Generate and return the Forward Fourier Transform (a.k.a. Fourier Analysis) of a periodic sequence of type complex or real of arbitrary kind type parameter. More...

Detailed Description

Generate and return the Forward Fourier Transform (a.k.a. Fourier Analysis) of a periodic sequence of type complex or real of arbitrary kind type parameter.

See the documentation of setFFTF for more details.

Parameters

[in]

data

: The input 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.

Returns: fft : The output vector of the same type, kind, and size as the input data, containing the FFT result.

Possible calling interfaces ⛓

: use pm_fftpack, only: getFFTF

fft = getFFTF(data(:))

pm_fftpack::getFFTF
Generate and return the Forward Fourier Transform (a.k.a. Fourier Analysis) of a periodic sequence of...
Definition: pm_fftpack.F90:746

pm_fftpack
This module contains procedures and generic interfaces for computing the Discrete Fourier Transform o...
Definition: pm_fftpack.F90:205

Remarks: The procedures under discussion are impure.

Note: This functional generic interface is simply a more flexible but slower wrapper around the subroutine generic interface setFFTF.
As such, this functional interface can be significantly slower than the corresponding subroutine interface.

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_fftpack, only: getfactorFFT

6 use pm_fftpack, only: getFFTF, getFFTI

7 use pm_distUnif, only: getUnifRand

8 use pm_mathCompare, only: isClose

9 use pm_err, only: setAsserted

10

11 implicit none

12

13 integer(IK) :: i

14 integer(IK) :: lenData

15 type(display_type) :: disp

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

17

18 do i = 1, 5

19 block

20 use pm_kind, only: TKG => CKS

21 real(TKG) :: reltol

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

23 call disp%show("lenData = getUnifRand(5, 11)")

24 lenData = getUnifRand(5, 11)

25 call disp%show("lenData")

26 call disp%show( lenData )

27 call disp%show("data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)")

28 data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

29 call disp%show("data")

30 call disp%show( data )

31 call disp%show("getFFTI(getFFTF(data))")

32 call disp%show( getFFTI(getFFTF(data)) )

33 call disp%show("reltol = sqrt(epsilon(1._TKG))")

34 reltol = sqrt(epsilon(1._TKG))

35 call disp%show("reltol")

36 call disp%show( reltol )

37 call disp%show("isClose(data, getFFTI(getFFTF(data)), reltol = reltol)")

38 call disp%show( isClose(data, getFFTI(getFFTF(data)), reltol = reltol) )

39 call disp%show("call setAsserted(all(isClose(data, getFFTI(getFFTF(data)), reltol = reltol)))")

40 call setAsserted(all(isClose(data, getFFTI(getFFTF(data)), reltol = reltol)))

41 call disp%skip()

42 end block

43

44 block

45 use pm_kind, only: TKG => CKD

46 real(TKG) :: reltol

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

48 call disp%show("lenData = getUnifRand(5, 11)")

49 lenData = getUnifRand(5, 11)

50 call disp%show("lenData")

51 call disp%show( lenData )

52 call disp%show("data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)")

53 data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

54 call disp%show("data")

55 call disp%show( data )

56 call disp%show("getFFTI(getFFTF(data))")

57 call disp%show( getFFTI(getFFTF(data)) )

58 call disp%show("reltol = sqrt(epsilon(1._TKG))")

59 reltol = sqrt(epsilon(1._TKG))

60 call disp%show("reltol")

61 call disp%show( reltol )

62 call disp%show("isClose(data, getFFTI(getFFTF(data)), reltol = reltol)")

63 call disp%show( isClose(data, getFFTI(getFFTF(data)), reltol = reltol) )

64 call disp%show("call setAsserted(all(isClose(data, getFFTI(getFFTF(data)), reltol = reltol)))")

65 call setAsserted(all(isClose(data, getFFTI(getFFTF(data)), reltol = reltol)))

66 call disp%skip()

67 end block

68

69 block

70 use pm_kind, only: TKG => CKH

71 real(TKG) :: reltol

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

73 call disp%show("lenData = getUnifRand(5, 11)")

74 lenData = getUnifRand(5, 11)

75 call disp%show("lenData")

76 call disp%show( lenData )

77 call disp%show("data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)")

78 data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

79 call disp%show("data")

80 call disp%show( data )

81 call disp%show("getFFTI(getFFTF(data))")

82 call disp%show( getFFTI(getFFTF(data)) )

83 call disp%show("reltol = sqrt(epsilon(1._TKG))")

84 reltol = sqrt(epsilon(1._TKG))

85 call disp%show("reltol")

86 call disp%show( reltol )

87 call disp%show("isClose(data, getFFTI(getFFTF(data)), reltol = reltol)")

88 call disp%show( isClose(data, getFFTI(getFFTF(data)), reltol = reltol) )

89 call disp%show("call setAsserted(all(isClose(data, getFFTI(getFFTF(data)), reltol = reltol)))")

90 call setAsserted(all(isClose(data, getFFTI(getFFTF(data)), reltol = reltol)))

91 call disp%skip()

92 end block

93

94 block

95 use pm_kind, only: TKG => RKS

96 real(TKG) :: reltol

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

98 call disp%show("lenData = getUnifRand(5, 11)")

99 lenData = getUnifRand(5, 11)

100 call disp%show("lenData")

101 call disp%show( lenData )

102 call disp%show("data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)")

103 data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

104 call disp%show("data")

105 call disp%show( data )

106 call disp%show("getFFTF(data)")

107 call disp%show( getFFTF(data) )

108 call disp%show("getFFTF(cmplx(data, kind = TKG))")

109 call disp%show( getFFTF(cmplx(data, kind = TKG)) )

110 call disp%show("getFFTI(getFFTF(data))")

111 call disp%show( getFFTI(getFFTF(data)) )

112 call disp%show("getFFTI(getFFTF(cmplx(data, kind = TKG)))")

113 call disp%show( getFFTI(getFFTF(cmplx(data, kind = TKG))) )

114 call disp%show("reltol = sqrt(epsilon(1._TKG))")

115 reltol = sqrt(epsilon(1._TKG))

116 call disp%show("reltol")

117 call disp%show( reltol )

118 call disp%show("isClose(data, getFFTI(getFFTF(data)), reltol = reltol)")

119 call disp%show( isClose(data, getFFTI(getFFTF(data)), reltol = reltol) )

120 call disp%show("call setAsserted(all(isClose(data, getFFTI(getFFTF(data)), reltol = reltol)))")

121 call setAsserted(all(isClose(data, getFFTI(getFFTF(data)), reltol = reltol)))

122 call disp%skip()

123 end block

124

125 block

126 use pm_kind, only: TKG => RKD

127 real(TKG) :: reltol

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

129 call disp%show("lenData = getUnifRand(5, 11)")

130 lenData = getUnifRand(5, 11)

131 call disp%show("lenData")

132 call disp%show( lenData )

133 call disp%show("data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)")

134 data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

135 call disp%show("data")

136 call disp%show( data )

137 call disp%show("getFFTF(data)")

138 call disp%show( getFFTF(data) )

139 call disp%show("getFFTF(cmplx(data, kind = TKG))")

140 call disp%show( getFFTF(cmplx(data, kind = TKG)) )

141 call disp%show("getFFTI(getFFTF(data))")

142 call disp%show( getFFTI(getFFTF(data)) )

143 call disp%show("getFFTI(getFFTF(cmplx(data, kind = TKG)))")

144 call disp%show( getFFTI(getFFTF(cmplx(data, kind = TKG))) )

145 call disp%show("reltol = sqrt(epsilon(1._TKG))")

146 reltol = sqrt(epsilon(1._TKG))

147 call disp%show("reltol")

148 call disp%show( reltol )

149 call disp%show("isClose(data, getFFTI(getFFTF(data)), reltol = reltol)")

