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

See the documentation of pm_fftnr 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 size getExpNext(size(data), 2) of the same type and kind as the input data, containing the FFT result.

Possible calling interfaces ⛓

: use pm_fftnr, only: getFFTF

type_of(data) :: fft(1 : getExpNext(size(data)))

fft(:) = getFFTF(data(:))

pm_fftnr::getFFTF
Generate and return the Forward Fourier Transform (a.k.a. Fourier Analysis) of a periodic sequence of...
Definition: pm_fftnr.F90:250

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

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_fftnr, only: getFFTF, getFFTI

6 use pm_distUnif, only: getUnifRand

7 use pm_mathCompare, only: isClose

8 use pm_err, only: setAsserted

9

10 implicit none

11

12 integer(IK) :: i

13 integer(IK) :: lenData

14 type(display_type) :: disp

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

16

17 do i = 1, 5

18 block

19 use pm_kind, only: TKG => CKS

20 real(TKG) :: reltol

21 complex(TKG), allocatable :: data(:), atad(:)

22 call disp%show("lenData = getUnifRand(5, 100)")

23 lenData = getUnifRand(5, 100)

24 call disp%show("lenData")

25 call disp%show( lenData )

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

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

28 call disp%show("data")

29 call disp%show( data )

30 call disp%skip()

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

32 atad = getFFTI(getFFTF(data))

33 call disp%show("atad")

34 call disp%show( atad )

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

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

37 call disp%show("reltol")

38 call disp%show( reltol )

39 call disp%show("isClose(data, atad(1:size(data)), reltol = reltol)")

40 call disp%show( isClose(data, atad(1:size(data)), reltol = reltol) )

41 call disp%show("call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))")

42 call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

43 call disp%skip()

44 end block

45

46 block

47 use pm_kind, only: TKG => CKD

48 real(TKG) :: reltol

49 complex(TKG), allocatable :: data(:), atad(:)

50 call disp%show("lenData = getUnifRand(5, 100)")

51 lenData = getUnifRand(5, 100)

52 call disp%show("lenData")

53 call disp%show( lenData )

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

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

56 call disp%show("data")

57 call disp%show( data )

58 call disp%skip()

59 call disp%show("atad = getFFTI(getFFTF(data))")

60 atad = getFFTI(getFFTF(data))

61 call disp%show("atad")

62 call disp%show( atad )

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

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

65 call disp%show("reltol")

66 call disp%show( reltol )

67 call disp%show("isClose(data, atad(1:size(data)), reltol = reltol)")

68 call disp%show( isClose(data, atad(1:size(data)), reltol = reltol) )

69 call disp%show("call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))")

70 call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

71 call disp%skip()

72 end block

73

74 block

75 use pm_kind, only: TKG => CKH

76 real(TKG) :: reltol

77 complex(TKG), allocatable :: data(:), atad(:)

78 call disp%show("lenData = getUnifRand(5, 100)")

79 lenData = getUnifRand(5, 100)

80 call disp%show("lenData")

81 call disp%show( lenData )

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

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

84 call disp%show("data")

85 call disp%show( data )

86 call disp%skip()

87 call disp%show("atad = getFFTI(getFFTF(data))")

88 atad = getFFTI(getFFTF(data))

89 call disp%show("atad")

90 call disp%show( atad )

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

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

93 call disp%show("reltol")

94 call disp%show( reltol )

95 call disp%show("isClose(data, atad(1:size(data)), reltol = reltol)")

96 call disp%show( isClose(data, atad(1:size(data)), reltol = reltol) )

97 call disp%show("call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))")

98 call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

99 call disp%skip()

100 end block

101

102 block

103 use pm_kind, only: TKG => RKS

104 real(TKG) :: reltol

105 real(TKG), allocatable :: data(:), atad(:)

106 call disp%show("lenData = getUnifRand(5, 100)")

107 lenData = getUnifRand(5, 100)

108 call disp%show("lenData")

109 call disp%show( lenData )

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

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

112 call disp%show("data")

113 call disp%show( data )

114 call disp%skip()

115 call disp%show("atad = getFFTI(getFFTF(data))")

116 atad = getFFTI(getFFTF(data))

117 call disp%show("atad")

118 call disp%show( atad )

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

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

121 call disp%show("reltol")

122 call disp%show( reltol )

123 call disp%show("isClose(data, atad(1:size(data)), reltol = reltol)")

124 call disp%show( isClose(data, atad(1:size(data)), reltol = reltol) )

125 call disp%show("call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))")

126 call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

127 call disp%skip()

128 end block

129

130 block

131 use pm_kind, only: TKG => RKD

132 real(TKG) :: reltol

133 real(TKG), allocatable :: data(:), atad(:)

134 call disp%show("lenData = getUnifRand(5, 100)")

135 lenData = getUnifRand(5, 100)

136 call disp%show("lenData")

137 call disp%show( lenData )

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

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

140 call disp%show("data")

141 call disp%show( data )

142 call disp%skip()

143 call disp%show("atad = getFFTI(getFFTF(data))")

144 atad = getFFTI(getFFTF(data))

145 call disp%show("atad")

146 call disp%show( atad )

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

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

149 call disp%show("reltol")

150 call disp%show( reltol )

151 call disp%show("isClose(data, atad(1:size(data)), reltol = reltol)")

152 call disp%show( isClose(data, atad(1:size(data)), reltol = reltol) )

153 call disp%show("call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))")

154 call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

155 call disp%skip()

156 end block

157

158 block

159 use pm_kind, only: TKG => RKH

160 real(TKG) :: reltol

161 real(TKG), allocatable :: data(:), atad(:)

162 call disp%show("lenData = getUnifRand(5, 100)")

163 lenData = getUnifRand(5, 100)

164 call disp%show("lenData")

165 call disp%show( lenData )

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

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

168 call disp%show("data")

169 call disp%show( data )

170 call disp%skip()

171 call disp%show("atad = getFFTI(getFFTF(data))")

172 atad = getFFTI(getFFTF(data))

173 call disp%show("atad")

174 call disp%show( atad )

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

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

177 call disp%show("reltol")

178 call disp%show( reltol )

179 call disp%show("isClose(data, atad(1:size(data)), reltol = reltol)")

180 call disp%show( isClose(data, atad(1:size(data)), reltol = reltol) )

181 call disp%show("call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))")

182 call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

183 call disp%skip()

184 end block

185 end do

186

187end 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_fftnr::getFFTI
Generate and return the Inverse (normalized by 2 / size(data)) Fourier Transform of a periodic sequen...
Definition: pm_fftnr.F90:428

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, 100)

2lenData

3+43

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

5data

6(+1.22610283, +0.531929076), (+1.50672483, +0.113173127), (+1.57787108, +0.387748778), (+1.15288997, +0.138619840), (+1.13602591, +0.285096765), (+1.51032066, +0.656002522), (+1.96869683, +0.856448293), (+1.29824543, +0.973886073), (+1.33452177, +0.608775616E-1), (+1.11668360, +0.786522746), (+1.86529517, +0.513481081), (+1.91050458, +0.284176469), (+1.65234160, +0.381369948), (+1.26110697, +0.666667223E-1), (+1.91385555, +0.230168462), (+1.91270256, +0.491228819), (+1.11699486, +0.692375600), (+1.79472351, +0.231518626), (+1.78486383, +0.223636329), (+1.89976621, +0.431723118), (+1.51349592, +0.833250165), (+1.29661226, +0.254572213), (+1.45832992, +0.763734698), (+1.80193830, +0.809514403), (+1.48805082, +0.137460053), (+1.82525253, +0.291980863), (+1.70809603, +0.464283347), (+1.07688093, +0.219451487), (+1.45338416, +0.394091487), (+1.35029352, +0.689985752E-1), (+1.38296986, +0.877215922), (+1.45688701, +0.780933917), (+1.55621552, +0.449297249), (+1.69865882, +0.916604519), (+1.28527904, +0.333553910), (+1.63160300, +0.300880969), (+1.44069242, +0.141880095), (+1.69595540, +0.727841377), (+1.87780070, +0.160028219), (+1.15625668, +0.647285461), (+1.86651635, +0.636300445), (+1.11574149, +0.293062329E-1), (+1.19483376, +0.277564347)

7

8atad = getFFTI(getFFTF(data))

9atad

10(+1.22610271, +0.531929076), (+1.50672483, +0.113173246), (+1.57787061, +0.387748778), (+1.15288973, +0.138619900), (+1.13602579, +0.285096705), (+1.51032066, +0.656002581), (+1.96869683, +0.856448174), (+1.29824519, +0.973885894), (+1.33452177, +0.608775616E-1), (+1.11668372, +0.786522627), (+1.86529493, +0.513481140), (+1.91050422, +0.284176677), (+1.65234137, +0.381370068), (+1.26110709, +0.666670650E-1), (+1.91385555, +0.230168685), (+1.91270232, +0.491228938), (+1.11699486, +0.692375541), (+1.79472351, +0.231518656), (+1.78486371, +0.223636225), (+1.89976633, +0.431722850), (+1.51349580, +0.833250046), (+1.29661238, +0.254572093), (+1.45832992, +0.763734698), (+1.80193841, +0.809514284), (+1.48805070, +0.137460113), (+1.82525229, +0.291980863), (+1.70809579, +0.464283347), (+1.07688081, +0.219451487), (+1.45338392, +0.394091606), (+1.35029340, +0.689986199E-1), (+1.38296962, +0.877215981), (+1.45688689, +0.780933857), (+1.55621541, +0.449297249), (+1.69865894, +0.916604280), (+1.28527904, +0.333554089), (+1.63160324, +0.300880849), (+1.44069231, +0.141880214), (+1.69595528, +0.727841318), (+1.87780070, +0.160028368), (+1.15625691, +0.647285342), (+1.86651611, +0.636300385), (+1.11574149, +0.293061435E-1), (+1.19483376, +0.277564228), (+0.476837158E-6, +0.298023224E-7), (+0.596046448E-7, -0.163912773E-6), (+0.00000000, -0.197440386E-6), (+0.238418579E-6, -0.104308128E-6), (+0.178813934E-6, -0.119209290E-6), (-0.596046448E-7, +0.298023224E-7), (+0.00000000, +0.521540642E-7), (+0.119209290E-6, +0.134110451E-6), (+0.119209290E-6, +0.208616257E-6), (-0.119209290E-6, -0.298023224E-7), (+0.00000000, +0.00000000), (+0.596046448E-7, +0.298023224E-7), (+0.119209290E-6, +0.208616257E-6), (+0.119209290E-6, -0.119209290E-6), (+0.178813934E-6, +0.745058060E-7), (-0.596046448E-7, +0.178813934E-6), (+0.238418579E-6, +0.186264515E-6), (+0.178813934E-6, -0.745058060E-7), (+0.178813934E-6, +0.484287739E-7), (+0.596046448E-7, +0.119209290E-6), (+0.119209290E-6, +0.00000000)

11reltol = sqrt(epsilon(1._TKG))

12reltol

13+0.345266977E-3

14isClose(data, atad(1:size(data)), reltol = reltol)

15T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

16call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

17

18lenData = getUnifRand(5, 100)

19lenData

20+42

21data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

22data

23(+1.1620747881130982, +0.65629585860341688), (+1.1566716803189609, +0.89600550279393276), (+1.8480974300134523, +0.14175508744477050), (+1.7259279562093468, +0.11750056677947651), (+1.6485205165314998, +0.88118439257305392), (+1.7349157323058941, +0.75939272680536096), (+1.6452701124269453, +0.27055692504611251), (+1.0398946713873192, +0.22762233325616821), (+1.2036279386906843, +0.56313321895755108), (+1.2709478553982203, +0.57601124207539911), (+1.6406813038508161, +0.84263375629950710), (+1.5590824491131494, +0.31402937988185553), (+1.2306104528865931, +0.62959876129759085), (+1.2945244492783337, +0.62838005911804184), (+1.3554638743343386, +0.91509808320251806), (+1.7017995057146562, +0.60821627539865653), (+1.9020249938370752, +0.82639986507564134), (+1.6387319669106066, +0.46857756815844420), (+1.5657415273465247, +0.81288674356700319), (+1.1980121939260444, +0.74415330673755953), (+1.3508377934802325, +0.63158660398840683), (+1.8110203330095187, +0.93014528997120149), (+1.2035883081338925, +0.96848112084969218), (+1.3571515228915025, +0.71719502916811673), (+1.2163089644980491, +0.78545600570893115), (+1.7164093519027825, +0.96425129958129385), (+1.9387121893445898, +0.43793417488492814), (+1.7237077878071843, +0.12448790400220966), (+1.0016315601828478, +0.67013547285426855), (+1.9810300424578762, +0.10077727705697148E-1), (+1.0973463144199824, +0.70761687641418880), (+1.2686412655085610, +0.90980210063570266E-1), (+1.0898622399920972, +0.51538912796669656), (+1.4393711107928113, +0.86615236002912199), (+1.8091781115163237, +0.45356559065738100E-1), (+1.6209759626938940, +0.30166205148120628E-1), (+1.3227703369282218, +0.45742483070230189), (+1.4145486048065150, +0.66984057979333822E-1), (+1.8458524094896780, +0.55947459097604402), (+1.2188368699278658, +0.93521071781545007E-1), (+1.0316469064782963, +0.13548294482737933), (+1.7360860770620525, +0.71031686451715625)

24

25atad = getFFTI(getFFTF(data))

26atad

27(+1.1620747881130982, +0.65629585860341688), (+1.1566716803189607, +0.89600550279393298), (+1.8480974300134521, +0.14175508744477075), (+1.7259279562093466, +0.11750056677947664), (+1.6485205165314998, +0.88118439257305403), (+1.7349157323058941, +0.75939272680536107), (+1.6452701124269451, +0.27055692504611240), (+1.0398946713873192, +0.22762233325616837), (+1.2036279386906843, +0.56313321895755108), (+1.2709478553982199, +0.57601124207539922), (+1.6406813038508159, +0.84263375629950688), (+1.5590824491131494, +0.31402937988185581), (+1.2306104528865931, +0.62959876129759107), (+1.2945244492783337, +0.62838005911804173), (+1.3554638743343383, +0.91509808320251818), (+1.7017995057146558, +0.60821627539865641), (+1.9020249938370752, +0.82639986507564100), (+1.6387319669106062, +0.46857756815844420), (+1.5657415273465247, +0.81288674356700286), (+1.1980121939260449, +0.74415330673755919), (+1.3508377934802325, +0.63158660398840671), (+1.8110203330095187, +0.93014528997120149), (+1.2035883081338927, +0.96848112084969218), (+1.3571515228915030, +0.71719502916811662), (+1.2163089644980494, +0.78545600570893104), (+1.7164093519027825, +0.96425129958129374), (+1.9387121893445896, +0.43793417488492781), (+1.7237077878071840, +0.12448790400220930), (+1.0016315601828480, +0.67013547285426855), (+1.9810300424578760, +0.10077727705696982E-1), (+1.0973463144199824, +0.70761687641418858), (+1.2686412655085610, +0.90980210063569919E-1), (+1.0898622399920972, +0.51538912796669667), (+1.4393711107928111, +0.86615236002912221), (+1.8091781115163239, +0.45356559065738065E-1), (+1.6209759626938938, +0.30166205148120392E-1), (+1.3227703369282215, +0.45742483070230189), (+1.4145486048065150, +0.66984057979333711E-1), (+1.8458524094896780, +0.55947459097604368), (+1.2188368699278660, +0.93521071781544632E-1), (+1.0316469064782963, +0.13548294482737927), (+1.7360860770620521, +0.71031686451715614), (+0.55511151231257827E-15, -0.11102230246251565E-15), (+0.22204460492503131E-15, -0.77715611723760958E-15), (+0.11102230246251565E-15, -0.16653345369377348E-15), (+0.11102230246251565E-15, -0.38857805861880479E-15), (+0.44408920985006262E-15, +0.0000000000000000), (+0.33306690738754696E-15, -0.11102230246251565E-15), (-0.33306690738754696E-15, +0.27755575615628914E-15), (-0.11102230246251565E-15, +0.11102230246251565E-15), (+0.22204460492503131E-15, +0.27755575615628914E-15), (+0.11102230246251565E-15, +0.55511151231257827E-16), (-0.44408920985006262E-15, +0.0000000000000000), (+0.0000000000000000, -0.27755575615628914E-15), (+0.22204460492503131E-15, +0.0000000000000000), (+0.0000000000000000, -0.55511151231257827E-16), (+0.0000000000000000, +0.55511151231257827E-16), (+0.0000000000000000, +0.55511151231257827E-16), (+0.33306690738754696E-15, +0.99920072216264089E-15), (+0.33306690738754696E-15, +0.52735593669694936E-15), (+0.22204460492503131E-15, +0.16653345369377348E-15), (+0.11102230246251565E-15, +0.16653345369377348E-15), (+0.22204460492503131E-15, +0.94368957093138306E-15), (+0.55511151231257827E-15, +0.56898930012039273E-15)

28reltol = sqrt(epsilon(1._TKG))

29reltol

30+0.14901161193847656E-7

31isClose(data, atad(1:size(data)), reltol = reltol)

32T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

33call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

34

35lenData = getUnifRand(5, 100)

36lenData

37+87

38data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

39data

40(+1.14935441743804830080994420561198767, +0.637078236369604748288896435913001583), (+1.25658801809825645855937091113198073, +0.300004466209259342095462670999542789), (+1.73474131150198675206973322404923375, +0.829288317068384522210048909532698304), (+1.60858385354569122537406231947843748, +0.873678953012845293977274152235066722E-1), (+1.24048026367161553667642351951947054, +0.964359592501388038310810674530325560), (+1.36832615616910626638832502838357963, +0.811546454809023951856590853327818836), (+1.63897297435421086497425893749356798, +0.790812921817568560609573672160579997), (+1.90556004104170661136640394238753048, +0.917580730459986105053058880543531848), (+1.64470790038112047333531301904048984, +0.849789119785959512784340967478191185), (+1.62385695875636447062072965370072939, +0.864671864106970241689309463589240435), (+1.90842492931004224973523025279948190, +0.570845437622505149788334965046117523), (+1.38709931583769258192095360565900491, +0.329983185757232606228653917780753655), 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41

