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+64

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

5data

6(+1.35363078, +0.850536585), (+1.76230478, +0.403125823), (+1.52058148, +0.323670328), (+1.74957347, +0.837254286), (+1.89248490, +0.272002220), (+1.53184855, +0.976671576), (+1.67865527, +0.795257330), (+1.23342073, +0.781225801), (+1.90733695, +0.831930518), (+1.07923627, +0.762972236), (+1.60210681, +0.434480309), (+1.60158896, +0.559628367), (+1.76661313, +0.347639322E-1), (+1.98842096, +0.273532033), (+1.45209193, +0.891226351), (+1.30424333, +0.111671805), (+1.18760407, +0.590125859), (+1.92758811, +0.453391016), (+1.93787980, +0.594763219), (+1.97947049, +0.854501426), (+1.46676672, +0.269058764), (+1.67572773, +0.231776237E-1), (+1.71333814, +0.791001797), (+1.94029117, +0.742974401), (+1.35541368, +0.245553970), (+1.06889057, +0.697220862), (+1.25309885, +0.105981171), (+1.54548120, +0.147362769), (+1.18408704, +0.911541045), (+1.11111450, +0.721559703), (+1.62080908, +0.403082013), (+1.51198697, +0.356970966), (+1.80021405, +0.169198036), (+1.66469741, +0.811996162), (+1.48282003, +0.141573191), (+1.65015531, +0.903929472E-1), (+1.86565232, +0.690945923), (+1.86191034, +0.499667227), (+1.65237296, +0.755773008), (+1.31166387, +0.766082644), (+1.91893578, +0.627252340), (+1.43700099, +0.218657553), (+1.93633425, +0.107619822), (+1.36725950, +0.184263170), (+1.11198890, +0.556634486), (+1.30699325, +0.920636296), (+1.07754564, +0.134777606), (+1.40671897, +0.999252319), (+1.34291434, +0.105310261), (+1.45951188, +0.175603390), (+1.11373353, +0.807050884), (+1.17138672, +0.678204298), (+1.91886711, +0.588972807), (+1.70391345, +0.799611449), (+1.73306704, +0.663352251), (+1.66409075, +0.840653718), (+1.90506005, +0.485615373), (+1.09792519, +0.690066516), (+1.95829320, +0.160754859), (+1.20487225, +0.312345922), (+1.53974223, +0.559602797), (+1.33024454, +0.682484448), (+1.68886077, +0.230791569), (+1.09768867, +0.898053169)

7

8atad = getFFTI(getFFTF(data))

9atad

10(+1.35363066, +0.850536525), (+1.76230478, +0.403125882), (+1.52058136, +0.323670328), (+1.74957323, +0.837254167), (+1.89248490, +0.272002161), (+1.53184843, +0.976671696), (+1.67865527, +0.795257330), (+1.23342061, +0.781225860), (+1.90733671, +0.831930399), (+1.07923627, +0.762972355), (+1.60210681, +0.434480250), (+1.60158885, +0.559628367), (+1.76661313, +0.347640514E-1), (+1.98842096, +0.273532242), (+1.45209193, +0.891226411), (+1.30424321, +0.111671805), (+1.18760395, +0.590125799), (+1.92758811, +0.453391075), (+1.93787980, +0.594763100), (+1.97947025, +0.854501367), (+1.46676683, +0.269058764), (+1.67572761, +0.231778622E-1), (+1.71333814, +0.791001797), (+1.94029117, +0.742974401), (+1.35541368, +0.245553866), (+1.06889057, +0.697220862), (+1.25309896, +0.105981231), (+1.54548109, +0.147362933), (+1.18408704, +0.911540926), (+1.11111450, +0.721559703), (+1.62080908, +0.403082013), (+1.51198697, +0.356971174), (+1.80021393, +0.169197977), (+1.66469741, +0.811996222), (+1.48281991, +0.141573191), (+1.65015507, +0.903929472E-1), (+1.86565232, +0.690945923), (+1.86191010, +0.499667436), (+1.65237296, +0.755773067), (+1.31166387, +0.766082585), (+1.91893554, +0.627252340), (+1.43700099, +0.218657702), (+1.93633437, +0.107619882), (+1.36725938, +0.184263200), (+1.11198890, +0.556634426), (+1.30699325, +0.920636296), (+1.07754588, +0.134777576), (+1.40671885, +0.999252200), (+1.34291434, +0.105310217), (+1.45951188, +0.175603509), (+1.11373353, +0.807050884), (+1.17138672, +0.678204417), (+1.91886711, +0.588972747), (+1.70391321, +0.799611509), (+1.73306704, +0.663352251), (+1.66409087, +0.840653777), (+1.90505981, +0.485615373), (+1.09792519, +0.690066516), (+1.95829296, +0.160754919), (+1.20487225, +0.312345982), (+1.53974223, +0.559602797), (+1.33024478, +0.682484448), (+1.68886089, +0.230791673), (+1.09768867, +0.898053050)

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, 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+6

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

22data

23(+1.4527844996036610, +0.42487785604050010), (+1.6253006952573625, +0.70084431551777326), (+1.9901380522242098, +0.92470327006204689), (+1.5261164643397804, +0.17653363403418165E-1), (+1.3121241976642661, +0.52543605295321527), (+1.5344847655056706, +0.52892090438213257)

24

25atad = getFFTI(getFFTF(data))

26atad

27(+1.4527844996036607, +0.42487785604050010), (+1.6253006952573625, +0.70084431551777326), (+1.9901380522242094, +0.92470327006204667), (+1.5261164643397802, +0.17653363403417943E-1), (+1.3121241976642659, +0.52543605295321527), (+1.5344847655056704, +0.52892090438213257), (-0.11102230246251565E-15, +0.33306690738754696E-15), (+0.22204460492503131E-15, +0.11102230246251565E-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

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

34

35lenData = getUnifRand(5, 100)

36lenData

37+71

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

39data

40(+1.56515681248848262646523217101561332, +0.588340114359993536686444910906638329), (+1.08400469598635654280794208367117010, +0.630018991104678718692225442106903883), (+1.58900950637769560929323436724028780, +0.173435458963164376610972474237054131), (+1.59710336701127325929449949381845179, +0.378248423275564587250970797383514626), (+1.49499434629993445331360363678496450, +0.285927646876043058824087057548904277), (+1.40011549713923926122746445244825880, +0.251908885282559651315293727152462286), (+1.65382061019234267876429580883735628, +0.919274667835967729538186492965165562), (+1.73885967515117260584931547950968273, +0.253827053255831027381394287826961947), (+1.11086288463499084444510834661070453, +0.582938406078561506406978579407352766), (+1.17227936855072861552701609985810030, +0.315607129297604398076045719551113319), (+1.76195548758425140218122792406259162, +0.882587559227106904767084081308708514), (+1.61411472428528963987221612320351579, +0.848055029819524548409087269364722127), 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41

42atad = getFFTI(getFFTF(data))

43atad

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(-0.288889491658085377958396691387739098E-33, -0.288889491658085377958396691387739098E-33), (-0.481482486096808963263994485646231830E-33, -0.132407683676622464897598483552713753E-33), (-0.962964972193617926527988971292463659E-34, -0.674075480535532548569592279904724561E-33), (-0.770371977754894341222391177033970927E-33, -0.577778983316170755916793382775478196E-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

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

51

52lenData = getUnifRand(5, 100)

53lenData

54+27

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

56data

57+1.25180006, +1.33400357, +1.63004518, +1.19320846, +1.44465721, +1.48478448, +1.40832245, +1.00324464, +1.64531720, +1.37458754, +1.71682763, +1.29110646, +1.23105419, +1.92984891, +1.86805439, +1.65615392, +1.40940702, +1.62369847, +1.68870759, +1.72368145, +1.56065726, +1.68650818, +1.72736859, +1.36455488, +1.41196156, +1.46949410, +1.86083508

58

59atad = getFFTI(getFFTF(data))

60atad

61+1.25180018, +1.33400357, +1.63004529, +1.19320869, +1.44465685, +1.48478460, +1.40832222, +1.00324488, +1.64531708, +1.37458754, +1.71682775, +1.29110658, +1.23105431, +1.92984879, +1.86805439, +1.65615392, +1.40940702, +1.62369835, +1.68870747, +1.72368145, +1.56065702, +1.68650818, +1.72736847, +1.36455488, +1.41196156, +1.46949410, +1.86083519, +0.119209290E-6, +0.00000000, +0.357627869E-6, -0.178813934E-6, +0.238418579E-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

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

68

69lenData = getUnifRand(5, 100)

70lenData

71+80

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

73data

74+1.9454465569218473, +1.2982274146864394, +1.3126376128342212, +1.1967733737878916, +1.4038684483726835, +1.5747581350803159, +1.5940200617499427, +1.8404723468025384, +1.2959445127860816, +1.9232281860922817, +1.5359141853070621, +1.3082667963604213, +1.0362018185054755, +1.8042908802512114, +1.1260735413935197, +1.3209036679791035, +1.6688158514216695, +1.7415855619419176, +1.0497005335683012, +1.3575858062900823, +1.3943089447697719, +1.2607719488985036, +1.8133933021087474, +1.2408640914605553, +1.2169090488942744, +1.8956265857104451, +1.8288920430952147, +1.4804362073739927, +1.1383953646290295, +1.0164757855819633, +1.3778178294809504, +1.8300205615454717, +1.9790458856787279, +1.8762233257436085, +1.0885657598406897, +1.5711442730031768, +1.6934873497002521, +1.2244391996296859, +1.6579141755227975, +1.0782476232200495, +1.0781849120459444, +1.2210756360324846, +1.5005289423976813, +1.2037101383172621, +1.6200340991476385, +1.4843324012152437, +1.6260295301776797, +1.4980414438583600, +1.7327085092622512, +1.7549970059289339, +1.8761234057055201, +1.3530960499893103, +1.8305113037196317, +1.6390617337096294, +1.2355726687439945, +1.3517430291423007, +1.4511642528610138, +1.7078914486765839, +1.4321666194410105, +1.5094540196936448, +1.6326331482545653, +1.1545423231127327, +1.2102760685616607, +1.4828299011993706, +1.1039182665895133, +1.9597628293472595, +1.1919850484517309, +1.2975306890138216, +1.9562546629417183, +1.1110955194372711, +1.4076062026409164, +1.3032454810694631, +1.8975309576569319, +1.6742948039997017, +1.0223670534359728, +1.4704260338720041, +1.3077745988351324, +1.3484656112646720, +1.4288346331539996, +1.5423615626148934

75

76atad = getFFTI(getFFTF(data))

77atad

78+1.9454465569218475, +1.2982274146864390, +1.3126376128342214, +1.1967733737878918, +1.4038684483726831, +1.5747581350803157, +1.5940200617499423, +1.8404723468025388, +1.2959445127860818, +1.9232281860922815, +1.5359141853070624, +1.3082667963604218, +1.0362018185054751, +1.8042908802512114, +1.1260735413935197, +1.3209036679791035, +1.6688158514216691, +1.7415855619419176, +1.0497005335683012, +1.3575858062900823, +1.3943089447697716, +1.2607719488985036, +1.8133933021087465, +1.2408640914605555, +1.2169090488942742, +1.8956265857104451, +1.8288920430952142, +1.4804362073739932, +1.1383953646290290, +1.0164757855819635, +1.3778178294809500, +1.8300205615454717, +1.9790458856787283, +1.8762233257436081, +1.0885657598406904, +1.5711442730031764, +1.6934873497002521, +1.2244391996296855, +1.6579141755227980, +1.0782476232200493, +1.0781849120459448, +1.2210756360324844, +1.5005289423976818, +1.2037101383172621, +1.6200340991476387, +1.4843324012152435, +1.6260295301776804, +1.4980414438583596, +1.7327085092622514, +1.7549970059289337, +1.8761234057055205, +1.3530960499893099, +1.8305113037196321, +1.6390617337096287, +1.2355726687439952, +1.3517430291423000, +1.4511642528610140, +1.7078914486765835, +1.4321666194410108, +1.5094540196936443, +1.6326331482545653, +1.1545423231127321, +1.2102760685616611, +1.4828299011993700, +1.1039182665895135, +1.9597628293472595, +1.1919850484517311, +1.2975306890138214, +1.9562546629417188, +1.1110955194372709, +1.4076062026409171, +1.3032454810694629, +1.8975309576569319, +1.6742948039997017, +1.0223670534359728, +1.4704260338720045, +1.3077745988351328, +1.3484656112646713, +1.4288346331540001, +1.5423615626148934, +0.0000000000000000, -0.33306690738754696E-15, -0.11102230246251565E-15, -0.66613381477509392E-15, +0.66613381477509392E-15, -0.22204460492503131E-15, +0.55511151231257827E-15, -0.22204460492503131E-15, +0.11102230246251565E-15, -0.44408920985006262E-15, +0.44408920985006262E-15, -0.33306690738754696E-15, +0.66613381477509392E-15, +0.22204460492503131E-15, +0.66613381477509392E-15, +0.11102230246251565E-15, -0.33306690738754696E-15, +0.11102230246251565E-15, -0.33306690738754696E-15, -0.11102230246251565E-15, -0.11102230246251565E-15, +0.55511151231257827E-15, +0.0000000000000000, +0.44408920985006262E-15, -0.11102230246251565E-15, -0.33306690738754696E-15, -0.11102230246251565E-15, -0.11102230246251565E-15, +0.0000000000000000, +0.55511151231257827E-15, +0.11102230246251565E-15, +0.33306690738754696E-15, -0.22204460492503131E-15, +0.33306690738754696E-15, +0.0000000000000000, +0.55511151231257827E-15, -0.33306690738754696E-15, +0.66613381477509392E-15, -0.11102230246251565E-15, +0.44408920985006262E-15, +0.0000000000000000, -0.11102230246251565E-15, -0.22204460492503131E-15, +0.55511151231257827E-15, -0.55511151231257827E-15, +0.11102230246251565E-14, -0.33306690738754696E-15, +0.99920072216264089E-15

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

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

85

86lenData = getUnifRand(5, 100)

87lenData

88+79

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

90data

91+1.54743331843261794109122145006511828, +1.95813808388322356639761956616574235, +1.29333229475773617330995621609245034, +1.35717973199000568692195697597980027, +1.12185418449418541968299757011585434, +1.92194443306658348950215585242892772, +1.01664552474786547707008133360791197, +1.70365087900303147958176370911687649, +1.60915174100778121037441970418534602, +1.08821475714323003240446137708386684, +1.30900977884277218107612565129268903, +1.91217778290227691953639812501280773, +1.03482433762910653274761000956639874, +1.83875166158621417160720961469826275, +1.71849998205030874244942388458440468, +1.37000730500372623707629380453327596, +1.56370007340358281443116863315968491, +1.23246356743316037534425967043332870, +1.93560914795401704351803150256740669, +1.89971637798319338439252322696386808, +1.05659837283051848304927190521898724, +1.03044755939259209598872649715110340, +1.67451593154193462497657208239020653, +1.79020423635789233519230320872579789, +1.46218138643111083694714838691052897, +1.96185971380078364514825359341060792, +1.22895855478661818847457021691617877, +1.42976667513904262061924480235745427, +1.30234898405649004174874855475162174, +1.29382593607477985225172771489226295, +1.39443796229609524677461731663012162, +1.23589641852666587406860987756195372, +1.95401378242954356602385138707533890, +1.11310260081642191552297458011029874, +1.98975217697398415464890575748128925, +1.14235025592630108610505192470394253, +1.27109509698591461342851458447856391, +1.84438998390234052692403386114429847, +1.95369116470599864557920350926952521, +1.59324813512677368231587860232197594, +1.18810839750507167514760187491313971, +1.36737914520759262235023549353964678, +1.33749766105050628817834867361709418, +1.07233072088528210007057538339360682, +1.50079775493299093519528278863471509, +1.45122949936803837766861769823021010, +1.80809738767243180518858436573380208, +1.87476347711087736856849868175744665, +1.26413754227546573200673318428271782, +1.43197422172101360620524133072330032, +1.32539310472558751603043916160054225, +1.38272720282588698521017818558540420, +1.66687544904904403874452570766362839, +1.64710668039811323808150329447102837, +1.80870202499890112068243333061570631, +1.19520797610896645800185114160094666, +1.13422810366331551226129395180684483, +1.90771411083114585474332851342253529, +1.28492324347023476555728766776078840, +1.21447201524288861409320073017033519, +1.47677336173868672305121447585361610, +1.81228106723371880562839237068740649, +1.33196271847789014152310897531359569, +1.72286018932322654721339596347046614, +1.05450346568367300341178199949004297, +1.89039331268008922518568078042810625, +1.18965265556586913712970832463161924, +1.20063178794160658797375326345388864, +1.32032080388798840185478676035814274, +1.73947482286345262126716659433845695, +1.66201595584534628139747082814655718, +1.12216248472118061799018015336742336, +1.85700731202132338951620866795188361, +1.16848635921567193603974604252005471, +1.04537334074751829564853742338702872, +1.94349545600871572900442850611547150, +1.22956614568732530884266734943263118, +1.36523990708583990337970773717967643, +1.23452246754105740556366074692485894

92

93atad = getFFTI(getFFTF(data))

