Return the Reverse (unnormalized) Fourier Transform of a periodic sequence of type complex or real of arbitrary kind parameter. More...

Detailed Description

Return the Reverse (unnormalized) Fourier Transform of a periodic sequence of type complex or real of arbitrary kind parameter.

See the documentation of pm_fftnr for more details.

Parameters

[in,out]

data

: The input/output contiguous vector of arbitrary size of,

type complex of kind any supported by the processor (e.g., CK, CK32, CK64, or CK128),
type real of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128),

containing the periodic sequence whose FFT is to be computed.
On output, data contains the FFT result.

Possible calling interfaces ⛓

: use pm_fftnr, only: setFFTR

call setFFTR(data(:))

pm_fftnr::setFFTR
Return the Reverse (unnormalized) Fourier Transform of a periodic sequence of type complex or real of...
Definition: pm_fftnr.F90:1107

pm_fftnr
This module contains procedures and generic interfaces for computing the Discrete Fourier Transform o...
Definition: pm_fftnr.F90:184

Warning: The condition 1 < size(data) .and. isIntPow(size(data)) must hold for the corresponding input arguments.
This condition is 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.

See also: getFFTF
getFFTR
getFFTI
setFFTF
setFFTR
setFFTI

Example usage ⛓

: 1program example

2

3 use pm_kind, only: SK, IK, LK

4 use pm_io, only: display_type

5 use pm_fftnr, only: setFFTF, setFFTR

6 use pm_arrayResize, only: setResized

7

8 implicit none

9

10 logical(LK) :: inwork

11 integer(IK), allocatable :: factor(:)

12

13 type(display_type) :: disp

14 disp = display_type(file = "main.out.F90")

15

16 block

17 use pm_kind, only: TKG => CKS

18 complex(TKG), allocatable :: data(:)

19 complex(TKG), parameter :: ZERO = 0._TKG

20 call disp%skip()

21 call disp%show("data = [complex(TKG) :: (1., -6.), (2., -5.), (3., -4.), (4., -3.), (5., -2.), (6., -1.), ZERO, ZERO]")

22 data = [complex(TKG) :: (1., -6.), (2., -5.), (3., -4.), (4., -3.), (5., -2.), (6., -1.), ZERO, ZERO]

23 call disp%show("call setFFTF(data)")

24 call setFFTF(data)

25 call disp%show("data")

26 call disp%show( data )

27 call disp%skip()

28 call disp%show("call setFFTR(data)")

29 call setFFTR(data)

30 call disp%show("data * 2 / size(data)")

31 call disp%show( data * 2 / size(data) )

32 call disp%skip()

33 end block

34

35 block

36 use pm_kind, only: TKG => CKD

37 complex(TKG), allocatable :: data(:)

38 complex(TKG), parameter :: ZERO = 0._TKG

39 call disp%skip()

40 call disp%show("data = [complex(TKG) :: (1., -6.), (2., -5.), (3., -4.), (4., -3.), (5., -2.), (6., -1.), ZERO, ZERO]")

41 data = [complex(TKG) :: (1., -6.), (2., -5.), (3., -4.), (4., -3.), (5., -2.), (6., -1.), ZERO, ZERO]

42 call disp%show("call setFFTF(data)")

43 call setFFTF(data)

44 call disp%show("data")

45 call disp%show( data )

46 call disp%skip()

47 call disp%show("call setFFTR(data)")

48 call setFFTR(data)

49 call disp%show("data * 2 / size(data)")

50 call disp%show( data * 2 / size(data) )

51 call disp%skip()

52 end block

53

54 block

55 use pm_kind, only: TKG => CKH

56 complex(TKG), allocatable :: data(:)

57 complex(TKG), parameter :: ZERO = 0._TKG

58 call disp%skip()

59 call disp%show("data = [complex(TKG) :: (1., -6.), (2., -5.), (3., -4.), (4., -3.), (5., -2.), (6., -1.), ZERO, ZERO]")

60 data = [complex(TKG) :: (1., -6.), (2., -5.), (3., -4.), (4., -3.), (5., -2.), (6., -1.), ZERO, ZERO]

