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 ⛓
integer(IK), allocatable :: factor(:)
Generate and return the factorization vector factor of the specified input sequence length and the co...
This module contains procedures and generic interfaces for computing the Discrete Fourier Transform o...
- 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.
- See also
- getFFTF
getFFTI
getFFTR
setFFTF
setFFTI
setFFTR
Example usage ⛓
11 integer(IK),
allocatable :: factor(:)
13 type(display_type) :: disp
18 complex(TKG),
allocatable :: coef(:)
22 call disp%show(
"factor = getfactorFFT(getFilled((0._TKG, 0._TKG), size(coef, 1, IK)), coef)")
23 factor
= getfactorFFT(
getFilled((
0._TKG,
0._TKG),
size(coef,
1,
IK)), coef)
28 call disp%show(
"call setAsserted(product([factor]) == size(coef, 1, IK))")
35 real(TKG),
allocatable :: coef(:)
39 call disp%show(
"factor = getfactorFFT(getFilled(0._TKG, size(coef, 1, IK)), coef)")
40 factor
= getfactorFFT(
getFilled(
0._TKG,
size(coef,
1,
IK)), coef)
45 call disp%show(
"call setAsserted(product([factor]) == size(coef, 1, IK))")
52 real(TKG),
allocatable :: coef(:)
54 call disp%show(
"allocate(coef(273))")
56 call disp%show(
"factor = getfactorFFT(getFilled(0._TKG, size(coef, 1, IK)), coef)")
57 factor
= getfactorFFT(
getFilled(
0._TKG,
size(coef,
1,
IK)), coef)
62 call disp%show(
"call setAsserted(product([factor]) == size(coef, 1, IK))")
Generate and return an array of the specified rank and shape of arbitrary intrinsic type and kind wit...
Verify the input assertion holds and if it does not, print the (optional) input message on stdout and...
Generate and return an object of type stop_type with the user-specified input attributes.
This is a generic method of the derived type display_type with pass attribute.
This module contains procedures and generic interfaces for convenient allocation and filling of array...
This module contains classes and procedures for reporting and handling errors.
This module contains classes and procedures for input/output (IO) or generic display operations on st...
type(display_type) disp
This is a scalar module variable an object of type display_type for general display.
This module defines the relevant Fortran kind type-parameters frequently used in the ParaMonte librar...
integer, parameter LK
The default logical kind in the ParaMonte library: kind(.true.) in Fortran, kind(....
integer, parameter CKS
The single-precision complex kind in Fortran mode. On most platforms, this is a 32-bit real kind.
integer, parameter IK
The default integer kind in the ParaMonte library: int32 in Fortran, c_int32_t in C-Fortran Interoper...
integer, parameter SK
The default character kind in the ParaMonte library: kind("a") in Fortran, c_char in C-Fortran Intero...
integer, parameter RKS
The single-precision real kind in Fortran mode. On most platforms, this is an 32-bit real kind.
Generate and return an object of type display_type.
Example Unix compile command via Intel ifort
compiler ⛓
3ifort -fpp -standard-semantics -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
Example Windows Batch compile command via Intel ifort
compiler ⛓
2set PATH=..\..\..\lib;%PATH%
3ifort /fpp /standard-semantics /O3 /I:..\..\..\include main.F90 ..\..\..\lib\libparamonte*.lib /exe:main.exe
Example Unix / MinGW compile command via GNU gfortran
compiler ⛓
3gfortran -cpp -ffree-line-length-none -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
Example output ⛓
3factor
= getfactorFFT(
getFilled((
0._TKG,
0._TKG),
size(coef,
1,
IK)), coef)
7(
+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)
12factor
= getfactorFFT(
getFilled(
0._TKG,
size(coef,
1,
IK)), coef)
16-0.129212331E+20,
+0.306562065E-40,
-0.129212276E+20,
+0.306562065E-40,
+0.00000000,
+0.00000000,
+0.574532370E-43,
+0.00000000,
+0.280259693E-44,
+0.00000000,
+0.140129846E-44,
+0.00000000,
-0.129368890E+20
21factor
= getfactorFFT(
getFilled(
0._TKG,
size(coef,
1,
IK)), coef)
25+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
- Test:
- test_pm_fftpack
- Todo:
- Low Priority: Extension to higher order factors may be worthwhile in future.
Final Remarks ⛓
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.
-
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.
-
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.