42atad = getFFTI(getFFTF(data))

43atad

44(+1.14935441743804830080994420561198767, +0.637078236369604748288896435913001680), (+1.25658801809825645855937091113198111, +0.300004466209259342095462670999542740), (+1.73474131150198675206973322404923432, +0.829288317068384522210048909532698400), (+1.60858385354569122537406231947843767, +0.873678953012845293977274152235062750E-1), (+1.24048026367161553667642351951947054, +0.964359592501388038310810674530325463), (+1.36832615616910626638832502838357963, +0.811546454809023951856590853327818644), (+1.63897297435421086497425893749356798, +0.790812921817568560609573672160579997), (+1.90556004104170661136640394238753086, +0.917580730459986105053058880543531559), (+1.64470790038112047333531301904049003, +0.849789119785959512784340967478191377), (+1.62385695875636447062072965370072997, +0.864671864106970241689309463589240435), (+1.90842492931004224973523025279948171, +0.570845437622505149788334965046117523), (+1.38709931583769258192095360565900530, +0.329983185757232606228653917780753318), 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(+1.97554148184332596518746507859966933, +0.953286884444548899952869020868676943E-1), (+1.15996423712093258099143325500040759, +0.172170441801876549454629065383961982), (+1.83526531292986844066365543336939373, +0.488543149248442333332149105935769899), (+1.86636328762675600780016325926841083, +0.362280800353367077311051822094553977), (+1.65440479630772494570214788778903765, +0.338529110727436478388680976693123189), (+1.40564094327929781474021773228929995, +0.143616037647610247781865045321046099), (+1.99807603096322430802154555432241391, +0.852052650958626159430288715306949225), (+1.27799754743262653700857736699033194, +0.879657657427686260351139798973738094E-1), (+1.51970290448240033434789050213277506, +0.719564428718892928661339986053475411), (+1.31397123325791731190245775446005185, +0.552816742311251720984914829791460839), (+1.59956591847155915457782585056662212, +0.527334738743922235843984963539437976E-1), (+1.30015540386849906413085738840453900, +0.949270263221195293842560822319006704), (+1.82853781762320220914595785489212611, +0.527666880459167842571301304662702080), (+1.41178386886622777648067001443657208, +0.757096485397990127035406978524472558E-1), (+1.63175774985347492563707024925076293, +0.445193710806826279840972662458865242), (+1.63529218656058324825392048616922988, +0.336317760752595435295133662549632208), (+0.288889491658085377958396691387739098E-33, +0.312963615962925826121596415670050689E-33), (-0.192592994438723585305597794258492732E-33, -0.962964972193617926527988971292463659E-34), (-0.192592994438723585305597794258492732E-33, -0.240741243048404481631997242823115915E-33), (-0.385185988877447170611195588516985464E-33, -0.144444745829042688979198345693869549E-33), (-0.192592994438723585305597794258492732E-33, +0.240741243048404481631997242823115915E-33), (-0.192592994438723585305597794258492732E-33, +0.144444745829042688979198345693869549E-33), (-0.481482486096808963263994485646231830E-33, -0.168518870133883137142398069976181140E-33), (-0.962964972193617926527988971292463659E-34, -0.481482486096808963263994485646231830E-34), (-0.192592994438723585305597794258492732E-33, -0.168518870133883137142398069976181140E-33), (-0.192592994438723585305597794258492732E-33, +0.240741243048404481631997242823115915E-34), (+0.00000000000000000000000000000000000, -0.144444745829042688979198345693869549E-33), (+0.962964972193617926527988971292463659E-34, -0.481482486096808963263994485646231830E-34), (-0.288889491658085377958396691387739098E-33, -0.601853107621011204079993107057789787E-34), (+0.00000000000000000000000000000000000, +0.120370621524202240815998621411557957E-33), (-0.962964972193617926527988971292463659E-34, +0.481482486096808963263994485646231830E-34), (+0.00000000000000000000000000000000000, -0.481482486096808963263994485646231830E-34), (-0.192592994438723585305597794258492732E-33, +0.216667118743564033468797518540804323E-33), (-0.192592994438723585305597794258492732E-33, -0.264815367353244929795196967105427506E-33), (+0.192592994438723585305597794258492732E-33, -0.240741243048404481631997242823115915E-33), (+0.00000000000000000000000000000000000, -0.240741243048404481631997242823115915E-33), (-0.192592994438723585305597794258492732E-33, -0.433334237487128066937595037081608647E-33), (-0.192592994438723585305597794258492732E-33, -0.481482486096808963263994485646231830E-34), (-0.481482486096808963263994485646231830E-33, -0.385185988877447170611195588516985464E-33), (-0.288889491658085377958396691387739098E-33, +0.00000000000000000000000000000000000), (-0.288889491658085377958396691387739098E-33, -0.625927231925851652243192831340101379E-33), (-0.192592994438723585305597794258492732E-33, -0.144444745829042688979198345693869549E-33), (-0.288889491658085377958396691387739098E-33, -0.240741243048404481631997242823115915E-34), (+0.00000000000000000000000000000000000, -0.337037740267766274284796139952362281E-33), (-0.192592994438723585305597794258492732E-33, -0.433334237487128066937595037081608647E-33), (-0.192592994438723585305597794258492732E-33, +0.144444745829042688979198345693869549E-33), (-0.192592994438723585305597794258492732E-33, +0.00000000000000000000000000000000000), (-0.288889491658085377958396691387739098E-33, -0.481482486096808963263994485646231830E-34), (-0.385185988877447170611195588516985464E-33, -0.962964972193617926527988971292463659E-34), (+0.00000000000000000000000000000000000, -0.337037740267766274284796139952362281E-33), (+0.288889491658085377958396691387739098E-33, -0.216667118743564033468797518540804323E-33), (+0.00000000000000000000000000000000000, -0.240741243048404481631997242823115915E-33), (-0.288889491658085377958396691387739098E-33, -0.722223729145213444895991728469347744E-33), (-0.288889491658085377958396691387739098E-33, -0.144444745829042688979198345693869549E-33), (-0.288889491658085377958396691387739098E-33, -0.529630734706489859590393934210855013E-33), (-0.288889491658085377958396691387739098E-33, -0.288889491658085377958396691387739098E-33), (-0.385185988877447170611195588516985464E-33, -0.625927231925851652243192831340101379E-33)

45reltol = sqrt(epsilon(1._TKG))

46reltol

47+0.138777878078144567552953958511352539E-16

48isClose(data, atad(1:size(data)), reltol = reltol)

49T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

50call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

51

52lenData = getUnifRand(5, 100)

53lenData

54+41

55data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

56data

57+1.54436719, +1.67511988, +1.80173755, +1.74204075, +1.21986794, +1.37581718, +1.58353329, +1.67617750, +1.51793587, +1.23355579, +1.14201403, +1.23705959, +1.21898568, +1.28429163, +1.10392451, +1.32709694, +1.05594337, +1.60828340, +1.79305005, +1.49384618, +1.99763346, +1.25128388, +1.69864094, +1.22022438, +1.16590202, +1.53152716, +1.95031309, +1.72486997, +1.18633699, +1.86355066, +1.32441092, +1.38986468, +1.03907573, +1.45192719, +1.29805136, +1.54822350, +1.24316263, +1.88864470, +1.69047093, +1.89972067, +1.88040042

58

59atad = getFFTI(getFFTF(data))

60atad

61+1.54436731, +1.67512000, +1.80173731, +1.74204051, +1.21986783, +1.37581742, +1.58353317, +1.67617738, +1.51793587, +1.23355567, +1.14201379, +1.23705947, +1.21898556, +1.28429174, +1.10392451, +1.32709718, +1.05594337, +1.60828352, +1.79304981, +1.49384606, +1.99763322, +1.25128388, +1.69864082, +1.22022450, +1.16590190, +1.53152704, +1.95031285, +1.72486973, +1.18633676, +1.86355042, +1.32441068, +1.38986468, +1.03907561, +1.45192707, +1.29805136, +1.54822314, +1.24316227, +1.88864458, +1.69047105, +1.89972055, +1.88040054, +0.00000000, +0.178813934E-6, +0.357627869E-6, +0.596046448E-7, +0.00000000, +0.238418579E-6, +0.298023224E-6, -0.119209290E-6, +0.596046448E-7, -0.596046448E-7, +0.357627869E-6, +0.00000000, -0.596046448E-7, +0.178813934E-6, +0.119209290E-6, +0.178813934E-6, +0.119209290E-6, +0.00000000, +0.178813934E-6, +0.238418579E-6, +0.00000000, +0.238418579E-6, +0.178813934E-6

62reltol = sqrt(epsilon(1._TKG))

63reltol

64+0.345266977E-3

65isClose(data, atad(1:size(data)), reltol = reltol)

66T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

67call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

68

69lenData = getUnifRand(5, 100)

70lenData

71+93

72data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

73data

74+1.1311613269545113, +1.1203545855745103, +1.6899399545822074, +1.5998470161217644, +1.5992605951426131, +1.6281893913915364, +1.8134255976606994, +1.7445975942063283, +1.2394521546313291, +1.8389530673276819, +1.7606576321024030, +1.6264670310591420, +1.6622855099605220, +1.2650971282101460, +1.0722852611435241, +1.5341650357256702, +1.2291463999197578, +1.1037480197768517, +1.1684472617035104, +1.5491730614299679, +1.9124158410257754, +1.1801568843506056, +1.5639156683856645, +1.3439404056221167, +1.7080393170675183, +1.6587431912698385, +1.3199421282897668, +1.5734067026720147, +1.4779903490408941, +1.3840427707633334, +1.3904449624760660, +1.9151868830219114, +1.6081346696611312, +1.9984102775325308, +1.5833220748422676, +1.9925690927539539, +1.4120264725326694, +1.0697512595976160, +1.6913240766978657, +1.1900273280062925, +1.1736251092864942, +1.9093077599492116, +1.2694584035730054, +1.6448362611490999, +1.1326828885896048, +1.1336436607548523, +1.4539837674469753, +1.1272150913114729, +1.4590158421139905, +1.1315573694024881, +1.5285283826747487, +1.0067247212837707, +1.0129371561818725, +1.1458927628336526, +1.1483890439247364, +1.1261738841454478, +1.7645660299817352, +1.7639994263471483, +1.4019523597888961, +1.1736072669421875, +1.9903129936933825, +1.0284152781848777, +1.1034905692471335, +1.6134454487084886, +1.3010926784204337, +1.5867550501718708, +1.0845625972105626, +1.1536541774581188, +1.2799402398239512, +1.7384314744962086, +1.7399496293178922, +1.6338412712692678, +1.4347449709809414, +1.9195641266758563, +1.5211315922007329, +1.7298121676781903, +1.5399893668521598, +1.4057583388727120, +1.9761764138903464, +1.4956710839481806, +1.2310263044366632, +1.4755348946076994, +1.4414732273580988, +1.8082717681095586, +1.7699916089160244, +1.0272536579641156, +1.4817990796475655, +1.1718840803538120, +1.2637973435212007, +1.3188381328788128, +1.9308246575812609, +1.7310769491515707, +1.8758019243574693

75

76atad = getFFTI(getFFTF(data))

77atad

78+1.1311613269545115, +1.1203545855745101, +1.6899399545822076, +1.5998470161217653, +1.5992605951426129, +1.6281893913915364, +1.8134255976606986, +1.7445975942063290, +1.2394521546313289, +1.8389530673276819, +1.7606576321024030, +1.6264670310591423, +1.6622855099605218, +1.2650971282101466, +1.0722852611435241, +1.5341650357256704, +1.2291463999197578, +1.1037480197768519, +1.1684472617035104, +1.5491730614299681, +1.9124158410257750, +1.1801568843506058, +1.5639156683856641, +1.3439404056221171, +1.7080393170675181, +1.6587431912698387, +1.3199421282897663, +1.5734067026720149, +1.4779903490408937, +1.3840427707633336, +1.3904449624760655, +1.9151868830219119, +1.6081346696611316, +1.9984102775325305, +1.5833220748422678, +1.9925690927539543, +1.4120264725326694, +1.0697512595976160, +1.6913240766978657, +1.1900273280062927, +1.1736251092864942, +1.9093077599492116, +1.2694584035730054, +1.6448362611491003, +1.1326828885896045, +1.1336436607548523, +1.4539837674469758, +1.1272150913114731, +1.4590158421139905, +1.1315573694024881, +1.5285283826747484, +1.0067247212837707, +1.0129371561818727, +1.1458927628336526, +1.1483890439247366, +1.1261738841454474, +1.7645660299817352, +1.7639994263471481, +1.4019523597888963, +1.1736072669421880, +1.9903129936933825, +1.0284152781848774, +1.1034905692471340, +1.6134454487084882, +1.3010926784204337, +1.5867550501718708, +1.0845625972105626, +1.1536541774581193, +1.2799402398239514, +1.7384314744962084, +1.7399496293178920, +1.6338412712692680, +1.4347449709809414, +1.9195641266758561, +1.5211315922007329, +1.7298121676781903, +1.5399893668521603, +1.4057583388727124, +1.9761764138903466, +1.4956710839481808, +1.2310263044366634, +1.4755348946076994, +1.4414732273580988, +1.8082717681095584, +1.7699916089160248, +1.0272536579641156, +1.4817990796475662, +1.1718840803538120, +1.2637973435212009, +1.3188381328788126, +1.9308246575812602, +1.7310769491515707, +1.8758019243574693, +0.0000000000000000, +0.12212453270876722E-14, +0.11102230246251565E-15, -0.11102230246251565E-15, +0.33306690738754696E-15, +0.11102230246251565E-15, +0.22204460492503131E-15, +0.55511151231257827E-15, +0.22204460492503131E-15, -0.11102230246251565E-15, +0.44408920985006262E-15, -0.22204460492503131E-15, -0.22204460492503131E-15, -0.11102230246251565E-15, -0.33306690738754696E-15, -0.11102230246251565E-15, +0.55511151231257827E-15, +0.11102230246251565E-15, +0.11102230246251565E-15, +0.11102230246251565E-15, +0.33306690738754696E-15, +0.33306690738754696E-15, +0.33306690738754696E-15, +0.22204460492503131E-15, +0.44408920985006262E-15, +0.33306690738754696E-15, +0.66613381477509392E-15, +0.0000000000000000, +0.22204460492503131E-15, +0.66613381477509392E-15, +0.0000000000000000, -0.33306690738754696E-15, +0.66613381477509392E-15, -0.44408920985006262E-15, +0.12212453270876722E-14

79reltol = sqrt(epsilon(1._TKG))

80reltol

81+0.14901161193847656E-7

82isClose(data, atad(1:size(data)), reltol = reltol)

83T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

84call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

85

86lenData = getUnifRand(5, 100)

87lenData

88+61

89data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

90data

91+1.18737479394263284624763774655655649, +1.96681088944344663602063462625535154, +1.20727776823117998822692651728821707, +1.44679265214550610125233814693371947, +1.50654197404042696821637649766165417, +1.22542895338698040334738560514964633, +1.36881973084483564510746616882840849, +1.01975266808557817688580156101771005, +1.89103631053063157114770340422370953, +1.25591922008833080399877481198908042, +1.91900646329554869861323614714047626, +1.22916068200770668584841933952714104, +1.38197021810241496501256560072989512, +1.65810118351164230757723856385065321, +1.97708194113688963323560152419709867, +1.57837214250497249070696568562830452, +1.88758823701695121168673520650257289, +1.33308704585671116984763869193580769, +1.79300022123389284973994518466338785, +1.25545709882330241690432674091913729, +1.10287380861209554064746906000883649, +1.02286175571527581987961047290969593, +1.40777745425203943359203039175347942, +1.98548886956635474559974921222868446, +1.73275448770388882901923459303983929, +1.00808089895799414220557347622605943, +1.63846432913459501656523761737401175, +1.99143719787459100488366544077692568, +1.60089135423368264325704194886863632, +1.30135734597136262357908280715570749, +1.37888501826304681739884037613971545, +1.32196056230373907130908455326499301, +1.34153808461993497779601605740239843, +1.18869839574103835555595801998829407, +1.30830864166708133907120702109342378, +1.05196111380667844515522248512827417, +1.61380781329876307677672726865606462, +1.04628531917938954623676138953718927, +1.77706962681773841842348591391217744, +1.94343084013282789435689456035056212, +1.28195084657294985141943388808696873, +1.95159764608899291569414457833268167, +1.16608264017753803484101287054385687, +1.61722476256767297737230197175387699, +1.70173235012807276351956338824558155, +1.70164925075832112083846680504495558, +1.07530243197197328253799457143035248, +1.84303710472026150787394825035241976, +1.23685949653177198356284720747784705, +1.02941062808169672964661157181292539, +1.20417032537950272044454207166678964, +1.98940230442055783440297666959186626, +1.76500991684770477068349716745308171, +1.26566583151949360829912687653769411, +1.65372891661228905998792497127092436, +1.28447823672296987679096917297768468, +1.96174361308922859396489299624025293, +1.27108409033575567352552036903679174, +1.28832157434670073965711895422441730, +1.59115690549739796861866598748442892, +1.06284119482231845238610339875625588

92

93atad = getFFTI(getFFTF(data))