61 call disp%show("call setFFTF(data)")

62 call setFFTF(data)

63 call disp%show("data")

64 call disp%show( data )

65 call disp%skip()

66 call disp%show("call setFFTR(data)")

67 call setFFTR(data)

68 call disp%show("data * 2 / size(data)")

69 call disp%show( data * 2 / size(data) )

70 call disp%skip()

71 end block

72

73 block

74 use pm_kind, only: TKG => RKS

75 real(TKG), allocatable :: data(:)

76 real(TKG), parameter :: ZERO = 0._TKG

77 call disp%skip()

78 call disp%show("data = [real(TKG) :: 1., 2., 3., 4., 5., 6.5, ZERO, ZERO]")

79 data = [real(TKG) :: 1., 2., 3., 4., 5., 6.5, ZERO, ZERO]

80 call disp%show("call setFFTF(data)")

81 call setFFTF(data)

82 call disp%show("data")

83 call disp%show( data )

84 call disp%skip()

85 call disp%show("call setFFTR(data)")

86 call setFFTR(data)

87 call disp%show("data * 2 / size(data)")

88 call disp%show( data * 2 / size(data) )

89 call disp%skip()

90 end block

91

92 block

93 use pm_kind, only: TKG => RKD

94 real(TKG), allocatable :: data(:)

95 real(TKG), parameter :: ZERO = 0._TKG

96 call disp%skip()

97 call disp%show("data = [real(TKG) :: 1., 2., 3., 4., 5., 6.5, ZERO, ZERO]")

98 data = [real(TKG) :: 1., 2., 3., 4., 5., 6.5, ZERO, ZERO]

99 call disp%show("call setFFTF(data)")

100 call setFFTF(data)

101 call disp%show("data")

102 call disp%show( data )

103 call disp%skip()

104 call disp%show("call setFFTR(data)")

105 call setFFTR(data)

106 call disp%show("data * 2 / size(data)")

107 call disp%show( data * 2 / size(data) )

108 call disp%skip()

109 end block

110

111 block

112 use pm_kind, only: TKG => RKH

113 real(TKG), allocatable :: data(:)

114 real(TKG), parameter :: ZERO = 0._TKG

115 call disp%skip()

116 call disp%show("data = [real(TKG) :: 1., 2., 3., 4., 5., 6.5, ZERO, ZERO]")

117 data = [real(TKG) :: 1., 2., 3., 4., 5., 6.5, ZERO, ZERO]

118 call disp%show("call setFFTF(data)")

119 call setFFTF(data)

120 call disp%show("data")

121 call disp%show( data )

122 call disp%skip()

123 call disp%show("call setFFTR(data)")

124 call setFFTR(data)

125 call disp%show("data * 2 / size(data)")

126 call disp%show( data * 2 / size(data) )

127 call disp%skip()

128 end block

129

130end program example

pm_arrayResize::setResized
Allocate or resize (shrink or expand) an input allocatable scalar string or array of rank 1....
Definition: pm_arrayResize.F90:249

pm_fftnr::setFFTF
Return the Forward Fourier Transform of a periodic sequence of type complex or real of arbitrary kind...
Definition: pm_fftnr.F90:783

pm_io::show
This is a generic method of the derived type display_type with pass attribute.
Definition: pm_io.F90:11726

pm_io::skip
This is a generic method of the derived type display_type with pass attribute.
Definition: pm_io.F90:11508

pm_arrayResize
This module contains procedures and generic interfaces for resizing allocatable arrays of various typ...
Definition: pm_arrayResize.F90:81

pm_io
This module contains classes and procedures for input/output (IO) or generic display operations on st...
Definition: pm_io.F90:252

pm_io::disp
type(display_type) disp
This is a scalar module variable an object of type display_type for general display.
Definition: pm_io.F90:11393

pm_kind
This module defines the relevant Fortran kind type-parameters frequently used in the ParaMonte librar...
Definition: pm_kind.F90:268

pm_kind::LK
integer, parameter LK
The default logical kind in the ParaMonte library: kind(.true.) in Fortran, kind(....
Definition: pm_kind.F90:541