150 call disp%show( isClose(data, getFFTI(getFFTF(data)), reltol = reltol) )

151 call disp%show("call setAsserted(all(isClose(data, getFFTI(getFFTF(data)), reltol = reltol)))")

152 call setAsserted(all(isClose(data, getFFTI(getFFTF(data)), reltol = reltol)))

153 call disp%skip()

154 end block

155

156 block

157 use pm_kind, only: TKG => RKH

158 real(TKG) :: reltol

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

160 call disp%show("lenData = getUnifRand(5, 11)")

161 lenData = getUnifRand(5, 11)

162 call disp%show("lenData")

163 call disp%show( lenData )

164 call disp%show("data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)")

165 data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

166 call disp%show("data")

167 call disp%show( data )

168 call disp%show("getFFTF(data)")

169 call disp%show( getFFTF(data) )

170 call disp%show("getFFTF(cmplx(data, kind = TKG))")

171 call disp%show( getFFTF(cmplx(data, kind = TKG)) )

172 call disp%show("getFFTI(getFFTF(data))")

173 call disp%show( getFFTI(getFFTF(data)) )

174 call disp%show("getFFTI(getFFTF(cmplx(data, kind = TKG)))")

175 call disp%show( getFFTI(getFFTF(cmplx(data, kind = TKG))) )

176 call disp%show("reltol = sqrt(epsilon(1._TKG))")

177 reltol = sqrt(epsilon(1._TKG))

178 call disp%show("reltol")

179 call disp%show( reltol )

180 call disp%show("isClose(data, getFFTI(getFFTF(data)), reltol = reltol)")

181 call disp%show( isClose(data, getFFTI(getFFTF(data)), reltol = reltol) )

182 call disp%show("call setAsserted(all(isClose(data, getFFTI(getFFTF(data)), reltol = reltol)))")

183 call setAsserted(all(isClose(data, getFFTI(getFFTF(data)), reltol = reltol)))

184 call disp%skip()

185 end block

186 end do

187

188end program example

pm_distUnif::getUnifRand
Generate and return a scalar or a contiguous array of rank 1 of length s1 of randomly uniformly distr...
Definition: pm_distUnif.F90:4150

pm_err::setAsserted
Verify the input assertion holds and if it does not, print the (optional) input message on stdout and...
Definition: pm_err.F90:735

pm_err::show
Generate and return an object of type stop_type with the user-specified input attributes.
Definition: pm_err.F90:1618

pm_fftpack::getFFTI
Generate and return the Inverse (normalized) Fourier Transform of a periodic sequence of type complex...
Definition: pm_fftpack.F90:1567

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

pm_mathCompare::isClose
Generate and return .true. if the two input values are sufficiently close to each other within the sp...
Definition: pm_mathCompare.F90:535

pm_distUnif
This module contains classes and procedures for computing various statistical quantities related to t...
Definition: pm_distUnif.F90:274

pm_err
This module contains classes and procedures for reporting and handling errors.
Definition: pm_err.F90:52

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_mathCompare
This module contains the procedures and interfaces for evaluating the relative or absolute proximity ...
Definition: pm_mathCompare.F90:205

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 ⛓
1lenData = getUnifRand(5, 11)

2lenData

3+8

4data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

5data

6(+1.50482452, +0.183970988), (+1.62449193, +0.410823226), (+1.01650548, +0.297196507E-1), (+1.41120148, +0.448471546), (+1.24040270, +0.710610628), (+1.35899663, +0.313088596), (+1.83887529, +0.147309959), (+1.14844108, +0.285040140E-1)

7getFFTI(getFFTF(data))

8(+1.50482464, +0.183970928), (+1.62449181, +0.410823256), (+1.01650536, +0.297196545E-1), (+1.41120148, +0.448471546), (+1.24040270, +0.710610628), (+1.35899651, +0.313088626), (+1.83887517, +0.147309959), (+1.14844108, +0.285040438E-1)

9reltol = sqrt(epsilon(1._TKG))

10reltol

11+0.345266977E-3

12isClose(data, getFFTI(getFFTF(data)), reltol = reltol)

13T, T, T, T, T, T, T, T

14call setAsserted(all(isClose(data, getFFTI(getFFTF(data)), reltol = reltol)))

15

16lenData = getUnifRand(5, 11)

17lenData

18+10

19data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

20data

21(+1.2876871853731551, +0.96276312344184101), (+1.9112587053356338, +0.50861641828784931), (+1.1521703936957692, +0.21326723168428929), (+1.5593319363391878, +0.92133314941521405), (+1.5736393013012990, +0.36046404076861471), (+1.7649096757535649, +0.20125991615059424), (+1.6511478248962850, +0.66981936894838989), (+1.4143579850673640, +0.68682691287349096), (+1.4210285900830870, +0.30522695205507666), (+1.5798683979405375, +0.26643291773239774)

22getFFTI(getFFTF(data))

23(+1.2876871853731555, +0.96276312344184134), (+1.9112587053356336, +0.50861641828784920), (+1.1521703936957692, +0.21326723168428924), (+1.5593319363391878, +0.92133314941521405), (+1.5736393013012988, +0.36046404076861482), (+1.7649096757535654, +0.20125991615059446), (+1.6511478248962850, +0.66981936894839000), (+1.4143579850673640, +0.68682691287349096), (+1.4210285900830872, +0.30522695205507655), (+1.5798683979405370, +0.26643291773239774)

24reltol = sqrt(epsilon(1._TKG))

25reltol

26+0.14901161193847656E-7

27isClose(data, getFFTI(getFFTF(data)), reltol = reltol)

28T, T, T, T, T, T, T, T, T, T

29call setAsserted(all(isClose(data, getFFTI(getFFTF(data)), reltol = reltol)))

30

31lenData = getUnifRand(5, 11)

32lenData

33+10

34data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

35data

36(+1.48653242384318593925747808624971667, +0.821897995847605863916567201554063852), (+1.18412769064399562573025788837068150, +0.922017434698187479938753669731087679), (+1.64050734740036198140618057407922775, +0.513090700640538073283250609613769371), (+1.52037263570319299552120277940985753, +0.139074947235701415161391136852142459), (+1.51585671340493005578248668348123914, +0.761236838352545588281079178765259515), (+1.09926358789766445668863923262354369, +0.423612444834393483820473268795699362), (+1.56955745078379823891678121125040597, +0.380693549602581167847191830267127358), (+1.31195310404397084579356659058609930, +0.419797873100377136658447909052772076), (+1.73041722228204085423505887502743899, +0.302193107564157693388089580412008000), (+1.95577226081875939273723323120693556, +0.387977865051097261411324968961482337)

37getFFTI(getFFTF(data))

38(+1.48653242384318593925747808624971667, +0.821897995847605863916567201554063852), (+1.18412769064399562573025788837068189, +0.922017434698187479938753669731087679), (+1.64050734740036198140618057407922795, +0.513090700640538073283250609613769467), (+1.52037263570319299552120277940985772, +0.139074947235701415161391136852142484), (+1.51585671340493005578248668348123933, +0.761236838352545588281079178765259419), (+1.09926358789766445668863923262354388, +0.423612444834393483820473268795699410), (+1.56955745078379823891678121125040616, +0.380693549602581167847191830267127358), (+1.31195310404397084579356659058609969, +0.419797873100377136658447909052772028), (+1.73041722228204085423505887502743899, +0.302193107564157693388089580412008000), (+1.95577226081875939273723323120693595, +0.387977865051097261411324968961482289)

39reltol = sqrt(epsilon(1._TKG))

40reltol

41+0.138777878078144567552953958511352539E-16

42isClose(data, getFFTI(getFFTF(data)), reltol = reltol)

43T, T, T, T, T, T, T, T, T, T

44call setAsserted(all(isClose(data, getFFTI(getFFTF(data)), reltol = reltol)))