94atad

95+1.18737479394263284624763774655655649, +1.96681088944344663602063462625535154, +1.20727776823117998822692651728821687, +1.44679265214550610125233814693371966, +1.50654197404042696821637649766165417, +1.22542895338698040334738560514964652, +1.36881973084483564510746616882840849, +1.01975266808557817688580156101771005, +1.89103631053063157114770340422370953, +1.25591922008833080399877481198908042, +1.91900646329554869861323614714047587, +1.22916068200770668584841933952714065, +1.38197021810241496501256560072989512, +1.65810118351164230757723856385065341, +1.97708194113688963323560152419709906, +1.57837214250497249070696568562830472, +1.88758823701695121168673520650257289, +1.33308704585671116984763869193580808, +1.79300022123389284973994518466338746, +1.25545709882330241690432674091913729, +1.10287380861209554064746906000883649, +1.02286175571527581987961047290969555, +1.40777745425203943359203039175347942, +1.98548886956635474559974921222868446, +1.73275448770388882901923459303983929, +1.00808089895799414220557347622605943, +1.63846432913459501656523761737401136, +1.99143719787459100488366544077692549, +1.60089135423368264325704194886863613, +1.30135734597136262357908280715570749, +1.37888501826304681739884037613971545, +1.32196056230373907130908455326499282, +1.34153808461993497779601605740239863, +1.18869839574103835555595801998829407, +1.30830864166708133907120702109342359, +1.05196111380667844515522248512827398, +1.61380781329876307677672726865606462, +1.04628531917938954623676138953718908, +1.77706962681773841842348591391217744, +1.94343084013282789435689456035056231, +1.28195084657294985141943388808696873, +1.95159764608899291569414457833268205, +1.16608264017753803484101287054385668, +1.61722476256767297737230197175387680, +1.70173235012807276351956338824558174, +1.70164925075832112083846680504495597, +1.07530243197197328253799457143035286, +1.84303710472026150787394825035241996, +1.23685949653177198356284720747784724, +1.02941062808169672964661157181292558, +1.20417032537950272044454207166678945, +1.98940230442055783440297666959186626, +1.76500991684770477068349716745308190, +1.26566583151949360829912687653769411, +1.65372891661228905998792497127092436, +1.28447823672296987679096917297768507, +1.96174361308922859396489299624025293, +1.27108409033575567352552036903679174, +1.28832157434670073965711895422441730, +1.59115690549739796861866598748442873, +1.06284119482231845238610339875625608, -0.288889491658085377958396691387739098E-33, +0.192592994438723585305597794258492732E-33, -0.385185988877447170611195588516985464E-33

96reltol = sqrt(epsilon(1._TKG))

97reltol

98+0.138777878078144567552953958511352539E-16

99isClose(data, atad(1:size(data)), reltol = reltol)

100T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

101call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

102

103lenData = getUnifRand(5, 100)

104lenData

105+57

106data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

107data

108(+1.54075491, +0.902749419), (+1.34111166, +0.266981125E-1), (+1.05799675, +0.166626573), (+1.06345236, +0.348644793), (+1.17796874, +0.443990290), (+1.79555643, +0.952303410), (+1.54819632, +0.921253681), (+1.88730156, +0.181934416), (+1.61842346, +0.655233622), (+1.23532259, +0.686792552), (+1.95509529, +0.535051823), (+1.81165338, +0.468168795), (+1.13565934, +0.934073329), (+1.39617646, +0.120104790), (+1.38969660, +0.933817387), (+1.68233681, +0.407180011), (+1.14305270, +0.612009466), (+1.07393169, +0.851728439), (+1.59510684, +0.219424248), (+1.50089741, +0.598864138), (+1.76777494, +0.133679807), (+1.96495366, +0.373612106), (+1.75637138, +0.869031250), (+1.58567333, +0.323964357E-1), (+1.16225791, +0.923814774E-1), (+1.92718589, +0.751026273), (+1.76004922, +0.370367050), (+1.61628175, +0.590242028), (+1.26842856, +0.804258227), (+1.46244955, +0.557377219), (+1.59802747, +0.656306565), (+1.25359225, +0.923976600), (+1.81711245, +0.360808313), (+1.69342864, +0.909801602), (+1.14226651, +0.999750257), (+1.75681829, +0.290049732), (+1.54860556, +0.450418055), (+1.21762204, +0.254657745), (+1.36939609, +0.516232014), (+1.26068425, +0.844050527), (+1.34981513, +0.271499276), (+1.44870806, +0.567358196), (+1.93663347, +0.108224094), (+1.46544743, +0.379599214), (+1.98785973, +0.304197907), (+1.02525651, +0.247622728), (+1.34182072, +0.242203593), (+1.90912056, +0.682979226), (+1.85114896, +0.886762738), (+1.46406746, +0.388016403), (+1.99342561, +0.288657606), (+1.27739930, +0.327388883), (+1.41740954, +0.675259590), (+1.29089379, +0.545636833), (+1.89759135, +0.298986495), (+1.59926867, +0.536249280), (+1.33112216, +0.144910336)

109

110atad = getFFTI(getFFTF(data))

111atad

112(+1.54075480, +0.902749419), (+1.34111166, +0.266982317E-1), (+1.05799663, +0.166626573), (+1.06345189, +0.348644853), (+1.17796898, +0.443990231), (+1.79555643, +0.952303290), (+1.54819643, +0.921253562), (+1.88730133, +0.181934297), (+1.61842322, +0.655233562), (+1.23532271, +0.686792552), (+1.95509517, +0.535051823), (+1.81165326, +0.468168855), (+1.13565934, +0.934073329), (+1.39617658, +0.120105051), (+1.38969684, +0.933817506), (+1.68233681, +0.407179981), (+1.14305258, +0.612009466), (+1.07393181, +0.851728439), (+1.59510672, +0.219424322), (+1.50089741, +0.598864138), (+1.76777506, +0.133679777), (+1.96495366, +0.373612106), (+1.75637138, +0.869031191), (+1.58567309, +0.323963761E-1), (+1.16225779, +0.923814625E-1), (+1.92718577, +0.751026154), (+1.76004910, +0.370366991), (+1.61628151, +0.590241790), (+1.26842856, +0.804258227), (+1.46244955, +0.557377219), (+1.59802747, +0.656306505), (+1.25359225, +0.923976541), (+1.81711221, +0.360808283), (+1.69342875, +0.909801483), (+1.14226663, +0.999750257), (+1.75681794, +0.290049613), (+1.54860568, +0.450418055), (+1.21762216, +0.254657745), (+1.36939633, +0.516232014), (+1.26068413, +0.844050467), (+1.34981489, +0.271499217), (+1.44870806, +0.567358077), (+1.93663323, +0.108224049), (+1.46544731, +0.379599094), (+1.98785961, +0.304198146), (+1.02525663, +0.247622699), (+1.34182072, +0.242203593), (+1.90912032, +0.682979107), (+1.85114884, +0.886762679), (+1.46406758, +0.388016343), (+1.99342549, +0.288657606), (+1.27739930, +0.327388883), (+1.41740966, +0.675259590), (+1.29089403, +0.545636773), (+1.89759147, +0.298986584), (+1.59926867, +0.536249220), (+1.33112204, +0.144910350), (+0.417232513E-6, -0.894069672E-7), (+0.536441803E-6, +0.134110451E-6), (+0.476837158E-6, +0.119209290E-6), (+0.238418579E-6, -0.149011612E-6), (+0.357627869E-6, -0.894069672E-7), (+0.417232513E-6, +0.894069672E-7), (+0.596046448E-7, -0.298023224E-7)

113reltol = sqrt(epsilon(1._TKG))

114reltol

115+0.345266977E-3

116isClose(data, atad(1:size(data)), reltol = reltol)

117T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

118call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

119

120lenData = getUnifRand(5, 100)

121lenData

122+58

123data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

124data

125(+1.0755413830011786, +0.17206821849351550), (+1.0669200356336392, +0.15813029480170238), (+1.0561993064760036, +0.50413575680906608), (+1.6138551657899425, +0.15936153523884222E-1), (+1.1223534384203293, +0.82784867623835845), (+1.8262506221155328, +0.58198209780247545), (+1.6131456230765862, +0.35906192344227983E-1), (+1.6596210286419755, +0.76259380555379064), (+1.4940686908851848, +0.38388446769174855), (+1.9003511546865666, +0.61428054504030860), (+1.5884948558500644, +0.51490901137154033), (+1.8772654369034680, +0.98853357789572860), (+1.1993402365111328, +0.57928163354630713), (+1.8132639509057817, +0.19183853389101313), (+1.6536632272145129, +0.47268683829203406), (+1.8727269792317682, +0.12634287421966595E-1), (+1.4413204059044504, +0.65679637580082328), (+1.1258216886973065, +0.90395318229763366), (+1.9306105523255486, +0.34366997000546839), (+1.6865010675201462, +0.15930904901437548), (+1.0156983888679498, +0.74187689643304711), (+1.2735437299324996, +0.36610097173314737), (+1.9368145228794167, +0.17343597729930538), (+1.6864413059798899, +0.43194766322492306), (+1.1416560422594553, +0.93168432371257837), (+1.5094833716165534, +0.47758647810445853), (+1.3834333931247871, +0.56849904954987540E-2), (+1.0250963227572942, +0.60121429208327226), (+1.0976543840605166, +0.64033752762227447E-1), (+1.0343448227904330, +0.54933954451726041), (+1.7925866995134601, +0.79560572735508672), (+1.3711068550753902, +0.82031368147771844), (+1.7268135109073603, +0.38895812368566451), (+1.4214530358414330, +0.76088587882119652), (+1.9501897780602220, +0.72674247738831610), (+1.8626737249813570, +0.89808088974358835), (+1.2694715431819428, +0.55182519244544403), (+1.1044834981103655, +0.16849114410046118), (+1.2540431813573560, +0.53852852264122575), (+1.1709654928321411, +0.77652691629393511), (+1.4665851443387923, +0.52927917825318305), (+1.4278725643992833, +0.15297605630314559), (+1.3189469539208003, +0.27742009220090369), (+1.2224380528629188, +0.52481574841219458), (+1.6250666900237696, +0.87114115613532517), (+1.0879112208758932, +0.56588751863159370), (+1.4667071766292574, +0.38779053097114069), (+1.2701210472138558, +0.12724509819607599E-1), (+1.9538522834397849, +0.46392754421445892), (+1.4928564501061015, +0.90427998724338798), (+1.5564492315629228, +0.47724095076666084), (+1.8784633940429789, +0.82873445334760110), (+1.5921400702271744, +0.78747232272442780), (+1.8960894472387975, +0.20560471904225663), (+1.0758988984513604, +0.22525622820238944), (+1.5285534663155267, +0.26065880786827722), (+1.6549611623632301, +0.19457486113691558), (+1.4878074140217328, +0.17533408358261371)

126

127atad = getFFTI(getFFTF(data))

128atad

129(+1.0755413830011789, +0.17206821849351542), (+1.0669200356336397, +0.15813029480170215), (+1.0561993064760038, +0.50413575680906608), (+1.6138551657899425, +0.15936153523884500E-1), (+1.1223534384203298, +0.82784867623835834), (+1.8262506221155328, +0.58198209780247567), (+1.6131456230765862, +0.35906192344228038E-1), (+1.6596210286419755, +0.76259380555379053), (+1.4940686908851848, +0.38388446769174867), (+1.9003511546865666, +0.61428054504030882), (+1.5884948558500644, +0.51490901137154044), (+1.8772654369034678, +0.98853357789572882), (+1.1993402365111328, +0.57928163354630724), (+1.8132639509057815, +0.19183853389101346), (+1.6536632272145129, +0.47268683829203456), (+1.8727269792317682, +0.12634287421967233E-1), (+1.4413204059044511, +0.65679637580082317), (+1.1258216886973065, +0.90395318229763355), (+1.9306105523255483, +0.34366997000546834), (+1.6865010675201459, +0.15930904901437548), (+1.0156983888679501, +0.74187689643304722), (+1.2735437299324994, +0.36610097173314748), (+1.9368145228794167, +0.17343597729930504), (+1.6864413059798902, +0.43194766322492290), (+1.1416560422594555, +0.93168432371257848), (+1.5094833716165534, +0.47758647810445842), (+1.3834333931247871, +0.56849904954987540E-2), (+1.0250963227572947, +0.60121429208327171), (+1.0976543840605169, +0.64033752762227281E-1), (+1.0343448227904330, +0.54933954451726019), (+1.7925866995134601, +0.79560572735508628), (+1.3711068550753902, +0.82031368147771799), (+1.7268135109073606, +0.38895812368566451), (+1.4214530358414335, +0.76088587882119640), (+1.9501897780602222, +0.72674247738831577), (+1.8626737249813570, +0.89808088974358835), (+1.2694715431819432, +0.55182519244544403), (+1.1044834981103655, +0.16849114410046107), (+1.2540431813573565, +0.53852852264122575), (+1.1709654928321416, +0.77652691629393489), (+1.4665851443387925, +0.52927917825318316), (+1.4278725643992833, +0.15297605630314554), (+1.3189469539208005, +0.27742009220090369), (+1.2224380528629191, +0.52481574841219436), (+1.6250666900237696, +0.87114115613532495), (+1.0879112208758930, +0.56588751863159337), (+1.4667071766292574, +0.38779053097114052), (+1.2701210472138560, +0.12724509819607793E-1), (+1.9538522834397853, +0.46392754421445870), (+1.4928564501061015, +0.90427998724338787), (+1.5564492315629230, +0.47724095076666057), (+1.8784633940429794, +0.82873445334760099), (+1.5921400702271746, +0.78747232272442769), (+1.8960894472387975, +0.20560471904225663), (+1.0758988984513609, +0.22525622820238933), (+1.5285534663155271, +0.26065880786827694), (+1.6549611623632303, +0.19457486113691558), (+1.4878074140217330, +0.17533408358261371), (+0.77715611723760958E-15, +0.44408920985006262E-15), (+0.77715611723760958E-15, +0.27755575615628914E-15), (+0.66613381477509392E-15, -0.16653345369377348E-15), (+0.11102230246251565E-15, +0.0000000000000000), (+0.44408920985006262E-15, +0.66613381477509392E-15), (+0.77715611723760958E-15, +0.33306690738754696E-15)

130reltol = sqrt(epsilon(1._TKG))

131reltol

132+0.14901161193847656E-7

133isClose(data, atad(1:size(data)), reltol = reltol)

134T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

135call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

136

137lenData = getUnifRand(5, 100)

138lenData

139+26

140data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

141data

142(+1.18949417321395666207237933754019015, +0.529588163159611287565903604995394086), (+1.36048062014479515000817247163113171, +0.419747533576677330363951359977742763), (+1.59058695073499981616131924287529969, +0.569692146346138138492356725831913682), (+1.65489270600210777182351080691553418, +0.209638469585927150198547559741401825), (+1.72190956704412421273053388745927987, +0.879915183095360283155065966682692589), (+1.40070127584756410127499494640729897, +0.854254418604338810037843313180201194), (+1.84472072944800305868921361968628135, +0.330731348610765178050635297049434271), (+1.20308753108444227924944365982545670, +0.840993222610602158711699471061877555), (+1.93044291007985466688141658517035488, +0.510907758025305731949265497373047307), (+1.70809676936365983199448188637496009, +0.547227478744077437356203311228127396E-1), (+1.42832338529943503048315760046105284, +0.780595203333762215811444093337814307), (+1.90365749290013304973949326337915660, +0.963986892541299553058643861828993254), (+1.56321029018656239480352410802608703, +0.463469929070112599439103289120904258), (+1.10654613133692274315581231982182439, +0.874261116505962751140111122269511743), (+1.98977684432166411016487914900241876, +0.163348187751458893868753450860129030), (+1.67059725308677158919883672234850651, +0.947609290084581527598183430279275531), (+1.28285003033919294719545556889737209, +0.671960690680748365034436698350670304), (+1.81601562479048497205552610720259424, +0.368838311581866897859430633414115077), (+1.24658194320515394074421263793592131, +0.556803601785528672525673594049099276), (+1.14159174533087401960018520415120766, +0.221856783943081552836232697256293468), (+1.53074255224335871686295243742398419, +0.576469039820298051244363588516839980E-1), (+1.86442732394315826926293979951115544, +0.218960457199986888435702414043702711), (+1.47129960071038759888256252088930661, +0.415682576340558233202987204892107219), (+1.94571881882562062525345448339194790, +0.249476141712095321052204086415658417), (+1.62949484934647969879201067878599684, +0.380017202007280570906513473592207225), (+1.13237415665038647942407561842118751, +0.882006011751083121745002581758279757)

143

144atad = getFFTI(getFFTF(data))

145atad

146(+1.18949417321395666207237933754018976, +0.529588163159611287565903604995394086), (+1.36048062014479515000817247163113152, +0.419747533576677330363951359977742812), (+1.59058695073499981616131924287529989, +0.569692146346138138492356725831913682), (+1.65489270600210777182351080691553456, +0.209638469585927150198547559741401632), (+1.72190956704412421273053388745928006, +0.879915183095360283155065966682692589), (+1.40070127584756410127499494640729897, +0.854254418604338810037843313180201001), (+1.84472072944800305868921361968628135, +0.330731348610765178050635297049434319), (+1.20308753108444227924944365982545670, +0.840993222610602158711699471061877651), (+1.93044291007985466688141658517035450, +0.510907758025305731949265497373047307), (+1.70809676936365983199448188637496009, +0.547227478744077437356203311228128359E-1), (+1.42832338529943503048315760046105265, +0.780595203333762215811444093337814307), (+1.90365749290013304973949326337915679, +0.963986892541299553058643861828993447), (+1.56321029018656239480352410802608684, +0.463469929070112599439103289120904162), (+1.10654613133692274315581231982182439, +0.874261116505962751140111122269511839), (+1.98977684432166411016487914900241857, +0.163348187751458893868753450860129126), (+1.67059725308677158919883672234850612, +0.947609290084581527598183430279275724), (+1.28285003033919294719545556889737189, +0.671960690680748365034436698350670401), (+1.81601562479048497205552610720259443, +0.368838311581866897859430633414115029), (+1.24658194320515394074421263793592131, +0.556803601785528672525673594049099469), (+1.14159174533087401960018520415120766, +0.221856783943081552836232697256293612), (+1.53074255224335871686295243742398438, +0.576469039820298051244363588516839980E-1), (+1.86442732394315826926293979951115544, +0.218960457199986888435702414043702711), (+1.47129960071038759888256252088930661, +0.415682576340558233202987204892107171), (+1.94571881882562062525345448339194771, +0.249476141712095321052204086415658417), (+1.62949484934647969879201067878599665, +0.380017202007280570906513473592207273), (+1.13237415665038647942407561842118751, +0.882006011751083121745002581758279564), (-0.192592994438723585305597794258492732E-33, -0.481482486096808963263994485646231830E-34), (+0.192592994438723585305597794258492732E-33, -0.144444745829042688979198345693869549E-33), (+0.962964972193617926527988971292463659E-34, +0.240741243048404481631997242823115915E-34), (+0.00000000000000000000000000000000000, +0.00000000000000000000000000000000000), (-0.962964972193617926527988971292463659E-34, -0.288889491658085377958396691387739098E-33), (+0.192592994438723585305597794258492732E-33, +0.481482486096808963263994485646231830E-34)