94atad

95+1.54743331843261794109122145006511809, +1.95813808388322356639761956616574273, +1.29333229475773617330995621609245034, +1.35717973199000568692195697597980046, +1.12185418449418541968299757011585396, +1.92194443306658348950215585242892791, +1.01664552474786547707008133360791177, +1.70365087900303147958176370911687649, +1.60915174100778121037441970418534640, +1.08821475714323003240446137708386665, +1.30900977884277218107612565129268980, +1.91217778290227691953639812501280773, +1.03482433762910653274761000956639894, +1.83875166158621417160720961469826275, +1.71849998205030874244942388458440526, +1.37000730500372623707629380453327596, +1.56370007340358281443116863315968452, +1.23246356743316037534425967043332870, +1.93560914795401704351803150256740631, +1.89971637798319338439252322696386846, +1.05659837283051848304927190521898685, +1.03044755939259209598872649715110301, +1.67451593154193462497657208239020615, +1.79020423635789233519230320872579750, +1.46218138643111083694714838691052877, +1.96185971380078364514825359341060811, +1.22895855478661818847457021691617877, +1.42976667513904262061924480235745446, +1.30234898405649004174874855475162136, +1.29382593607477985225172771489226256, +1.39443796229609524677461731663012162, +1.23589641852666587406860987756195410, +1.95401378242954356602385138707533909, +1.11310260081642191552297458011029836, +1.98975217697398415464890575748128944, +1.14235025592630108610505192470394253, +1.27109509698591461342851458447856391, +1.84438998390234052692403386114429847, +1.95369116470599864557920350926952521, +1.59324813512677368231587860232197594, +1.18810839750507167514760187491313971, +1.36737914520759262235023549353964658, +1.33749766105050628817834867361709456, +1.07233072088528210007057538339360682, +1.50079775493299093519528278863471528, +1.45122949936803837766861769823020990, +1.80809738767243180518858436573380285, +1.87476347711087736856849868175744704, +1.26413754227546573200673318428271743, +1.43197422172101360620524133072329993, +1.32539310472558751603043916160054225, +1.38272720282588698521017818558540420, +1.66687544904904403874452570766362839, +1.64710668039811323808150329447102799, +1.80870202499890112068243333061570631, +1.19520797610896645800185114160094647, +1.13422810366331551226129395180684445, +1.90771411083114585474332851342253548, +1.28492324347023476555728766776078840, +1.21447201524288861409320073017033538, +1.47677336173868672305121447585361610, +1.81228106723371880562839237068740688, +1.33196271847789014152310897531359530, +1.72286018932322654721339596347046614, +1.05450346568367300341178199949004278, +1.89039331268008922518568078042810645, +1.18965265556586913712970832463161924, +1.20063178794160658797375326345388883, +1.32032080388798840185478676035814293, +1.73947482286345262126716659433845695, +1.66201595584534628139747082814655737, +1.12216248472118061799018015336742336, +1.85700731202132338951620866795188322, +1.16848635921567193603974604252005528, +1.04537334074751829564853742338702834, +1.94349545600871572900442850611547246, +1.22956614568732530884266734943263118, +1.36523990708583990337970773717967701, +1.23452246754105740556366074692485914, -0.674075480535532548569592279904724561E-33, -0.962964972193617926527988971292463659E-34, -0.962964972193617926527988971292463659E-34, +0.288889491658085377958396691387739098E-33, -0.192592994438723585305597794258492732E-33, +0.385185988877447170611195588516985464E-33, +0.962964972193617926527988971292463659E-34, +0.385185988877447170611195588516985464E-33, +0.962964972193617926527988971292463659E-34, -0.385185988877447170611195588516985464E-33, +0.962964972193617926527988971292463659E-34, -0.385185988877447170611195588516985464E-33, -0.962964972193617926527988971292463659E-34, -0.288889491658085377958396691387739098E-33, +0.962964972193617926527988971292463659E-34, +0.00000000000000000000000000000000000, -0.385185988877447170611195588516985464E-33, -0.192592994438723585305597794258492732E-33, +0.385185988877447170611195588516985464E-33, +0.962964972193617926527988971292463659E-34, +0.962964972193617926527988971292463659E-34, +0.962964972193617926527988971292463659E-34, +0.385185988877447170611195588516985464E-33, +0.00000000000000000000000000000000000, +0.192592994438723585305597794258492732E-33, +0.00000000000000000000000000000000000, +0.385185988877447170611195588516985464E-33, +0.962964972193617926527988971292463659E-34, -0.385185988877447170611195588516985464E-33, -0.288889491658085377958396691387739098E-33, -0.962964972193617926527988971292463659E-34, -0.288889491658085377958396691387739098E-33, -0.962964972193617926527988971292463659E-34, -0.962964972193617926527988971292463659E-34, +0.481482486096808963263994485646231830E-33, +0.962964972193617926527988971292463659E-34, +0.00000000000000000000000000000000000, -0.385185988877447170611195588516985464E-33, +0.481482486096808963263994485646231830E-33, -0.962964972193617926527988971292463659E-34, -0.962964972193617926527988971292463659E-34, +0.00000000000000000000000000000000000, +0.00000000000000000000000000000000000, +0.192592994438723585305597794258492732E-33, -0.577778983316170755916793382775478196E-33, -0.288889491658085377958396691387739098E-33, -0.962964972193617926527988971292463659E-34, -0.481482486096808963263994485646231830E-33, -0.481482486096808963263994485646231830E-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, 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+68

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

107data

108(+1.64631510, +0.365983665), (+1.76745200, +0.149792731), (+1.17439389, +0.614043772), (+1.85118592, +0.411059439), (+1.06522822, +0.711008847), (+1.40478849, +0.373242319), (+1.33908057, +0.626225829), (+1.16138566, +0.503990889), (+1.68011332, +0.566571414), (+1.63083267, +0.896306396), (+1.88988245, +0.140628994), (+1.18190694, +0.631485462), (+1.96884894, +0.183727443), (+1.48285246, +0.993193805), (+1.57236719, +0.655704975), (+1.40318894, +0.289670229), (+1.25026822, +0.777505636E-1), (+1.93827987, +0.199810863E-1), (+1.37442255, +0.911904752), (+1.12689567, +0.845775127), (+1.45663989, +0.465329051), (+1.48303437, +0.632429242), (+1.21653652, +0.765025795), (+1.75699699, +0.828684509), (+1.79522240, +0.618468523E-1), (+1.85159159, +0.772437751), (+1.50252914, +0.977091908), (+1.28212285, +0.603873849), (+1.72178030, +0.168807685), (+1.27148068, +0.654257715), (+1.67875791, +0.405740321), (+1.12120926, +0.624014020), (+1.75440955, +0.630726874), (+1.16027021, +0.913848281E-1), (+1.10274386, +0.181998134), (+1.48640513, +0.566578507E-1), (+1.98826647, +0.760188997), (+1.87978268, +0.503049672), (+1.14567876, +0.975671053), (+1.07370150, +0.244176745), (+1.62057841, +0.561169446), (+1.78311729, +0.575906038E-1), (+1.94261003, +0.758237064), (+1.29938817, +0.116151273), (+1.37410355, +0.527051985), (+1.98540390, +0.594857633), (+1.05995309, +0.465359688E-1), (+1.97199440, +0.855516672), (+1.20440626, +0.621168733), (+1.56345510, +0.607424676), (+1.21327639, +0.268305600), (+1.87525272, +0.342294157), (+1.19911587, +0.571439862E-1), (+1.65156806, +0.987595320E-1), (+1.90742910, +0.856912553), (+1.71540856, +0.365718246), (+1.41042614, +0.305342078E-1), (+1.50423837, +0.305848598), (+1.34019041, +0.261076748), (+1.14455962, +0.341371298E-1), (+1.31595612, +0.733026743), (+1.34725070, +0.925665736), (+1.20535779, +0.355152011), (+1.89849377, +0.569838047), (+1.05260122, +0.537180722), (+1.10395885, +0.709676087), (+1.96628761, +0.212313235), (+1.75327718, +0.534370959)

109

110atad = getFFTI(getFFTF(data))

111atad

112(+1.64631546, +0.365983605), (+1.76745188, +0.149792761), (+1.17439365, +0.614043832), (+1.85118556, +0.411059320), (+1.06522810, +0.711008847), (+1.40478849, +0.373242199), (+1.33908033, +0.626225710), (+1.16138554, +0.503990591), (+1.68011355, +0.566571414), (+1.63083267, +0.896306396), (+1.88988233, +0.140629292), (+1.18190694, +0.631485462), (+1.96884894, +0.183727682), (+1.48285246, +0.993193746), (+1.57236731, +0.655704975), (+1.40318882, +0.289669901), (+1.25026822, +0.777506679E-1), (+1.93827987, +0.199812353E-1), (+1.37442243, +0.911904573), (+1.12689567, +0.845775008), (+1.45663977, +0.465329111), (+1.48303425, +0.632429242), (+1.21653652, +0.765025735), (+1.75699699, +0.828684270), (+1.79522228, +0.618470758E-1), (+1.85159159, +0.772437871), (+1.50252891, +0.977091968), (+1.28212261, +0.603873849), (+1.72178018, +0.168807954), (+1.27148080, +0.654257774), (+1.67875791, +0.405740470), (+1.12120950, +0.624014258), (+1.75440979, +0.630726755), (+1.16027021, +0.913847461E-1), (+1.10274386, +0.181998014), (+1.48640513, +0.566578954E-1), (+1.98826647, +0.760188580), (+1.87978268, +0.503049433), (+1.14567876, +0.975670815), (+1.07370150, +0.244176596), (+1.62057829, +0.561169505), (+1.78311753, +0.575906932E-1), (+1.94260979, +0.758236945), (+1.29938793, +0.116151392), (+1.37410355, +0.527052045), (+1.98540401, +0.594857693), (+1.05995309, +0.465359241E-1), (+1.97199416, +0.855516553), (+1.20440614, +0.621168613), (+1.56345499, +0.607424617), (+1.21327627, +0.268305540), (+1.87525249, +0.342294097), (+1.19911587, +0.571438968E-1), (+1.65156794, +0.987593830E-1), (+1.90742910, +0.856912255), (+1.71540833, +0.365718067), (+1.41042590, +0.305343270E-1), (+1.50423813, +0.305848777), (+1.34019017, +0.261076659), (+1.14455950, +0.341372117E-1), (+1.31595588, +0.733026683), (+1.34725058, +0.925665796), (+1.20535779, +0.355152071), (+1.89849341, +0.569838047), (+1.05260146, +0.537180781), (+1.10395873, +0.709676147), (+1.96628761, +0.212313056), (+1.75327706, +0.534370720), (+0.238418579E-6, +0.178813934E-6), (+0.596046448E-7, +0.596046448E-7), (+0.298023224E-6, +0.894069672E-7), (+0.238418579E-6, +0.298023224E-6), (-0.119209290E-6, +0.596046448E-7), (-0.238418579E-6, +0.00000000), (+0.596046448E-7, -0.119209290E-6), (+0.00000000, +0.298023224E-7), (+0.596046448E-7, -0.670552254E-7), (+0.00000000, -0.298023224E-7), (+0.119209290E-6, +0.00000000), (-0.119209290E-6, +0.894069672E-7), (+0.596046448E-7, -0.149011612E-7), (-0.119209290E-6, -0.298023224E-7), (+0.119209290E-6, +0.894069672E-7), (-0.596046448E-7, +0.119209290E-6), (+0.178813934E-6, +0.149011612E-7), (+0.119209290E-6, -0.298023224E-7), (+0.178813934E-6, +0.149011612E-6), (-0.119209290E-6, +0.00000000), (+0.596046448E-7, -0.134110451E-6), (-0.596046448E-7, -0.119209290E-6), (+0.238418579E-6, +0.00000000), (-0.596046448E-7, -0.894069672E-7), (+0.119209290E-6, -0.596046448E-7), (+0.00000000, -0.119209290E-6), (+0.119209290E-6, -0.894069672E-7), (-0.238418579E-6, -0.298023224E-6), (+0.119209290E-6, +0.178813934E-6), (-0.238418579E-6, +0.819563866E-7), (+0.178813934E-6, +0.268220901E-6), (-0.119209290E-6, +0.104308128E-6), (+0.596046448E-7, +0.476837158E-6), (+0.00000000, +0.178813934E-6), (+0.596046448E-7, +0.387430191E-6), (-0.119209290E-6, +0.819563866E-7), (+0.178813934E-6, +0.298023224E-7), (-0.178813934E-6, -0.894069672E-7), (+0.119209290E-6, +0.298023224E-6), (-0.596046448E-7, +0.596046448E-7), (+0.596046448E-7, +0.298023224E-7), (+0.00000000, +0.894069672E-7), (+0.119209290E-6, +0.134110451E-6), (+0.00000000, -0.149011612E-6), (+0.238418579E-6, +0.894069672E-7), (+0.00000000, +0.298023224E-7), (+0.119209290E-6, +0.372529030E-6), (+0.596046448E-7, +0.119209290E-6), (+0.119209290E-6, +0.268220901E-6), (+0.178813934E-6, +0.208616257E-6), (+0.119209290E-6, +0.268220901E-6), (+0.596046448E-7, +0.104308128E-6), (+0.298023224E-6, -0.149011612E-6), (+0.417232513E-6, -0.119209290E-6), (+0.178813934E-6, +0.327825546E-6), (+0.119209290E-6, +0.968575478E-7), (+0.178813934E-6, -0.596046448E-7), (+0.119209290E-6, -0.596046448E-7), (+0.119209290E-6, +0.178813934E-6), (+0.00000000, -0.596046448E-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, 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+62

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

124data

125(+1.2872980938995009, +0.59912709631339556), (+1.2634282241966681, +0.36179328226779861), (+1.9219795974356311, +0.31570215959909365), (+1.8217843277895449, +0.74166518686822014), (+1.4512768023516989, +0.59822942392313316), (+1.5247515976919153, +0.26156705941277059E-2), (+1.3192944387774013, +0.75500687081711881), (+1.4751333840168215, +0.25911674398703743), (+1.4819337407829019, +0.51136136714432867), (+1.8123476851831022, +0.45575273210710698), (+1.1642458165297129, +0.32137107379572905), (+1.8364011274355532, +0.17374682038260869), (+1.2365029926200037, +0.23389230272273187), (+1.3371769160492692, +0.74161772995483533), (+1.9571866099454147, +0.88693383378207280), (+1.6344649734811294, +0.84883308943383540), (+1.7297176900530222, +0.75826513029872533E-1), (+1.2500968634859317, +0.34137623369850456), (+1.6066557293724966, +0.13392253988492619), (+1.8497394667157399, +0.15866596374875974), (+1.5096199805698380, +0.43790164980056578), (+1.5129425494899400, +0.33013328028452882), (+1.7913105031677183, +0.20701271423144163), (+1.5445467469781624, +0.25499110311381867), (+1.4419676327211715, +0.17342668857120858), (+1.0517346934995206, +0.52458350150402455E-1), (+1.0653734308692169, +0.97592213069522404), (+1.9071930245219870, +0.93974458682175954), (+1.7132828734900145, +0.58200987564220752), (+1.0815262486400452, +0.12947780059959746), (+1.6773437490565675, +0.27538483116819290), (+1.9068011539666601, +0.23591306644723109), (+1.2518785806541075, +0.87182137029628104), (+1.2553301217488366, +0.82309786327986756), (+1.8922243657735689, +0.71307132526242600), (+1.3390449915647489, +0.36773008488871695), (+1.0217049965250555, +0.70914849518770473E-1), (+1.1778971840916963, +0.90485600957613055), (+1.7149343319692618, +0.98983939120382713), (+1.6322492282650991, +0.30261414592105740), (+1.8959443062197510, +0.18888917724069176), (+1.5024289248093234, +0.47970689072690254), (+1.5482268791132938, +0.53877902211087636), (+1.2800513803428974, +0.65629709216006860), (+1.6440760391556437, +0.21826596511537988), (+1.3346249094779417, +0.62870593755032744), (+1.4423552923063594, +0.52722031537022307), (+1.5171878097795988, +0.47936330648653147), (+1.6400022651989348, +0.77522338834197790E-1), (+1.1234865422904456, +0.23164186756402882), (+1.6306411340135245, +0.45853874222417712), (+1.6348978618113941, +0.61088086509094464), (+1.7881355063921698, +0.18276007610748157), (+1.9594281260362316, +0.78892378415951059), (+1.9660558663538370, +0.27298845568781349), (+1.4957364907661157, +0.34238921906493625), (+1.6345002936100419, +0.16204782353631242), (+1.8194037072621436, +0.84296393932676505), (+1.4895719834664201, +0.25145863281962533), (+1.9811777827049686, +0.68320398925550629), (+1.6059372412010116, +0.86705824210367521), (+1.1987192638337882, +0.13882835967150942)

126

127atad = getFFTI(getFFTF(data))

128atad

129(+1.2872980938995011, +0.59912709631339556), (+1.2634282241966683, +0.36179328226779872), (+1.9219795974356311, +0.31570215959909365), (+1.8217843277895449, +0.74166518686822025), (+1.4512768023516991, +0.59822942392313316), (+1.5247515976919150, +0.26156705941275393E-2), (+1.3192944387774010, +0.75500687081711848), (+1.4751333840168215, +0.25911674398703743), (+1.4819337407829019, +0.51136136714432867), (+1.8123476851831022, +0.45575273210710698), (+1.1642458165297129, +0.32137107379572938), (+1.8364011274355532, +0.17374682038260905), (+1.2365029926200042, +0.23389230272273201), (+1.3371769160492690, +0.74161772995483521), (+1.9571866099454145, +0.88693383378207280), (+1.6344649734811294, +0.84883308943383562), (+1.7297176900530224, +0.75826513029872533E-1), (+1.2500968634859317, +0.34137623369850439), (+1.6066557293724968, +0.13392253988492636), (+1.8497394667157396, +0.15866596374875999), (+1.5096199805698380, +0.43790164980056590), (+1.5129425494899400, +0.33013328028452893), (+1.7913105031677179, +0.20701271423144169), (+1.5445467469781624, +0.25499110311381878), (+1.4419676327211719, +0.17342668857120869), (+1.0517346934995206, +0.52458350150402566E-1), (+1.0653734308692173, +0.97592213069522382), (+1.9071930245219870, +0.93974458682175943), (+1.7132828734900145, +0.58200987564220763), (+1.0815262486400450, +0.12947780059959760), (+1.6773437490565672, +0.27538483116819285), (+1.9068011539666601, +0.23591306644723109), (+1.2518785806541077, +0.87182137029628104), (+1.2553301217488364, +0.82309786327986756), (+1.8922243657735689, +0.71307132526242589), (+1.3390449915647489, +0.36773008488871700), (+1.0217049965250558, +0.70914849518770418E-1), (+1.1778971840916961, +0.90485600957613044), (+1.7149343319692616, +0.98983939120382702), (+1.6322492282650991, +0.30261414592105740), (+1.8959443062197510, +0.18888917724069187), (+1.5024289248093234, +0.47970689072690254), (+1.5482268791132938, +0.53877902211087636), (+1.2800513803428979, +0.65629709216006871), (+1.6440760391556437, +0.21826596511537996), (+1.3346249094779414, +0.62870593755032744), (+1.4423552923063589, +0.52722031537022296), (+1.5171878097795988, +0.47936330648653125), (+1.6400022651989350, +0.77522338834197790E-1), (+1.1234865422904456, +0.23164186756402888), (+1.6306411340135247, +0.45853874222417718), (+1.6348978618113941, +0.61088086509094475), (+1.7881355063921700, +0.18276007610748160), (+1.9594281260362316, +0.78892378415951070), (+1.9660558663538370, +0.27298845568781333), (+1.4957364907661157, +0.34238921906493625), (+1.6345002936100421, +0.16204782353631253), (+1.8194037072621434, +0.84296393932676494), (+1.4895719834664201, +0.25145863281962499), (+1.9811777827049686, +0.68320398925550607), (+1.6059372412010116, +0.86705824210367521), (+1.1987192638337880, +0.13882835967150950), (+0.66613381477509392E-15, +0.61062266354383610E-15), (+0.88817841970012523E-15, +0.43021142204224816E-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, T, T, T, T