45

46lenData = getUnifRand(5, 11)

47lenData

48+6

49data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

50data

51+1.07149625, +1.76320672, +1.67985272, +1.74203897, +1.04487586, +1.24271965

52getFFTF(data)

53+8.54419041, -0.529943824, -1.00066113, -0.517922491E-1, +0.991510749E-1, -0.951740503

54getFFTF(cmplx(data, kind = TKG))

55(+8.54418945, +0.00000000), (-0.529943883, -1.00066113), (-0.517921448E-1, +0.991510674E-1), (-0.951740444, +0.00000000), (-0.517921448E-1, -0.991510674E-1), (-0.529943764, +1.00066113)

56getFFTI(getFFTF(data))

57+1.07149637, +1.76320684, +1.67985296, +1.74203908, +1.04487610, +1.24271965

58getFFTI(getFFTF(cmplx(data, kind = TKG)))

59(+1.07149625, +0.00000000), (+1.76320648, -0.993410776E-8), (+1.67985249, -0.172063785E-7), (+1.74203897, +0.135702436E-7), (+1.04487574, +0.172063785E-7), (+1.24271953, -0.363613561E-8)

60reltol = sqrt(epsilon(1._TKG))

61reltol

62+0.345266977E-3

63isClose(data, getFFTI(getFFTF(data)), reltol = reltol)

64T, T, T, T, T, T

65call setAsserted(all(isClose(data, getFFTI(getFFTF(data)), reltol = reltol)))

66

67lenData = getUnifRand(5, 11)

68lenData

69+5

70data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

71data

72+1.0524827582568805, +1.7457841237541529, +1.3987859471095072, +1.5114542989253945, +1.3447511334563305

73getFFTF(data)

74+7.0532582615022656, -0.34692314230629417, -0.31518024307459669, -0.54849909280263653, -0.34287524755454507

75getFFTF(cmplx(data, kind = TKG))

76(+7.0532582615022656, +0.0000000000000000), (-0.34692314230629417, -0.31518024307459669), (-0.54849909280263653, -0.34287524755454507), (-0.54849909280263653, +0.34287524755454507), (-0.34692314230629417, +0.31518024307459669)

77getFFTI(getFFTF(data))

78+1.0524827582568808, +1.7457841237541531, +1.3987859471095072, +1.5114542989253945, +1.3447511334563305

79getFFTI(getFFTF(cmplx(data, kind = TKG)))

80(+1.0524827582568808, +0.0000000000000000), (+1.7457841237541531, +0.0000000000000000), (+1.3987859471095072, +0.0000000000000000), (+1.5114542989253945, +0.0000000000000000), (+1.3447511334563305, +0.0000000000000000)

81reltol = sqrt(epsilon(1._TKG))

82reltol

83+0.14901161193847656E-7

84isClose(data, getFFTI(getFFTF(data)), reltol = reltol)

85T, T, T, T, T

86call setAsserted(all(isClose(data, getFFTI(getFFTF(data)), reltol = reltol)))

87

88lenData = getUnifRand(5, 11)

89lenData

90+6

91data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

92data

93+1.38805066421846178816331615286867292, +1.64830129487409695726429697638538548, +1.56388008047860648120891663695537561, +1.16670498325146190109845622760785800, +1.78025095717321329260064906414498362, +1.06803183634886227618598951719794766

94getFFTF(data)

95+8.61521981634470269652162457516022426, -0.925532722474303831147796784976981722E-1, -0.315145416266454089678803331950643750, -0.475476436967465814368153716865315217, -0.689910767979733788629739013477351951, +0.849143587395860427424139132777841221

96getFFTF(cmplx(data, kind = TKG))

97(+8.61521981634470269652162457516022426, +0.00000000000000000000000000000000000), (-0.925532722474303831147796784976981722E-1, -0.315145416266454089678803331950643750), (-0.475476436967465814368153716865315072, -0.689910767979733788629739013477351951), (+0.849143587395860427424139132777841028, -0.240741243048404481631997242823115915E-34), (-0.475476436967465814368153716865315072, +0.689910767979733788629739013477351951), (-0.925532722474303831147796784976981241E-1, +0.315145416266454089678803331950643799)

98getFFTI(getFFTF(data))

99+1.38805066421846178816331615286867312, +1.64830129487409695726429697638538548, +1.56388008047860648120891663695537581, +1.16670498325146190109845622760785800, +1.78025095717321329260064906414498362, +1.06803183634886227618598951719794785

100getFFTI(getFFTF(cmplx(data, kind = TKG)))

101(+1.38805066421846178816331615286867292, +0.401235405080674136053328738038526505E-35), (+1.64830129487409695726429697638538548, +0.361111864572606722447995864234673872E-34), (+1.56388008047860648120891663695537561, -0.802470810161348272106657476077053011E-35), (+1.16670498325146190109845622760785819, -0.398354664482285140321949953964150378E-34), (+1.78025095717321329260064906414498343, -0.802470810161348272106657476077053011E-35), (+1.06803183634886227618598951719794766, +0.157613421433880658689952711141034463E-34)

102reltol = sqrt(epsilon(1._TKG))

103reltol

104+0.138777878078144567552953958511352539E-16

105isClose(data, getFFTI(getFFTF(data)), reltol = reltol)

106T, T, T, T, T, T

107call setAsserted(all(isClose(data, getFFTI(getFFTF(data)), reltol = reltol)))

108

109lenData = getUnifRand(5, 11)

110lenData

111+10

112data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

113data

114(+1.23968399, +0.955482066), (+1.21911621, +0.976786733), (+1.84466374, +0.265725970), (+1.95516396, +0.691450953), (+1.20274580, +0.550195575E-1), (+1.80945778, +0.789554715), (+1.87069678, +0.659685493), (+1.46079803, +0.904396713), (+1.80528784, +0.579334676), (+1.95619297, +0.617053866)

115getFFTI(getFFTF(data))

116(+1.23968399, +0.955482006), (+1.21911621, +0.976786733), (+1.84466398, +0.265725911), (+1.95516396, +0.691450953), (+1.20274580, +0.550196171E-1), (+1.80945778, +0.789554656), (+1.87069690, +0.659685493), (+1.46079826, +0.904396832), (+1.80528796, +0.579334676), (+1.95619321, +0.617053866)

117reltol = sqrt(epsilon(1._TKG))

118reltol

119+0.345266977E-3

120isClose(data, getFFTI(getFFTF(data)), reltol = reltol)

121T, T, T, T, T, T, T, T, T, T

122call setAsserted(all(isClose(data, getFFTI(getFFTF(data)), reltol = reltol)))

123

124lenData = getUnifRand(5, 11)

125lenData

126+8

127data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

128data

129(+1.2873016607028103, +0.16508843215673585), (+1.8329903926842372, +0.42587912807969264), (+1.4258785236640157, +0.11658408827298850), (+1.0671722806611512, +0.25153721181253175), (+1.9611743157575181, +0.13371095541660016), (+1.2602205143843936, +0.39196299396836742), (+1.2103157305646870, +0.72967201218501632), (+1.5335435270420585, +0.31672340566433121)

130getFFTI(getFFTF(data))

131(+1.2873016607028105, +0.16508843215673585), (+1.8329903926842372, +0.42587912807969269), (+1.4258785236640159, +0.11658408827298855), (+1.0671722806611514, +0.25153721181253180), (+1.9611743157575185, +0.13371095541660016), (+1.2602205143843936, +0.39196299396836748), (+1.2103157305646872, +0.72967201218501621), (+1.5335435270420588, +0.31672340566433127)

132reltol = sqrt(epsilon(1._TKG))

133reltol

134+0.14901161193847656E-7

135isClose(data, getFFTI(getFFTF(data)), reltol = reltol)

136T, T, T, T, T, T, T, T

137call setAsserted(all(isClose(data, getFFTI(getFFTF(data)), reltol = reltol)))