pm_kind::CKH
integer, parameter CKH
The scalar integer constant of intrinsic default kind, representing the highest-precision complex kin...
Definition: pm_kind.F90:843

pm_kind::CKS
integer, parameter CKS
The single-precision complex kind in Fortran mode. On most platforms, this is a 32-bit real kind.
Definition: pm_kind.F90:570

pm_kind::IK
integer, parameter IK
The default integer kind in the ParaMonte library: int32 in Fortran, c_int32_t in C-Fortran Interoper...
Definition: pm_kind.F90:540

pm_kind::CKD
integer, parameter CKD
The double precision complex kind in Fortran mode. On most platforms, this is a 64-bit real kind.
Definition: pm_kind.F90:571

pm_kind::RKD
integer, parameter RKD
The double precision real kind in Fortran mode. On most platforms, this is an 64-bit real kind.
Definition: pm_kind.F90:568

pm_kind::SK
integer, parameter SK
The default character kind in the ParaMonte library: kind("a") in Fortran, c_char in C-Fortran Intero...
Definition: pm_kind.F90:539

pm_kind::RKH
integer, parameter RKH
The scalar integer constant of intrinsic default kind, representing the highest-precision real kind t...
Definition: pm_kind.F90:858

pm_kind::RKS
integer, parameter RKS
The single-precision real kind in Fortran mode. On most platforms, this is an 32-bit real kind.
Definition: pm_kind.F90:567

pm_io::display_type
Generate and return an object of type display_type.
Definition: pm_io.F90:10282

Example Unix compile command via Intel ifort compiler ⛓
1#!/usr/bin/env sh

2rm main.exe

3ifort -fpp -standard-semantics -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe

4./main.exe

Example Windows Batch compile command via Intel ifort compiler ⛓
1del main.exe

2set PATH=..\..\..\lib;%PATH%

3ifort /fpp /standard-semantics /O3 /I:..\..\..\include main.F90 ..\..\..\lib\libparamonte*.lib /exe:main.exe

4main.exe

Example Unix / MinGW compile command via GNU gfortran compiler ⛓
1#!/usr/bin/env sh

2rm main.exe

3gfortran -cpp -ffree-line-length-none -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe

4./main.exe

Example output ⛓
1

2data = [complex(TKG) :: (1., -6.), (2., -5.), (3., -4.), (4., -3.), (5., -2.), (6., -1.), ZERO, ZERO]

3call setFFTF(data)

4data

5(+21.0000000, -21.0000000), (-0.707106352, -1.70710707), (+5.99999905, -0.238418579E-6), (+2.60659981, -6.29289198), (-3.00000000, -3.00000000), (+0.707106352, -0.292893469), (+0.715255737E-6, -8.00000000), (-18.6065998, -7.70710802)

6

7call setFFTR(data)

8data * 2 / size(data)

9(+2.00000000, -12.0000000), (+4.00000143, -9.99999905), (+5.99999905, -8.00000000), (+7.99999905, -5.99999905), (+10.0000000, -4.00000000), (+11.9999981, -2.00000000), (+0.715255737E-6, -0.238418579E-6), (+0.119209290E-5, -0.166893005E-5)

10

11

12data = [complex(TKG) :: (1., -6.), (2., -5.), (3., -4.), (4., -3.), (5., -2.), (6., -1.), ZERO, ZERO]

13call setFFTF(data)

14data

15(+21.000000000000000, -21.000000000000000), (-0.70710678118654524, -1.7071067811865483), (+5.9999999999999991, -0.88817841970012523E-15), (+2.6066017177982097, -6.2928932188134530), (-3.0000000000000000, -3.0000000000000000), (+0.70710678118654702, -0.29289321881345343), (+0.88817841970012523E-15, -7.9999999999999991), (-18.606601717798210, -7.7071067811865452)

16

17call setFFTR(data)

18data * 2 / size(data)