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

136

137lenData = getUnifRand(5, 100)

138lenData

139+95

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

141data

142(+1.73622062392813149880840898063388333, +0.801208572453290661653307094638786480), (+1.72249456053305511132328316649448693, +0.182896755268771364624549468322879765), (+1.42878224428446606083063508406486088, +0.812360055131961906239632914193645595), (+1.20086329721358974280831261279444659, +0.867037731903091975824266769258328304), (+1.68024679587476621093100567625034492, +0.851281872022113222597011716308615018), (+1.60889355914589215379011649508103752, +0.602469738059299851663076276312900815), (+1.29141818672572144912876845458483537, +0.943150251812655085362344344455704393), (+1.62498548892502252429800979349013477, +0.325096862094713411331214102771128134), (+1.86890055286701512531696228598500961, +0.332853619453493526065928210270757672), (+1.39859610357789933674594530261852337, +0.603906542563563334031562916506978253), (+1.44700285552916247731394862438548529, +0.453025975982851216175578162623703527), (+1.68868086020364076977950015493863127, +0.711115765896288935648912840271956268), (+1.66615221234588114008289471573487446, +0.308615843484322834699900507735361589), (+1.38738543787532874301030973279501328, +0.538639650241527165406803529624429759), (+1.14784809400954398338682259016500334, +0.827052093950873999376866880722379084), (+1.23841026972345439738251133826600280, +0.601534222901458955559169293032552395), (+1.21884855319975896268606029444464880, +0.681810413321157249157277676088942297), (+1.00861498435821039637467267191023978, +0.170726044144970129236163265379136886), (+1.98891524625878994297314222805993111, +0.525224703713855441296915019757112828E-3), (+1.13517262691190931089844086343492591, +0.748234512626445292381500302934265401), (+1.29891086702954254596959652640865111, +0.203223782848510082014189477645285295), (+1.22951900499338218589888047686347185, +0.930385865968816323206305085968691873), (+1.24380900267617081537007574070180605, +0.832838543227171991117335661051935431), (+1.89158848964222954207843743743600142, +0.347732814351654318679289986545872781), 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143

144atad = getFFTI(getFFTF(data))

145atad

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-0.962964972193617926527988971292463659E-34), (+0.00000000000000000000000000000000000, -0.337037740267766274284796139952362281E-33), (-0.674075480535532548569592279904724561E-33, -0.144444745829042688979198345693869549E-33), (-0.577778983316170755916793382775478196E-33, -0.240741243048404481631997242823115915E-34), (-0.962964972193617926527988971292463659E-33, +0.240741243048404481631997242823115915E-34), (-0.962964972193617926527988971292463659E-34, -0.264815367353244929795196967105427506E-33), (-0.962964972193617926527988971292463659E-33, -0.962964972193617926527988971292463659E-34), (+0.00000000000000000000000000000000000, -0.120370621524202240815998621411557957E-33), (-0.385185988877447170611195588516985464E-33, +0.240741243048404481631997242823115915E-33), (-0.192592994438723585305597794258492732E-33, -0.168518870133883137142398069976181140E-33), (-0.385185988877447170611195588516985464E-33, +0.722223729145213444895991728469347744E-34), (-0.288889491658085377958396691387739098E-33, +0.192592994438723585305597794258492732E-33), (-0.481482486096808963263994485646231830E-33, +0.385185988877447170611195588516985464E-33), (+0.288889491658085377958396691387739098E-33, -0.168518870133883137142398069976181140E-33), (-0.577778983316170755916793382775478196E-33, +0.240741243048404481631997242823115915E-33), (-0.288889491658085377958396691387739098E-33, -0.168518870133883137142398069976181140E-33), (-0.288889491658085377958396691387739098E-33, -0.240741243048404481631997242823115915E-33), (-0.192592994438723585305597794258492732E-33, -0.433334237487128066937595037081608647E-33), (+0.00000000000000000000000000000000000, -0.240741243048404481631997242823115915E-33), (+0.00000000000000000000000000000000000, -0.216667118743564033468797518540804323E-33), (-0.577778983316170755916793382775478196E-33, -0.288889491658085377958396691387739098E-33), (+0.962964972193617926527988971292463659E-34, -0.361111864572606722447995864234673872E-33), (-0.674075480535532548569592279904724561E-33, -0.385185988877447170611195588516985464E-33)

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, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, 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+27

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

158data

159+1.68201399, +1.00232470, +1.61510587, +1.25331771, +1.22081971, +1.80239987, +1.36975908, +1.12721646, +1.26581764, +1.39944518, +1.66443300, +1.79228187, +1.66711020, +1.97970533, +1.96673226, +1.97569263, +1.91853428, +1.04102755, +1.00205755, +1.14863598, +1.03359127, +1.52666187, +1.38653708, +1.40941858, +1.51484489, +1.14087069, +1.21848845

160

161atad = getFFTI(getFFTF(data))

162atad

163+1.68201411, +1.00232458, +1.61510587, +1.25331795, +1.22081971, +1.80239987, +1.36975873, +1.12721658, +1.26581776, +1.39944506, +1.66443300, +1.79228210, +1.66711044, +1.97970510, +1.96673203, +1.97569227, +1.91853440, +1.04102755, +1.00205731, +1.14863598, +1.03359151, +1.52666187, +1.38653696, +1.40941834, +1.51484501, +1.14087057, +1.21848822, +0.238418579E-6, -0.178813934E-6, +0.417232513E-6, -0.596046448E-7, +0.476837158E-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

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

170

171lenData = getUnifRand(5, 100)

172lenData

173+82

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

175data

176+1.9943623569838891, +1.5491322962711496, +1.6232942389539748, +1.7814318896761567, +1.8637469705443299, +1.3730671369136673, +1.3667746790771433, +1.8950572178111100, +1.5419981065123345, +1.3697483422247263, +1.6148117046539017, +1.8705250372574493, +1.4828584665170998, +1.2814257161442681, +1.5859449354544675, +1.1162752679376173, +1.5742722315367830, +1.3596378602419601, +1.1130849139888594, +1.6741419732947769, +1.7846273959758077, +1.8500025902508854, +1.4050989478426561, +1.7288993565463500, +1.0990820194184980, +1.7804507596681252, +1.1905780439004345, +1.4672198744580769, +1.2491475795972062, +1.5505750475340703, +1.8128760303260654, +1.6660219434387125, +1.5578093761687515, +1.6460762626635033, +1.0311203004165930, +1.6581479387034086, +1.3288054982859172, +1.8714790531930787, +1.0616583250369538, +1.3378567968151454, +1.6696850417401539, +1.5324230289119154, +1.2227478932806335, +1.9646640147479286, +1.4047594994508883, +1.6290725264096655, +1.7434236142112103, +1.6842864124322103, +1.2973776062131843, +1.3428290890968451, +1.9381919468716933, +1.0704606544831070, +1.1340668924869377, +1.6804158297150624, +1.2759966240719041, +1.7865424696909664, +1.5475666078832440, +1.3181831584657275, +1.5374920050044243, +1.0294706814018280, +1.8270461720422406, +1.7918704417094260, +1.4936518888366010, +1.7613740913337677, +1.4686830741659256, +1.3482161618731352, +1.2972672400960463, +1.8658649000320779, +1.7852341469017698, +1.6496690379778176, +1.0481402721591317, +1.6132039481627720, +1.8750185725381434, +1.2539617983732447, +1.7649960741059949, +1.1666558260201889, +1.8969774119277361, +1.2545129684021026, +1.7009905049586762, +1.0253010874005537, +1.7805666140397396, +1.5959600186141971

177

178atad = getFFTI(getFFTF(data))

179atad

180+1.9943623569838891, +1.5491322962711496, +1.6232942389539751, +1.7814318896761572, +1.8637469705443293, +1.3730671369136673, +1.3667746790771431, +1.8950572178111100, +1.5419981065123345, +1.3697483422247263, +1.6148117046539019, +1.8705250372574498, +1.4828584665170996, +1.2814257161442679, +1.5859449354544672, +1.1162752679376173, +1.5742722315367825, +1.3596378602419601, +1.1130849139888592, +1.6741419732947778, +1.7846273959758072, +1.8500025902508850, +1.4050989478426559, +1.7288993565463500, +1.0990820194184980, +1.7804507596681245, +1.1905780439004343, +1.4672198744580771, +1.2491475795972060, +1.5505750475340703, +1.8128760303260649, +1.6660219434387122, +1.5578093761687515, +1.6460762626635028, +1.0311203004165934, +1.6581479387034090, +1.3288054982859179, +1.8714790531930783, +1.0616583250369540, +1.3378567968151449, +1.6696850417401543, +1.5324230289119150, +1.2227478932806342, +1.9646640147479291, +1.4047594994508885, +1.6290725264096648, +1.7434236142112103, +1.6842864124322101, +1.2973776062131850, +1.3428290890968446, +1.9381919468716937, +1.0704606544831072, +1.1340668924869384, +1.6804158297150615, +1.2759966240719045, +1.7865424696909655, +1.5475666078832440, +1.3181831584657266, +1.5374920050044247, +1.0294706814018275, +1.8270461720422402, +1.7918704417094249, +1.4936518888366010, +1.7613740913337668, +1.4686830741659256, +1.3482161618731348, +1.2972672400960461, +1.8658649000320784, +1.7852341469017698, +1.6496690379778172, +1.0481402721591320, +1.6132039481627718, +1.8750185725381434, +1.2539617983732447, +1.7649960741059951, +1.1666558260201891, +1.8969774119277358, +1.2545129684021021, +1.7009905049586762, +1.0253010874005537, +1.7805666140397391, +1.5959600186141967, +0.22204460492503131E-15, -0.77715611723760958E-15, +0.33306690738754696E-15, -0.33306690738754696E-15, +0.11102230246251565E-14, -0.33306690738754696E-15, +0.44408920985006262E-15, -0.33306690738754696E-15, +0.33306690738754696E-15, -0.11102230246251565E-15, +0.66613381477509392E-15, -0.11102230246251565E-15, +0.88817841970012523E-15, +0.33306690738754696E-15, -0.33306690738754696E-15, +0.11102230246251565E-15, +0.0000000000000000, -0.22204460492503131E-15, -0.11102230246251565E-15, +0.11102230246251565E-15, +0.44408920985006262E-15, +0.11102230246251565E-15, -0.11102230246251565E-15, -0.22204460492503131E-15, +0.22204460492503131E-15, -0.22204460492503131E-15, +0.0000000000000000, +0.66613381477509392E-15, -0.11102230246251565E-15, +0.22204460492503131E-15, +0.55511151231257827E-15, -0.11102230246251565E-15, +0.0000000000000000, +0.22204460492503131E-15, -0.11102230246251565E-15, +0.55511151231257827E-15, +0.11102230246251565E-15, +0.55511151231257827E-15, +0.33306690738754696E-15, +0.11102230246251565E-15, +0.33306690738754696E-15, +0.22204460492503131E-15, -0.33306690738754696E-15, +0.99920072216264089E-15, +0.0000000000000000, +0.12212453270876722E-14

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, T, T, T, T, T, T, T, T, T, T, T, T, T, T, 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+89

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

192data

193+1.82900799641165078697561870506615269, +1.98311621191317144987332467730561899, +1.40442817704097775540090628238025953, +1.13700317489691300715148895373934973, +1.40631311017523963154614638358385200, +1.36081773756427833727016325121661505, +1.65537545132086323737696629802464763, +1.48260377521187948060801145328255090, +1.53775965245809372255332047396932601, +1.14545173492478986360466359100546650, +1.18368972000999853954866750933330756, +1.67203052627280312953325762446501027, +1.31553128097371255697466375679319056, +1.38024322709594665554311356206392051, +1.07350652395294603274559570802286201, +1.65406530891075149738808446962091834, +1.71898653446424155075667594123731864, +1.05392766267149392785352325540449827, +1.70030995304648623725020625636083233, +1.98294663256918093955966426013757329, +1.45309319785955896309917027062459581, +1.44470666667655417311562941903731803, +1.71341542234626829332748695341593702, +1.22903083174438617727241274961937927, +1.63052676489086300248973995253443442, +1.85559852721967892737946518089438066, +1.68817904132405256241422768483157729, +1.40889581942286247815931563638314873, +1.44539200129294392345776803998272210, +1.44576067933892762624439537933266990, +1.54218143039497395390448611702798055, +1.90400833594768892596940525814119872, +1.55380592555790071341206303268025521, +1.39559041454803985402230388036001769, +1.37607803922678982182806749313228014, +1.23684228804096478963145807821653864, +1.81836849595423462240856153161564264, +1.11234556673832645753989237492425999, +1.44116839009773534378268215051541716, +1.87773616233692500096427829478146265, +1.66211322533169658330084245629237070, +1.56424060968110895799186881280273631, +1.71954037514040166379464446405875739, +1.35768612891127513616746257053025424, +1.83225877410400473807279305199667210, +1.04358748601216831195593523947587292, +1.04073101127189413742146183194080298, +1.95944381940483950452059261816763330, +1.07314550699362485878212650150508815, +1.02679086151511805104454365266985544, +1.89391759472159716821760492313418429, +1.06779642689604510905536635572467158, +1.89165812432340483599336728237273873, +1.45428670057552789638455404172747990, +1.07942193868506600158179253860830709, +1.13847831375314126984292826880335538, +1.64597185985876603488166121354044319, +1.08271971803090395677175254917182570, +1.62334145115778483176916898301607541, +1.25127551196282978844648928771755731, +1.35180217333654305056465067968945195, +1.67017380572833819527121633747183921, +1.17946432636548101585623242885075194, +1.26452909646612357519555867821127582, +1.42275044307933663717064728782058032, +1.58612650544524545297803786560550062, +1.96111873467371105969613938813650671, +1.78546236863488572904505710022999202, +1.58633609542241374140915799730604390, +1.95784811421922035815703250194234796, +1.97852124894023021158901485967910835, +1.21178957225518242761231014679072706, +1.64263768885529000873115712726736461, +1.89118840564397214240297424346517650, +1.56640533675318040097623102971498802, +1.88988714104159542528009937888915673, +1.60710098416214016220766403341528625, +1.98565277530174705879900912170733334, +1.26050701126629603127439065672425226, +1.02232458370087927528484356374275198, +1.90831472414350656965840784270628515, +1.40520813059863483679849075070422351, +1.02686180219155271729687841698465383, +1.09752041898950644035363513640816546, +1.31394419553872626174671063365193772, +1.51129684808091214625027847515700738, +1.80940833984721548490943303929372799, +1.08429043025774324737074551104550148, +1.76850941213020008574957439105995574

194

195atad = getFFTI(getFFTF(data))