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

148reltol

149+0.138777878078144567552953958511352539E-16

150isClose(data, atad(1:size(data)), reltol = reltol)

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

152call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

153

154lenData = getUnifRand(5, 100)

155lenData

156+61

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

158data

159+1.35942876, +1.93164742, +1.10042310, +1.90382242, +1.55297971, +1.72515547, +1.84496474, +1.69391561, +1.25007725, +1.64773464, +1.02833319, +1.63574290, +1.94827437, +1.06451178, +1.14697480, +1.79786229, +1.29033828, +1.60345328, +1.75608671, +1.13393354, +1.46604943, +1.85667872, +1.87688231, +1.83545411, +1.73954391, +1.70850801, +1.73772168, +1.88497901, +1.44667673, +1.31763709, +1.34403515, +1.20474219, +1.71809030, +1.25402570, +1.01439798, +1.38168383, +1.57722771, +1.42129040, +1.18488383, +1.04788387, +1.03466558, +1.41051078, +1.90075541, +1.88486814, +1.07475424, +1.17726791, +1.69991577, +1.16013503, +1.91691279, +1.31935799, +1.07144022, +1.42948794, +1.25531960, +1.98413575, +1.31893110, +1.08624077, +1.21240246, +1.12690663, +1.98800969, +1.21922445, +1.69166613

160

161atad = getFFTI(getFFTF(data))

162atad

163+1.35942876, +1.93164730, +1.10042310, +1.90382242, +1.55297995, +1.72515512, +1.84496462, +1.69391525, +1.25007737, +1.64773452, +1.02833343, +1.63574278, +1.94827461, +1.06451178, +1.14697480, +1.79786217, +1.29033828, +1.60345292, +1.75608683, +1.13393342, +1.46604943, +1.85667861, +1.87688243, +1.83545375, +1.73954391, +1.70850778, +1.73772156, +1.88497877, +1.44667661, +1.31763685, +1.34403515, +1.20474243, +1.71809018, +1.25402546, +1.01439786, +1.38168383, +1.57722807, +1.42129016, +1.18488395, +1.04788363, +1.03466570, +1.41051066, +1.90075541, +1.88486803, +1.07475424, +1.17726779, +1.69991565, +1.16013515, +1.91691279, +1.31935763, +1.07144022, +1.42948782, +1.25531983, +1.98413551, +1.31893122, +1.08624053, +1.21240258, +1.12690663, +1.98800957, +1.21922445, +1.69166625, +0.00000000, +0.178813934E-6, +0.178813934E-6

164reltol = sqrt(epsilon(1._TKG))

165reltol

166+0.345266977E-3

167isClose(data, atad(1:size(data)), reltol = reltol)

168T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

169call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

170

171lenData = getUnifRand(5, 100)

172lenData

173+44

174data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

175data

176+1.4272589655733410, +1.4909955397287358, +1.4794151357813057, +1.4369736833193318, +1.4673874592624725, +1.0955717092332029, +1.7582492963652965, +1.5684701417038398, +1.3521243116759445, +1.2967895630622328, +1.8028781241533518, +1.2237000013988952, +1.7319466097107643, +1.1312161418876032, +1.0983866269942877, +1.6565141817757665, +1.0732472210522488, +1.5425862748422161, +1.1046405996643833, +1.2982634188757030, +1.2679204446075365, +1.8615623505926471, +1.9381692694039532, +1.6079162439837469, +1.2078999370028347, +1.9695564300293182, +1.9969659099889450, +1.7067543390262756, +1.2750986094636354, +1.1149300539734566, +1.5066386266707734, +1.6749032329642746, +1.0890260364761015, +1.5386283140514254, +1.9341780109211340, +1.9027036040368728, +1.0510894157315813, +1.0219040784710256, +1.3482295594907465, +1.2804801178952592, +1.7907481483022809, +1.4682746838189582, +1.9725553656559565, +1.4517838458357013

177

178atad = getFFTI(getFFTF(data))

179atad

180+1.4272589655733410, +1.4909955397287358, +1.4794151357813050, +1.4369736833193323, +1.4673874592624720, +1.0955717092332029, +1.7582492963652958, +1.5684701417038402, +1.3521243116759445, +1.2967895630622328, +1.8028781241533511, +1.2237000013988955, +1.7319466097107634, +1.1312161418876028, +1.0983866269942872, +1.6565141817757660, +1.0732472210522483, +1.5425862748422157, +1.1046405996643829, +1.2982634188757025, +1.2679204446075361, +1.8615623505926462, +1.9381692694039527, +1.6079162439837467, +1.2078999370028347, +1.9695564300293178, +1.9969659099889441, +1.7067543390262747, +1.2750986094636352, +1.1149300539734557, +1.5066386266707728, +1.6749032329642737, +1.0890260364761013, +1.5386283140514250, +1.9341780109211333, +1.9027036040368723, +1.0510894157315813, +1.0219040784710249, +1.3482295594907463, +1.2804801178952587, +1.7907481483022809, +1.4682746838189580, +1.9725553656559562, +1.4517838458357011, +0.22204460492503131E-15, -0.55511151231257827E-15, +0.33306690738754696E-15, +0.0000000000000000, +0.0000000000000000, -0.33306690738754696E-15, +0.0000000000000000, +0.0000000000000000, -0.22204460492503131E-15, -0.22204460492503131E-15, +0.0000000000000000, +0.44408920985006262E-15, +0.55511151231257827E-15, +0.33306690738754696E-15, +0.33306690738754696E-15, +0.12212453270876722E-14, +0.0000000000000000, +0.11102230246251565E-15, +0.22204460492503131E-15, +0.88817841970012523E-15

181reltol = sqrt(epsilon(1._TKG))

182reltol

183+0.14901161193847656E-7

184isClose(data, atad(1:size(data)), reltol = reltol)

185T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

186call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

187

188lenData = getUnifRand(5, 100)

189lenData

190+61

191data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

192data

193+1.49449065196501015851272384059823664, +1.22893403534742157801640064752742160, +1.63533177231424081874653793615824048, +1.38096693474505084699811975125141860, +1.61109201991196599473335075253109454, +1.51628396573179416721209614407498686, +1.69272916803812802058467034366212688, +1.43917617057213848112512794416022117, +1.37746053477475253307094616615181263, +1.53851263208790030548642140322163465, +1.40577718321953754121627460629089663, +1.08199304397021282941742218280921596, +1.14755948749266814346581398278794866, +1.43138767733357909586059996367324608, +1.64709175007446615774516288971004143, +1.65872419210300210116488234147357431, +1.04568749194036548778554327258748643, +1.72318755620801630538239399181166138, +1.82534364360197191604681073005228735, +1.96716328212191191133951992350597145, +1.37849799236361786986076992090490862, +1.80093900911433053807078515954325967, +1.67873844081941006741297251801707355, +1.60790437844027046526479444284441721, +1.61311565115060795373842259440059778, +1.57987140856762456121348207904303403, +1.48140808528950887894246800395159635, +1.73978966574104407059450214246786623, +1.58929167593610806190760689286660692, +1.80769124981774006600225374239480561, +1.02655608581436462508993509199350104, +1.83215470512523928150884493433912275, +1.26291309454212040546780667241350221, +1.70256490949810725857098306800078409, +1.72597675982775919889444746464387744, +1.08193504344738920937902093213745905, +1.11322422334343077619947633163910385, +1.83425033872636012861263908012266073, +1.44927712499787388638099478600388158, +1.50552859464589680398384926207588781, +1.87450002560152032102593918086548200, +1.69124500436169659788305248016124908, +1.90381670275496954400418142111020765, +1.51863405652953385473149108643356242, +1.26872804468755021439363288213450922, +1.26699647491787059640316550148845012, +1.19600784514839136737543846938897692, +1.94362645443385725826778076098296573, +1.73999280211374476644736876237893779, +1.15434207704182720094387208322092549, +1.31562010126138867930027371219546616, +1.91540206236203394335512989840270822, +1.50726671828999308398393568833858074, +1.92098026392826682584748952132504504, +1.85228736950559004818454447051557626, +1.73769805062067729500666091209151979, +1.27639315125321003983647900184480587, +1.65235855629767301126711276542539720, +1.84349376991856159413995388283450156, +1.55374239332003157705833929038900684, +1.62648853639884674824256884035528580

194

195atad = getFFTI(getFFTF(data))

196atad

197+1.49449065196501015851272384059823626, +1.22893403534742157801640064752742179, +1.63533177231424081874653793615824028, +1.38096693474505084699811975125141841, +1.61109201991196599473335075253109454, +1.51628396573179416721209614407498725, +1.69272916803812802058467034366212688, +1.43917617057213848112512794416022079, +1.37746053477475253307094616615181244, +1.53851263208790030548642140322163484, +1.40577718321953754121627460629089644, +1.08199304397021282941742218280921557, +1.14755948749266814346581398278794846, +1.43138767733357909586059996367324608, +1.64709175007446615774516288971004200, +1.65872419210300210116488234147357412, +1.04568749194036548778554327258748643, +1.72318755620801630538239399181166157, +1.82534364360197191604681073005228716, +1.96716328212191191133951992350597125, +1.37849799236361786986076992090490842, +1.80093900911433053807078515954325987, +1.67873844081941006741297251801707375, +1.60790437844027046526479444284441682, +1.61311565115060795373842259440059778, +1.57987140856762456121348207904303403, +1.48140808528950887894246800395159616, +1.73978966574104407059450214246786603, +1.58929167593610806190760689286660692, +1.80769124981774006600225374239480561, +1.02655608581436462508993509199350066, +1.83215470512523928150884493433912236, +1.26291309454212040546780667241350182, +1.70256490949810725857098306800078429, +1.72597675982775919889444746464387725, +1.08193504344738920937902093213745866, +1.11322422334343077619947633163910346, +1.83425033872636012861263908012266092, +1.44927712499787388638099478600388158, +1.50552859464589680398384926207588761, +1.87450002560152032102593918086548162, +1.69124500436169659788305248016124908, +1.90381670275496954400418142111020727, +1.51863405652953385473149108643356203, +1.26872804468755021439363288213450903, +1.26699647491787059640316550148845012, +1.19600784514839136737543846938897730, +1.94362645443385725826778076098296573, +1.73999280211374476644736876237893760, +1.15434207704182720094387208322092568, +1.31562010126138867930027371219546616, +1.91540206236203394335512989840270803, +1.50726671828999308398393568833858055, +1.92098026392826682584748952132504504, +1.85228736950559004818454447051557626, +1.73769805062067729500666091209151960, +1.27639315125321003983647900184480568, +1.65235855629767301126711276542539701, +1.84349376991856159413995388283450137, +1.55374239332003157705833929038900665, +1.62648853639884674824256884035528599, +0.00000000000000000000000000000000000, -0.385185988877447170611195588516985464E-33, -0.288889491658085377958396691387739098E-33

198reltol = sqrt(epsilon(1._TKG))

199reltol

200+0.138777878078144567552953958511352539E-16

201isClose(data, atad(1:size(data)), reltol = reltol)

202T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

203call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

204

205lenData = getUnifRand(5, 100)

206lenData

207+39

208data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

209data

210(+1.19681048, +0.608822346), (+1.97817254, +0.180851400), (+1.34614670, +0.676657557), (+1.45736599, +0.273793936E-2), (+1.42150950, +0.559445977), (+1.27174973, +0.797274947), (+1.65489364, +0.681914389), (+1.47308540, +0.206903756), (+1.39021707, +0.356060445), (+1.78821874, +0.729504704), (+1.06266832, +0.107736349), (+1.07657743, +0.636109412), (+1.76759243, +0.791803122), (+1.78432655, +0.692153096), (+1.94817209, +0.302317560), (+1.30428338, +0.411117911), (+1.79617500, +0.676033437), (+1.54248166, +0.966536403E-1), (+1.69189620, +0.867174089), (+1.82334614, +0.324174285), (+1.40427434, +0.631652236), (+1.34079671, +0.871210456), (+1.99622369, +0.952312052), (+1.67784059, +0.784517586), (+1.84782565, +0.943243682), (+1.60478425, +0.208824098), (+1.57867265, +0.833718479), (+1.51894546, +0.522803366), (+1.82527208, +0.120299697), (+1.00673795, +0.222580135), (+1.12848711, +0.432655632), (+1.83486748, +0.116591990), (+1.37129760, +0.665915072), (+1.09607983, +0.808141828E-1), (+1.63880146, +0.386994720), (+1.96849227, +0.648964822), (+1.22014892, +0.334461272), (+1.71180725, +0.240131915), (+1.38004589, +0.257454395)

211

212atad = getFFTI(getFFTF(data))

213atad

214(+1.19681060, +0.608822346), (+1.97817230, +0.180851460), (+1.34614658, +0.676657677), (+1.45736575, +0.273802876E-2), (+1.42150950, +0.559445977), (+1.27174973, +0.797274888), (+1.65489352, +0.681914330), (+1.47308528, +0.206903636), (+1.39021707, +0.356060624), (+1.78821850, +0.729504824), (+1.06266832, +0.107736483), (+1.07657719, +0.636109471), (+1.76759243, +0.791803360), (+1.78432631, +0.692153335), (+1.94817185, +0.302317739), (+1.30428326, +0.411118031), (+1.79617512, +0.676033378), (+1.54248166, +0.966537371E-1), (+1.69189620, +0.867173791), (+1.82334590, +0.324174136), (+1.40427446, +0.631652176), (+1.34079671, +0.871210456), (+1.99622369, +0.952311993), (+1.67784047, +0.784517527), (+1.84782553, +0.943243563), (+1.60478401, +0.208824143), (+1.57867265, +0.833718419), (+1.51894522, +0.522803247), (+1.82527208, +0.120299697), (+1.00673783, +0.222580075), (+1.12848711, +0.432655573), (+1.83486724, +0.116592109), (+1.37129772, +0.665915012), (+1.09607983, +0.808142126E-1), (+1.63880157, +0.386994630), (+1.96849275, +0.648964524), (+1.22014880, +0.334461212), (+1.71180725, +0.240132034), (+1.38004601, +0.257454336), (+0.357627869E-6, +0.596046448E-7), (+0.178813934E-6, -0.238418579E-6), (+0.298023224E-6, -0.238418579E-6), (+0.298023224E-6, -0.745058060E-7), (+0.476837158E-6, -0.298023224E-7), (+0.596046448E-7, -0.268220901E-6), (+0.298023224E-6, -0.894069672E-7), (+0.178813934E-6, +0.596046448E-7), (+0.238418579E-6, -0.104308128E-6), (+0.119209290E-6, -0.298023224E-7), (+0.238418579E-6, +0.521540642E-7), (+0.238418579E-6, +0.327825546E-6), (+0.417232513E-6, +0.149011612E-6), (-0.596046448E-7, -0.596046448E-7), (+0.596046448E-7, -0.298023224E-7), (+0.00000000, +0.894069672E-7), (+0.238418579E-6, +0.894069672E-7), (+0.298023224E-6, +0.596046448E-7), (+0.298023224E-6, +0.447034836E-7), (+0.238418579E-6, +0.238418579E-6), (+0.238418579E-6, +0.178813934E-6), (+0.178813934E-6, -0.178813934E-6), (+0.238418579E-6, +0.521540642E-7), (+0.596046448E-7, -0.149011612E-7), (+0.596046448E-7, +0.894069672E-7)

215reltol = sqrt(epsilon(1._TKG))

216reltol

217+0.345266977E-3

218isClose(data, atad(1:size(data)), reltol = reltol)

219T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

220call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

221

222lenData = getUnifRand(5, 100)

223lenData

224+51

225data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

226data

227(+1.3448530159276730, +0.51234202851343291), (+1.4645809673329784, +0.61337333325541343), (+1.2504956048902054, +0.64426466929485204), (+1.4747828647732053, +0.75984243348870484), (+1.6883529984110073, +0.84790074628893830), (+1.9361763842583635, +0.64824312822507557E-1), (+1.3299021497271828, +0.34041935943960966), (+1.4906832283867504, +0.21339426923508664), (+1.5349499502649970, +0.14164475550313294), (+1.8841629397962696, +0.20779228655628124), (+1.3376022160320857, +0.99456793963784029), (+1.4618061144167283, +0.23230175079587989), (+1.6786847420940336, +0.11197575393073944), (+1.5830417941778396, +0.96997042236435593), (+1.2583625494455235, +0.25345347288337805), (+1.9368171453902638, +0.50355273593455419), (+1.0604156232825801, +0.82449306316935189), (+1.3024262613287627, +0.12668914535011111), (+1.5452190166364423, +0.15651267037636218), (+1.5225775685591463, +0.67464690357855683), (+1.1837865654942301, +0.65187368266293588), (+1.1032711092754459, +0.58846843041182673), (+1.9600239897197482, +0.12326883077673034), (+1.1474866380445368, +0.80792814350439435), (+1.4583988347103296, +0.23239274544192701), (+1.5232700729650253, +0.77681567836657250), (+1.8678563918951148, +0.39299672044276546), (+1.6713677132924940, +0.29909720554617025), (+1.6817192104063134, +0.96926479723108749), (+1.7152504037954346, +0.83508741018595500), (+1.7676946840397081, +0.41872857835155564), (+1.9173628075199050, +0.10605235055738171), (+1.9215876346265588, +0.39285955309272758), (+1.9924865559112395, +0.75488824777815977), (+1.3731992587579245, +0.36396585678767901), (+1.8913969059332698, +0.62071448206636948), (+1.9513666059749153, +0.98051333704718868), (+1.2936236103464078, +0.44874365491204449), (+1.0854855886572277, +0.49563054216189451E-1), (+1.8210869098108549, +0.80725807598521848), (+1.0574297608878591, +0.52033025940107247), (+1.6731369812709769, +0.78390107693287714), (+1.4829462969261025, +0.52149365739033560), (+1.4806260356841006, +0.22305617374788556), (+1.8268257529274627, +0.25269236653087268), (+1.6009052468621034, +0.49285935008127391E-1), (+1.2385303225885504, +0.94283530302930252), (+1.6607958364859250, +0.78425748170846132E-2), (+1.8392028825513265, +0.81918790420998044), (+1.9943476472232811, +0.11685359017169694), (+1.0753885550591153, +0.33985865264907522)