138

139lenData = getUnifRand(5, 11)

140lenData

141+6

142data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

143data

144(+1.35812246747021005199738823565633052, +0.816840770106499451999156599833851879), (+1.92993046880000938469099277619671815, +0.964103924386550140104247862725691656), (+1.11164974579160057278786320500580377, +0.359719380037589930683851567075949264), (+1.61170160036394081969186063693055235, +0.123526239446056477126295493858295503), (+1.14887050029196823243396806303750609, +0.187081923321911801849171188072151937), (+1.10941251257399605077430601288917442, +0.877129891220744738744795492633855708)

145getFFTI(getFFTF(data))

146(+1.35812246747021005199738823565633052, +0.816840770106499451999156599833851783), (+1.92993046880000938469099277619671815, +0.964103924386550140104247862725691656), (+1.11164974579160057278786320500580358, +0.359719380037589930683851567075949360), (+1.61170160036394081969186063693055235, +0.123526239446056477126295493858295467), (+1.14887050029196823243396806303750590, +0.187081923321911801849171188072151961), (+1.10941251257399605077430601288917442, +0.877129891220744738744795492633855708)

147reltol = sqrt(epsilon(1._TKG))

148reltol

149+0.138777878078144567552953958511352539E-16

150isClose(data, getFFTI(getFFTF(data)), reltol = reltol)

151T, T, T, T, T, T

152call setAsserted(all(isClose(data, getFFTI(getFFTF(data)), reltol = reltol)))

153

154lenData = getUnifRand(5, 11)

155lenData

156+6

157data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

158data

159+1.81022394, +1.21831799, +1.03354335, +1.82940269, +1.05461729, +1.47110808

160getFFTF(data)

161+8.41721344, +0.281454027, +0.237173304, +1.25083327, +0.200672165, -0.620444298

162getFFTF(cmplx(data, kind = TKG))

163(+8.41721344, +0.00000000), (+0.281453997, +0.237173185), (+1.25083303, +0.200672075), (-0.620444179, +0.372529030E-7), (+1.25083303, -0.200672075), (+0.281453907, -0.237173229)

164getFFTI(getFFTF(data))

165+1.81022394, +1.21831799, +1.03354335, +1.82940280, +1.05461729, +1.47110832

166getFFTI(getFFTF(cmplx(data, kind = TKG)))

167(+1.81022394, -0.124176347E-8), (+1.21831810, -0.161429252E-7), (+1.03354347, +0.271404872E-7), (+1.82940269, +0.159646163E-7), (+1.05461740, -0.727227123E-8), (+1.47110820, -0.184481426E-7)

168reltol = sqrt(epsilon(1._TKG))

169reltol

170+0.345266977E-3

171isClose(data, getFFTI(getFFTF(data)), reltol = reltol)

172T, T, T, T, T, T

173call setAsserted(all(isClose(data, getFFTI(getFFTF(data)), reltol = reltol)))

174

175lenData = getUnifRand(5, 11)

176lenData

177+7

178data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

179data

180+1.6877273227986480, +1.8662472608576652, +1.2953250661586628, +1.5649115742010631, +1.7123636108150095, +1.1136053042752727, +1.7349234753745797

181getFFTF(data)

182+10.975103614480901, +0.44426020247824827, -0.21585969695614776, +0.75936783427269705, -0.16446861862213275, -0.78413421419612694, +0.22885008194954778

183getFFTF(cmplx(data, kind = TKG))

184(+10.975103614480901, +0.0000000000000000), (+0.44426020247824871, -0.21585969695614776), (+0.75936783427269727, -0.16446861862213266), (-0.78413421419612817, +0.22885008194954767), (-0.78413421419612817, -0.22885008194954767), (+0.75936783427269727, +0.16446861862213266), (+0.44426020247824871, +0.21585969695614776)

185getFFTI(getFFTF(data))

186+1.6877273227986480, +1.8662472608576648, +1.2953250661586633, +1.5649115742010624, +1.7123636108150091, +1.1136053042752729, +1.7349234753745792

187getFFTI(getFFTF(cmplx(data, kind = TKG)))

188(+1.6877273227986480, +0.0000000000000000), (+1.8662472608576650, +0.0000000000000000), (+1.2953250661586628, +0.0000000000000000), (+1.5649115742010624, +0.0000000000000000), (+1.7123636108150091, +0.0000000000000000), (+1.1136053042752727, +0.0000000000000000), (+1.7349234753745795, +0.0000000000000000)

189reltol = sqrt(epsilon(1._TKG))

190reltol

191+0.14901161193847656E-7

192isClose(data, getFFTI(getFFTF(data)), reltol = reltol)

193T, T, T, T, T, T, T

194call setAsserted(all(isClose(data, getFFTI(getFFTF(data)), reltol = reltol)))

195

196lenData = getUnifRand(5, 11)

197lenData

198+8

199data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

200data

201+1.61914537357424413539835045170324887, +1.20402708834020014294988727873580287, +1.90942145360377714246287661280087619, +1.62409948019466998410009696799575611, +1.58221034057349833894146951951494547, +1.99102508248787309486122546956044597, +1.93143463557260312918955517778229040, +1.68184086290133939654332213391285887

202getFFTF(data)

203+13.5432043172482053644467836120062259, -0.478727262174311003263290604585065892, +0.619334123677829961373452496206300892, -0.639500375028637797312611819364972439, +0.110888172267936142832306353612365940, +0.552597328175802596177052468961672695, +0.575307759740177987920095366243472474, +0.541219289400040127537719911596497104

204getFFTF(cmplx(data, kind = TKG))

205(+13.5432043172482053644467836120062259, +0.00000000000000000000000000000000000), (-0.478727262174311003263290604585065892, +0.619334123677829961373452496206300892), (-0.639500375028637797312611819364972439, +0.110888172267936142832306353612365940), (+0.552597328175802596177052468961672598, +0.575307759740177987920095366243472570), (+0.541219289400040127537719911596497104, +0.00000000000000000000000000000000000), (+0.552597328175802596177052468961672695, -0.575307759740177987920095366243472474), (-0.639500375028637797312611819364972439, -0.110888172267936142832306353612365940), (-0.478727262174311003263290604585065796, -0.619334123677829961373452496206300989)

206getFFTI(getFFTF(data))

207+1.61914537357424413539835045170324906, +1.20402708834020014294988727873580306, +1.90942145360377714246287661280087619, +1.62409948019466998410009696799575630, +1.58221034057349833894146951951494566, +1.99102508248787309486122546956044597, +1.93143463557260312918955517778229059, +1.68184086290133939654332213391285906

208getFFTI(getFFTF(cmplx(data, kind = TKG)))

209(+1.61914537357424413539835045170324906, +0.00000000000000000000000000000000000), (+1.20402708834020014294988727873580306, -0.108350606829402246200904653637676773E-34), (+1.90942145360377714246287661280087619, +0.00000000000000000000000000000000000), (+1.62409948019466998410009696799575630, -0.120200146947999946150939677738811856E-35), (+1.58221034057349833894146951951494566, +0.00000000000000000000000000000000000), (+1.99102508248787309486122546956044597, +0.132390636219002235431092589185439153E-34), (+1.93143463557260312918955517778229059, +0.00000000000000000000000000000000000), (+1.68184086290133939654332213391285906, -0.120200146947999946150939677738811856E-35)

210reltol = sqrt(epsilon(1._TKG))

211reltol

212+0.138777878078144567552953958511352539E-16

213isClose(data, getFFTI(getFFTF(data)), reltol = reltol)

214T, T, T, T, T, T, T, T

215call setAsserted(all(isClose(data, getFFTI(getFFTF(data)), reltol = reltol)))

216

217lenData = getUnifRand(5, 11)