196atad

197+1.82900799641165078697561870506615308, +1.98311621191317144987332467730561918, +1.40442817704097775540090628238025953, +1.13700317489691300715148895373934973, +1.40631311017523963154614638358385219, +1.36081773756427833727016325121661486, +1.65537545132086323737696629802464744, +1.48260377521187948060801145328255109, +1.53775965245809372255332047396932697, +1.14545173492478986360466359100546650, +1.18368972000999853954866750933330814, +1.67203052627280312953325762446501027, +1.31553128097371255697466375679319094, +1.38024322709594665554311356206392071, +1.07350652395294603274559570802286258, +1.65406530891075149738808446962091834, +1.71898653446424155075667594123731864, +1.05392766267149392785352325540449808, +1.70030995304648623725020625636083233, +1.98294663256918093955966426013757329, +1.45309319785955896309917027062459581, +1.44470666667655417311562941903731803, +1.71341542234626829332748695341593683, +1.22903083174438617727241274961937946, +1.63052676489086300248973995253443461, +1.85559852721967892737946518089438124, +1.68817904132405256241422768483157787, +1.40889581942286247815931563638314873, +1.44539200129294392345776803998272191, +1.44576067933892762624439537933267010, +1.54218143039497395390448611702798093, +1.90400833594768892596940525814119949, +1.55380592555790071341206303268025560, +1.39559041454803985402230388036001769, +1.37607803922678982182806749313228053, +1.23684228804096478963145807821653864, +1.81836849595423462240856153161564302, +1.11234556673832645753989237492425999, +1.44116839009773534378268215051541755, +1.87773616233692500096427829478146304, +1.66211322533169658330084245629237128, +1.56424060968110895799186881280273650, +1.71954037514040166379464446405875797, +1.35768612891127513616746257053025462, +1.83225877410400473807279305199667249, +1.04358748601216831195593523947587273, +1.04073101127189413742146183194080336, +1.95944381940483950452059261816763446, +1.07314550699362485878212650150508815, +1.02679086151511805104454365266985506, +1.89391759472159716821760492313418468, +1.06779642689604510905536635572467120, +1.89165812432340483599336728237273873, +1.45428670057552789638455404172747951, +1.07942193868506600158179253860830748, +1.13847831375314126984292826880335519, +1.64597185985876603488166121354044396, +1.08271971803090395677175254917182570, +1.62334145115778483176916898301607579, +1.25127551196282978844648928771755750, +1.35180217333654305056465067968945234, +1.67017380572833819527121633747183921, +1.17946432636548101585623242885075233, +1.26452909646612357519555867821127582, +1.42275044307933663717064728782058070, +1.58612650544524545297803786560550082, +1.96111873467371105969613938813650651, +1.78546236863488572904505710022999202, +1.58633609542241374140915799730604410, +1.95784811421922035815703250194234815, +1.97852124894023021158901485967910874, +1.21178957225518242761231014679072667, +1.64263768885529000873115712726736461, +1.89118840564397214240297424346517708, +1.56640533675318040097623102971498783, +1.88988714104159542528009937888915750, +1.60710098416214016220766403341528664, +1.98565277530174705879900912170733392, +1.26050701126629603127439065672425245, +1.02232458370087927528484356374275218, +1.90831472414350656965840784270628535, +1.40520813059863483679849075070422332, +1.02686180219155271729687841698465402, +1.09752041898950644035363513640816508, +1.31394419553872626174671063365193811, +1.51129684808091214625027847515700719, +1.80940833984721548490943303929372818, +1.08429043025774324737074551104550129, +1.76850941213020008574957439105995593, -0.577778983316170755916793382775478196E-33, -0.192592994438723585305597794258492732E-33, -0.674075480535532548569592279904724561E-33, +0.00000000000000000000000000000000000, +0.192592994438723585305597794258492732E-33, +0.481482486096808963263994485646231830E-33, -0.385185988877447170611195588516985464E-33, +0.962964972193617926527988971292463659E-34, -0.288889491658085377958396691387739098E-33, +0.00000000000000000000000000000000000, -0.192592994438723585305597794258492732E-33, +0.288889491658085377958396691387739098E-33, +0.962964972193617926527988971292463659E-34, +0.385185988877447170611195588516985464E-33, +0.962964972193617926527988971292463659E-34, +0.192592994438723585305597794258492732E-33, -0.192592994438723585305597794258492732E-33, +0.962964972193617926527988971292463659E-34, -0.385185988877447170611195588516985464E-33, +0.962964972193617926527988971292463659E-34, +0.962964972193617926527988971292463659E-34, +0.481482486096808963263994485646231830E-33, -0.962964972193617926527988971292463659E-34, +0.962964972193617926527988971292463659E-34, -0.962964972193617926527988971292463659E-34, +0.481482486096808963263994485646231830E-33, +0.962964972193617926527988971292463659E-34, +0.288889491658085377958396691387739098E-33, +0.962964972193617926527988971292463659E-34, +0.385185988877447170611195588516985464E-33, +0.962964972193617926527988971292463659E-34, +0.481482486096808963263994485646231830E-33, -0.288889491658085377958396691387739098E-33, +0.288889491658085377958396691387739098E-33, -0.385185988877447170611195588516985464E-33, +0.288889491658085377958396691387739098E-33, -0.192592994438723585305597794258492732E-33, +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, T, T, T, T, 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+62

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

209data

210(+1.85071564, +0.419135690E-1), (+1.51691031, +0.572207093), (+1.00296378, +0.946370602), (+1.49922299, +0.463548899E-1), (+1.52788281, +0.878078640), (+1.87015128, +0.903750300), (+1.80691087, +0.379768252), (+1.77514458, +0.120518208E-1), (+1.91453230, +0.413053989), (+1.82080364, +0.124681950), (+1.20228934, +0.831910431), (+1.81690693, +0.410019159), (+1.88452089, +0.288110495), (+1.76407242, +0.669558644), (+1.46151233, +0.860551059), (+1.61853552, +0.345108926), (+1.90025353, +0.791506052), (+1.65427887, +0.937721014), (+1.03618622, +0.938274860), (+1.11484575, +0.291123986E-1), (+1.60527611, +0.306969225), (+1.90393710, +0.550005734), (+1.42275262, +0.281945944), (+1.68483591, +0.455856740), (+1.13853574, +0.553468466E-1), (+1.57550168, +0.409046590), (+1.77681637, +0.620706618), (+1.28798318, +0.491065025), (+1.47290468, +0.498378396), (+1.86268044, +0.461289585), (+1.09498048, +0.260646284), (+1.21951509, +0.502201915E-1), (+1.33304965, +0.556609631E-1), (+1.43893003, +0.254619956), (+1.20546460, +0.763327241), (+1.15875173, +0.830578327), (+1.17064631, +0.245153546), (+1.13371563, +0.928914189), (+1.70110798, +0.713871956), (+1.95944691, +0.573145032), (+1.81949055, +0.428452492), (+1.99875295, +0.388777316), (+1.31643140, +0.203176737E-1), (+1.30618739, +0.557358563), (+1.52900374, +0.271800935), (+1.79807591, +0.904367387), (+1.66528964, +0.291920304E-1), (+1.04084706, +0.666687846), (+1.25582838, +0.699002504), (+1.15339088, +0.519800723), (+1.65965486, +0.456891656), (+1.44883275, +0.173589766), (+1.04228163, +0.873485625), (+1.01408708, +0.185068548), (+1.70601606, +0.271433055), (+1.26930869, +0.285949290), (+1.33953726, +0.587063968), (+1.52994990, +0.933203161), (+1.84912848, +0.511943102E-1), (+1.39219785, +0.994023442), (+1.91552889, +0.371736586), (+1.56714177, +0.735446215E-1)

211

212atad = getFFTI(getFFTF(data))

213atad

214(+1.85071588, +0.419135392E-1), (+1.51691031, +0.572207093), (+1.00296378, +0.946370542), (+1.49922276, +0.463550091E-1), (+1.52788281, +0.878078580), (+1.87015128, +0.903750241), (+1.80691075, +0.379768133), (+1.77514458, +0.120517313E-1), (+1.91453242, +0.413054019), (+1.82080376, +0.124682039), (+1.20228946, +0.831910312), (+1.81690669, +0.410019130), (+1.88452077, +0.288110495), (+1.76407242, +0.669558585), (+1.46151233, +0.860551178), (+1.61853552, +0.345109046), (+1.90025365, +0.791506112), (+1.65427887, +0.937720954), (+1.03618622, +0.938274860), (+1.11484575, +0.291123986E-1), (+1.60527611, +0.306969285), (+1.90393710, +0.550005674), (+1.42275262, +0.281946033), (+1.68483579, +0.455856740), (+1.13853610, +0.553468466E-1), (+1.57550168, +0.409046710), (+1.77681637, +0.620706618), (+1.28798318, +0.491065025), (+1.47290444, +0.498378307), (+1.86268067, +0.461289585), (+1.09498048, +0.260646343), (+1.21951485, +0.502202734E-1), (+1.33305001, +0.556609333E-1), (+1.43893003, +0.254619956), (+1.20546460, +0.763327301), (+1.15875173, +0.830578208), (+1.17064643, +0.245153517), (+1.13371563, +0.928914130), (+1.70110798, +0.713871956), (+1.95944691, +0.573144913), (+1.81949067, +0.428452581), (+1.99875295, +0.388777405), (+1.31643140, +0.203178525E-1), (+1.30618739, +0.557358503), (+1.52900362, +0.271800935), (+1.79807591, +0.904367268), (+1.66528964, +0.291922092E-1), (+1.04084706, +0.666687906), (+1.25582850, +0.699002564), (+1.15339100, +0.519800723), (+1.65965462, +0.456891626), (+1.44883275, +0.173589736), (+1.04228163, +0.873485684), (+1.01408720, +0.185068697), (+1.70601606, +0.271433085), (+1.26930869, +0.285949349), (+1.33953750, +0.587063909), (+1.52994990, +0.933203042), (+1.84912848, +0.511943698E-1), (+1.39219785, +0.994023323), (+1.91552877, +0.371736676), (+1.56714201, +0.735446811E-1), (+0.298023224E-6, +0.447034836E-7), (+0.238418579E-6, +0.156462193E-6)

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, 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+46

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

226data

227(+1.3532427665443199, +0.58328395666718913), (+1.7268456495309361, +0.33326731326424053E-2), (+1.6339345384966617, +0.21061643406505115), (+1.7814160899386213, +0.21203854215859907), (+1.1242372285389386, +0.52008001666520975), (+1.9180373045598134, +0.62000173616153775), (+1.8045535713217626, +0.40438274929972762), (+1.6993596422912933, +0.62168993444443310), (+1.4480337370749232, +0.54187562528934030), (+1.6177771214230385, +0.44920156665396904), (+1.1426243411295411, +0.97110103360792555), (+1.3276285112779127, +0.76184171188714267), (+1.0883127935900934, +0.70584206790073223), (+1.2293350190550947, +0.60096347066169709), (+1.0751026886048183, +0.20421826084935180), (+1.3202513937602363, +0.46436577624177788), (+1.1589376948954526, +0.76455853438720334), (+1.4493364855794004, +0.54190417873060470), (+1.9006558965844702, +0.26734407127565818), (+1.4749570762146222, +0.75321007205217527), (+1.4029270564560026, +0.90206813448301448), (+1.1465174121010755, +0.70727111134896092), (+1.3926575056413408, +0.48438168700315132), (+1.5784692910657292, +0.91500397794518684), (+1.9524735785245348, +0.18169791794732904), (+1.2452169059731921, +0.12093529295584138), (+1.1598350933384154, +0.17657490524527575), (+1.6986746619545867, +0.10741042392567335), (+1.1015837882743131, +0.43588069183007228), (+1.2780550473704406, +0.76514151587047308), (+1.4100239824416203, +0.72236269649626961), (+1.4627021538291292, +0.23398398731938208), (+1.3053135416877293, +0.44418759433660604), (+1.1683261365447513, +0.55160298670646202), (+1.9402706015644120, +0.63282871718226330E-1), (+1.7521342443537717, +0.61936806948218459E-1), (+1.0816272930735233, +0.15469425297773376), (+1.7723519103545906, +0.91692046004307137E-1), (+1.7504709410415877, +0.41384547815284101), (+1.1572224359897332, +0.37040484094415183), (+1.4176799022268709, +0.35249205415753515), (+1.2298727076378264, +0.50353570149949156), (+1.1214189164587320, +0.25222361072007626), (+1.5813064029322337, +0.12363021051729217), (+1.6452838836274191, +0.63139676012892487), (+1.1354686947080057, +0.84981816409583555)

228

229atad = getFFTI(getFFTF(data))

230atad

231(+1.3532427665443199, +0.58328395666718924), (+1.7268456495309363, +0.33326731326424053E-2), (+1.6339345384966613, +0.21061643406505157), (+1.7814160899386211, +0.21203854215859941), (+1.1242372285389384, +0.52008001666520998), (+1.9180373045598134, +0.62000173616153809), (+1.8045535713217622, +0.40438274929972767), (+1.6993596422912931, +0.62168993444443310), (+1.4480337370749234, +0.54187562528934063), (+1.6177771214230381, +0.44920156665396915), (+1.1426243411295411, +0.97110103360792543), (+1.3276285112779127, +0.76184171188714278), (+1.0883127935900931, +0.70584206790073245), (+1.2293350190550942, +0.60096347066169731), (+1.0751026886048181, +0.20421826084935243), (+1.3202513937602360, +0.46436577624177833), (+1.1589376948954526, +0.76455853438720323), (+1.4493364855794004, +0.54190417873060492), (+1.9006558965844700, +0.26734407127565796), (+1.4749570762146225, +0.75321007205217516), (+1.4029270564560026, +0.90206813448301437), (+1.1465174121010753, +0.70727111134896092), (+1.3926575056413411, +0.48438168700315098), (+1.5784692910657294, +0.91500397794518684), (+1.9524735785245348, +0.18169791794732901), (+1.2452169059731921, +0.12093529295584132), (+1.1598350933384156, +0.17657490524527583), (+1.6986746619545872, +0.10741042392567332), (+1.1015837882743131, +0.43588069183007216), (+1.2780550473704406, +0.76514151587047308), (+1.4100239824416203, +0.72236269649626927), (+1.4627021538291289, +0.23398398731938175), (+1.3053135416877293, +0.44418759433660621), (+1.1683261365447513, +0.55160298670646224), (+1.9402706015644118, +0.63282871718226358E-1), (+1.7521342443537717, +0.61936806948218279E-1), (+1.0816272930735233, +0.15469425297773370), (+1.7723519103545904, +0.91692046004307248E-1), (+1.7504709410415877, +0.41384547815284073), (+1.1572224359897334, +0.37040484094415144), (+1.4176799022268707, +0.35249205415753493), (+1.2298727076378260, +0.50353570149949156), (+1.1214189164587323, +0.25222361072007582), (+1.5813064029322339, +0.12363021051729156), (+1.6452838836274191, +0.63139676012892476), (+1.1354686947080053, +0.84981816409583510), (+0.66613381477509392E-15, +0.27755575615628914E-16), (+0.44408920985006262E-15, -0.77715611723760958E-15), (+0.0000000000000000, +0.38857805861880479E-15), (-0.22204460492503131E-15, -0.16653345369377348E-15), (+0.22204460492503131E-15, +0.41633363423443370E-15), (+0.33306690738754696E-15, -0.11102230246251565E-15), (+0.0000000000000000, +0.22204460492503131E-15), (-0.55511151231257827E-15, -0.49960036108132044E-15), (+0.33306690738754696E-15, +0.33306690738754696E-15), (+0.33306690738754696E-15, -0.55511151231257827E-16), (+0.44408920985006262E-15, +0.41633363423443370E-15), (+0.11102230246251565E-15, -0.16653345369377348E-15), (+0.66613381477509392E-15, +0.47184478546569153E-15), (+0.77715611723760958E-15, +0.30531133177191805E-15), (+0.33306690738754696E-15, +0.13877787807814457E-15), (+0.0000000000000000, -0.16653345369377348E-15), (+0.11102230246251565E-15, +0.83266726846886741E-15), (+0.44408920985006262E-15, +0.65225602696727947E-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

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

238

239lenData = getUnifRand(5, 100)

240lenData

241+44

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

243data

244(+1.99288783386318952565238514847986358, +0.622973892817481745882368815072716481), (+1.35387471331460121713164624862298983, +0.380595413100220118215593007100841496), (+1.01637637211927198499182725597926923, +0.839718313846387089524236910711668108), (+1.85769565395745514129608872008935845, +0.765645322476601066024607727572131553), (+1.99032214344889918381036637961141231, +0.860292615016914249693048220511367678), (+1.07035288626646627379375556510024834, +0.987222481099684074554124092991090909), (+1.90816593453251576191445568512139263, +0.868156134154063094428678252464122750), (+1.87814742616824792847530015058993161, +0.801603558541520281103337998227778462), (+1.60713152155952069341479130071971525, +0.994047894949773492811129857159482237), (+1.67627073829230116175227527156441992, +0.587316025111869892197668405871366128), (+1.48724061840698959414885581770490235, +0.460123746557947489220424376256425695), (+1.25939873556829048102956604327336936, +0.184729382305047478487878352542880754), (+1.44392269859080410563583809618939908, +0.269831843074531773516982252363834717), (+1.07990408692294437288353050583374684, +0.832356353210373298964832085407430550), (+1.15877219026318172285322513854955472, +0.588912363330316058229466698685011185), (+1.39836377826071773594465307417161429, +0.920266405372786304060117826840942045), (+1.05710100548582516665827152891220056, +0.600467011296220637309525745223182610), (+1.58998725898010430830890236636895802, +0.188864684017770785360681704152801590), (+1.92945514464877316881071040036946798, +0.123061179495823923058969916597772785), (+1.17742283547286287313383971586127959, +0.661208470409158552013367449932076473), (+1.57445573508373870182037285472928528, +0.968579429344948524052546929520690620), (+1.44731147730519755968818966284919249, +0.279783072885672276228457591778993297), (+1.89493311948004120789982957072062054, +0.614848553800964816156219205586298580), (+1.44834102335428028621037253293777686, +0.422801475007475823677148031424818545), (+1.24768229649414685895802718827437647, +0.528241381249870339446891762219666521), (+1.40244857596648981472543087623982006, +0.809475655556552048006368934884221985), (+1.90002519219489401765892353610523806, +0.321912321098226959230026515749560586), (+1.36418909655478984690746893499857133, +0.215800030259320529482636842353598167), (+1.34269692071362276196943602729100331, +0.222300672970445340108425462475894185), (+1.32782726637371664467063954549965404, +0.130701323901298211028144887873094491), (+1.80826550089568724588922574572529581, +0.267964274656401854720840816827184829E-1), (+1.07144617171881327518697883685428599, +0.805933250336321453434825430468546340E-1), (+1.70744545120328722984509146694533938, +0.647538128209182864203680578236905383), (+1.20952276628617670530393521287705436, +0.777784574784859307721881423048723146), (+1.85487447775431437484715486248522058, +0.123787132621637822579253954027616327), (+1.30144411772095544722309166789410239, +0.915204822145983314329134687094762892E-1), (+1.12108346597606046296666078385607773, +0.760773424821429120080626010121375037), (+1.78141154463290846715736217694176394, +0.201709051075464922102802222934087587), (+1.48972665612977692617647988328285260, +0.932821510409836156215625843551769190), (+1.06987383910247279918197823800932643, +0.601296519659206255431867850231173896), (+1.98413226229363927694315995684732599, +0.237217538768183690004151341063860676E-1), (+1.98360732712810285193125693891875392, +0.351434009443686827843150692603502514), (+1.92195934264819956667890232258902025, +0.618348710970881730078443825629777247), (+1.76625341271626339568211914696463024, +0.435722600291172816317397116583682241)

245

246atad = getFFTI(getFFTF(data))