228

229atad = getFFTI(getFFTF(data))

230atad

231(+1.3448530159276730, +0.51234202851343302), (+1.4645809673329784, +0.61337333325541366), (+1.2504956048902049, +0.64426466929485215), (+1.4747828647732055, +0.75984243348870495), (+1.6883529984110073, +0.84790074628893841), (+1.9361763842583637, +0.64824312822507862E-1), (+1.3299021497271828, +0.34041935943960988), (+1.4906832283867502, +0.21339426923508703), (+1.5349499502649966, +0.14164475550313307), (+1.8841629397962696, +0.20779228655628157), (+1.3376022160320857, +0.99456793963784018), (+1.4618061144167280, +0.23230175079588028), (+1.6786847420940334, +0.11197575393073958), (+1.5830417941778396, +0.96997042236435616), (+1.2583625494455237, +0.25345347288337833), (+1.9368171453902634, +0.50355273593455407), (+1.0604156232825799, +0.82449306316935189), (+1.3024262613287632, +0.12668914535011103), (+1.5452190166364419, +0.15651267037636224), (+1.5225775685591465, +0.67464690357855661), (+1.1837865654942303, +0.65187368266293577), (+1.1032711092754459, +0.58846843041182650), (+1.9600239897197480, +0.12326883077673020), (+1.1474866380445370, +0.80792814350439413), (+1.4583988347103292, +0.23239274544192673), (+1.5232700729650253, +0.77681567836657217), (+1.8678563918951143, +0.39299672044276529), (+1.6713677132924940, +0.29909720554617025), (+1.6817192104063130, +0.96926479723108716), (+1.7152504037954346, +0.83508741018595478), (+1.7676946840397076, +0.41872857835155541), (+1.9173628075199045, +0.10605235055738144), (+1.9215876346265586, +0.39285955309272763), (+1.9924865559112397, +0.75488824777815999), (+1.3731992587579245, +0.36396585678767884), (+1.8913969059332698, +0.62071448206636937), (+1.9513666059749148, +0.98051333704718890), (+1.2936236103464076, +0.44874365491204471), (+1.0854855886572277, +0.49563054216189423E-1), (+1.8210869098108549, +0.80725807598521859), (+1.0574297608878584, +0.52033025940107225), (+1.6731369812709769, +0.78390107693287692), (+1.4829462969261022, +0.52149365739033549), (+1.4806260356841008, +0.22305617374788517), (+1.8268257529274625, +0.25269236653087279), (+1.6009052468621032, +0.49285935008126946E-1), (+1.2385303225885504, +0.94283530302930196), (+1.6607958364859248, +0.78425748170841414E-2), (+1.8392028825513262, +0.81918790420998033), (+1.9943476472232811, +0.11685359017169691), (+1.0753885550591153, +0.33985865264907511), (+0.0000000000000000, -0.11102230246251565E-15), (+0.0000000000000000, -0.11102230246251565E-15), (-0.33306690738754696E-15, -0.11102230246251565E-15), (+0.44408920985006262E-15, +0.30531133177191805E-15), (+0.33306690738754696E-15, -0.16653345369377348E-15), (+0.0000000000000000, +0.16653345369377348E-15), (+0.33306690738754696E-15, +0.11102230246251565E-15), (+0.66613381477509392E-15, +0.49960036108132044E-15), (+0.44408920985006262E-15, +0.41633363423443370E-15), (+0.11102230246251565E-15, +0.0000000000000000), (+0.55511151231257827E-15, +0.33306690738754696E-15), (+0.44408920985006262E-15, +0.74940054162198066E-15), (+0.44408920985006262E-15, +0.63837823915946501E-15)

232reltol = sqrt(epsilon(1._TKG))

233reltol

234+0.14901161193847656E-7

235isClose(data, atad(1:size(data)), reltol = reltol)

236T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

237call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

238

239lenData = getUnifRand(5, 100)

240lenData

241+25

242data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

243data

244(+1.31731573137508162074819334382405401, +0.190592130603650948132907188736216182), (+1.55618564568919074006460635190799937, +0.870830278013099354125996532379082895), (+1.75951511523961333920609522186443459, +0.919196666862807276569876289100217866), (+1.19838229798570939314375640166956306, +0.875257724018442735004580873716789079), (+1.36937326904555531734213846478981803, +0.724629917895636733031905858818270633), (+1.87736243108996585583764397200049990, +0.962759841570265535742970189435248578), (+1.37314293612122726503451812225091725, +0.278071788782711862070326573656196385), (+1.11391731261436465784205860612940124, +0.139781096969629979271113099456551416), (+1.63446156681881229125050548013066252, +0.707270404737088231805032035999738606), (+1.81326052073561504390322199478075766, +0.110893330333556580026469871986206774), (+1.59656747131744147565277258101009915, +0.743188224790038364381267635221618532), (+1.45360370953516644991387293141047755, +0.761137313239986676541719025965924436E-1), (+1.63574914214581095615295525931143577, +0.286774727221936323855057410367115083E-1), (+1.85593635083245166625768861037890313, +0.194916415622871951845546613498906661), (+1.37180788157588681968090849778151492, +0.551068448387246908136768415087571893), (+1.54818266070550828091979326652622985, +0.493100800961539116312904152094174848), (+1.14592197835022449669198572206683353, +0.315623560321790009738723894623905334), (+1.63662890993034241444908932742360295, +0.914669114587823152551045215890159009), (+1.22348048466601075241853899910368258, +0.630070872897385127211496555574559574), (+1.86343792463237448666444461505045729, +0.591639831429313399219163128076907673), (+1.55379595295209775022527774740828876, +0.959454981255864291704501740703773189), (+1.18666087785321229647712291331648853, +0.147938498517677151359469505471735127), (+1.53903334083084461272703854152820886, +0.695841204022427833168295441255335763), (+1.12537546039092708350917257172725600, +0.890997224431432606382763712832854517E-1), (+1.57867274806858511174645367281027972, +0.721991193100467462421646938691960655E-1)

245

246atad = getFFTI(getFFTF(data))

247atad

248(+1.31731573137508162074819334382405381, +0.190592130603650948132907188736216230), (+1.55618564568919074006460635190799937, +0.870830278013099354125996532379082798), (+1.75951511523961333920609522186443440, +0.919196666862807276569876289100217962), (+1.19838229798570939314375640166956306, +0.875257724018442735004580873716789079), (+1.36937326904555531734213846478981803, +0.724629917895636733031905858818270633), (+1.87736243108996585583764397200049990, +0.962759841570265535742970189435248481), (+1.37314293612122726503451812225091705, +0.278071788782711862070326573656196288), (+1.11391731261436465784205860612940124, +0.139781096969629979271113099456551223), (+1.63446156681881229125050548013066213, +0.707270404737088231805032035999738606), (+1.81326052073561504390322199478075766, +0.110893330333556580026469871986206846), (+1.59656747131744147565277258101009876, +0.743188224790038364381267635221618436), (+1.45360370953516644991387293141047716, +0.761137313239986676541719025965924436E-1), (+1.63574914214581095615295525931143519, +0.286774727221936323855057410367115564E-1), (+1.85593635083245166625768861037890274, +0.194916415622871951845546613498906805), (+1.37180788157588681968090849778151434, +0.551068448387246908136768415087572181), (+1.54818266070550828091979326652622946, +0.493100800961539116312904152094175040), (+1.14592197835022449669198572206683334, +0.315623560321790009738723894623905382), (+1.63662890993034241444908932742360295, +0.914669114587823152551045215890158816), (+1.22348048466601075241853899910368239, +0.630070872897385127211496555574559670), (+1.86343792463237448666444461505045748, +0.591639831429313399219163128076907961), (+1.55379595295209775022527774740828857, +0.959454981255864291704501740703773285), (+1.18666087785321229647712291331648911, +0.147938498517677151359469505471735127), (+1.53903334083084461272703854152820867, +0.695841204022427833168295441255335860), (+1.12537546039092708350917257172725638, +0.890997224431432606382763712832854517E-1), (+1.57867274806858511174645367281027934, +0.721991193100467462421646938691960655E-1), (+0.481482486096808963263994485646231830E-33, -0.722223729145213444895991728469347744E-34), (-0.577778983316170755916793382775478196E-33, -0.962964972193617926527988971292463659E-34), (-0.962964972193617926527988971292463659E-34, -0.192592994438723585305597794258492732E-33), (-0.192592994438723585305597794258492732E-33, -0.144444745829042688979198345693869549E-33), (-0.962964972193617926527988971292463659E-34, -0.481482486096808963263994485646231830E-34), (-0.385185988877447170611195588516985464E-33, -0.385185988877447170611195588516985464E-33), (-0.962964972193617926527988971292463659E-34, +0.00000000000000000000000000000000000)

249reltol = sqrt(epsilon(1._TKG))

250reltol

251+0.138777878078144567552953958511352539E-16

252isClose(data, atad(1:size(data)), reltol = reltol)

253T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

254call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

255

256lenData = getUnifRand(5, 100)

257lenData

258+21

259data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

260data

261+1.77173269, +1.38999343, +1.85208774, +1.14375556, +1.59002256, +1.17782044, +1.73891044, +1.60386086, +1.13627625, +1.42661500, +1.49950099, +1.94666600, +1.11533260, +1.78470612, +1.77622890, +1.74556816, +1.52672791, +1.65044188, +1.26784897, +1.88418984, +1.66507983

262

263atad = getFFTI(getFFTF(data))

264atad

265+1.77173281, +1.38999367, +1.85208786, +1.14375591, +1.59002233, +1.17782056, +1.73891020, +1.60386109, +1.13627625, +1.42661476, +1.49950099, +1.94666576, +1.11533284, +1.78470588, +1.77622867, +1.74556804, +1.52672791, +1.65044188, +1.26784861, +1.88418984, +1.66507983, +0.119209290E-6, +0.178813934E-6, -0.596046448E-7, +0.178813934E-6, +0.178813934E-6, -0.178813934E-6, +0.178813934E-6, -0.596046448E-7, +0.298023224E-6, +0.178813934E-6, +0.655651093E-6

266reltol = sqrt(epsilon(1._TKG))

267reltol

268+0.345266977E-3

269isClose(data, atad(1:size(data)), reltol = reltol)

270T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

271call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

272

273lenData = getUnifRand(5, 100)

274lenData

275+51

276data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

277data

278+1.5197504475461243, +1.4241192448256723, +1.2668550052342173, +1.6575719902823929, +1.7571397959424195, +1.0093219153149144, +1.9835316885250345, +1.0133030031266448, +1.6969087535372180, +1.3405398096793744, +1.5094911146380343, +1.2816777610860424, +1.8144127772472605, +1.8992104364016644, +1.8973069404978320, +1.6787348430552158, +1.8513197430637782, +1.6971333381752007, +1.4428383243229477, +1.5050089604666284, +1.9367687991597637, +1.2773199759220986, +1.1050888380684589, +1.9110590159469640, +1.0180856850601361, +1.6948940389299993, +1.2487530741954356, +1.5106325053234473, +1.9123165509158075, +1.9840971941444261, +1.8469895121277153, +1.0321936803830489, +1.8544199557309127, +1.6760338380565609, +1.5728993378656775, +1.9362226755272807, +1.7708121508674726, +1.8021337528021939, +1.0599882163657648, +1.0278279726616164, +1.4732551250347397, +1.0470611191336356, +1.6801283787588224, +1.3414469134778439, +1.7433013014714385, +1.1487715396339035, +1.8281362722877694, +1.9835749173471307, +1.0260591486502646, +1.5309124722446081, +1.3245571806831418

279

280atad = getFFTI(getFFTF(data))

281atad

282+1.5197504475461243, +1.4241192448256732, +1.2668550052342171, +1.6575719902823935, +1.7571397959424193, +1.0093219153149147, +1.9835316885250340, +1.0133030031266452, +1.6969087535372180, +1.3405398096793744, +1.5094911146380341, +1.2816777610860428, +1.8144127772472602, +1.8992104364016642, +1.8973069404978313, +1.6787348430552163, +1.8513197430637780, +1.6971333381752012, +1.4428383243229472, +1.5050089604666284, +1.9367687991597635, +1.2773199759220986, +1.1050888380684585, +1.9110590159469640, +1.0180856850601363, +1.6948940389299991, +1.2487530741954351, +1.5106325053234471, +1.9123165509158071, +1.9840971941444254, +1.8469895121277142, +1.0321936803830489, +1.8544199557309127, +1.6760338380565614, +1.5728993378656768, +1.9362226755272809, +1.7708121508674723, +1.8021337528021941, +1.0599882163657646, +1.0278279726616164, +1.4732551250347399, +1.0470611191336356, +1.6801283787588221, +1.3414469134778444, +1.7433013014714382, +1.1487715396339033, +1.8281362722877692, +1.9835749173471307, +1.0260591486502644, +1.5309124722446086, +1.3245571806831413, +0.22204460492503131E-15, +0.33306690738754696E-15, -0.11102230246251565E-15, +0.0000000000000000, +0.66613381477509392E-15, +0.44408920985006262E-15, +0.44408920985006262E-15, +0.22204460492503131E-15, +0.11102230246251565E-14, +0.22204460492503131E-15, +0.22204460492503131E-15, +0.33306690738754696E-15, +0.99920072216264089E-15

283reltol = sqrt(epsilon(1._TKG))

284reltol

285+0.14901161193847656E-7

286isClose(data, atad(1:size(data)), reltol = reltol)

287T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

288call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

289

290lenData = getUnifRand(5, 100)

291lenData

292+52

293data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

294data

295+1.58303118345957071824973777230568484, +1.60355298485885031363591107737400525, +1.73467221880684838522946476210401237, +1.01501310969575012990433736162879024, +1.09716857408031183489645701409354278, +1.99278193133095918401255063988881099, +1.29605400865654451902084156412006192, +1.27009878622529311889572775514123937, +1.69018521762621931752489825386834679, +1.34549696744115384064356041121415394, +1.39382814833148378781309194562356302, +1.35410228797790177031487390647083433, +1.03833585332267431742728442826767892, +1.80281095192845096470424076919852297, +1.12915635832646583417948804862140696, +1.20735156519118835530541961462714664, +1.25228424152901690228376091000253838, +1.77707710980822847815372774363142881, +1.40959458255584724448312077977184291, +1.42088462005237047450492595988168800, +1.05146940330867788438372127574801094, +1.07634978090040717251538108926036858, +1.31716936036946262757596764922264738, +1.19455379551083028769943409017243452, +1.94927360655989152730800587871368966, +1.54286002850573693548185825787117863, +1.09592801405954137212264516268523642, +1.00498786373342718924857212828415403, +1.12437577285471929413238782848980081, +1.54566424714869794992203246945715774, +1.35978718897672385001449946338722463, +1.08309647184984278902059530486756771, +1.95407068586988022365388356065405095, +1.15780506997071810821460595415999010, +1.81060707365623897226409987748990312, +1.72410048087470904100742223505466685, +1.36971134494098476703428670748839313, +1.43861204350824880249924870404917001, +1.28990135717383390951602742728955841, +1.17210342970665571646840190616621373, +1.83678211080578337565900849195468435, +1.12036407671993345616435336645997778, +1.15655992381690869664466361645411666, +1.28552403693603662859744013383696245, +1.92735559630228341843598469706690358, +1.10903708246270414150610108529891747, +1.98737063322600407108968791075043439, +1.78746562920553503903060688444083478, +1.00666806345283930505008889255019375, +1.02086306732113548642733807410541519, +1.36461659274827257889378466110175456, +1.23147690153739784649172193464784618

296

297atad = getFFTI(getFFTF(data))