218lenData

219+10

220data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

221data

222(+1.52937317, +0.611593425), (+1.11563897, +0.744267941), (+1.91574693, +0.109144449E-1), (+1.23989487, +0.365248919), (+1.04607272, +0.142463207), (+1.32786751, +0.175406218), (+1.17816067, +0.492155671), (+1.35010159, +0.402815759), (+1.45186448, +0.958017945), (+1.07411742, +0.661279857)

223getFFTI(getFFTF(data))

224(+1.52937305, +0.611593425), (+1.11563909, +0.744267941), (+1.91574705, +0.109144691E-1), (+1.23989499, +0.365248919), (+1.04607284, +0.142463252), (+1.32786739, +0.175406113), (+1.17816091, +0.492155612), (+1.35010183, +0.402815729), (+1.45186460, +0.958017945), (+1.07411754, +0.661279857)

225reltol = sqrt(epsilon(1._TKG))

226reltol

227+0.345266977E-3

228isClose(data, getFFTI(getFFTF(data)), reltol = reltol)

229T, T, T, T, T, T, T, T, T, T

230call setAsserted(all(isClose(data, getFFTI(getFFTF(data)), reltol = reltol)))

231

232lenData = getUnifRand(5, 11)

233lenData

234+10

235data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

236data

237(+1.5579835428276509, +0.60342515664803786), (+1.8212757199928022, +0.31297921699278397), (+1.4809901106723280, +0.48431340641187104), (+1.2369247567644677, +0.35342813029943176), (+1.5629378795264639, +0.63421326984553761), (+1.1300946481767118, +0.70186982341054427), (+1.1869067279996601, +0.94694260100124439), (+1.7112508772496828, +0.51933114672504432), (+1.9118252671646478, +0.43822712582658963), (+1.8208118860010849, +0.74387815112035094)

238getFFTI(getFFTF(data))

239(+1.5579835428276514, +0.60342515664803797), (+1.8212757199928025, +0.31297921699278380), (+1.4809901106723280, +0.48431340641187104), (+1.2369247567644679, +0.35342813029943165), (+1.5629378795264639, +0.63421326984553761), (+1.1300946481767120, +0.70186982341054438), (+1.1869067279996601, +0.94694260100124450), (+1.7112508772496833, +0.51933114672504421), (+1.9118252671646474, +0.43822712582658963), (+1.8208118860010849, +0.74387815112035094)

240reltol = sqrt(epsilon(1._TKG))

241reltol

242+0.14901161193847656E-7

243isClose(data, getFFTI(getFFTF(data)), reltol = reltol)

244T, T, T, T, T, T, T, T, T, T

245call setAsserted(all(isClose(data, getFFTI(getFFTF(data)), reltol = reltol)))

246

247lenData = getUnifRand(5, 11)

248lenData

249+11

250data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

251data

252(+1.09102632283523799444037602325832972, +0.817754749272559526016832445401952289), (+1.43037286084032752834667360975339728, +0.206249727057588135964548132393017447), (+1.24650435764316188791599737396385978, +0.326348681950039759322688366271152057), (+1.60752618934052214673409811015022407, +0.719008117390192223588679881651369912), (+1.05911084007507555531056681073473419, +0.192042609359491784364551675359272206), (+1.25009609667148097608596399700856438, +0.232718957573458947739998687103017485), (+1.73870330569369192046741196629056863, +0.554464848270990824464296916735782306), (+1.64223479300377657756451942402213175, +0.479708852976604401340702404159327875), (+1.30693214611148999492110626674076501, +0.585579536253301620877538449193880373), (+1.98522002110761335818841218712504626, +0.612425308075019463504947992696451844), (+1.41903368352170193348402924198903008, +0.982280368408265137192280227062103770)

253getFFTI(getFFTF(data))

254(+1.09102632283523799444037602325832934, +0.817754749272559526016832445401952385), (+1.43037286084032752834667360975339747, +0.206249727057588135964548132393017471), (+1.24650435764316188791599737396385978, +0.326348681950039759322688366271152105), (+1.60752618934052214673409811015022426, +0.719008117390192223588679881651370105), (+1.05911084007507555531056681073473381, +0.192042609359491784364551675359272230), (+1.25009609667148097608596399700856457, +0.232718957573458947739998687103017485), (+1.73870330569369192046741196629056901, +0.554464848270990824464296916735782402), (+1.64223479300377657756451942402213155, +0.479708852976604401340702404159327971), (+1.30693214611148999492110626674076521, +0.585579536253301620877538449193880470), (+1.98522002110761335818841218712504626, +0.612425308075019463504947992696451940), (+1.41903368352170193348402924198903027, +0.982280368408265137192280227062103867)

255reltol = sqrt(epsilon(1._TKG))

256reltol

257+0.138777878078144567552953958511352539E-16

258isClose(data, getFFTI(getFFTF(data)), reltol = reltol)

259T, T, T, T, T, T, T, T, T, T, T

260call setAsserted(all(isClose(data, getFFTI(getFFTF(data)), reltol = reltol)))

261

262lenData = getUnifRand(5, 11)

263lenData

264+7

265data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

266data

267+1.41285288, +1.22124147, +1.76275432, +1.06383920, +1.40564048, +1.01384842, +1.75190532

268getFFTF(data)

269+9.63208199, +0.423803329, -0.166937515, -0.210672021, +0.575066149, -0.841874480E-1, +1.14899611

270getFFTF(cmplx(data, kind = TKG))

271(+9.63208199, +0.00000000), (+0.423803091, -0.166937545), (-0.210671425, +0.575066209), (-0.841867924E-1, +1.14899600), (-0.841867924E-1, -1.14899600), (-0.210671425, -0.575066209), (+0.423803091, +0.166937545)

272getFFTI(getFFTF(data))

273+1.41285288, +1.22124159, +1.76275420, +1.06383920, +1.40564036, +1.01384842, +1.75190556

274getFFTI(getFFTF(cmplx(data, kind = TKG)))

275(+1.41285336, +0.00000000), (+1.22124135, +0.00000000), (+1.76275420, +0.00000000), (+1.06383932, +0.00000000), (+1.40564048, +0.00000000), (+1.01384854, +0.00000000), (+1.75190520, +0.00000000)

276reltol = sqrt(epsilon(1._TKG))

277reltol

278+0.345266977E-3

279isClose(data, getFFTI(getFFTF(data)), reltol = reltol)

280T, T, T, T, T, T, T

281call setAsserted(all(isClose(data, getFFTI(getFFTF(data)), reltol = reltol)))

282

283lenData = getUnifRand(5, 11)

284lenData

285+5

286data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

287data

288+1.9771999813286913, +1.1125870761256931, +1.6452455899212712, +1.4043949461569349, +1.5484889931314831

289getFFTF(data)

290+7.6879165866640733, +0.33230668963165000, +0.27299890222408080, +0.76673497035804195, +0.48527929246797574

291getFFTF(cmplx(data, kind = TKG))

292(+7.6879165866640733, +0.0000000000000000), (+0.33230668963165000, +0.27299890222408080), (+0.76673497035804195, +0.48527929246797574), (+0.76673497035804195, -0.48527929246797574), (+0.33230668963165000, -0.27299890222408080)

293getFFTI(getFFTF(data))

294+1.9771999813286918, +1.1125870761256931, +1.6452455899212712, +1.4043949461569349, +1.5484889931314834

295getFFTI(getFFTF(cmplx(data, kind = TKG)))

296(+1.9771999813286918, +0.0000000000000000), (+1.1125870761256931, +0.0000000000000000), (+1.6452455899212712, +0.0000000000000000), (+1.4043949461569349, +0.0000000000000000), (+1.5484889931314834, +0.0000000000000000)

297reltol = sqrt(epsilon(1._TKG))

298reltol

299+0.14901161193847656E-7

300isClose(data, getFFTI(getFFTF(data)), reltol = reltol)