247atad

248(+1.99288783386318952565238514847986358, +0.622973892817481745882368815072716577), (+1.35387471331460121713164624862298983, +0.380595413100220118215593007100841496), (+1.01637637211927198499182725597926884, +0.839718313846387089524236910711668301), (+1.85769565395745514129608872008935864, +0.765645322476601066024607727572131842), (+1.99032214344889918381036637961141269, +0.860292615016914249693048220511367774), (+1.07035288626646627379375556510024834, +0.987222481099684074554124092991090813), (+1.90816593453251576191445568512139244, +0.868156134154063094428678252464122653), (+1.87814742616824792847530015058993238, +0.801603558541520281103337998227778365), (+1.60713152155952069341479130071971487, +0.994047894949773492811129857159482333), (+1.67627073829230116175227527156441954, +0.587316025111869892197668405871366321), (+1.48724061840698959414885581770490216, +0.460123746557947489220424376256425839), (+1.25939873556829048102956604327336916, +0.184729382305047478487878352542880995), (+1.44392269859080410563583809618939908, +0.269831843074531773516982252363834814), (+1.07990408692294437288353050583374646, +0.832356353210373298964832085407430647), (+1.15877219026318172285322513854955433, +0.588912363330316058229466698685011185), (+1.39836377826071773594465307417161410, +0.920266405372786304060117826840942045), (+1.05710100548582516665827152891220056, +0.600467011296220637309525745223182514), (+1.58998725898010430830890236636895802, +0.188864684017770785360681704152801590), (+1.92945514464877316881071040036946779, +0.123061179495823923058969916597772881), (+1.17742283547286287313383971586127959, +0.661208470409158552013367449932076473), (+1.57445573508373870182037285472928528, +0.968579429344948524052546929520690813), (+1.44731147730519755968818966284919211, +0.279783072885672276228457591778993104), (+1.89493311948004120789982957072062035, +0.614848553800964816156219205586298484), (+1.44834102335428028621037253293777725, +0.422801475007475823677148031424818593), (+1.24768229649414685895802718827437628, +0.528241381249870339446891762219666521), (+1.40244857596648981472543087623982006, +0.809475655556552048006368934884221889), (+1.90002519219489401765892353610523787, +0.321912321098226959230026515749560394), (+1.36418909655478984690746893499857133, +0.215800030259320529482636842353597975), (+1.34269692071362276196943602729100293, +0.222300672970445340108425462475894137), (+1.32782726637371664467063954549965385, +0.130701323901298211028144887873094203), (+1.80826550089568724588922574572529542, +0.267964274656401854720840816827182663E-1), (+1.07144617171881327518697883685428561, +0.805933250336321453434825430468545137E-1), (+1.70744545120328722984509146694533938, +0.647538128209182864203680578236905383), (+1.20952276628617670530393521287705436, +0.777784574784859307721881423048723146), (+1.85487447775431437484715486248522058, +0.123787132621637822579253954027616279), (+1.30144411772095544722309166789410239, +0.915204822145983314329134687094761448E-1), (+1.12108346597606046296666078385607753, +0.760773424821429120080626010121375423), (+1.78141154463290846715736217694176394, +0.201709051075464922102802222934087924), (+1.48972665612977692617647988328285241, +0.932821510409836156215625843551769479), (+1.06987383910247279918197823800932663, +0.601296519659206255431867850231173992), (+1.98413226229363927694315995684732561, +0.237217538768183690004151341063859713E-1), (+1.98360732712810285193125693891875354, +0.351434009443686827843150692603502514), (+1.92195934264819956667890232258902006, +0.618348710970881730078443825629776862), (+1.76625341271626339568211914696463004, +0.435722600291172816317397116583682000), (-0.288889491658085377958396691387739098E-33, -0.192592994438723585305597794258492732E-33), (-0.674075480535532548569592279904724561E-33, +0.00000000000000000000000000000000000), (-0.674075480535532548569592279904724561E-33, -0.144444745829042688979198345693869549E-33), (-0.192592994438723585305597794258492732E-33, -0.481482486096808963263994485646231830E-34), (-0.962964972193617926527988971292463659E-34, -0.481482486096808963263994485646231830E-34), (-0.962964972193617926527988971292463659E-34, -0.132407683676622464897598483552713753E-33), (+0.00000000000000000000000000000000000, +0.192592994438723585305597794258492732E-33), (-0.962964972193617926527988971292463659E-34, +0.144444745829042688979198345693869549E-33), (-0.192592994438723585305597794258492732E-33, -0.288889491658085377958396691387739098E-33), (-0.288889491658085377958396691387739098E-33, -0.240741243048404481631997242823115915E-34), (-0.674075480535532548569592279904724561E-33, +0.00000000000000000000000000000000000), (+0.962964972193617926527988971292463659E-34, +0.144444745829042688979198345693869549E-33), (+0.00000000000000000000000000000000000, +0.962964972193617926527988971292463659E-34), (-0.962964972193617926527988971292463659E-34, -0.481482486096808963263994485646231830E-34), (+0.00000000000000000000000000000000000, +0.216667118743564033468797518540804323E-33), (+0.962964972193617926527988971292463659E-34, +0.481482486096808963263994485646231830E-34), (-0.962964972193617926527988971292463659E-34, -0.433334237487128066937595037081608647E-33), (+0.00000000000000000000000000000000000, -0.108333559371782016734398759270402162E-33), (-0.770371977754894341222391177033970927E-33, -0.722223729145213444895991728469347744E-34), (-0.962964972193617926527988971292463659E-34, +0.120370621524202240815998621411557957E-33)

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, 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+14

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

260data

261+1.93936205, +1.15372944, +1.34803295, +1.09325993, +1.79897416, +1.31385911, +1.31966233, +1.91820049, +1.04904628, +1.49916005, +1.44679356, +1.94508529, +1.36509144, +1.45832741

262

263atad = getFFTI(getFFTF(data))

264atad

265+1.93936193, +1.15372956, +1.34803271, +1.09326017, +1.79897404, +1.31385922, +1.31966233, +1.91820025, +1.04904616, +1.49916017, +1.44679332, +1.94508517, +1.36509132, +1.45832753, +0.238418579E-6, +0.298023224E-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

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

272

273lenData = getUnifRand(5, 100)

274lenData

275+72

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

277data

278+1.1476646657885401, +1.7448391990525698, +1.6984124166597079, +1.7748291036067694, +1.2302431809353545, +1.8340980289858015, +1.2498309151597575, +1.1964492578172736, +1.2170697434348607, +1.2282482678615108, +1.9074781391765605, +1.2653617739690537, +1.7281902705014502, +1.9314985911281979, +1.8044737456576638, +1.2243544203781891, +1.1419061740382999, +1.3148758664288738, +1.6267273915087135, +1.7905285135509235, +1.7892116093624066, +1.3091964307567303, +1.5793578261341989, +1.7319931039770622, +1.0567243538819955, +1.8618229731427676, +1.2264126038607754, +1.7631729787843018, +1.8014778962143627, +1.6344760086300174, +1.2305093198787658, +1.0987226157931325, +1.5063568728644232, +1.9704236280434322, +1.2190384785421542, +1.2532577345319966, +1.7726740781615113, +1.2059870710506535, +1.2774438717377197, +1.6536546674274994, +1.9027067319176525, +1.6518839601341870, +1.4235612281040209, +1.4790285782546158, +1.9524749502939081, +1.6938807654594126, +1.3117871725439680, +1.8490380366783938, +1.3155031429490156, +1.8124420672468209, +1.1985111289056574, +1.7185300699202655, +1.7121353096916361, +1.0673846253478545, +1.9730546789303465, +1.5248990661224073, +1.8089709092634330, +1.1060890042886342, +1.5327827658136473, +1.0785656445281315, +1.5441101509235413, +1.8920879004907174, +1.3170044200785533, +1.9175720474362241, +1.4870860119458409, +1.1138993692980534, +1.4317685375816351, +1.4344269564453085, +1.8703144621921917, +1.5848569781130142, +1.1882017828199585, +1.3983444351254988

279

280atad = getFFTI(getFFTF(data))

281atad

282+1.1476646657885401, +1.7448391990525698, +1.6984124166597079, +1.7748291036067700, +1.2302431809353536, +1.8340980289858013, +1.2498309151597571, +1.1964492578172741, +1.2170697434348612, +1.2282482678615110, +1.9074781391765607, +1.2653617739690541, +1.7281902705014500, +1.9314985911281979, +1.8044737456576634, +1.2243544203781895, +1.1419061740382996, +1.3148758664288742, +1.6267273915087133, +1.7905285135509239, +1.7892116093624053, +1.3091964307567303, +1.5793578261341981, +1.7319931039770617, +1.0567243538819953, +1.8618229731427673, +1.2264126038607750, +1.7631729787843020, +1.8014778962143616, +1.6344760086300174, +1.2305093198787649, +1.0987226157931327, +1.5063568728644232, +1.9704236280434322, +1.2190384785421542, +1.2532577345319966, +1.7726740781615109, +1.2059870710506528, +1.2774438717377197, +1.6536546674274990, +1.9027067319176525, +1.6518839601341868, +1.4235612281040206, +1.4790285782546158, +1.9524749502939081, +1.6938807654594124, +1.3117871725439678, +1.8490380366783934, +1.3155031429490158, +1.8124420672468204, +1.1985111289056576, +1.7185300699202650, +1.7121353096916356, +1.0673846253478538, +1.9730546789303460, +1.5248990661224064, +1.8089709092634325, +1.1060890042886338, +1.5327827658136473, +1.0785656445281313, +1.5441101509235411, +1.8920879004907167, +1.3170044200785531, +1.9175720474362232, +1.4870860119458409, +1.1138993692980534, +1.4317685375816351, +1.4344269564453087, +1.8703144621921917, +1.5848569781130140, +1.1882017828199585, +1.3983444351254986, +0.0000000000000000, -0.11102230246251565E-15, +0.0000000000000000, -0.33306690738754696E-15, +0.22204460492503131E-15, +0.11102230246251565E-15, +0.33306690738754696E-15, -0.55511151231257827E-15, +0.66613381477509392E-15, -0.11102230246251565E-15, +0.55511151231257827E-15, -0.22204460492503131E-15, +0.33306690738754696E-15, +0.33306690738754696E-15, +0.66613381477509392E-15, +0.11102230246251565E-15, +0.55511151231257827E-15, +0.0000000000000000, +0.55511151231257827E-15, -0.44408920985006262E-15, +0.88817841970012523E-15, +0.11102230246251565E-15, +0.55511151231257827E-15, -0.22204460492503131E-15, -0.22204460492503131E-15, +0.33306690738754696E-15, +0.22204460492503131E-15, +0.33306690738754696E-15, -0.22204460492503131E-15, +0.55511151231257827E-15, -0.11102230246251565E-15, +0.55511151231257827E-15, -0.11102230246251565E-15, +0.44408920985006262E-15, +0.22204460492503131E-15, +0.11102230246251565E-15, -0.33306690738754696E-15, +0.55511151231257827E-15, -0.11102230246251565E-15, +0.33306690738754696E-15, +0.0000000000000000, +0.55511151231257827E-15, +0.0000000000000000, +0.33306690738754696E-15, -0.22204460492503131E-15, +0.11102230246251565E-14, +0.0000000000000000, +0.88817841970012523E-15, +0.11102230246251565E-15, +0.77715611723760958E-15, +0.0000000000000000, +0.22204460492503131E-15, -0.44408920985006262E-15, +0.88817841970012523E-15, -0.11102230246251565E-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, 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+29

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

294data

295+1.99031949043579523194747923205459192, +1.03788623487274758523944017117788750, +1.04751117934634024578784202532112087, +1.17301167796431941788941404225907669, +1.56086837114725794064871398370311761, +1.07317014862888536640412457983659621, +1.18361534050705771420850428736745229, +1.88896700601977593806108529739358918, +1.44227136247595314879570839393121994, +1.78579260148120646362293568364231289, +1.84966284297974811708052008717466900, +1.43237190675286770981602881052353287, +1.28834447585028828312734316502681482, +1.80379922597514013652606604367912888, +1.54878711048712355902036739166405027, +1.15754073996267302947521668478366574, +1.89579865094221849417630513201617023, +1.73752783001008999832232965235086463, +1.93608146413362323604740491500185490, +1.83867529761986196652404448470910455, +1.42886190576943923098834531082810230, +1.17161438883358000245236017868015350, +1.49950514801924772935351916516825101, +1.73918241153003854759745097116994161, +1.63965835684583820375642648257542680, +1.22760130799154511824607531233281517, +1.33376107672332555039592800589509386, +1.38098095380180663967104327086721046, +1.10319336665416135683688255887507934

296

297atad = getFFTI(getFFTF(data))

298atad

299+1.99031949043579523194747923205459173, +1.03788623487274758523944017117788750, +1.04751117934634024578784202532112125, +1.17301167796431941788941404225907669, +1.56086837114725794064871398370311761, +1.07317014862888536640412457983659659, +1.18361534050705771420850428736745229, +1.88896700601977593806108529739358938, +1.44227136247595314879570839393121975, +1.78579260148120646362293568364231328, +1.84966284297974811708052008717466939, +1.43237190675286770981602881052353287, +1.28834447585028828312734316502681501, +1.80379922597514013652606604367912927, +1.54878711048712355902036739166405085, +1.15754073996267302947521668478366574, +1.89579865094221849417630513201617004, +1.73752783001008999832232965235086463, +1.93608146413362323604740491500185528, +1.83867529761986196652404448470910513, +1.42886190576943923098834531082810230, +1.17161438883358000245236017868015350, +1.49950514801924772935351916516825081, +1.73918241153003854759745097116994180, +1.63965835684583820375642648257542680, +1.22760130799154511824607531233281517, +1.33376107672332555039592800589509367, +1.38098095380180663967104327086721046, +1.10319336665416135683688255887507914, -0.962964972193617926527988971292463659E-34, -0.481482486096808963263994485646231830E-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

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

306

307lenData = getUnifRand(5, 100)

308lenData

309+37

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

311data

312(+1.28388023, +0.679135621), (+1.62055683, +0.632081568), (+1.10525489, +0.956767082), (+1.02820706, +0.554713011E-1), (+1.45134985, +0.249545991), (+1.24468541, +0.650671124E-1), (+1.75359654, +0.295577228), (+1.86462414, +0.423409939E-1), (+1.79844582, +0.265492439), (+1.11592078, +0.726555169), (+1.44368720, +0.210435569), (+1.39592826, +0.947424591), (+1.26280618, +0.619368494), (+1.08347821, +0.512089491), (+1.51225388, +0.749766886), (+1.18776321, +0.986686885), (+1.19956374, +0.631551147E-1), (+1.49506998, +0.158718169), (+1.23925614, +0.162278712), (+1.10504723, +0.462690532), (+1.82812405, +0.528158247), (+1.01500154, +0.391506672), (+1.78335094, +0.189334512), (+1.76128912, +0.519298196), (+1.39701200, +0.360585034), (+1.71391702, +0.159029186), (+1.90852106, +0.760363996), (+1.88242042, +0.985730052), (+1.76545262, +0.115747809), (+1.56871843, +0.354975522), (+1.12439644, +0.573829830), (+1.69112349, +0.523168385), (+1.35980558, +0.355942249E-1), (+1.27308595, +0.553343415), (+1.25602400, +0.301479876), (+1.40362144, +0.535042882), (+1.59117460, +0.920210361)

313

314atad = getFFTI(getFFTF(data))

315atad

316(+1.28388023, +0.679135561), (+1.62055683, +0.632081509), (+1.10525465, +0.956766963), (+1.02820683, +0.554713905E-1), (+1.45134974, +0.249546081), (+1.24468541, +0.650672242E-1), (+1.75359654, +0.295577168), (+1.86462379, +0.423409119E-1), (+1.79844570, +0.265492529), (+1.11592066, +0.726555228), (+1.44368696, +0.210435629), (+1.39592814, +0.947424471), (+1.26280594, +0.619368672), (+1.08347821, +0.512089610), (+1.51225376, +0.749767005), (+1.18776321, +0.986686826), (+1.19956374, +0.631550997E-1), (+1.49506986, +0.158718035), (+1.23925602, +0.162278637), (+1.10504711, +0.462690502), (+1.82812381, +0.528158307), (+1.01500142, +0.391506702), (+1.78335094, +0.189334556), (+1.76128888, +0.519298017), (+1.39701176, +0.360585034), (+1.71391678, +0.159029216), (+1.90852082, +0.760363817), (+1.88242006, +0.985729694), (+1.76545238, +0.115747988), (+1.56871796, +0.354975581), (+1.12439632, +0.573829770), (+1.69112325, +0.523168445), (+1.35980558, +0.355942547E-1), (+1.27308607, +0.553343296), (+1.25602412, +0.301479727), (+1.40362167, +0.535042644), (+1.59117436, +0.920210481), (-0.596046448E-7, -0.670552254E-7), (-0.596046448E-7, +0.104308128E-6), (+0.417232513E-6, +0.968575478E-7), (+0.596046448E-7, -0.298023224E-7), (+0.119209290E-6, -0.894069672E-7), (+0.119209290E-6, +0.596046448E-7), (+0.417232513E-6, -0.596046448E-7), (-0.596046448E-7, -0.178813934E-6), (+0.596046448E-7, -0.178813934E-6), (-0.596046448E-7, -0.596046448E-7), (+0.596046448E-7, -0.298023224E-7), (-0.596046448E-7, +0.149011612E-7), (+0.238418579E-6, +0.149011612E-7), (-0.119209290E-6, +0.193715096E-6), (+0.119209290E-6, +0.178813934E-6), (+0.00000000, -0.119209290E-6), (+0.119209290E-6, -0.298023224E-7), (-0.596046448E-7, +0.447034836E-7), (+0.178813934E-6, +0.178813934E-6), (+0.00000000, +0.00000000), (+0.298023224E-6, +0.298023224E-7), (+0.00000000, +0.149011612E-6), (+0.298023224E-6, +0.208616257E-6), (+0.178813934E-6, -0.119209290E-6), (+0.298023224E-6, -0.298023224E-7), (-0.596046448E-7, +0.00000000), (+0.178813934E-6, +0.119209290E-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