19(+2.0000000000000004, -12.000000000000000), (+4.0000000000000018, -9.9999999999999982), (+5.9999999999999982, -7.9999999999999991), (+7.9999999999999973, -5.9999999999999991), (+10.000000000000000, -4.0000000000000000), (+11.999999999999998, -1.9999999999999996), (+0.13322676295501878E-14, -0.88817841970012523E-15), (+0.26645352591003757E-14, -0.26645352591003757E-14)

20

21

22data = [complex(TKG) :: (1., -6.), (2., -5.), (3., -4.), (4., -3.), (5., -2.), (6., -1.), ZERO, ZERO]

23call setFFTF(data)

24data

25(+21.0000000000000000000000000000000000, -21.0000000000000000000000000000000000), (-0.707106781186547524400844362104848511, -1.70710678118654752440084436210484928), (+6.00000000000000000000000000000000000, -0.385185988877447170611195588516985464E-33), (+2.60660171779821286601266543157273536, -6.29289321881345247559915563789515226), (-3.00000000000000000000000000000000000, -3.00000000000000000000000000000000000), (+0.707106781186547524400844362104848511, -0.292893218813452475599155637895151393), (-0.385185988877447170611195588516985464E-33, -8.00000000000000000000000000000000000), (-18.6066017177982128660126654315727354, -7.70710678118654752440084436210484774)

26

27call setFFTR(data)

28data * 2 / size(data)

29(+2.00000000000000000000000000000000000, -12.0000000000000000000000000000000000), (+4.00000000000000000000000000000000000, -10.0000000000000000000000000000000000), (+6.00000000000000000000000000000000000, -8.00000000000000000000000000000000000), (+8.00000000000000000000000000000000000, -5.99999999999999999999999999999999923), (+10.0000000000000000000000000000000000, -4.00000000000000000000000000000000000), (+12.0000000000000000000000000000000000, -2.00000000000000000000000000000000000), (-0.385185988877447170611195588516985464E-33, -0.385185988877447170611195588516985464E-33), (+0.00000000000000000000000000000000000, -0.770371977754894341222391177033970927E-33)

30

31

32data = [real(TKG) :: 1., 2., 3., 4., 5., 6.5, ZERO, ZERO]

33call setFFTF(data)

34data

35+21.5000000, -3.50000000, -10.0104074, +2.64644647, +3.00000000, +4.50000000, +2.01040721, -3.35355353

36

37call setFFTR(data)

38data * 2 / size(data)

39+1.00000000, +2.00000024, +3.00000000, +4.00000000, +5.00000000, +6.50000000, +0.119209290E-6, +0.00000000

40

41

42data = [real(TKG) :: 1., 2., 3., 4., 5., 6.5, ZERO, ZERO]

43call setFFTF(data)

44data

45+21.500000000000000, -3.5000000000000000, -10.010407640085653, +2.6464466094067260, +3.0000000000000000, +4.5000000000000000, +2.0104076400856532, -3.3535533905932753

46

47call setFFTR(data)

48data * 2 / size(data)

49+1.0000000000000000, +2.0000000000000000, +3.0000000000000000, +3.9999999999999996, +5.0000000000000000, +6.5000000000000000, +0.0000000000000000, +0.44408920985006262E-15

50

51

52data = [real(TKG) :: 1., 2., 3., 4., 5., 6.5, ZERO, ZERO]

53call setFFTF(data)

54data

55+21.5000000000000000000000000000000000, -3.50000000000000000000000000000000000, -10.0104076400856539574071770778912162, +2.64644660940672623779957781894757574, +3.00000000000000000000000000000000000, +4.50000000000000000000000000000000000, +2.01040764008565395740717707789121696, -3.35355339059327376220042218105242426

56

57call setFFTR(data)

58data * 2 / size(data)

59+1.00000000000000000000000000000000039, +2.00000000000000000000000000000000000, +3.00000000000000000000000000000000000, +4.00000000000000000000000000000000000, +5.00000000000000000000000000000000000, +6.50000000000000000000000000000000000, +0.192592994438723585305597794258492732E-33, +0.192592994438723585305597794258492732E-33

60

61

Test:: test_pm_fftnr

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 1107 of file pm_fftnr.F90.

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

src/fortran/main/pm_fftnr.F90