301T, T, T, T, T

302call setAsserted(all(isClose(data, getFFTI(getFFTF(data)), reltol = reltol)))

303

304lenData = getUnifRand(5, 11)

305lenData

306+8

307data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

308data

309+1.50378782018398580325428367229299325, +1.40588795441137902718268083824114261, +1.91132070443048554956477405805852728, +1.77572813164737960027737790004925900, +1.09253052179062686754519085146756255, +1.73166426948215097766866248558681775, +1.03050499676491728536113515445208611, +1.05010279905489394894003616692223109

310getFFTF(data)

311+11.5015271977658190597941411270706197, -0.332195936420039693612526619630545242, -1.16355165940595068116902662483261738, -0.345507359220790164126434688750057590, -0.311721293191256455633929256856470267, +1.15471053320675756503071226128140664, +0.598079755925185847238251182380264961, -0.425239111425788048343373654528280478

312getFFTF(cmplx(data, kind = TKG))

313(+11.5015271977658190597941411270706197, +0.00000000000000000000000000000000000), (-0.332195936420039693612526619630545194, -1.16355165940595068116902662483261738), (-0.345507359220790164126434688750057590, -0.311721293191256455633929256856470267), (+1.15471053320675756503071226128140664, +0.598079755925185847238251182380265153), (-0.425239111425788048343373654528280478, +0.00000000000000000000000000000000000), (+1.15471053320675756503071226128140664, -0.598079755925185847238251182380264961), (-0.345507359220790164126434688750057590, +0.311721293191256455633929256856470267), (-0.332195936420039693612526619630545290, +1.16355165940595068116902662483261719)

314getFFTI(getFFTF(data))

315+1.50378782018398580325428367229299345, +1.40588795441137902718268083824114242, +1.91132070443048554956477405805852728, +1.77572813164737960027737790004925900, +1.09253052179062686754519085146756275, +1.73166426948215097766866248558681755, +1.03050499676491728536113515445208611, +1.05010279905489394894003616692223109

316getFFTI(getFFTF(cmplx(data, kind = TKG)))

317(+1.50378782018398580325428367229299345, +0.00000000000000000000000000000000000), (+1.40588795441137902718268083824114242, -0.274531091399294768388453203420177028E-34), (+1.91132070443048554956477405805852728, +0.00000000000000000000000000000000000), (+1.77572813164737960027737790004925900, +0.154160469875092527572454582008619071E-34), (+1.09253052179062686754519085146756275, +0.00000000000000000000000000000000000), (+1.73166426948215097766866248558681755, +0.206951394697514194875541282226054802E-34), (+1.03050499676491728536113515445208611, +0.00000000000000000000000000000000000), (+1.05010279905489394894003616692223109, -0.865807731733119540595426608144968443E-35)

318reltol = sqrt(epsilon(1._TKG))

319reltol

320+0.138777878078144567552953958511352539E-16

321isClose(data, getFFTI(getFFTF(data)), reltol = reltol)

322T, T, T, T, T, T, T, T

323call setAsserted(all(isClose(data, getFFTI(getFFTF(data)), reltol = reltol)))

324

325lenData = getUnifRand(5, 11)

326lenData

327+7

328data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

329data

330(+1.36101508, +0.788269222), (+1.30688977, +0.332791388), (+1.71389198, +0.193755150), (+1.31971192, +0.694915354), (+1.22592103, +0.227993727), (+1.30582786, +0.850414097), (+1.26622248, +0.262608409)

331getFFTI(getFFTF(data))

332(+1.36101556, +0.788269341), (+1.30688977, +0.332791239), (+1.71389186, +0.193755224), (+1.31971192, +0.694915414), (+1.22592103, +0.227993876), (+1.30582774, +0.850414097), (+1.26622236, +0.262608379)

333reltol = sqrt(epsilon(1._TKG))

334reltol

335+0.345266977E-3

336isClose(data, getFFTI(getFFTF(data)), reltol = reltol)

337T, T, T, T, T, T, T

338call setAsserted(all(isClose(data, getFFTI(getFFTF(data)), reltol = reltol)))

339

340lenData = getUnifRand(5, 11)

341lenData

342+7

343data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

344data

345(+1.5461340038437839, +0.18773812612390139), (+1.6842876454069304, +0.63358258473945994), (+1.4436233571317494, +0.33172281381478819), (+1.6029711214686682, +0.25789954233520163), (+1.5406228733155571, +0.32354055560988515), (+1.4639702266173042, +0.90262390325072550E-1), (+1.4470603430116242, +0.77196930849858325)

346getFFTI(getFFTF(data))

347(+1.5461340038437834, +0.18773812612390156), (+1.6842876454069304, +0.63358258473945994), (+1.4436233571317494, +0.33172281381478830), (+1.6029711214686677, +0.25789954233520157), (+1.5406228733155567, +0.32354055560988515), (+1.4639702266173042, +0.90262390325072633E-1), (+1.4470603430116242, +0.77196930849858314)

348reltol = sqrt(epsilon(1._TKG))

349reltol

350+0.14901161193847656E-7

351isClose(data, getFFTI(getFFTF(data)), reltol = reltol)

352T, T, T, T, T, T, T

353call setAsserted(all(isClose(data, getFFTI(getFFTF(data)), reltol = reltol)))

354

355lenData = getUnifRand(5, 11)

356lenData

357+7

358data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

359data

360(+1.64294974422416703843133969876822584, +0.441438593307731449195871638545195848), (+1.84338410726523072627904335817738281, +0.648425942246592719532020936695459654), (+1.20907998989869295007702562501427352, +0.519502169668440983389386432802197096), (+1.29522866356001058630696140098118986, +0.332864848194502922336705549165352682), (+1.58767544594666017957722221916576944, +0.849846048122833698939232153112488511), (+1.15325812378029330013968422037496184, +0.591513836826836621960673272511245011), (+1.03275349016232867124259853329889971, +0.711478113500873654600039151164568001)

361getFFTI(getFFTF(data))

362(+1.64294974422416703843133969876822584, +0.441438593307731449195871638545195945), (+1.84338410726523072627904335817738281, +0.648425942246592719532020936695459751), (+1.20907998989869295007702562501427352, +0.519502169668440983389386432802197096), (+1.29522866356001058630696140098118967, +0.332864848194502922336705549165352538), (+1.58767544594666017957722221916576924, +0.849846048122833698939232153112488415), (+1.15325812378029330013968422037496184, +0.591513836826836621960673272511245011), (+1.03275349016232867124259853329889952, +0.711478113500873654600039151164568097)

363reltol = sqrt(epsilon(1._TKG))

364reltol

365+0.138777878078144567552953958511352539E-16

366isClose(data, getFFTI(getFFTF(data)), reltol = reltol)

367T, T, T, T, T, T, T

368call setAsserted(all(isClose(data, getFFTI(getFFTF(data)), reltol = reltol)))

369

370lenData = getUnifRand(5, 11)

371lenData

372+11

373data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

374data

375+1.09827006, +1.94380343, +1.56084466, +1.73355579, +1.46036911, +1.22790742, +1.82479024, +1.06183362, +1.51450348, +1.78785431, +1.18730807

376getFFTF(data)

377+16.4010391, +0.804471970E-1, -0.552351415, -0.701294422, -0.383075833, -1.08837473, -0.377865285, +0.151801109, -1.57007265, -0.602615952, +0.451919526

378getFFTF(cmplx(data, kind = TKG))

379(+16.4010391, +0.00000000), (+0.804469585E-1, -0.552351415), (-0.701293945, -0.383075774), (-1.08837438, -0.377865106), (+0.151800871, -1.57007265), (-0.602614284, +0.451919556), (-0.602614284, -0.451919556), (+0.151800871, +1.57007265), (-1.08837438, +0.377865106), (-0.701293945, +0.383075774), (+0.804469585E-1, +0.552351415)

