0.322120428, +0.946698725, -0.862004608E-1, +0.996277809, -0.479937583, +0.877302647, -0.792476892, +0.609901965, +0.00000000, +0.00000000, +0.00000000, +0.00000000, +0.00000000, +0.00000000, +0.00000000, +0.00000000, +0.00000000, +0.00000000, +0.00000000, +0.00000000, +0.00000000, +0.00000000
call setAsserted(product([factor]) == size(coef, 1, IK))
 
 

Test:

test_pm_fftpack

Todo:

Low Priority: Extension to higher order factors may be worthwhile in future.

Final Remarks ⛓

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If you believe this algorithm or its documentation can be improved, we appreciate your contribution and help to edit this page's documentation and source file on GitHub.
For details on the naming abbreviations, see this page.
For details on the naming conventions, see this page.
This software is distributed under the MIT license with additional terms outlined below.

1. If you use any parts or concepts from this library to any extent, please acknowledge the usage by citing the relevant publications of the ParaMonte library.
   
2. If you regenerate any parts/ideas from this library in a programming environment other than those currently supported by this ParaMonte library (i.e., other than C, C++, Fortran, MATLAB, Python, R), please also ask the end users to cite this original ParaMonte library.
   

This software is available to the public under a highly permissive license.
Help us justify its continued development and maintenance by acknowledging its benefit to society, distributing it, and contributing to it.

Copyright

Computational Data Science Lab

Author:

Fatemeh Bagheri, Tuesday 11:34 PM, August 10, 2021, Dallas, TX

Definition at line 292 of file pm_fftpack.F90.

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

• src/fortran/main/pm_fftpack.F90