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

323

324lenData = getUnifRand(5, 100)

325lenData

326+98

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

328data

329(+1.9381444032650132, +0.50482728875689220), (+1.0412957218538830, +0.11170170732801765), (+1.8612852516777423, +0.81792163116127015), (+1.2400791361741552, +0.70306328120003092), (+1.4162715052396841, +0.32242027741854684), (+1.3194049116666204, +0.92113791304896298), (+1.2658448079519720, +0.16929500427812394), (+1.2456058975154503, +0.17162937510398923), (+1.7011593749372791, +0.58521660483579563), (+1.2261937021586695, +0.29556011036907537), (+1.5664880248492832, +0.57788702972730310E-1), (+1.2178420576145610, +0.54558179110515448), (+1.4376340220743666, +0.38533955776808160), (+1.4642256812211976, +0.24539510722493418), (+1.9549378546033898, +0.26232383313809970), (+1.1323736133083835, +0.78812046056053164), (+1.5340721695824875, +0.64116826084257539), (+1.6479337550509066, +0.12944521420307997E-1), (+1.7155630623469493, +0.75348567134264777), (+1.4290879945785582, +0.44792763690998505), (+1.8221806467035404, +0.84571567977158668), (+1.8867551302164154, +0.94031271519760162), (+1.6577011445398728, +0.91974421237452142), (+1.2463575701062961, +0.53401165496433489), (+1.0243000840134953, +0.37323519086792334), (+1.6763661687282250, +0.51876077182836466), (+1.7433150991897355, +0.20829490779829318), (+1.1178886337474900, +0.68481145901761364), (+1.8999008022597383, +0.81491950325310902), (+1.0381945959838186, +0.87408769760349303), (+1.5366730975225420, +0.28299728722552253), (+1.0879729844975139, +0.48659117402786090), (+1.5316957636061503, +0.34433205735467620), (+1.7329556174635403, +0.33402494104751268E-1), (+1.7361533778546570, +0.67895280752357312), (+1.3904317247729387, +0.42634827211494131), (+1.9614623787315533, +0.87291815139914464E-1), (+1.1263612604243183, +0.80625955467873023), (+1.2157653460211379, +0.40456739582395251), (+1.3181542749001960, +0.52194368681317771E-1), (+1.2094356415950889, +0.44591688085485892), (+1.1541241788581598, +0.31589439839092393), (+1.8760312358819009, +0.43158649747503253), (+1.0896418158009407, +0.24793242326574116), (+1.5687814293098978, +0.23501915924135308), (+1.6903614094782204, +0.42849912073099439), (+1.6066060649941041, +0.64248681869520263), (+1.8491632187280223, +0.27469756885138075), (+1.4961264898053450, +0.64070520873393422), (+1.0124707454642072, +0.74483467337742248), (+1.7310118692331598, +0.44139706062343442), (+1.6878870834318151, +0.40341917432554664), (+1.4212394568771183, +0.70535364607882700), (+1.1036957258266429, +0.44465324708210896), (+1.3943902727693334, +0.45039477286756524), (+1.1566676720856686, +0.32561659179609492), (+1.3679223278906076, +0.83177305419554659), (+1.7120528068823675, +0.76776712971376893E-1), (+1.6476003858622095, +0.18524704711215945), (+1.7791429235195195, +0.92580890148890371E-1), (+1.7270022456256569, +0.47965167631583705), (+1.8474166254459223, +0.28471188563070315), (+1.8837901451541290, +0.18305895685295748), (+1.4562070983881217, +0.65471099654214837), (+1.3908175065822261, +0.36747369234447957), (+1.0512389419144563, +0.56042200406520970E-1), (+1.1806198067372820, +0.71489607175349179), (+1.0536450097327899, +0.61381535336467208), (+1.5562299219763827, +0.71195219420933942), (+1.3669754847928215, +0.86403407158834322E-1), (+1.9988617274787543, +0.99824062095464905E-1), (+1.4892156969066268, +0.83290450221880086), (+1.2515085013502683, +0.31328056291731077E-1), (+1.9677448624100851, +0.15796497952501998), (+1.7462313189995213, +0.83514024665689479), (+1.3058251830019489, +0.72925737386154432), (+1.6940306320710943, +0.34087258517669849), (+1.9315299558700361, +0.86262947164526005), (+1.4955962095170978, +0.48380082951477810), (+1.0632148809949808, +0.78831306717048011), (+1.7302345971366742, +0.54433094487683842), (+1.1732909185079383, +0.27672588881123972), (+1.6708289871216515, +0.84860899926167110), (+1.1464036963871413, +0.61442076725804518), (+1.4342107385588430, +0.98698400412252862), (+1.1458315640098178, +0.43439927972050874E-1), (+1.5562589335979820, +0.25959429898579245E-1), (+1.5577199129554553, +0.25394681317007073), (+1.6187751172704310, +0.77468050878123174), (+1.4220802058914834, +0.89823922367407960), (+1.8003610897351199, +0.12671481485137426), (+1.2190708513271742, +0.51103683234875819), (+1.9001068330717894, +0.44327408349602848), (+1.2805249072532656, +0.73094532910685228), (+1.8357963716240628, +0.69476547186045667), (+1.1163026468714321, +0.95356545652746250), (+1.9046762256231506, +0.29212854187173609), (+1.9118235010155247, +0.10978176428490483)

330

331atad = getFFTI(getFFTF(data))

332atad

333(+1.9381444032650130, +0.50482728875689220), (+1.0412957218538834, +0.11170170732801769), (+1.8612852516777425, +0.81792163116127026), (+1.2400791361741559, +0.70306328120003114), (+1.4162715052396837, +0.32242027741854717), (+1.3194049116666204, +0.92113791304896309), (+1.2658448079519715, +0.16929500427812411), (+1.2456058975154503, +0.17162937510398951), (+1.7011593749372786, +0.58521660483579585), (+1.2261937021586697, +0.29556011036907542), (+1.5664880248492830, +0.57788702972730421E-1), (+1.2178420576145610, +0.54558179110515459), (+1.4376340220743666, +0.38533955776808193), (+1.4642256812211971, +0.24539510722493452), (+1.9549378546033893, +0.26232383313809982), (+1.1323736133083837, +0.78812046056053187), (+1.5340721695824868, +0.64116826084257539), (+1.6479337550509066, +0.12944521420308053E-1), (+1.7155630623469489, +0.75348567134264777), (+1.4290879945785582, +0.44792763690998522), (+1.8221806467035400, +0.84571567977158657), (+1.8867551302164149, +0.94031271519760151), (+1.6577011445398724, +0.91974421237452120), (+1.2463575701062959, +0.53401165496433478), (+1.0243000840134946, +0.37323519086792334), (+1.6763661687282250, +0.51876077182836478), (+1.7433150991897350, +0.20829490779829307), (+1.1178886337474900, +0.68481145901761342), (+1.8999008022597379, +0.81491950325310913), (+1.0381945959838186, +0.87408769760349281), (+1.5366730975225411, +0.28299728722552259), (+1.0879729844975143, +0.48659117402786117), (+1.5316957636061501, +0.34433205735467620), (+1.7329556174635405, +0.33402494104751330E-1), (+1.7361533778546572, +0.67895280752357268), (+1.3904317247729387, +0.42634827211494125), (+1.9614623787315533, +0.87291815139914214E-1), (+1.1263612604243183, +0.80625955467873012), (+1.2157653460211377, +0.40456739582395218), (+1.3181542749001958, +0.52194368681317604E-1), (+1.2094356415950884, +0.44591688085485887), (+1.1541241788581600, +0.31589439839092348), (+1.8760312358819007, +0.43158649747503219), (+1.0896418158009407, +0.24793242326574086), (+1.5687814293098976, +0.23501915924135280), (+1.6903614094782200, +0.42849912073099422), (+1.6066060649941036, +0.64248681869520252), (+1.8491632187280223, +0.27469756885138080), (+1.4961264898053450, +0.64070520873393411), (+1.0124707454642072, +0.74483467337742226), (+1.7310118692331595, +0.44139706062343420), (+1.6878870834318151, +0.40341917432554625), (+1.4212394568771183, +0.70535364607882700), (+1.1036957258266427, +0.44465324708210863), (+1.3943902727693329, +0.45039477286756491), (+1.1566676720856686, +0.32561659179609476), (+1.3679223278906072, +0.83177305419554637), (+1.7120528068823673, +0.76776712971376754E-1), (+1.6476003858622090, +0.18524704711215925), (+1.7791429235195193, +0.92580890148890427E-1), (+1.7270022456256564, +0.47965167631583672), (+1.8474166254459217, +0.28471188563070282), (+1.8837901451541281, +0.18305895685295712), (+1.4562070983881212, +0.65471099654214793), (+1.3908175065822259, +0.36747369234447969), (+1.0512389419144565, +0.56042200406520984E-1), (+1.1806198067372817, +0.71489607175349179), (+1.0536450097327899, +0.61381535336467186), (+1.5562299219763827, +0.71195219420933964), (+1.3669754847928215, +0.86403407158834322E-1), (+1.9988617274787539, +0.99824062095464752E-1), (+1.4892156969066268, +0.83290450221880086), (+1.2515085013502678, +0.31328056291731354E-1), (+1.9677448624100848, +0.15796497952502048), (+1.7462313189995207, +0.83514024665689490), (+1.3058251830019485, +0.72925737386154443), (+1.6940306320710945, +0.34087258517669861), (+1.9315299558700354, +0.86262947164525983), (+1.4955962095170972, +0.48380082951477799), (+1.0632148809949806, +0.78831306717047989), (+1.7302345971366737, +0.54433094487683842), (+1.1732909185079381, +0.27672588881123955), (+1.6708289871216508, +0.84860899926167110), (+1.1464036963871416, +0.61442076725804506), (+1.4342107385588427, +0.98698400412252862), (+1.1458315640098173, +0.43439927972050874E-1), (+1.5562589335979813, +0.25959429898579023E-1), (+1.5577199129554551, +0.25394681317007040), (+1.6187751172704301, +0.77468050878123151), (+1.4220802058914828, +0.89823922367407938), (+1.8003610897351194, +0.12671481485137415), (+1.2190708513271742, +0.51103683234875785), (+1.9001068330717890, +0.44327408349602826), (+1.2805249072532652, +0.73094532910685195), (+1.8357963716240624, +0.69476547186045634), (+1.1163026468714321, +0.95356545652746183), (+1.9046762256231504, +0.29212854187173598), (+1.9118235010155245, +0.10978176428490460), (-0.11102230246251565E-15, -0.55511151231257827E-16), (+0.22204460492503131E-15, -0.16653345369377348E-15), (-0.11102230246251565E-15, +0.19428902930940239E-15), (-0.33306690738754696E-15, -0.38857805861880479E-15), (+0.0000000000000000, +0.44408920985006262E-15), (+0.11102230246251565E-15, -0.16653345369377348E-15), (-0.44408920985006262E-15, -0.33306690738754696E-15), (-0.22204460492503131E-15, -0.47184478546569153E-15), (-0.22204460492503131E-15, -0.27755575615628914E-16), (+0.0000000000000000, -0.24980018054066022E-15), (-0.22204460492503131E-15, +0.16653345369377348E-15), (-0.33306690738754696E-15, +0.16653345369377348E-15), (-0.33306690738754696E-15, +0.0000000000000000), (+0.33306690738754696E-15, -0.16653345369377348E-15), (-0.22204460492503131E-15, +0.11102230246251565E-15), (-0.11102230246251565E-15, -0.16653345369377348E-15), (+0.22204460492503131E-15, +0.44408920985006262E-15), (+0.55511151231257827E-15, +0.27755575615628914E-15), (+0.0000000000000000, +0.66613381477509392E-15), (+0.44408920985006262E-15, +0.11102230246251565E-15), (+0.22204460492503131E-15, +0.61062266354383610E-15), (+0.55511151231257827E-15, +0.33306690738754696E-15), (-0.33306690738754696E-15, +0.22204460492503131E-15), (+0.0000000000000000, -0.83266726846886741E-16), (+0.0000000000000000, +0.30531133177191805E-15), (+0.66613381477509392E-15, +0.38857805861880479E-15), (-0.11102230246251565E-15, +0.58286708792820718E-15), (+0.33306690738754696E-15, +0.44408920985006262E-15), (-0.33306690738754696E-15, +0.69388939039072284E-15), (+0.55511151231257827E-15, +0.66613381477509392E-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, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, 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+40

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

345data

346(+1.97251352091524457384038642691126482, +0.306317326355574246504708677065074418), (+1.70407695429628259700002964549996344, +0.176352837210014960007487358395935744), (+1.82980503216072094627788663416475682, +0.602438117441155246952035536620250508E-1), (+1.94760802940045444027617073402557159, +0.389260582033054610093332367317568665), (+1.53217750729628443899650562840748818, +0.217028757659997275213153727744190248), (+1.88357695967411422763049819882679890, +0.709851613558302832839191137306557409), (+1.81736661619675611644290905383924352, +0.182095573224484922538110460746391263), (+1.01403387203468806887936584419381546, +0.128524180641373388735433094543113812), (+1.07935591599036215316341397698751206, +0.519423546590704468582601996111726115), (+1.75024478076425552923404596745608055, +0.912642476595749689058148057645802083), (+1.89034925186771810545747601537247027, +0.167880150453813613122715926585827368), (+1.91375271942154989264120232205568100, +0.239770113514176902035406638157525491), (+1.20031882878378770675948345991778396, +0.606159152229401343394218553257308259), (+1.21669054102038050144274463589048240, +0.764051640231645285296286936080876780), (+1.71515828860865810310227084930113599, +0.813335976548641660302772733507667699), (+1.20099829955875887507886164007484013, +0.929015438959957846412518461571541880E-1), (+1.01239951072188872228244545697015823, +0.871773180029705370091792459123198094), (+1.43692089523964421928443801938263480, +0.897182647448158327244264811107948318), (+1.66077270269326718867096424045885314, +0.140790239954023012391769151036764218), (+1.22678081409699464804912423837296427, +0.655465638919585112946871462691547027), (+1.87007244760874001480607437061339752, +0.731549103556831668790031223120673967), (+1.33508376486721033275049645168634663, +0.847475982963352049161436697632628894), (+1.41091649853586421909993423615471428, +0.744587120873378511637453282193933882), (+1.56650278623533023795275899434087960, +0.969978510264119642199886246010169081), (+1.93864211274235028965461108179685998, +0.930178067006667490506622236639123729), (+1.44175927720003178119562671848131998, +0.468115560619237335409423956678724559), (+1.48896449997532568745491216942465695, +0.942336618824417459743182926480510508), (+1.74554408485176378488477275596795746, +0.715220456787033184133197325408563810), (+1.90739987405406038171531288885892667, +0.204041169470848667934032338127245822), (+1.18542811246676925126706717698800770, +0.306884987965915949755134025781420227), (+1.56219016990806754178064532667779926, +0.106057186102763183656802180878222078), (+1.38134510034752533660061465478812081, +0.595731680405058302739901467783547378), (+1.08882909459864947408441389272907405, +0.817301082312980642566204264366915629), (+1.23957974773543335396732441573234515, +0.562304359616905500048207106250859387), (+1.12644755510848984071802387902228198, +0.949734320965325718026278544749876346), (+1.78640666220745904772279987338391836, +0.424753354461987042250262491647147348), (+1.56705333687512090592359604315914517, +0.101954251570293460133109354788435552), (+1.64594997472549213155588435316954273, +0.471860523222460216579351513565409697), (+1.12247429383757029044439214432765474, +0.690664885745302238167576184521465648), (+1.69321563602656924182467146843907272, +0.388148319944517068769690217777071197)

347

348atad = getFFTI(getFFTF(data))