380getFFTI(getFFTF(data))

381+1.09826970, +1.94380367, +1.56084406, +1.73355579, +1.46036875, +1.22790802, +1.82479072, +1.06183338, +1.51450336, +1.78785396, +1.18730831

382getFFTI(getFFTF(cmplx(data, kind = TKG)))

383(+1.09827006, +0.00000000), (+1.94380331, +0.00000000), (+1.56084430, +0.00000000), (+1.73355544, +0.00000000), (+1.46036875, +0.00000000), (+1.22790778, +0.00000000), (+1.82479072, +0.00000000), (+1.06183338, +0.00000000), (+1.51450336, +0.00000000), (+1.78785419, +0.00000000), (+1.18730795, +0.00000000)

384reltol = sqrt(epsilon(1._TKG))

385reltol

386+0.345266977E-3

387isClose(data, getFFTI(getFFTF(data)), reltol = reltol)

388T, T, T, T, T, T, T, T, T, T, T

389call setAsserted(all(isClose(data, getFFTI(getFFTF(data)), reltol = reltol)))

390

391lenData = getUnifRand(5, 11)

392lenData

393+7

394data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

395data

396+1.4819008839638541, +1.7001441875833683, +1.5912171888584496, +1.3411205106844764, +1.1616507577449191, +1.8480897518883932, +1.9207482760795624

397getFFTF(data)

398+11.044871556803022, +0.71925361973188151, +0.34503844565514524, -0.86207960732864342, +0.24393535829113155, -0.19295669693125994, -0.28008460151086417

399getFFTF(cmplx(data, kind = TKG))

400(+11.044871556803022, +0.0000000000000000), (+0.71925361973188151, +0.34503844565514513), (-0.86207960732864208, +0.24393535829113144), (-0.19295669693126050, -0.28008460151086401), (-0.19295669693126050, +0.28008460151086401), (-0.86207960732864208, -0.24393535829113144), (+0.71925361973188151, -0.34503844565514513)

401getFFTI(getFFTF(data))

402+1.4819008839638537, +1.7001441875833683, +1.5912171888584499, +1.3411205106844759, +1.1616507577449182, +1.8480897518883934, +1.9207482760795624

403getFFTI(getFFTF(cmplx(data, kind = TKG)))

404(+1.4819008839638539, +0.0000000000000000), (+1.7001441875833683, +0.0000000000000000), (+1.5912171888584494, +0.0000000000000000), (+1.3411205106844761, +0.0000000000000000), (+1.1616507577449191, +0.0000000000000000), (+1.8480897518883928, +0.0000000000000000), (+1.9207482760795624, +0.0000000000000000)

405reltol = sqrt(epsilon(1._TKG))

406reltol

407+0.14901161193847656E-7

408isClose(data, getFFTI(getFFTF(data)), reltol = reltol)

409T, T, T, T, T, T, T

410call setAsserted(all(isClose(data, getFFTI(getFFTF(data)), reltol = reltol)))

411

412lenData = getUnifRand(5, 11)

413lenData

414+7

415data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

416data

417+1.29652883795269382248986026196638047, +1.51408256786813238831622765311911293, +1.15833658555863191984873501639751566, +1.49578943242343641015870213694515006, +1.47612605706554453449077216742969664, +1.42371606782959479027324972854606710, +1.39415276331144604964466337211749074

418getFFTF(data)

419+9.75873231200947991522221033652141283, -0.142380193674461442197634654982471309, +0.156429348873713767907951535193333792, +0.175995539588620471718340621195495321, -0.216693310111245530595503229129635583, -0.375130569084470608417300217591399549, -0.278687999557315208259567907633228986

420getFFTF(cmplx(data, kind = TKG))

421(+9.75873231200947991522221033652141283, +0.00000000000000000000000000000000000), (-0.142380193674461442197634654982470924, +0.156429348873713767907951535193333792), (+0.175995539588620471718340621195495513, -0.216693310111245530595503229129635535), (-0.375130569084470608417300217591399356, -0.278687999557315208259567907633228938), (-0.375130569084470608417300217591399356, +0.278687999557315208259567907633228938), (+0.175995539588620471718340621195495513, +0.216693310111245530595503229129635535), (-0.142380193674461442197634654982470924, -0.156429348873713767907951535193333792)

422getFFTI(getFFTF(data))

423+1.29652883795269382248986026196638009, +1.51408256786813238831622765311911254, +1.15833658555863191984873501639751547, +1.49578943242343641015870213694515006, +1.47612605706554453449077216742969645, +1.42371606782959479027324972854606691, +1.39415276331144604964466337211749036

424getFFTI(getFFTF(cmplx(data, kind = TKG)))

425(+1.29652883795269382248986026196638028, +0.00000000000000000000000000000000000), (+1.51408256786813238831622765311911293, +0.00000000000000000000000000000000000), (+1.15833658555863191984873501639751547, +0.00000000000000000000000000000000000), (+1.49578943242343641015870213694514967, +0.00000000000000000000000000000000000), (+1.47612605706554453449077216742969645, +0.00000000000000000000000000000000000), (+1.42371606782959479027324972854606691, +0.00000000000000000000000000000000000), (+1.39415276331144604964466337211749055, +0.00000000000000000000000000000000000)

426reltol = sqrt(epsilon(1._TKG))

427reltol

428+0.138777878078144567552953958511352539E-16

429isClose(data, getFFTI(getFFTF(data)), reltol = reltol)

430T, T, T, T, T, T, T

431call setAsserted(all(isClose(data, getFFTI(getFFTF(data)), reltol = reltol)))

432

433lenData = getUnifRand(5, 11)

434lenData

435+5

436data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

437data

438(+1.84127951, +0.312046468), (+1.61808658, +0.195453227), (+1.78725553, +0.869305968), (+1.94271827, +0.816134095), (+1.97408986, +0.976683080)

439getFFTI(getFFTF(data))

440(+1.84127927, +0.312046379), (+1.61808670, +0.195453286), (+1.78725564, +0.869306087), (+1.94271839, +0.816134155), (+1.97408986, +0.976683140)

441reltol = sqrt(epsilon(1._TKG))

442reltol

443+0.345266977E-3

444isClose(data, getFFTI(getFFTF(data)), reltol = reltol)

445T, T, T, T, T

446call setAsserted(all(isClose(data, getFFTI(getFFTF(data)), reltol = reltol)))

447

448lenData = getUnifRand(5, 11)

449lenData

450+8

451data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

452data

453(+1.7596382562032997, +0.69812149496674825), (+1.0243392729070080, +0.72065185068512394), (+1.6158880993398164, +0.71924619251023003), (+1.3174256042059684, +0.91848281455658598E-1), (+1.6477429927493774, +0.30492738173010037), (+1.0734050771531951, +0.62906641826615417), (+1.3057953934721858, +0.98041281815040737), (+1.8593169191734686, +0.47942545706314466)

454getFFTI(getFFTF(data))

455(+1.7596382562032995, +0.69812149496674814), (+1.0243392729070080, +0.72065185068512394), (+1.6158880993398164, +0.71924619251022981), (+1.3174256042059684, +0.91848281455658487E-1), (+1.6477429927493772, +0.30492738173010026), (+1.0734050771531951, +0.62906641826615417), (+1.3057953934721858, +0.98041281815040726), (+1.8593169191734686, +0.47942545706314466)

456reltol = sqrt(epsilon(1._TKG))

457reltol

458+0.14901161193847656E-7

459isClose(data, getFFTI(getFFTF(data)), reltol = reltol)

460T, T, T, T, T, T, T, T

461call setAsserted(all(isClose(data, getFFTI(getFFTF(data)), reltol = reltol)))

462

463lenData = getUnifRand(5, 11)