298atad

299+1.58303118345957071824973777230568465, +1.60355298485885031363591107737400525, +1.73467221880684838522946476210401217, +1.01501310969575012990433736162879024, +1.09716857408031183489645701409354278, +1.99278193133095918401255063988881137, +1.29605400865654451902084156412006192, +1.27009878622529311889572775514123937, +1.69018521762621931752489825386834698, +1.34549696744115384064356041121415394, +1.39382814833148378781309194562356302, +1.35410228797790177031487390647083452, +1.03833585332267431742728442826767873, +1.80281095192845096470424076919852316, +1.12915635832646583417948804862140715, +1.20735156519118835530541961462714703, +1.25228424152901690228376091000253819, +1.77707710980822847815372774363142900, +1.40959458255584724448312077977184272, +1.42088462005237047450492595988168800, +1.05146940330867788438372127574801056, +1.07634978090040717251538108926036858, +1.31716936036946262757596764922264738, +1.19455379551083028769943409017243452, +1.94927360655989152730800587871368927, +1.54286002850573693548185825787117825, +1.09592801405954137212264516268523603, +1.00498786373342718924857212828415403, +1.12437577285471929413238782848980004, +1.54566424714869794992203246945715812, +1.35978718897672385001449946338722444, +1.08309647184984278902059530486756733, +1.95407068586988022365388356065405057, +1.15780506997071810821460595415999029, +1.81060707365623897226409987748990332, +1.72410048087470904100742223505466647, +1.36971134494098476703428670748839274, +1.43861204350824880249924870404917039, +1.28990135717383390951602742728955880, +1.17210342970665571646840190616621373, +1.83678211080578337565900849195468416, +1.12036407671993345616435336645997797, +1.15655992381690869664466361645411666, +1.28552403693603662859744013383696264, +1.92735559630228341843598469706690319, +1.10903708246270414150610108529891805, +1.98737063322600407108968791075043459, +1.78746562920553503903060688444083478, +1.00666806345283930505008889255019356, +1.02086306732113548642733807410541539, +1.36461659274827257889378466110175437, +1.23147690153739784649172193464784618, -0.577778983316170755916793382775478196E-33, +0.962964972193617926527988971292463659E-34, +0.00000000000000000000000000000000000, -0.192592994438723585305597794258492732E-33, +0.00000000000000000000000000000000000, +0.288889491658085377958396691387739098E-33, -0.481482486096808963263994485646231830E-33, +0.192592994438723585305597794258492732E-33, -0.385185988877447170611195588516985464E-33, +0.962964972193617926527988971292463659E-34, -0.192592994438723585305597794258492732E-33, -0.192592994438723585305597794258492732E-33

300reltol = sqrt(epsilon(1._TKG))

301reltol

302+0.138777878078144567552953958511352539E-16

303isClose(data, atad(1:size(data)), reltol = reltol)

304T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

305call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

306

307lenData = getUnifRand(5, 100)

308lenData

309+79

310data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

311data

312(+1.21084237, +0.256814957), (+1.29714227, +0.703296661), (+1.53773487, +0.310187936), (+1.22163999, +0.286281109E-2), (+1.82533598, +0.892612696), (+1.08429110, +0.907999337), (+1.69222069, +0.599057376), (+1.40739393, +0.473366320), (+1.93294001, +0.451930702), (+1.89216006, +0.925168514), (+1.21789551, +0.705972433), (+1.22928166, +0.571495652), (+1.71439373, +0.635824978), (+1.14511168, +0.371032059), (+1.23705471, +0.591828287), (+1.01724410, +0.368666768), (+1.71252108, +0.198441386), (+1.26182961, +0.208364546), (+1.84849513, +0.558248401), (+1.83866024, +0.699936509), (+1.83447504, +0.842546463), (+1.98976827, +0.330204010), (+1.07953203, +0.670978129), (+1.67853796, +0.638161302), (+1.81984389, +0.558188140), (+1.67996454, +0.198122680), (+1.45735741, +0.166734815), (+1.10779560, +0.774345815), (+1.72721434, +0.497132659), (+1.77301252, +0.192709208), (+1.45860469, +0.964731574E-1), (+1.41847444, +0.910284579), (+1.68235874, +0.935652792), (+1.56821847, +0.812927961), (+1.92103994, +0.212540686), (+1.72570705, +0.548171401E-1), (+1.06545496, +0.771466315), (+1.08656061, +0.133051991), (+1.12319350, +0.878174365), (+1.77876568, +0.486248851), (+1.27623963, +0.572353601E-2), (+1.88873219, +0.661569536), (+1.65765381, +0.698415756), (+1.18224514, +0.642110646), (+1.26693392, +0.513545632), (+1.36475563, +0.138498962), (+1.57138097, +0.233092248), (+1.14837360, +0.798974037), (+1.14332378, +0.728131950), (+1.81283402, +0.917397320), (+1.43818772, +0.393382967), (+1.96418142, +0.115564466), (+1.23514950, +0.323862612), (+1.94352078, +0.306658268), (+1.95555019, +0.206994474), (+1.22785711, +0.828353882), (+1.76574326, +0.396081507), (+1.40589702, +0.103179991), (+1.76584029, +0.171444476), (+1.83614326, +0.750900269), (+1.96008015, +0.379524350), (+1.46792948, +0.556951344), (+1.94739258, +0.102204800), (+1.98178101, +0.468701482), (+1.42512619, +0.563184798), (+1.95956039, +0.769008517), (+1.90134811, +0.731589556), (+1.61492491, +0.586832523), (+1.84717476, +0.414892316), (+1.91940653, +0.229735255), (+1.80330110, +0.266434014), (+1.40221083, +0.403068900), (+1.58810532, +0.334410667), (+1.59189391, +0.451433539), (+1.76791191, +0.103597045), (+1.93984628, +0.245802402E-1), (+1.08079314, +0.811697543), (+1.43008304, +0.167798340), (+1.69346189, +0.136441350)

313

314atad = getFFTI(getFFTF(data))

315atad

316(+1.21084261, +0.256815016), (+1.29714239, +0.703296781), (+1.53773463, +0.310188055), (+1.22163987, +0.286287069E-2), (+1.82533574, +0.892612636), (+1.08429086, +0.907999158), (+1.69222045, +0.599057078), (+1.40739381, +0.473366350), (+1.93294001, +0.451930761), (+1.89216018, +0.925168633), (+1.21789551, +0.705972314), (+1.22928166, +0.571495771), (+1.71439385, +0.635825038), (+1.14511168, +0.371032119), (+1.23705482, +0.591828346), (+1.01724410, +0.368666947), (+1.71252108, +0.198441401), (+1.26182961, +0.208364755), (+1.84849477, +0.558248281), (+1.83866000, +0.699936509), (+1.83447492, +0.842546344), (+1.98976791, +0.330204070), (+1.07953191, +0.670978069), (+1.67853773, +0.638161182), (+1.81984377, +0.558188319), (+1.67996454, +0.198122829), (+1.45735741, +0.166734919), (+1.10779548, +0.774345875), (+1.72721434, +0.497132868), (+1.77301240, +0.192709506), (+1.45860457, +0.964732766E-1), (+1.41847444, +0.910284698), (+1.68235898, +0.935652554), (+1.56821847, +0.812927842), (+1.92103958, +0.212540478), (+1.72570682, +0.548170134E-1), (+1.06545496, +0.771466196), (+1.08656049, +0.133051917), (+1.12319350, +0.878174186), (+1.77876568, +0.486248553), (+1.27623987, +0.572344661E-2), (+1.88873219, +0.661569476), (+1.65765381, +0.698415637), (+1.18224514, +0.642110467), (+1.26693380, +0.513545513), (+1.36475551, +0.138498917), (+1.57138109, +0.233092174), (+1.14837360, +0.798974037), (+1.14332366, +0.728131771), (+1.81283367, +0.917397082), (+1.43818736, +0.393382758), (+1.96418118, +0.115564272), (+1.23514938, +0.323862493), (+1.94352043, +0.306658030), (+1.95554996, +0.206994295), (+1.22785687, +0.828353584), (+1.76574302, +0.396081507), (+1.40589690, +0.103179850), (+1.76584005, +0.171444401), (+1.83614302, +0.750900030), (+1.96008003, +0.379524380), (+1.46792912, +0.556951165), (+1.94739223, +0.102204740), (+1.98178077, +0.468701392), (+1.42512631, +0.563184738), (+1.95956028, +0.769008398), (+1.90134799, +0.731589317), (+1.61492515, +0.586832345), (+1.84717488, +0.414892256), (+1.91940653, +0.229735225), (+1.80330110, +0.266433835), (+1.40221107, +0.403068811), (+1.58810520, +0.334410727), (+1.59189391, +0.451433510), (+1.76791191, +0.103597075), (+1.93984628, +0.245801806E-1), (+1.08079314, +0.811697721), (+1.43008292, +0.167798400), (+1.69346189, +0.136441365), (+0.119209290E-6, -0.134110451E-6), (+0.238418579E-6, -0.447034836E-7), (+0.178813934E-6, -0.149011612E-6), (+0.238418579E-6, +0.00000000), (+0.298023224E-6, -0.894069672E-7), (+0.119209290E-6, +0.178813934E-6), (+0.119209290E-6, -0.149011612E-7), (+0.417232513E-6, +0.894069672E-7), (+0.238418579E-6, +0.894069672E-7), (-0.596046448E-7, -0.298023224E-6), (+0.178813934E-6, -0.230967999E-6), (+0.00000000, -0.745058060E-7), (+0.596046448E-7, -0.238418579E-6), (-0.596046448E-7, -0.149011612E-6), (+0.596046448E-7, -0.216066837E-6), (-0.596046448E-7, -0.633299351E-7), (+0.178813934E-6, -0.596046448E-7), (+0.596046448E-7, +0.119209290E-6), (+0.417232513E-6, +0.298023224E-7), (+0.00000000, +0.208616257E-6), (+0.178813934E-6, +0.126659870E-6), (+0.00000000, +0.298023224E-6), (-0.596046448E-7, +0.134110451E-6), (+0.596046448E-7, +0.357627869E-6), (+0.238418579E-6, +0.298023224E-6), (+0.596046448E-7, -0.298023224E-7), (+0.178813934E-6, +0.596046448E-7), (+0.596046448E-7, +0.208616257E-6), (+0.119209290E-6, -0.298023224E-7), (+0.119209290E-6, -0.298023224E-7), (+0.119209290E-6, -0.447034836E-7), (-0.596046448E-7, +0.447034836E-7), (+0.178813934E-6, +0.149011612E-6), (+0.178813934E-6, +0.119209290E-6), (+0.238418579E-6, +0.178813934E-6), (+0.178813934E-6, +0.268220901E-6), (+0.417232513E-6, +0.163912773E-6), (+0.596046448E-7, +0.253319740E-6), (+0.119209290E-6, +0.134110451E-6), (+0.596046448E-7, +0.365078449E-6), (+0.119209290E-6, +0.238418579E-6), (+0.178813934E-6, +0.149011612E-7), (+0.476837158E-6, -0.141561031E-6), (+0.596046448E-7, +0.104308128E-6), (+0.178813934E-6, +0.208616257E-6), (+0.00000000, +0.298023224E-7), (+0.178813934E-6, -0.596046448E-7), (-0.596046448E-7, +0.160187483E-6), (+0.238418579E-6, +0.298023224E-6)

317reltol = sqrt(epsilon(1._TKG))

318reltol

319+0.345266977E-3

320isClose(data, atad(1:size(data)), reltol = reltol)

321T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

322call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

323

324lenData = getUnifRand(5, 100)

325lenData

326+27

327data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

328data

329(+1.4081053578390756, +0.15190996466992024), (+1.4656259287108169, +0.71998370144619961), (+1.7690602669280646, +0.94746004671163697), (+1.7270561375899225, +0.87024771002120771), (+1.2033586363254707, +0.50509022003559334E-1), (+1.6249942079177102, +0.22832163544538098E-1), (+1.0780380487468568, +0.70879081363869001), (+1.3212304937821342, +0.99919024427789882), (+1.8651191964656335, +0.88695990057155860), (+1.1003090072873984, +0.27234482525539683), (+1.6048294351310655, +0.29703524683950033), (+1.6286677155739602, +0.83473720421282538E-1), (+1.6028987637696592, +0.13510471851344341), (+1.0335871690041212, +0.58160179189418371), (+1.5695370165683493, +0.41116757048147456), (+1.1400543701118009, +0.51478734822210914), (+1.5888356957840271, +0.90469451993978112), (+1.8141328716812231, +0.20278577665989839E-1), (+1.6719556416828918, +0.33166724440087214), (+1.0730758648225591, +0.21592921797665965), (+1.9059256867993806, +0.48051909909635238), (+1.3014030866044046, +0.87658814180248901), (+1.5108328478066497, +0.67836316051767587), (+1.3498333941710736, +0.99251685373764831), (+1.6990746891078996, +0.18720737527952624), (+1.1941535411555637, +0.18844522425732180), (+1.7153816362262271, +0.60435902731223046)

330

331atad = getFFTI(getFFTF(data))

332atad

333(+1.4081053578390759, +0.15190996466992024), (+1.4656259287108167, +0.71998370144619961), (+1.7690602669280646, +0.94746004671163697), (+1.7270561375899223, +0.87024771002120782), (+1.2033586363254707, +0.50509022003559195E-1), (+1.6249942079177098, +0.22832163544538264E-1), (+1.0780380487468568, +0.70879081363868990), (+1.3212304937821342, +0.99919024427789849), (+1.8651191964656335, +0.88695990057155849), (+1.1003090072873984, +0.27234482525539688), (+1.6048294351310657, +0.29703524683950050), (+1.6286677155739597, +0.83473720421282427E-1), (+1.6028987637696592, +0.13510471851344319), (+1.0335871690041207, +0.58160179189418360), (+1.5695370165683489, +0.41116757048147445), (+1.1400543701118007, +0.51478734822210892), (+1.5888356957840271, +0.90469451993978112), (+1.8141328716812228, +0.20278577665989783E-1), (+1.6719556416828918, +0.33166724440087209), (+1.0730758648225591, +0.21592921797665965), (+1.9059256867993803, +0.48051909909635226), (+1.3014030866044042, +0.87658814180248856), (+1.5108328478066497, +0.67836316051767576), (+1.3498333941710738, +0.99251685373764797), (+1.6990746891078996, +0.18720737527952619), (+1.1941535411555635, +0.18844522425732163), (+1.7153816362262273, +0.60435902731223035), (+0.55511151231257827E-15, -0.11102230246251565E-15), (+0.44408920985006262E-15, +0.12490009027033011E-15), (+0.22204460492503131E-15, +0.44408920985006262E-15), (+0.55511151231257827E-15, +0.13877787807814457E-15), (+0.66613381477509392E-15, +0.33306690738754696E-15)

334reltol = sqrt(epsilon(1._TKG))

335reltol

336+0.14901161193847656E-7

337isClose(data, atad(1:size(data)), reltol = reltol)

338T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

339call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

340

341lenData = getUnifRand(5, 100)

342lenData

343+93

344data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

345data

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347

348atad = getFFTI(getFFTF(data))

349atad

350(+1.16405483086705635005452283254615231, +0.971179540061829417867564165450890360), (+1.81002375352007596007720482812344177, +0.762738471736909372692071929758056089), (+1.24689490443620547503405478359019546, +0.905302545466475896808368804496701374), (+1.19978347569462698956695672799503019, +0.871597517579597902324986137071375282), (+1.07870266775897234211646833687165101, +0.834634893003478867637141940341698542), (+1.54306627857534695232063772993061688, +0.130946368533899433791185780893307897E-1), (+1.86391351752708053441175604031821188, +0.694951003970476427669868505136709058E-1), (+1.80533445195776669489856230404541004, +0.761498653607466011227342934511599467), (+1.61514060998263681413938076037817550, +0.543483663907784355814653625241774614), (+1.11048382123979035181316930595837845, +0.679695688145841253502383022905308122), (+1.30241287412466301976329641592566285, +0.620530844073251657906247845345110900), (+1.65809707493649374792995527916331373, 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(+1.03115032099467251148914898083307090, +0.136159979534430803620917876935636101), (+1.94168586880366363862823251086496945, +0.820610117578847053052967463597580002E-1), (+1.50616904170557076400931468596137449, +0.910819383181867779626844714427589170), (+1.85107113986836203238648213601995628, +0.111407629953323636146649603559545281), (+1.59510255631787265769259962370403844, +0.323279971287351841817245489810336736), (+1.97915979641922995381413008215778834, +0.258742799850951171400760352885597437), (+1.62297490986040840801888241332852026, +0.419452529115139266650832895825974549), (+1.04033114584577510525080704586095075, +0.415391109853799270825572365496217429E-1), (+1.28019385581411181624028330476750434, +0.664099085028860988808415522952381128), (+1.54860643559247373473795246910976663, +0.128888727606730517615470692079077474), (+1.92340672072665363862924660665800876, +0.857849983902708781005561383605721932), (+1.60443168437029049495010188912000691, +0.983646012601066254684129608796563559), (+1.26136825606299147786824117493722467, +0.223936444940420166994939310352912690E-1), (+1.15852895203410447629287643787770437, +0.920685639873799191258975320010087369), (+1.06565093972680664482838465048532513, +0.311331633115194114796078730662089843), (+1.08413516969683687469394076492001695, +0.166041873001132802064292452241393042), (+1.57269896628875130549272792206107448, +0.698044755552963443351089415326536237), (+1.19053843778026330249756784021071778, +0.354156496171530422986417497032850848), (+1.76246354275655549481094124721633290, +0.318789412065929438995203212761093612), (+1.79377063101891884083496225220969557, +0.584532814123041580490302208784024584), (+1.24279775845380175481774084758087145, +0.469610303011664148072869573376084465), (+1.86542598772901577335889662383446086, +0.588536893515536800480933279025845310), (-0.962964972193617926527988971292463659E-34, +0.782409039907314565303991039175126723E-34), (-0.288889491658085377958396691387739098E-33, -0.481482486096808963263994485646231830E-34), (-0.385185988877447170611195588516985464E-33, -0.144444745829042688979198345693869549E-33), (-0.481482486096808963263994485646231830E-33, -0.144444745829042688979198345693869549E-33), (-0.288889491658085377958396691387739098E-33, +0.361111864572606722447995864234673872E-34), (-0.962964972193617926527988971292463659E-34, -0.192592994438723585305597794258492732E-33), (-0.962964972193617926527988971292463659E-34, -0.481482486096808963263994485646231830E-34), (-0.288889491658085377958396691387739098E-33, +0.722223729145213444895991728469347744E-34), (-0.962964972193617926527988971292463659E-34, +0.144444745829042688979198345693869549E-33), (-0.962964972193617926527988971292463659E-34, -0.481482486096808963263994485646231830E-34), (-0.962964972193617926527988971292463659E-34, +0.00000000000000000000000000000000000), (-0.192592994438723585305597794258492732E-33, -0.216667118743564033468797518540804323E-33), (-0.577778983316170755916793382775478196E-33, -0.192592994438723585305597794258492732E-33), (-0.288889491658085377958396691387739098E-33, -0.288889491658085377958396691387739098E-33), (-0.385185988877447170611195588516985464E-33, -0.529630734706489859590393934210855013E-33), (-0.577778983316170755916793382775478196E-33, -0.240741243048404481631997242823115915E-33), (-0.674075480535532548569592279904724561E-33, -0.192592994438723585305597794258492732E-33), (-0.481482486096808963263994485646231830E-33, -0.120370621524202240815998621411557957E-33), (-0.192592994438723585305597794258492732E-33, -0.144444745829042688979198345693869549E-33), (-0.385185988877447170611195588516985464E-33, +0.00000000000000000000000000000000000), (-0.385185988877447170611195588516985464E-33, -0.144444745829042688979198345693869549E-33), (-0.962964972193617926527988971292463659E-34, -0.192592994438723585305597794258492732E-33), (-0.192592994438723585305597794258492732E-33, -0.144444745829042688979198345693869549E-33), (-0.577778983316170755916793382775478196E-33, +0.144444745829042688979198345693869549E-33), (-0.481482486096808963263994485646231830E-33, +0.00000000000000000000000000000000000), (-0.962964972193617926527988971292463659E-34, -0.962964972193617926527988971292463659E-34), (-0.192592994438723585305597794258492732E-33, +0.240741243048404481631997242823115915E-33), (-0.385185988877447170611195588516985464E-33, -0.216667118743564033468797518540804323E-33), (-0.770371977754894341222391177033970927E-33, -0.529630734706489859590393934210855013E-33), (+0.00000000000000000000000000000000000, +0.722223729145213444895991728469347744E-34), (+0.288889491658085377958396691387739098E-33, -0.385185988877447170611195588516985464E-33), (-0.192592994438723585305597794258492732E-33, -0.240741243048404481631997242823115915E-33), (-0.577778983316170755916793382775478196E-33, -0.475463955020598851223194554575653932E-33), (-0.481482486096808963263994485646231830E-33, -0.180555932286303361223997932117336936E-33), (-0.770371977754894341222391177033970927E-33, -0.517593672554069635508794072069699217E-33)