349atad

350(+1.97251352091524457384038642691126482, +0.306317326355574246504708677065074466), (+1.70407695429628259700002964549996344, +0.176352837210014960007487358395935888), (+1.82980503216072094627788663416475644, +0.602438117441155246952035536620251471E-1), (+1.94760802940045444027617073402557159, +0.389260582033054610093332367317568713), (+1.53217750729628443899650562840748838, +0.217028757659997275213153727744190007), (+1.88357695967411422763049819882679928, +0.709851613558302832839191137306557505), (+1.81736661619675611644290905383924371, +0.182095573224484922538110460746390974), (+1.01403387203468806887936584419381546, +0.128524180641373388735433094543113860), (+1.07935591599036215316341397698751206, +0.519423546590704468582601996111726307), (+1.75024478076425552923404596745608055, +0.912642476595749689058148057645802565), (+1.89034925186771810545747601537246989, +0.167880150453813613122715926585827609), (+1.91375271942154989264120232205568062, +0.239770113514176902035406638157525900), (+1.20031882878378770675948345991778377, +0.606159152229401343394218553257308548), (+1.21669054102038050144274463589048240, +0.764051640231645285296286936080876972), (+1.71515828860865810310227084930113619, +0.813335976548641660302772733507667699), (+1.20099829955875887507886164007484013, +0.929015438959957846412518461571541278E-1), (+1.01239951072188872228244545697015823, +0.871773180029705370091792459123198190), (+1.43692089523964421928443801938263480, +0.897182647448158327244264811107948511), (+1.66077270269326718867096424045885314, +0.140790239954023012391769151036764098), (+1.22678081409699464804912423837296427, +0.655465638919585112946871462691547220), (+1.87007244760874001480607437061339752, +0.731549103556831668790031223120673871), (+1.33508376486721033275049645168634663, +0.847475982963352049161436697632628894), (+1.41091649853586421909993423615471428, +0.744587120873378511637453282193933882), (+1.56650278623533023795275899434087998, +0.969978510264119642199886246010169177), (+1.93864211274235028965461108179685998, +0.930178067006667490506622236639123632), (+1.44175927720003178119562671848131998, +0.468115560619237335409423956678724414), (+1.48896449997532568745491216942465695, +0.942336618824417459743182926480509930), (+1.74554408485176378488477275596795746, +0.715220456787033184133197325408563425), (+1.90739987405406038171531288885892648, +0.204041169470848667934032338127246039), (+1.18542811246676925126706717698800731, +0.306884987965915949755134025781420227), (+1.56219016990806754178064532667779926, +0.106057186102763183656802180878221837), (+1.38134510034752533660061465478812081, +0.595731680405058302739901467783547185), (+1.08882909459864947408441389272907424, +0.817301082312980642566204264366915822), (+1.23957974773543335396732441573234496, +0.562304359616905500048207106250859387), (+1.12644755510848984071802387902228217, +0.949734320965325718026278544749876154), (+1.78640666220745904772279987338391855, +0.424753354461987042250262491647147589), (+1.56705333687512090592359604315914497, +0.101954251570293460133109354788435997), (+1.64594997472549213155588435316954292, +0.471860523222460216579351513565409890), (+1.12247429383757029044439214432765493, +0.690664885745302238167576184521465841), (+1.69321563602656924182467146843907311, +0.388148319944517068769690217777071342), (+0.385185988877447170611195588516985464E-33, -0.962964972193617926527988971292463659E-34), (+0.00000000000000000000000000000000000, -0.240741243048404481631997242823115915E-33), (+0.481482486096808963263994485646231830E-33, -0.481482486096808963263994485646231830E-34), (+0.288889491658085377958396691387739098E-33, -0.168518870133883137142398069976181140E-33), (-0.288889491658085377958396691387739098E-33, -0.192592994438723585305597794258492732E-33), (-0.288889491658085377958396691387739098E-33, -0.144444745829042688979198345693869549E-33), (+0.00000000000000000000000000000000000, +0.962964972193617926527988971292463659E-34), (-0.962964972193617926527988971292463659E-34, +0.156481807981462913060798207835025345E-33), (-0.192592994438723585305597794258492732E-33, +0.00000000000000000000000000000000000), (+0.00000000000000000000000000000000000, -0.240741243048404481631997242823115915E-33), (+0.288889491658085377958396691387739098E-33, +0.120370621524202240815998621411557957E-33), (-0.962964972193617926527988971292463659E-34, +0.481482486096808963263994485646231830E-34), (-0.385185988877447170611195588516985464E-33, +0.481482486096808963263994485646231830E-34), (-0.962964972193617926527988971292463659E-34, -0.962964972193617926527988971292463659E-34), (+0.00000000000000000000000000000000000, +0.00000000000000000000000000000000000), (-0.288889491658085377958396691387739098E-33, +0.00000000000000000000000000000000000), (+0.962964972193617926527988971292463659E-34, +0.144444745829042688979198345693869549E-33), (+0.00000000000000000000000000000000000, +0.240741243048404481631997242823115915E-33), (+0.962964972193617926527988971292463659E-34, +0.481482486096808963263994485646231830E-33), (+0.962964972193617926527988971292463659E-34, +0.192592994438723585305597794258492732E-33), (-0.192592994438723585305597794258492732E-33, -0.264815367353244929795196967105427506E-33), (-0.962964972193617926527988971292463659E-34, -0.120370621524202240815998621411557957E-33), (-0.962964972193617926527988971292463659E-34, -0.962964972193617926527988971292463659E-34), (-0.962964972193617926527988971292463659E-34, +0.192592994438723585305597794258492732E-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

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

357

358lenData = getUnifRand(5, 100)

359lenData

360+21

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

362data

363+1.06727362, +1.63840890, +1.91055048, +1.22645462, +1.15550542, +1.31867409, +1.83845198, +1.89843822, +1.45993853, +1.23270595, +1.12358928, +1.36467934, +1.98654413, +1.39795280, +1.71688628, +1.83153701, +1.16211677, +1.78751802, +1.64093351, +1.29210567, +1.47868896

364

365atad = getFFTI(getFFTF(data))

366atad

367+1.06727326, +1.63840890, +1.91055071, +1.22645473, +1.15550518, +1.31867409, +1.83845174, +1.89843798, +1.45993853, +1.23270583, +1.12358963, +1.36467934, +1.98654425, +1.39795256, +1.71688628, +1.83153665, +1.16211665, +1.78751802, +1.64093339, +1.29210567, +1.47868896, -0.596046448E-7, +0.119209290E-6, +0.00000000, -0.357627869E-6, +0.596046448E-7, -0.119209290E-6, +0.00000000, -0.238418579E-6, +0.119209290E-6, -0.596046448E-7, +0.119209290E-6

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

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

374

375lenData = getUnifRand(5, 100)

376lenData

377+74

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

379data

380+1.8319193246240557, +1.9839980037352931, +1.2092893884633857, +1.2796459038976682, +1.1617439225464858, +1.9138292445028311, +1.2014814949198944, +1.0675606791666699, +1.1845488481021968, +1.1297383423465153, +1.2378021706523215, +1.4765609996458418, +1.2392546601177767, +1.8808712938532652, +1.4929894287092100, +1.3296673723038395, +1.8238057281243591, +1.1975482071242785, +1.2008422681407840, +1.2207531736216306, +1.0420598030424268, +1.9629369032225870, +1.2775609241182959, +1.1170294403547747, +1.3622123880211963, +1.3842948431611917, +1.1522396310766378, +1.5884559287777527, +1.3865936955334865, +1.0043705305746782, +1.3382840339822040, +1.3981004026886208, +1.6616322676030779, +1.0920553770535446, +1.0103386437585580, +1.4995575963024934, +1.8562876153162731, +1.8690422335998247, +1.0968628246370307, +1.5601775328725971, +1.9388030191614531, +1.3005722945664149, +1.4086864568797703, +1.3797357615488091, +1.0277907761049052, +1.6947186453486829, +1.4018286790292447, +1.7779742998750447, +1.2815642500728348, +1.2848198772455799, +1.5036481479958499, +1.2845572318644169, +1.4779007784886766, +1.1938279188183309, +1.6431106945084166, +1.8117974097879441, +1.8461607287407764, +1.1578721079008014, +1.7620257064402269, +1.3297672606911242, +1.8343951515472228, +1.9294609593469307, +1.7211024287639722, +1.8983065685513334, +1.3626994363910636, +1.3463644246035793, +1.3140903600491365, +1.0024977436141116, +1.5966028685819402, +1.9050396523119317, +1.7906461800155065, +1.1215480294014259, +1.9405898673165853, +1.1822843639141181

381

382atad = getFFTI(getFFTF(data))

383atad

384+1.8319193246240562, +1.9839980037352931, +1.2092893884633862, +1.2796459038976689, +1.1617439225464852, +1.9138292445028309, +1.2014814949198938, +1.0675606791666707, +1.1845488481021971, +1.1297383423465150, +1.2378021706523215, +1.4765609996458426, +1.2392546601177763, +1.8808712938532652, +1.4929894287092096, +1.3296673723038399, +1.8238057281243591, +1.1975482071242785, +1.2008422681407835, +1.2207531736216310, +1.0420598030424268, +1.9629369032225861, +1.2775609241182952, +1.1170294403547749, +1.3622123880211960, +1.3842948431611917, +1.1522396310766374, +1.5884559287777531, +1.3865936955334861, +1.0043705305746786, +1.3382840339822035, +1.3981004026886208, +1.6616322676030784, +1.0920553770535444, +1.0103386437585578, +1.4995575963024934, +1.8562876153162731, +1.8690422335998240, +1.0968628246370304, +1.5601775328725966, +1.9388030191614536, +1.3005722945664147, +1.4086864568797703, +1.3797357615488091, +1.0277907761049057, +1.6947186453486824, +1.4018286790292445, +1.7779742998750447, +1.2815642500728353, +1.2848198772455794, +1.5036481479958499, +1.2845572318644169, +1.4779007784886766, +1.1938279188183301, +1.6431106945084162, +1.8117974097879430, +1.8461607287407769, +1.1578721079008012, +1.7620257064402265, +1.3297672606911237, +1.8343951515472225, +1.9294609593469296, +1.7211024287639722, +1.8983065685513325, +1.3626994363910643, +1.3463644246035793, +1.3140903600491367, +1.0024977436141114, +1.5966028685819407, +1.9050396523119313, +1.7906461800155067, +1.1215480294014251, +1.9405898673165856, +1.1822843639141183, +0.11102230246251565E-15, -0.66613381477509392E-15, +0.99920072216264089E-15, -0.11102230246251565E-15, +0.66613381477509392E-15, -0.55511151231257827E-15, +0.44408920985006262E-15, -0.44408920985006262E-15, +0.55511151231257827E-15, -0.22204460492503131E-15, +0.44408920985006262E-15, +0.11102230246251565E-15, +0.11102230246251565E-14, +0.22204460492503131E-15, +0.77715611723760958E-15, -0.44408920985006262E-15, +0.77715611723760958E-15, -0.33306690738754696E-15, +0.11102230246251565E-14, -0.11102230246251565E-15, +0.99920072216264089E-15, +0.22204460492503131E-15, +0.22204460492503131E-15, +0.22204460492503131E-15, +0.22204460492503131E-15, -0.11102230246251565E-15, -0.11102230246251565E-15, +0.22204460492503131E-15, +0.44408920985006262E-15, +0.77715611723760958E-15, +0.22204460492503131E-15, +0.0000000000000000, +0.33306690738754696E-15, +0.11102230246251565E-15, +0.22204460492503131E-15, +0.66613381477509392E-15, +0.22204460492503131E-15, +0.55511151231257827E-15, +0.11102230246251565E-15, +0.11102230246251565E-15, +0.22204460492503131E-15, +0.33306690738754696E-15, -0.11102230246251565E-15, +0.55511151231257827E-15, +0.33306690738754696E-15, +0.12212453270876722E-14, +0.11102230246251565E-15, -0.22204460492503131E-15, +0.44408920985006262E-15, +0.44408920985006262E-15, -0.11102230246251565E-15, +0.77715611723760958E-15, +0.22204460492503131E-15, +0.13322676295501878E-14

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, T, T, T, T, T, T, T, T, T, T, T, T, T, T, 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+57

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

396data

397+1.87643627600905417078360487843758173, +1.16666126619364419202193041612508029, +1.22347070445380124173721956705303265, +1.40180952089034171054646311423610630, +1.80318078783927304325520764605535172, +1.80993395138609937349798240953470897, +1.84301480172057887765311219412449157, +1.33344961721037487554056566457645420, +1.91278811136413681643632886292986757, +1.06009637494199213155785628357295252, +1.50444335236880677029077569655674802, +1.97850682309275529611925652196288020, +1.29873832445447999393397671944715072, +1.00279253343295486106112856490833543, +1.00044919037680801808067342691218382, +1.70237013808147151881033443964232348, +1.64438860600031301047537192190276323, +1.39010132016314032595903436023390392, +1.33419196988308412426889841363870163, +1.49906315404507905711373404131669533, +1.81344132791090747381854511855428444, +1.05017366269449940387220498299911099, +1.22130951099978547799163238843685012, +1.43389054233812905685476535735535801, +1.30162515603341168233562217567105638, +1.72323707792805776066974597904668761, +1.54881546180695259790701413733376986, +1.38171687473509978019932268173945213, +1.03006499079599859369871188158878992, +1.30371188574330306381719695659253473, +1.56955341322016679699641345855105049, +1.42244315302079481818723530039796768, +1.05044753345790746142608107586324173, +1.99003377512381224498153361553016449, +1.07712284045672170307689895917583722, +1.13464630876090685470140136099693130, +1.97307701667296589764999496507680491, +1.68702838418107022690158787684608043, +1.59804267821094091876639915826461338, +1.10470510621137651790755974366288454, +1.35500322991973209805284332407158080, +1.19196908698801974443355054448285191, +1.29270896056645315633995786996795628, +1.61430027678423461097425121105106372, +1.20624719991367658780630014011743010, +1.35834297239496128898136102028747467, +1.46430202771266722750310402005420127, +1.90532502933269633109698222097868758, +1.57932808043700948118798820119804052, +1.70886759289655529791633035873066788, +1.43211992429219872110011726871710010, +1.11423404858248443370950298901401010, +1.09280839158820473027431033919406443, +1.50747107940235738768326211065197479, +1.58921983776552666087854811175048272, +1.68033025426079200740833083011549323, +1.91081409077331664016447621203580669

398

399atad = getFFTI(getFFTF(data))

400atad

401+1.87643627600905417078360487843758154, +1.16666126619364419202193041612508029, +1.22347070445380124173721956705303246, +1.40180952089034171054646311423610649, +1.80318078783927304325520764605535210, +1.80993395138609937349798240953470858, +1.84301480172057887765311219412449118, +1.33344961721037487554056566457645420, +1.91278811136413681643632886292986757, +1.06009637494199213155785628357295233, +1.50444335236880677029077569655674821, +1.97850682309275529611925652196288001, +1.29873832445447999393397671944715052, +1.00279253343295486106112856490833485, +1.00044919037680801808067342691218382, +1.70237013808147151881033443964232309, +1.64438860600031301047537192190276285, +1.39010132016314032595903436023390392, +1.33419196988308412426889841363870163, +1.49906315404507905711373404131669533, +1.81344132791090747381854511855428482, +1.05017366269449940387220498299911079, +1.22130951099978547799163238843684992, +1.43389054233812905685476535735535801, +1.30162515603341168233562217567105600, +1.72323707792805776066974597904668742, +1.54881546180695259790701413733376947, +1.38171687473509978019932268173945174, +1.03006499079599859369871188158878973, +1.30371188574330306381719695659253434, +1.56955341322016679699641345855105010, +1.42244315302079481818723530039796691, +1.05044753345790746142608107586324154, +1.99003377512381224498153361553016449, +1.07712284045672170307689895917583702, +1.13464630876090685470140136099693130, +1.97307701667296589764999496507680529, +1.68702838418107022690158787684608004, +1.59804267821094091876639915826461300, +1.10470510621137651790755974366288434, +1.35500322991973209805284332407158080, +1.19196908698801974443355054448285191, +1.29270896056645315633995786996795608, +1.61430027678423461097425121105106372, +1.20624719991367658780630014011743010, +1.35834297239496128898136102028747429, +1.46430202771266722750310402005420147, +1.90532502933269633109698222097868758, +1.57932808043700948118798820119804013, +1.70886759289655529791633035873066788, +1.43211992429219872110011726871710029, +1.11423404858248443370950298901401010, +1.09280839158820473027431033919406443, +1.50747107940235738768326211065197441, +1.58921983776552666087854811175048234, +1.68033025426079200740833083011549323, +1.91081409077331664016447621203580650, -0.962964972193617926527988971292463659E-34, -0.962964972193617926527988971292463659E-34, -0.385185988877447170611195588516985464E-33, -0.192592994438723585305597794258492732E-33, -0.385185988877447170611195588516985464E-33, -0.385185988877447170611195588516985464E-33, -0.577778983316170755916793382775478196E-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, T, T, T, T, T, 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+31

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

413data

414(+1.05330098, +0.570981503), (+1.12381792, +0.226024628), (+1.34139991, +0.527821660), (+1.87132072, +0.970324039), (+1.80778468, +0.876167893), (+1.60152745, +0.884584367), (+1.51388478, +0.591989756), (+1.38611209, +0.933717906), (+1.09009314, +0.506116509), (+1.40811801, +0.221579313), (+1.84293365, +0.808480680), (+1.98885918, +0.982287347), (+1.21131539, +0.430110753), (+1.15548944, +0.674404919), (+1.78455091, +0.119534016), (+1.05831063, +0.525059521), (+1.47939062, +0.275494456E-1), (+1.80608177, +0.719535053), (+1.93523884, +0.761157155), (+1.05014229, +0.334705830), (+1.29425931, +0.824767888), (+1.58141792, +0.975707412), (+1.51656032, +0.286217570), (+1.31976008, +0.400033712), (+1.11410570, +0.458095908), (+1.81255078, +0.595530868), (+1.83827448, +0.203299522E-2), (+1.87667549, +0.964090824), (+1.10389841, +0.122344315), (+1.79050016, +0.257408023), (+1.74101675, +0.656070828)

415

416atad = getFFTI(getFFTF(data))

417atad

418(+1.05330086, +0.570981503), (+1.12381768, +0.226024568), (+1.34139979, +0.527821660), (+1.87132049, +0.970324039), (+1.80778468, +0.876167774), (+1.60152733, +0.884584308), (+1.51388478, +0.591989696), (+1.38611186, +0.933717847), (+1.09009314, +0.506116509), (+1.40811777, +0.221579298), (+1.84293342, +0.808480680), (+1.98885894, +0.982287288), (+1.21131527, +0.430110753), (+1.15548921, +0.674404919), (+1.78455091, +0.119534105), (+1.05831027, +0.525059462), (+1.47939062, +0.275494754E-1), (+1.80608153, +0.719534993), (+1.93523872, +0.761157155), (+1.05014205, +0.334705859), (+1.29425943, +0.824767828), (+1.58141768, +0.975707412), (+1.51656032, +0.286217570), (+1.31975996, +0.400033832), (+1.11410570, +0.458095938), (+1.81255054, +0.595530808), (+1.83827424, +0.203305483E-2), (+1.87667537, +0.964090705), (+1.10389841, +0.122344375), (+1.79050016, +0.257408082), (+1.74101663, +0.656070828), (-0.596046448E-7, +0.298023224E-7)

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

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

425

426lenData = getUnifRand(5, 100)