464lenData

465+5

466data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

467data

468(+1.44040461200878120915042350190060879, +0.924607714851226801448614270567289011), (+1.74361935003476398229178067231922682, +0.294821015817620662276946100442257440), (+1.98210726252160574667286997692192449, +0.191582787265808034546885688851576128), (+1.17109916915748884656303247360408785, +0.236530774363450737315745495666113231), (+1.03074561670585863346333366635338972, +0.118771869672068773697547866049543301)

469getFFTI(getFFTF(data))

470(+1.44040461200878120915042350190060860, +0.924607714851226801448614270567289107), (+1.74361935003476398229178067231922682, +0.294821015817620662276946100442257440), (+1.98210726252160574667286997692192449, +0.191582787265808034546885688851576128), (+1.17109916915748884656303247360408804, +0.236530774363450737315745495666113231), (+1.03074561670585863346333366635338953, +0.118771869672068773697547866049543301)

471reltol = sqrt(epsilon(1._TKG))

472reltol

473+0.138777878078144567552953958511352539E-16

474isClose(data, getFFTI(getFFTF(data)), reltol = reltol)

475T, T, T, T, T

476call setAsserted(all(isClose(data, getFFTI(getFFTF(data)), reltol = reltol)))

477

478lenData = getUnifRand(5, 11)

479lenData

480+5

481data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

482data

483+1.42326653, +1.27218866, +1.98083615, +1.87721300, +1.74493527

484getFFTF(data)

485+8.29843998, -0.765618563, +0.388700604, +0.174564362, +0.376424938

486getFFTF(cmplx(data, kind = TKG))

487(+8.29843998, +0.00000000), (-0.765618563, +0.388700604), (+0.174564362, +0.376424938), (+0.174564362, -0.376424938), (-0.765618563, -0.388700604)

488getFFTI(getFFTF(data))

489+1.42326629, +1.27218878, +1.98083627, +1.87721312, +1.74493539

490getFFTI(getFFTF(cmplx(data, kind = TKG)))

491(+1.42326629, +0.00000000), (+1.27218878, +0.00000000), (+1.98083627, +0.00000000), (+1.87721312, +0.00000000), (+1.74493539, +0.00000000)

492reltol = sqrt(epsilon(1._TKG))

493reltol

494+0.345266977E-3

495isClose(data, getFFTI(getFFTF(data)), reltol = reltol)

496T, T, T, T, T

497call setAsserted(all(isClose(data, getFFTI(getFFTF(data)), reltol = reltol)))

498

499lenData = getUnifRand(5, 11)

500lenData

501+5

502data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

503data

504+1.0546952647132146, +1.4044371849577799, +1.5515966496795492, +1.9130698622650300, +1.0551799218662694

505getFFTF(data)

506+6.9789788834818438, -0.98821533762774960, -0.11969477247006430, +0.13546405766986536, -0.54906972279678690

507getFFTF(cmplx(data, kind = TKG))

508(+6.9789788834818438, +0.0000000000000000), (-0.98821533762774960, -0.11969477247006430), (+0.13546405766986536, -0.54906972279678690), (+0.13546405766986536, +0.54906972279678690), (-0.98821533762774960, +0.11969477247006430)

509getFFTI(getFFTF(data))

510+1.0546952647132153, +1.4044371849577804, +1.5515966496795492, +1.9130698622650302, +1.0551799218662696

511getFFTI(getFFTF(cmplx(data, kind = TKG)))

512(+1.0546952647132153, +0.0000000000000000), (+1.4044371849577804, +0.0000000000000000), (+1.5515966496795492, +0.0000000000000000), (+1.9130698622650302, +0.0000000000000000), (+1.0551799218662696, +0.0000000000000000)

513reltol = sqrt(epsilon(1._TKG))

514reltol

515+0.14901161193847656E-7

516isClose(data, getFFTI(getFFTF(data)), reltol = reltol)

517T, T, T, T, T

518call setAsserted(all(isClose(data, getFFTI(getFFTF(data)), reltol = reltol)))

519

520lenData = getUnifRand(5, 11)

521lenData

522+11

523data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

524data

525+1.13798357243188471846978881380190435, +1.57301668421122624776416989289771849, +1.86297648605203739394217199992518790, +1.43427768626068571356495805849810268, +1.81683762880228069712830452872656057, +1.11277395615051322656763231718767288, +1.84098308896093961002361837047410652, +1.28378089494844782387123241415030410, +1.70947089778060736340053612454012680, +1.07182750620217080530061216447087480, +1.34464716545860504646283515901534593

526getFFTF(data)

527+16.1885755672593986464958598436879043, -0.500344291825488479311256373915709878, -0.768425345856134642689407295519436115, -0.544673109503414530059883590109138357, -0.749242208834071458131838049017545070, -0.113099956449841141053883871320766927, +0.867434232074922876019039269148341461E-2, -0.293643136530606628403668185220356949, -0.532950228647081767638067569456027322E-1, -0.383617640944982592835399425367504039, +1.77704792952563765231174798914096997

528getFFTF(cmplx(data, kind = TKG))

529(+16.1885755672593986464958598436879043, +0.00000000000000000000000000000000000), (-0.500344291825488479311256373915710648, -0.768425345856134642689407295519436212), (-0.544673109503414530059883590109137587, -0.749242208834071458131838049017544877), (-0.113099956449841141053883871320767890, +0.867434232074922876019039269148312572E-2), (-0.293643136530606628403668185220356372, -0.532950228647081767638067569456023470E-1), (-0.383617640944982592835399425367506350, +1.77704792952563765231174798914096958), (-0.383617640944982592835399425367506350, -1.77704792952563765231174798914096958), (-0.293643136530606628403668185220356372, +0.532950228647081767638067569456023470E-1), (-0.113099956449841141053883871320767890, -0.867434232074922876019039269148312572E-2), (-0.544673109503414530059883590109137587, +0.749242208834071458131838049017544877), (-0.500344291825488479311256373915710648, +0.768425345856134642689407295519436212)

530getFFTI(getFFTF(data))

531+1.13798357243188471846978881380190454, +1.57301668421122624776416989289771811, +1.86297648605203739394217199992518848, +1.43427768626068571356495805849810211, +1.81683762880228069712830452872656115, +1.11277395615051322656763231718767192, +1.84098308896093961002361837047410614, +1.28378089494844782387123241415030430, +1.70947089778060736340053612454012642, +1.07182750620217080530061216447087480, +1.34464716545860504646283515901534574

532getFFTI(getFFTF(cmplx(data, kind = TKG)))

533(+1.13798357243188471846978881380190435, +0.00000000000000000000000000000000000), (+1.57301668421122624776416989289771869, +0.00000000000000000000000000000000000), (+1.86297648605203739394217199992518809, +0.00000000000000000000000000000000000), (+1.43427768626068571356495805849810249, +0.00000000000000000000000000000000000), (+1.81683762880228069712830452872656096, +0.00000000000000000000000000000000000), (+1.11277395615051322656763231718767249, +0.00000000000000000000000000000000000), (+1.84098308896093961002361837047410614, +0.00000000000000000000000000000000000), (+1.28378089494844782387123241415030449, +0.00000000000000000000000000000000000), (+1.70947089778060736340053612454012680, +0.00000000000000000000000000000000000), (+1.07182750620217080530061216447087480, +0.00000000000000000000000000000000000), (+1.34464716545860504646283515901534612, +0.00000000000000000000000000000000000)

534reltol = sqrt(epsilon(1._TKG))

535reltol

536+0.138777878078144567552953958511352539E-16

537isClose(data, getFFTI(getFFTF(data)), reltol = reltol)

538T, T, T, T, T, T, T, T, T, T, T

539call setAsserted(all(isClose(data, getFFTI(getFFTF(data)), reltol = reltol)))

540

541

Test:: test_pm_fftpack

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.
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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.
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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 746 of file pm_fftpack.F90.

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

src/fortran/main/pm_fftpack.F90