351reltol = sqrt(epsilon(1._TKG))

352reltol

353+0.138777878078144567552953958511352539E-16

354isClose(data, atad(1:size(data)), reltol = reltol)

355T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

356call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

357

358lenData = getUnifRand(5, 100)

359lenData

360+98

361data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

362data

363+1.73412704, +1.46524572, +1.74941027, +1.87184739, +1.74546862, +1.84083486, +1.22509766, +1.63008106, +1.23557115, +1.70244873, +1.66441405, +1.17684937, +1.11964417, +1.01612616, +1.33740699, +1.41267574, +1.33862388, +1.08813989, +1.35962415, +1.25829673, +1.45384705, +1.04724908, +1.60577238, +1.84776080, +1.04493451, +1.37842929, +1.09944940, +1.78341508, +1.26047659, +1.44904947, +1.85017729, +1.79374838, +1.95963264, +1.63177204, +1.25160205, +1.33086681, +1.55143976, +1.69570374, +1.65546381, +1.23297560, +1.35194290, +1.16175866, +1.91959453, +1.31011176, +1.75966573, +1.33547688, +1.95131373, +1.49218726, +1.49287498, +1.25759864, +1.05141401, +1.98082685, +1.27633905, +1.97661972, +1.19667709, +1.04430747, +1.14659822, +1.54198337, +1.59824765, +1.25768948, +1.22690082, +1.21312058, +1.28368890, +1.53524244, +1.65712070, +1.36596799, +1.09858847, +1.41719961, +1.35183764, +1.33479357, +1.02048564, +1.23916137, +1.89250636, +1.16692042, +1.51966023, +1.58691633, +1.15471220, +1.89772439, +1.30650735, +1.62303841, +1.50842404, +1.74718964, +1.35477185, +1.46610200, +1.58941269, +1.82154107, +1.65437746, +1.59698987, +1.73596799, +1.05728102, +1.80649054, +1.79891288, +1.58598578, +1.46549678, +1.61942172, +1.89824772, +1.45493758, +1.86913514

364

365atad = getFFTI(getFFTF(data))

366atad

367+1.73412669, +1.46524560, +1.74940991, +1.87184739, +1.74546814, +1.84083450, +1.22509730, +1.63008082, +1.23557103, +1.70244861, +1.66441405, +1.17684925, +1.11964428, +1.01612604, +1.33740675, +1.41267562, +1.33862364, +1.08813953, +1.35962391, +1.25829661, +1.45384669, +1.04724884, +1.60577226, +1.84776068, +1.04493427, +1.37842917, +1.09944916, +1.78341496, +1.26047647, +1.44904959, +1.85017729, +1.79374850, +1.95963240, +1.63177192, +1.25160193, +1.33086681, +1.55143964, +1.69570315, +1.65546370, +1.23297548, +1.35194290, +1.16175842, +1.91959405, +1.31011128, +1.75966573, +1.33547664, +1.95131373, +1.49218726, +1.49287474, +1.25759840, +1.05141377, +1.98082650, +1.27633882, +1.97661948, +1.19667709, +1.04430723, +1.14659810, +1.54198313, +1.59824729, +1.25768924, +1.22690082, +1.21312058, +1.28368890, +1.53524232, +1.65712035, +1.36596787, +1.09858847, +1.41719961, +1.35183740, +1.33479321, +1.02048552, +1.23916137, +1.89250624, +1.16692042, +1.51966012, +1.58691609, +1.15471208, +1.89772427, +1.30650723, +1.62303829, +1.50842369, +1.74718952, +1.35477161, +1.46610177, +1.58941245, +1.82154083, +1.65437722, +1.59698987, +1.73596764, +1.05728102, +1.80648994, +1.79891264, +1.58598554, +1.46549690, +1.61942172, +1.89824760, +1.45493722, +1.86913502, +0.00000000, +0.298023224E-6, -0.119209290E-6, +0.238418579E-6, +0.00000000, +0.536441803E-6, -0.119209290E-6, +0.00000000, -0.596046448E-7, +0.596046448E-7, -0.596046448E-7, +0.238418579E-6, -0.596046448E-7, +0.536441803E-6, -0.119209290E-6, -0.596046448E-7, +0.00000000, +0.119209290E-6, -0.178813934E-6, +0.178813934E-6, +0.119209290E-6, +0.178813934E-6, +0.119209290E-6, -0.238418579E-6, +0.178813934E-6, -0.596046448E-7, -0.596046448E-7, +0.00000000, -0.119209290E-6, +0.596046448E-7

368reltol = sqrt(epsilon(1._TKG))

369reltol

370+0.345266977E-3

371isClose(data, atad(1:size(data)), reltol = reltol)

372T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

373call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

374

375lenData = getUnifRand(5, 100)

376lenData

377+36

378data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

379data

380+1.2374369391245372, +1.5806157290391434, +1.6892379729135116, +1.2336123820044165, +1.1107866779578774, +1.7364025697728169, +1.1417658635251735, +1.1467621222970441, +1.9146403362266391, +1.6820164405378795, +1.1134335493050211, +1.8851271476614428, +1.4738085683154749, +1.5490751431754166, +1.0176573413542194, +1.6793753409038028, +1.5867667294186591, +1.3129107171415335, +1.9097168092559880, +1.5740582672991139, +1.5908708539740419, +1.3284893979646200, +1.1237805494273232, +1.9393631193788312, +1.8922035167644404, +1.7420172396220175, +1.2571255800487591, +1.9529382668797699, +1.0106780505734148, +1.8268881643228654, +1.8855266819944401, +1.1044958385861918, +1.7148484669875153, +1.1393313952516022, +1.2950044536395229, +1.8186762435528911

381

382atad = getFFTI(getFFTF(data))

383atad

384+1.2374369391245372, +1.5806157290391436, +1.6892379729135114, +1.2336123820044167, +1.1107866779578772, +1.7364025697728172, +1.1417658635251731, +1.1467621222970439, +1.9146403362266384, +1.6820164405378795, +1.1134335493050207, +1.8851271476614426, +1.4738085683154747, +1.5490751431754164, +1.0176573413542187, +1.6793753409038024, +1.5867667294186589, +1.3129107171415333, +1.9097168092559875, +1.5740582672991135, +1.5908708539740415, +1.3284893979646200, +1.1237805494273228, +1.9393631193788305, +1.8922035167644400, +1.7420172396220166, +1.2571255800487591, +1.9529382668797692, +1.0106780505734145, +1.8268881643228647, +1.8855266819944394, +1.1044958385861912, +1.7148484669875150, +1.1393313952516024, +1.2950044536395233, +1.8186762435528909, +0.0000000000000000, +0.22204460492503131E-15, +0.55511151231257827E-15, -0.44408920985006262E-15, +0.44408920985006262E-15, +0.0000000000000000, +0.66613381477509392E-15, +0.22204460492503131E-15, +0.55511151231257827E-15, +0.22204460492503131E-15, +0.88817841970012523E-15, +0.22204460492503131E-15, +0.44408920985006262E-15, +0.11102230246251565E-15, +0.55511151231257827E-15, +0.55511151231257827E-15, +0.33306690738754696E-15, +0.22204460492503131E-15, +0.55511151231257827E-15, +0.33306690738754696E-15, +0.33306690738754696E-15, +0.77715611723760958E-15, +0.33306690738754696E-15, +0.66613381477509392E-15, +0.22204460492503131E-15, +0.66613381477509392E-15, +0.44408920985006262E-15, +0.55511151231257827E-15

385reltol = sqrt(epsilon(1._TKG))

386reltol

387+0.14901161193847656E-7

388isClose(data, atad(1:size(data)), reltol = reltol)

389T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

390call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

391

392lenData = getUnifRand(5, 100)

393lenData

394+28

395data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

396data

397+1.03269704713098344715872501408918646, +1.55494717825777696535308993637179205, +1.74600852777137806023835438745062883, +1.00323375281022965468878439104050171, +1.20936615920732151561999004285270211, +1.75573380593610678356062553559987964, +1.60916873342600436308128443968548906, +1.87458569142059182513481439097077621, +1.76133287226642943483859244263974381, +1.54210249746291903244965744565084490, +1.69510189565894971192344206431409958, +1.53004832586801265598839009492931295, +1.76395922743662149878491924130582570, +1.67956585512538677091600025209940952, +1.08151667333229385354027351864164033, +1.78422929088609555725021544739148820, +1.68662111523350626010381458152776753, +1.61128137299154039179420589821462278, +1.85862228962052179894102272846785775, +1.85912439822015864222248720187706078, +1.27965841499107047355007088479415244, +1.57415167451108519706844334479021343, +1.77458752833209423401623338639011650, +1.02656802811137792854178799280323731, +1.01654969543804706722056445402249080, +1.20345088202386947229799168266277560, +1.64135662014996107981129644258977918, +1.74679174514821730636585748117459378

398

399atad = getFFTI(getFFTF(data))

400atad

401+1.03269704713098344715872501408918646, +1.55494717825777696535308993637179166, +1.74600852777137806023835438745062922, +1.00323375281022965468878439104050151, +1.20936615920732151561999004285270230, +1.75573380593610678356062553559987945, +1.60916873342600436308128443968548906, +1.87458569142059182513481439097077621, +1.76133287226642943483859244263974400, +1.54210249746291903244965744565084451, +1.69510189565894971192344206431409996, +1.53004832586801265598839009492931276, +1.76395922743662149878491924130582647, +1.67956585512538677091600025209940933, +1.08151667333229385354027351864164072, +1.78422929088609555725021544739148820, +1.68662111523350626010381458152776753, +1.61128137299154039179420589821462278, +1.85862228962052179894102272846785794, +1.85912439822015864222248720187706059, +1.27965841499107047355007088479415283, +1.57415167451108519706844334479021323, +1.77458752833209423401623338639011650, +1.02656802811137792854178799280323731, +1.01654969543804706722056445402249118, +1.20345088202386947229799168266277541, +1.64135662014996107981129644258977918, +1.74679174514821730636585748117459378, -0.288889491658085377958396691387739098E-33, -0.385185988877447170611195588516985464E-33, -0.385185988877447170611195588516985464E-33, -0.481482486096808963263994485646231830E-33

402reltol = sqrt(epsilon(1._TKG))

403reltol

404+0.138777878078144567552953958511352539E-16

405isClose(data, atad(1:size(data)), reltol = reltol)

406T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

407call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

408

409lenData = getUnifRand(5, 100)

410lenData

411+47

412data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

413data

414(+1.49069738, +0.626179695), (+1.70965600, +0.742014587), (+1.24839187, +0.732341170), (+1.88026774, +0.198023856), (+1.47840261, +0.209167302), (+1.43841231, +0.617518365), (+1.11941028, +0.631217360), (+1.57763529, +0.649158299), (+1.93126786, +0.438494325), (+1.35266054, +0.633824825), (+1.63179040, +0.325381339), (+1.97061098, +0.901455522), (+1.88742507, +0.238064289), (+1.03249454, +0.179025114), (+1.95820308, +0.250066996), (+1.32066536, +0.639807343), (+1.96702361, +0.668791115), (+1.63522029, +0.638181746), (+1.34496188, +0.423119009), (+1.12413001, +0.126281857), (+1.58038640, +0.251354337), (+1.23957801, +0.675930977), (+1.45665717, +0.435712397), (+1.92082417, +0.108609080), (+1.98365963, +0.318418324), (+1.55529606, +0.859211087E-1), (+1.12911153, +0.575146854), (+1.15525293, +0.839388549), (+1.27447248, +0.405299485), (+1.76000893, +0.330076814), (+1.08612180, +0.217195570), (+1.30925584, +0.147652566), (+1.30957198, +0.815255642), (+1.63645041, +0.561843276), (+1.14604306, +0.409537435), (+1.80272532, +0.706663013), (+1.29158068, +0.298599899), (+1.55246544, +0.389424801), (+1.98362207, +0.422068655), (+1.14605165, +0.172736883), (+1.22292209, +0.435135961), (+1.03853345, +0.374697566), (+1.41953087, +0.373231351), (+1.07663822, +0.199892819), (+1.07292652, +0.706483781), (+1.01372802, +0.552900374), (+1.11757135, +0.106690645)

415

416atad = getFFTI(getFFTF(data))

417atad

418(+1.49069750, +0.626179695), (+1.70965576, +0.742014647), (+1.24839163, +0.732341051), (+1.88026726, +0.198023796), (+1.47840261, +0.209167391), (+1.43841219, +0.617518425), (+1.11941016, +0.631217301), (+1.57763505, +0.649158120), (+1.93126810, +0.438494444), (+1.35266030, +0.633824825), (+1.63179004, +0.325381458), (+1.97061086, +0.901455343), (+1.88742507, +0.238064632), (+1.03249466, +0.179025114), (+1.95820284, +0.250067145), (+1.32066524, +0.639807284), (+1.96702373, +0.668790996), (+1.63522017, +0.638181567), (+1.34496164, +0.423118919), (+1.12412977, +0.126281813), (+1.58038640, +0.251354277), (+1.23957789, +0.675930798), (+1.45665717, +0.435712278), (+1.92082405, +0.108608872), (+1.98365963, +0.318418324), (+1.55529571, +0.859213024E-1), (+1.12911141, +0.575146675), (+1.15525270, +0.839388251), (+1.27447248, +0.405299544), (+1.76000857, +0.330076993), (+1.08612156, +0.217195451), (+1.30925536, +0.147652686), (+1.30957210, +0.815255523), (+1.63645029, +0.561843157), (+1.14604282, +0.409537315), (+1.80272520, +0.706662834), (+1.29158068, +0.298599929), (+1.55246520, +0.389424831), (+1.98362195, +0.422068536), (+1.14605165, +0.172736883), (+1.22292221, +0.435135841), (+1.03853309, +0.374697566), (+1.41953075, +0.373231232), (+1.07663846, +0.199892819), (+1.07292640, +0.706483662), (+1.01372802, +0.552900255), (+1.11757135, +0.106690645), (+0.00000000, +0.596046448E-7), (+0.119209290E-6, -0.596046448E-7), (+0.00000000, +0.119209290E-6), (+0.178813934E-6, +0.149011612E-6), (+0.00000000, +0.223517418E-6), (-0.596046448E-7, -0.447034836E-7), (+0.119209290E-6, +0.596046448E-7), (+0.178813934E-6, +0.149011612E-7), (+0.00000000, +0.894069672E-7), (+0.357627869E-6, -0.134110451E-6), (+0.00000000, +0.134110451E-6), (+0.119209290E-6, +0.00000000), (+0.178813934E-6, +0.268220901E-6), (+0.298023224E-6, -0.283122063E-6), (+0.238418579E-6, -0.596046448E-7), (+0.119209290E-6, -0.141561031E-6), (-0.178813934E-6, +0.171363354E-6)

419reltol = sqrt(epsilon(1._TKG))

420reltol

421+0.345266977E-3

422isClose(data, atad(1:size(data)), reltol = reltol)

423T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

424call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

425

426lenData = getUnifRand(5, 100)

427lenData

428+39

429data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

430data

431(+1.9047351399619983, +0.37611307292669038), (+1.6007932721278726, +0.47375059661943331), (+1.9796844385461858, +0.59591025009503273), (+1.6675177145106930, +0.25599844292258478E-1), (+1.4032821815492573, +0.77832894013145559), (+1.8686261916275499, +0.27680428001911672), (+1.2749424668933376, +0.60824614635244934), (+1.0244977110526143, +0.42734213102487673), (+1.2200327768905077, +0.64925766788201533), (+1.1780960187582012, +0.34878046592270340E-1), (+1.9559657023751094, +0.96170448424686605), (+1.3148919639828880, +0.98780883633431371), (+1.3188849357143035, +0.79662154652911610), (+1.4949472439577114, +0.85335662282066227), (+1.4941570135610898, +0.59549816475393547), (+1.4292184425676320, +0.42640176946378849), (+1.0378703981009623, +0.35744451834477009), (+1.2066569503897808, +0.81820870590688166), (+1.2615565571694924, +0.23600406654472039), (+1.8600992276357116, +0.42854385217755486), (+1.6022398101774455, +0.72662239992281830E-1), (+1.5327800788597723, +0.96536508704356228), (+1.9769940262267847, +0.88331515541647410), (+1.8735486823800214, +0.56368710252261289), (+1.0692522807912717, +0.63046534716199687), (+1.9169405262624983, +0.60685596151866994), (+1.6220235188262770, +0.76257407559527013), (+1.6038926760956094, +0.68490890723598441), (+1.4282525720463917, +0.58612686779778389), (+1.5500683152743528, +0.23948063027984390), (+1.1996162749103028, +0.50185016173980124), (+1.6034867101936561, +0.45977284461210233), (+1.1179758136013382, +0.76544929433461284), (+1.7930443720457352, +0.71998710058857152), (+1.4290058149217986, +0.66665178253465396), (+1.3517163986341618, +0.27005295968981313), (+1.3796053423552688, +0.41717065712785839), (+1.1021002867843608, +0.83592998363965876), (+1.9844749392957077, +0.75032646960094385)

432

433atad = getFFTI(getFFTF(data))

434atad

435(+1.9047351399619981, +0.37611307292669044), (+1.6007932721278726, +0.47375059661943336), (+1.9796844385461854, +0.59591025009503262), (+1.6675177145106928, +0.25599844292258672E-1), (+1.4032821815492571, +0.77832894013145548), (+1.8686261916275504, +0.27680428001911683), (+1.2749424668933373, +0.60824614635244956), (+1.0244977110526143, +0.42734213102487684), (+1.2200327768905077, +0.64925766788201544), (+1.1780960187582015, +0.34878046592270479E-1), (+1.9559657023751091, +0.96170448424686605), (+1.3148919639828880, +0.98780883633431382), (+1.3188849357143035, +0.79662154652911621), (+1.4949472439577112, +0.85335662282066249), (+1.4941570135610895, +0.59549816475393547), (+1.4292184425676320, +0.42640176946378872), (+1.0378703981009623, +0.35744451834477009), (+1.2066569503897808, +0.81820870590688155), (+1.2615565571694927, +0.23600406654472067), (+1.8600992276357111, +0.42854385217755459), (+1.6022398101774455, +0.72662239992281719E-1), (+1.5327800788597723, +0.96536508704356261), (+1.9769940262267847, +0.88331515541647376), (+1.8735486823800211, +0.56368710252261267), (+1.0692522807912717, +0.63046534716199676), (+1.9169405262624981, +0.60685596151866972), (+1.6220235188262773, +0.76257407559526946), (+1.6038926760956094, +0.68490890723598385), (+1.4282525720463917, +0.58612686779778356), (+1.5500683152743528, +0.23948063027984381), (+1.1996162749103028, +0.50185016173980079), (+1.6034867101936561, +0.45977284461210194), (+1.1179758136013382, +0.76544929433461273), (+1.7930443720457347, +0.71998710058857163), (+1.4290058149217986, +0.66665178253465385), (+1.3517163986341620, +0.27005295968981269), (+1.3796053423552685, +0.41717065712785834), (+1.1021002867843606, +0.83592998363965854), (+1.9844749392957077, +0.75032646960094329), (+0.11102230246251565E-15, -0.47184478546569153E-15), (-0.11102230246251565E-15, -0.33306690738754696E-15), (-0.22204460492503131E-15, -0.83266726846886741E-16), (+0.99920072216264089E-15, -0.27755575615628914E-15), (+0.55511151231257827E-15, -0.49960036108132044E-15), (-0.11102230246251565E-15, -0.16653345369377348E-15), (+0.11102230246251565E-15, -0.33306690738754696E-15), (+0.33306690738754696E-15, +0.0000000000000000), (+0.55511151231257827E-15, -0.22204460492503131E-15), (+0.0000000000000000, +0.11102230246251565E-15), (-0.33306690738754696E-15, -0.11102230246251565E-15), (+0.22204460492503131E-15, +0.38857805861880479E-15), (+0.33306690738754696E-15, +0.16653345369377348E-15), (-0.44408920985006262E-15, +0.0000000000000000), (-0.33306690738754696E-15, -0.27755575615628914E-15), (+0.0000000000000000, +0.16653345369377348E-15), (+0.22204460492503131E-15, +0.16653345369377348E-15), (-0.33306690738754696E-15, +0.16653345369377348E-15), (-0.22204460492503131E-15, -0.55511151231257827E-16), (+0.22204460492503131E-15, +0.88817841970012523E-15), (+0.33306690738754696E-15, +0.55511151231257827E-15), (-0.33306690738754696E-15, +0.38857805861880479E-15), (+0.44408920985006262E-15, +0.24980018054066022E-15), (+0.0000000000000000, +0.88817841970012523E-15), (+0.55511151231257827E-15, +0.83266726846886741E-15)

436reltol = sqrt(epsilon(1._TKG))

437reltol

438+0.14901161193847656E-7

439isClose(data, atad(1:size(data)), reltol = reltol)

440T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

441call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

442

443lenData = getUnifRand(5, 100)

444lenData

445+35

446data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

447data

448(+1.62130593364137533184764577367962512, +0.383061094545414257486010648583624719), (+1.50672811897635832956025188100904381, +0.635638088445651407569346055391068342), (+1.02937513724212656461142814406419373, +0.740573651789058730926429433092834783), (+1.47121681538268895766184519352798756, +0.542326129052610819580573860736109636E-3), (+1.09460718890969628460134482384601916, +0.970916969090479917649790568950804521), (+1.66493490045738647141988438928468677, +0.591936366652679973730265857355298007), (+1.51862998029208926528510812931891977, +0.417018689330315694672824277950673379), (+1.91730845294407775795865186006703658, +0.722669411660003002532233328576880478), (+1.50061551239826329033162950297824153, +0.708251637358003720213787427470136923), (+1.17839875348355797464592701096858827, +0.163616419856491797955671734224218524), (+1.70543499065818327505804795432357591, +0.508632388236930517811394014179628693), (+1.63934190674465540588346627257973216, +0.359900080591138389255431344246745557), (+1.73163302205091719849895051174042561, +0.345390728755733145619909494826521613), (+1.03840742722821080912508560623713667, +0.863220248585887440024139867518251392), (+1.28351579748434460771647389904070790, +0.204910153527783223775105920327238172), (+1.30005640967774988853920203419972190, +0.585558886935632846183346548711729005), (+1.23018658516367571270379403518288387, +0.711470205561996690499239892060640443), (+1.53518669469958414008050852472855266, +0.914718076126065695405289759334937509E-2), (+1.20989649868747096010372191720622722, +0.208458973436696970716496995712069841), (+1.83606720388102342892867107908688274, +0.583343268884284772421456766964099675E-1), (+1.23288636010232602773972720710753286, +0.794675580263459550313353958520049661), (+1.40318159140419818805163999721771025, +0.343596187817517508566463803365152428), (+1.64166005450924115286679648824499177, +0.325322970978148741735783106768245720), (+1.60455028034486808798954080209351161, +0.202003933001978264801576451500232058), (+1.90363245471006541982495414864468738, +0.983136885762669823452589636028735996), (+1.39537047806093606852281111332004322, +0.380071184076045498169230949668114551), (+1.42379072634068411297915175552295533, +0.803890515355403356640095172163799393), (+1.98200139854359937423862398290449372, +0.858933249203185091283862997776547571), (+1.74856369489590345168157210949845724, +0.168448678086033878069823937554911705E-1), (+1.02112782559571050028746920650476312, +0.173191729499280455732733235522989657), (+1.15367727760358263865844663345957166, +0.239288951025762452034447091307489353), (+1.08596133874757201913017719101779957, +0.122298338377892633882042232980248486), (+1.13733733316969414286470971898844773, +0.126027406027569027021260344494375105), (+1.39391042980820618664887226990212136, +0.513163205944634587301925608101369445), (+1.78450982514046149528561091062257892, +0.623245043362175292080694745909838211)

449

450atad = getFFTI(getFFTF(data))

451atad

452(+1.62130593364137533184764577367962531, +0.383061094545414257486010648583624719), (+1.50672811897635832956025188100904381, +0.635638088445651407569346055391068439), (+1.02937513724212656461142814406419354, +0.740573651789058730926429433092834590), (+1.47121681538268895766184519352798756, +0.542326129052610819580573860736296210E-3), (+1.09460718890969628460134482384601935, +0.970916969090479917649790568950804424), (+1.66493490045738647141988438928468716, +0.591936366652679973730265857355298199), (+1.51862998029208926528510812931891996, +0.417018689330315694672824277950673283), (+1.91730845294407775795865186006703696, +0.722669411660003002532233328576880190), (+1.50061551239826329033162950297824153, +0.708251637358003720213787427470136826), (+1.17839875348355797464592701096858827, +0.163616419856491797955671734224218765), (+1.70543499065818327505804795432357572, +0.508632388236930517811394014179628790), (+1.63934190674465540588346627257973235, +0.359900080591138389255431344246745750), (+1.73163302205091719849895051174042561, +0.345390728755733145619909494826521517), (+1.03840742722821080912508560623713667, +0.863220248585887440024139867518251585), (+1.28351579748434460771647389904070790, +0.204910153527783223775105920327238196), (+1.30005640967774988853920203419972210, +0.585558886935632846183346548711729197), (+1.23018658516367571270379403518288407, +0.711470205561996690499239892060640347), (+1.53518669469958414008050852472855286, +0.914718076126065695405289759334937509E-2), (+1.20989649868747096010372191720622722, +0.208458973436696970716496995712069745), (+1.83606720388102342892867107908688312, +0.583343268884284772421456766964099976E-1), (+1.23288636010232602773972720710753247, +0.794675580263459550313353958520049854), (+1.40318159140419818805163999721771045, +0.343596187817517508566463803365152524), (+1.64166005450924115286679648824499177, +0.325322970978148741735783106768245672), (+1.60455028034486808798954080209351199, +0.202003933001978264801576451500231841), (+1.90363245471006541982495414864468738, +0.983136885762669823452589636028735804), (+1.39537047806093606852281111332004322, +0.380071184076045498169230949668114407), (+1.42379072634068411297915175552295513, +0.803890515355403356640095172163799104), (+1.98200139854359937423862398290449372, +0.858933249203185091283862997776547090), (+1.74856369489590345168157210949845705, +0.168448678086033878069823937554912668E-1), (+1.02112782559571050028746920650476293, +0.173191729499280455732733235522989826), (+1.15367727760358263865844663345957166, +0.239288951025762452034447091307489522), (+1.08596133874757201913017719101779977, +0.122298338377892633882042232980248498), (+1.13733733316969414286470971898844793, +0.126027406027569027021260344494375032), (+1.39391042980820618664887226990212136, +0.513163205944634587301925608101369348), (+1.78450982514046149528561091062257872, +0.623245043362175292080694745909838211), (+0.192592994438723585305597794258492732E-33, -0.541667796858910083671993796352010808E-34), (-0.481482486096808963263994485646231830E-33, +0.240741243048404481631997242823115915E-33), (-0.288889491658085377958396691387739098E-33, -0.144444745829042688979198345693869549E-33), (-0.192592994438723585305597794258492732E-33, +0.962964972193617926527988971292463659E-34), (-0.962964972193617926527988971292463659E-34, +0.144444745829042688979198345693869549E-33), (+0.962964972193617926527988971292463659E-34, -0.962964972193617926527988971292463659E-34), (-0.962964972193617926527988971292463659E-34, -0.962964972193617926527988971292463659E-34), (-0.962964972193617926527988971292463659E-34, +0.00000000000000000000000000000000000), (+0.962964972193617926527988971292463659E-34, -0.120370621524202240815998621411557957E-33), (-0.962964972193617926527988971292463659E-34, -0.168518870133883137142398069976181140E-33), (-0.288889491658085377958396691387739098E-33, -0.144444745829042688979198345693869549E-33), (-0.962964972193617926527988971292463659E-34, -0.722223729145213444895991728469347744E-34), (-0.192592994438723585305597794258492732E-33, -0.144444745829042688979198345693869549E-33), (+0.00000000000000000000000000000000000, -0.481482486096808963263994485646231830E-34), (+0.00000000000000000000000000000000000, +0.00000000000000000000000000000000000), (-0.192592994438723585305597794258492732E-33, +0.962964972193617926527988971292463659E-34), (-0.192592994438723585305597794258492732E-33, +0.300926553810505602039996553528894894E-34), (-0.288889491658085377958396691387739098E-33, -0.192592994438723585305597794258492732E-33), (-0.385185988877447170611195588516985464E-33, -0.192592994438723585305597794258492732E-33), (+0.00000000000000000000000000000000000, +0.481482486096808963263994485646231830E-34), (+0.00000000000000000000000000000000000, +0.722223729145213444895991728469347744E-34), (+0.962964972193617926527988971292463659E-34, +0.481482486096808963263994485646231830E-34), (-0.962964972193617926527988971292463659E-34, +0.192592994438723585305597794258492732E-33), (+0.00000000000000000000000000000000000, +0.240741243048404481631997242823115915E-33), (+0.962964972193617926527988971292463659E-34, +0.240741243048404481631997242823115915E-33), (+0.192592994438723585305597794258492732E-33, -0.288889491658085377958396691387739098E-33), (+0.00000000000000000000000000000000000, -0.264815367353244929795196967105427506E-33), (-0.962964972193617926527988971292463659E-34, -0.120370621524202240815998621411557957E-33), (+0.192592994438723585305597794258492732E-33, -0.108333559371782016734398759270402162E-33)

453reltol = sqrt(epsilon(1._TKG))

454reltol

455+0.138777878078144567552953958511352539E-16

456isClose(data, atad(1:size(data)), reltol = reltol)

457T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

458call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

459

460lenData = getUnifRand(5, 100)

461lenData

462+10

463data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

464data

465+1.03976917, +1.77719593, +1.66510940, +1.94274569, +1.70135534, +1.95070076, +1.79022098, +1.26747739, +1.88558507, +1.05052388

466

467atad = getFFTI(getFFTF(data))

468atad

469+1.03976905, +1.77719581, +1.66510892, +1.94274557, +1.70135522, +1.95070028, +1.79022074, +1.26747692, +1.88558495, +1.05052388, +0.178813934E-6, +0.119209290E-6, -0.119209290E-6, +0.417232513E-6, +0.00000000, +0.357627869E-6

470reltol = sqrt(epsilon(1._TKG))

471reltol

472+0.345266977E-3

473isClose(data, atad(1:size(data)), reltol = reltol)

474T, T, T, T, T, T, T, T, T, T

475call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

476

477lenData = getUnifRand(5, 100)

478lenData

479+24

480data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

481data

482+1.3908871021914566, +1.8073277025935446, +1.7312545509986614, +1.0544677239891327, +1.6092417378284058, +1.1831457373670624, +1.0566545623904031, +1.8926204248115250, +1.6736328340213413, +1.6631625485361297, +1.0995500617259844, +1.7993307148047391, +1.3406399804340374, +1.5920663516304607, +1.9351383550829619, +1.3834765106212461, +1.7535066000860033, +1.3517850527487427, +1.9038024784080956, +1.8603583614584933, +1.2549222664449649, +1.5173827787628145, +1.2864848361436017, +1.0452249622587799

483

484atad = getFFTI(getFFTF(data))

485atad

486+1.3908871021914568, +1.8073277025935446, +1.7312545509986617, +1.0544677239891329, +1.6092417378284054, +1.1831457373670626, +1.0566545623904031, +1.8926204248115248, +1.6736328340213413, +1.6631625485361297, +1.0995500617259848, +1.7993307148047388, +1.3406399804340379, +1.5920663516304607, +1.9351383550829624, +1.3834765106212457, +1.7535066000860033, +1.3517850527487432, +1.9038024784080951, +1.8603583614584931, +1.2549222664449649, +1.5173827787628142, +1.2864848361436017, +1.0452249622587793, -0.11102230246251565E-15, +0.55511151231257827E-15, +0.0000000000000000, +0.0000000000000000, +0.11102230246251565E-15, +0.77715611723760958E-15, +0.66613381477509392E-15, +0.66613381477509392E-15

487reltol = sqrt(epsilon(1._TKG))

488reltol

489+0.14901161193847656E-7

490isClose(data, atad(1:size(data)), reltol = reltol)

491T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

492call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

493

494lenData = getUnifRand(5, 100)

495lenData

496+12

497data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

498data

499+1.00933329698023457000141414209882899, +1.15415461482710398582592931858453078, +1.64129544495926771795052849614689080, +1.55039213655490191447302503345617029, +1.96955081292262196785392606359271832, +1.64506326439615580978303760453917596, +1.78934933800051423535012568245749575, +1.70272683270232163900917680888343606, +1.39911517612565988288917970274503314, +1.63460200719158683620252791293035959, +1.33860176667633256442016465737051129, +1.82171261384765496740066748935458353

500

501atad = getFFTI(getFFTF(data))

502atad

503+1.00933329698023457000141414209882899, +1.15415461482710398582592931858453039, +1.64129544495926771795052849614689099, +1.55039213655490191447302503345617010, +1.96955081292262196785392606359271832, +1.64506326439615580978303760453917596, +1.78934933800051423535012568245749575, +1.70272683270232163900917680888343587, +1.39911517612565988288917970274503295, +1.63460200719158683620252791293035959, +1.33860176667633256442016465737051148, +1.82171261384765496740066748935458372, -0.288889491658085377958396691387739098E-33, -0.288889491658085377958396691387739098E-33, +0.288889491658085377958396691387739098E-33, -0.192592994438723585305597794258492732E-33

504reltol = sqrt(epsilon(1._TKG))

505reltol

506+0.138777878078144567552953958511352539E-16

507isClose(data, atad(1:size(data)), reltol = reltol)

508T, T, T, T, T, T, T, T, T, T, T, T

509call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

510

511

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 250 of file pm_fftnr.F90.

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

src/fortran/main/pm_fftnr.F90