427lenData

428+81

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

430data

431(+1.5779112666288369, +0.76126606446266432), (+1.1791682871593072, +0.10535753914361246), (+1.4305090462627628, +0.87044523908718530E-1), (+1.9196114402342173, +0.23194371305671324), (+1.0694650801624896, +0.60087896931323082), (+1.7873496352298528, +0.30200758472041134), (+1.9001823547521703, +0.32091069553523766), (+1.1961401718492544, +0.83962503476290029), (+1.3412314562991650, +0.96861228608956340), (+1.5861515154919479, +0.76200035417668555), (+1.6559239682445455, +0.63038780740661526), (+1.4694739260391185, +0.96016108779606657), (+1.3025007264299662, +0.91514688914414111), (+1.7651527157246414, +0.21948905238130967), (+1.9286807985846424, +0.13124108604667561), (+1.2661200228206626, +0.80590820654670736), (+1.7131565637898942, +0.22599441282300570), (+1.3048259994225233, +0.17677827493248366), (+1.9895721195358518, +0.40036640473176888), (+1.9675961077812050, +0.92835658258245490), (+1.0979543846613624, +0.79348546748712223), (+1.4450633908103196, +0.51960771175666520), (+1.4568114408605366, +0.32009726950140671), (+1.3400613483264854, +0.96224674504910668), (+1.7002268936375495, +0.31500584789030661), (+1.6154668441976869, +0.75667686680555346E-1), (+1.3551114172663503, +0.51033501794056613), (+1.6898598331084693, +0.49773887645861159), (+1.0525987678156321, +0.11176642890598776), (+1.4808726789216142, +0.37674316212362724E-1), (+1.1968965450775895, +0.24567159442737674), (+1.0131856876839276, +0.70706661774479040E-1), (+1.0469278983057650, +0.69099704466605782), (+1.8855851843930196, +0.60848103732769288), (+1.7967615457615917, +0.85436741357771551), (+1.4987379250761643, +0.80114488415673080), (+1.3650316153822168, +0.46249459128479098), (+1.2759836439043781, +0.46511819203802740), (+1.1646081067365679, +0.96445999776892521), (+1.5639192015305414, +0.17192096134221291), (+1.4441782790721738, +0.10351005315665829), (+1.5407095895412255, +0.37459241709450808), (+1.8415534190220875, +0.58654389591815936), (+1.8989190859422613, +0.61704252194874132), (+1.1826594782068209, +0.69517924114937535), (+1.8506549830810477, +0.67214606317621783), (+1.2629136809793202, +0.93476343308632981), (+1.9260396502780426, +0.47922844154330135), (+1.8562431567587283, +0.53582770300530513), (+1.5912521481670932, +0.97244298759317860), (+1.6236241973204715, +0.78452025375282253), (+1.2610454472674122, +0.26780650846561094), (+1.9776878517059688, +0.62575784742863472), (+1.9342928611616319, +0.15913504168088011), (+1.9329807894574627, +0.62787044640440959), (+1.3120031162412493, +0.91832178330470771), (+1.1072186010492988, +0.46135195515417060), (+1.2250692636923799, +0.41545192865140124), (+1.4241749647970083, +0.54778656998913688), (+1.1240349608239193, +0.40803577712182137), (+1.6256007730507875, +0.97331814427622509E-2), (+1.2962702711625247, +0.71740600392230713), (+1.8377247645582897, +0.73715894292654660), (+1.1592458321433299, +0.66532217956142703), (+1.9966496311211901, +0.98655475514794089), (+1.3330786533203165, +0.89374979113887598), (+1.7530407906462870, +0.66296701808720782), (+1.0785009108759493, +0.24753355110329500), (+1.6054948930254551, +0.20582064685527501), (+1.5915396123992558, +0.59673130173835998), (+1.0505675163025039, +0.46129590960579692), (+1.7469236615531831, +0.92113693134483432), (+1.7989172106848967, +0.64863931355065618), (+1.3785910366511636, +0.77787856171433389), (+1.9943054286463089, +0.13097071697440121), (+1.4517658223905161, +0.23397060828419258), (+1.2750306212373710, +0.25948459301311455), (+1.6621795924243887, +0.36454799666728577), (+1.9692970592784493, +0.56044912156221982), (+1.4751775605024444, +0.92379467764453282), (+1.7997408503542061, +0.57286923169633575E-1)

432

433atad = getFFTI(getFFTF(data))

434atad

435(+1.5779112666288375, +0.76126606446266432), (+1.1791682871593072, +0.10535753914361262), (+1.4305090462627628, +0.87044523908718863E-1), (+1.9196114402342173, +0.23194371305671352), (+1.0694650801624896, +0.60087896931323070), (+1.7873496352298526, +0.30200758472041189), (+1.9001823547521703, +0.32091069553523788), (+1.1961401718492539, +0.83962503476290062), (+1.3412314562991647, +0.96861228608956373), (+1.5861515154919477, +0.76200035417668577), (+1.6559239682445450, +0.63038780740661560), (+1.4694739260391183, +0.96016108779606701), (+1.3025007264299662, +0.91514688914414088), (+1.7651527157246412, +0.21948905238131036), (+1.9286807985846424, +0.13124108604667595), (+1.2661200228206626, +0.80590820654670758), (+1.7131565637898942, +0.22599441282300592), (+1.3048259994225231, +0.17677827493248413), (+1.9895721195358518, +0.40036640473176888), (+1.9675961077812045, +0.92835658258245479), (+1.0979543846613624, +0.79348546748712190), (+1.4450633908103194, +0.51960771175666542), (+1.4568114408605364, +0.32009726950140660), (+1.3400613483264854, +0.96224674504910634), (+1.7002268936375495, +0.31500584789030661), (+1.6154668441976869, +0.75667686680555374E-1), (+1.3551114172663499, +0.51033501794056602), (+1.6898598331084695, +0.49773887645861215), (+1.0525987678156326, +0.11176642890598781), (+1.4808726789216138, +0.37674316212363043E-1), (+1.1968965450775890, +0.24567159442737660), (+1.0131856876839276, +0.70706661774479346E-1), (+1.0469278983057655, +0.69099704466605760), (+1.8855851843930196, +0.60848103732769276), (+1.7967615457615915, +0.85436741357771528), (+1.4987379250761643, +0.80114488415673080), (+1.3650316153822168, +0.46249459128479076), (+1.2759836439043779, +0.46511819203802734), (+1.1646081067365679, +0.96445999776892499), (+1.5639192015305414, +0.17192096134221274), (+1.4441782790721733, +0.10351005315665793), (+1.5407095895412257, +0.37459241709450802), (+1.8415534190220870, +0.58654389591815914), (+1.8989190859422616, +0.61704252194874143), (+1.1826594782068212, +0.69517924114937502), (+1.8506549830810473, +0.67214606317621750), (+1.2629136809793204, +0.93476343308632948), (+1.9260396502780424, +0.47922844154330146), (+1.8562431567587285, +0.53582770300530480), (+1.5912521481670929, +0.97244298759317838), (+1.6236241973204715, +0.78452025375282242), (+1.2610454472674120, +0.26780650846561049), (+1.9776878517059688, +0.62575784742863427), (+1.9342928611616315, +0.15913504168087991), (+1.9329807894574627, +0.62787044640440892), (+1.3120031162412489, +0.91832178330470726), (+1.1072186010492988, +0.46135195515417049), (+1.2250692636923799, +0.41545192865140124), (+1.4241749647970083, +0.54778656998913666), (+1.1240349608239195, +0.40803577712182115), (+1.6256007730507875, +0.97331814427621885E-2), (+1.2962702711625245, +0.71740600392230647), (+1.8377247645582901, +0.73715894292654593), (+1.1592458321433294, +0.66532217956142681), (+1.9966496311211905, +0.98655475514794078), (+1.3330786533203165, +0.89374979113887609), (+1.7530407906462870, +0.66296701808720759), (+1.0785009108759493, +0.24753355110329506), (+1.6054948930254551, +0.20582064685527512), (+1.5915396123992558, +0.59673130173835975), (+1.0505675163025039, +0.46129590960579681), (+1.7469236615531829, +0.92113693134483410), (+1.7989172106848965, +0.64863931355065640), (+1.3785910366511633, +0.77787856171433400), (+1.9943054286463084, +0.13097071697440138), (+1.4517658223905159, +0.23397060828419225), (+1.2750306212373710, +0.25948459301311433), (+1.6621795924243890, +0.36454799666728510), (+1.9692970592784493, +0.56044912156221915), (+1.4751775605024440, +0.92379467764453227), (+1.7997408503542058, +0.57286923169633477E-1), (+0.11102230246251565E-15, -0.52735593669694936E-15), (+0.33306690738754696E-15, +0.11102230246251565E-15), (+0.22204460492503131E-15, -0.11102230246251565E-15), (+0.55511151231257827E-15, +0.55511151231257827E-16), (+0.44408920985006262E-15, -0.33306690738754696E-15), (+0.66613381477509392E-15, +0.27755575615628914E-16), (+0.22204460492503131E-15, -0.16653345369377348E-15), (+0.0000000000000000, -0.30531133177191805E-15), (+0.11102230246251565E-15, -0.30531133177191805E-15), (-0.22204460492503131E-15, -0.33306690738754696E-15), (-0.11102230246251565E-15, -0.55511151231257827E-15), (+0.11102230246251565E-15, +0.20816681711721685E-16), (+0.77715611723760958E-15, -0.31918911957973251E-15), (+0.77715611723760958E-15, +0.83266726846886741E-16), (+0.0000000000000000, -0.31225022567582528E-15), (-0.11102230246251565E-15, +0.16653345369377348E-15), (-0.22204460492503131E-15, +0.0000000000000000), (-0.11102230246251565E-15, +0.16653345369377348E-15), (-0.11102230246251565E-15, +0.11102230246251565E-15), (+0.11102230246251565E-15, +0.30531133177191805E-15), (+0.22204460492503131E-15, -0.55511151231257827E-16), (-0.11102230246251565E-15, +0.27755575615628914E-15), (+0.11102230246251565E-15, +0.38857805861880479E-15), (-0.44408920985006262E-15, -0.83266726846886741E-16), (+0.22204460492503131E-15, -0.16653345369377348E-15), (-0.88817841970012523E-15, +0.11102230246251565E-15), (-0.33306690738754696E-15, +0.0000000000000000), (-0.22204460492503131E-15, +0.11102230246251565E-15), (+0.44408920985006262E-15, +0.11102230246251565E-15), (+0.66613381477509392E-15, +0.44408920985006262E-15), (+0.11102230246251565E-15, +0.33306690738754696E-15), (+0.22204460492503131E-15, +0.33306690738754696E-15), (+0.0000000000000000, +0.27755575615628914E-15), (+0.11102230246251565E-15, +0.27755575615628914E-15), (+0.22204460492503131E-15, +0.24980018054066022E-15), (+0.22204460492503131E-15, +0.27755575615628914E-15), (+0.44408920985006262E-15, +0.69388939039072284E-15), (+0.0000000000000000, +0.83266726846886741E-15), (+0.11102230246251565E-15, +0.72164496600635175E-15), (+0.0000000000000000, +0.27755575615628914E-16), (+0.11102230246251565E-15, +0.30531133177191805E-15), (-0.11102230246251565E-15, +0.27755575615628914E-15), (+0.0000000000000000, +0.47184478546569153E-15), (+0.22204460492503131E-15, +0.54817261840867104E-15), (+0.22204460492503131E-15, +0.83266726846886741E-15), (+0.11102230246251565E-15, +0.88817841970012523E-15), (+0.22204460492503131E-15, +0.72164496600635175E-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, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, 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+60

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

447data

448(+1.71445715331162679396527968816107247, +0.565224515193281039215704126372768055), (+1.39504236289909125365433297117195371, +0.150712204033637527722195919658704895E-1), (+1.64060105402644245421828092519155963, +0.916467926217319790298963104524820530E-1), (+1.87677295725910268719335904260320062, +0.461434840031229293341520798659292082), (+1.27477824687371501120596258459444124, +0.635877726824130076008499128906509976), (+1.08657661911217698061152433223015851, +0.176315624501791561909968663758306261), (+1.13565100660515832653405801700586989, +0.887670416876935543458177530326218751), (+1.65285342364071797448622482727696359, +0.693004087818300086157040466491424106), (+1.62958692805775691478991671750385463, +0.867768735223997982655215157178443491), (+1.90679963268258214015741991114335904, +0.477252653219170293270245342528754458), (+1.58269863465346161276265676759652761, +0.951822214318278165206126707915365315), (+1.76690253717794571363987962516794249, +0.675534557439905036062957352555982335), (+1.72788365919308113640889094435116589, +0.519681278162364941448041711882665478), (+1.35271406682733834680591765162119724, +0.480724760675026983627487831693829913), (+1.80673497992755177055280586677753095, +0.198924577725615149922498995130507033), (+1.38870230778663436008610227087308547, +0.488392330691817848310866602945596511), (+1.40396608865460273105835000571844117, +0.192479053687103195727870787199381870), (+1.60364615705870341681194197629727858, +0.251170770093998055545474476711846741), (+1.72547293756768451179406170770441636, +0.325867112324954238696357853841645024), (+1.07856214994310796512537756412683022, +0.977300984424416290819252172740793941), (+1.43506150263682381505163293140667311, +0.944779023379844802288551922573496448), (+1.53884068950494837293534699874088562, +0.186501155351148969775365206203539709E-1), (+1.38609589817423635655501246625572541, +0.952680826661836048407558106948925133), (+1.90210865759044012230117734153382924, +0.614313795923866061390022840022034731E-2), (+1.92374702984788629910326991229112607, +0.843162586631049721707358093623376280), (+1.51209279201841388121501323789348353, +0.794248312264039199169047307441487778), (+1.55118006881084276033961740737611962, +0.543981113801531177196722393016490484), (+1.07916587577282471628454681135981945, +0.882024277415694355750289029631668891), (+1.53819359284139329451744212065724092, +0.260782710352638861610235370290314421), (+1.77315055268688860519403991063856510, +0.140041855175053885296404413348020492), (+1.47870499891694170489354357064539442, +0.723965912496438739971306126782994035), (+1.78530556287267538466570574775584324, +0.122732297804289083200672302006031851), (+1.08678036669267673762090587925127482, +0.482954198679320816891108627429566819), (+1.63504523777724998881099695587017875, +0.632919337027077523770345512880234587), (+1.94226769619637933106422539796265415, +0.181500357885934656256474407545975850), (+1.00778792608212595300399484801014139, +0.246780488598931549663780084545771528), (+1.69124236127920792618346080954971649, +0.499855132780480375342631071131582905), (+1.22760793592676902732869014721885065, +0.583899884978976982051286744434317006), (+1.42435170612294646685425862152063344, +0.365048355137115084479271508023946958), (+1.06386894785612564994225348285300021, +0.397838512144940560233251899721368399), (+1.13051791623769727542007345562783095, +0.574703947493464429734456341488044572), (+1.22872516647729180619895877593038393, +0.247489776990070907563631266074151829), (+1.30909392300253821796972561423609520, +0.874750042302726124385816822848804599E-1), (+1.49394034858329650229977275723383544, +0.427016434870529820108929797227054580), (+1.83469435184257060959331628342883427, +0.968194099908147324327468947070800559E-1), (+1.12828027399081417019069451817033811, +0.462468144428114740236950027941600656), (+1.06610554361403557347148549220778602, +0.509781300047969770409029371123230551), (+1.92874481730044548003256070355688187, +0.802966459680921162226385540535575562), (+1.17719641223573780792303020014958712, +0.303020490991080894365544970049879693), (+1.57378434321949921958328036766383360, +0.558756680917287035967422198499086214), (+1.29973543790489377302844523047093528, +0.545529564230632176299276885377460244), (+1.49984016915180172529675390355831054, +0.469508571672150464055968199362378617), (+1.78640578436554886258526488760931142, +0.109409994802100516613990691054528909), (+1.80807957134526135163225609094180045, +0.233611822535615971463558500999119597), (+1.12844334345605685619730697085747038, +0.471207440304959074397012340671763081), (+1.24598800792134759161347919412930347, +0.158060727830845328579275104261756864), (+1.97813093547929297252075413181270238, +0.924772021501580004420804791088522558), (+1.85023135239550168610742998639293346, +0.533923576835610230633858980771448634E-1), (+1.93498414287165554192180194903618145, +0.903446427026422462044993449479858530), (+1.92856657331754765231580334294180374, +0.384407189402869360562374617520206711)

449

450atad = getFFTI(getFFTF(data))

451atad

452(+1.71445715331162679396527968816107285, +0.565224515193281039215704126372767863), (+1.39504236289909125365433297117195390, +0.150712204033637527722195919658704895E-1), (+1.64060105402644245421828092519155943, +0.916467926217319790298963104524821614E-1), (+1.87677295725910268719335904260320043, +0.461434840031229293341520798659292226), (+1.27477824687371501120596258459444163, +0.635877726824130076008499128906509784), (+1.08657661911217698061152433223015851, +0.176315624501791561909968663758306116), (+1.13565100660515832653405801700586989, +0.887670416876935543458177530326218558), (+1.65285342364071797448622482727696359, +0.693004087818300086157040466491424010), (+1.62958692805775691478991671750385483, +0.867768735223997982655215157178443395), (+1.90679963268258214015741991114335923, +0.477252653219170293270245342528754362), (+1.58269863465346161276265676759652761, +0.951822214318278165206126707915365219), (+1.76690253717794571363987962516794249, +0.675534557439905036062957352555982431), (+1.72788365919308113640889094435116589, +0.519681278162364941448041711882665478), (+1.35271406682733834680591765162119724, +0.480724760675026983627487831693830057), (+1.80673497992755177055280586677753095, +0.198924577725615149922498995130507129), (+1.38870230778663436008610227087308547, +0.488392330691817848310866602945596415), (+1.40396608865460273105835000571844136, +0.192479053687103195727870787199381726), (+1.60364615705870341681194197629727858, +0.251170770093998055545474476711846789), (+1.72547293756768451179406170770441616, +0.325867112324954238696357853841644928), (+1.07856214994310796512537756412683002, +0.977300984424416290819252172740793941), (+1.43506150263682381505163293140667311, +0.944779023379844802288551922573496544), (+1.53884068950494837293534699874088581, +0.186501155351148969775365206203539228E-1), (+1.38609589817423635655501246625572580, +0.952680826661836048407558106948925229), (+1.90210865759044012230117734153382924, +0.614313795923866061390022840022039546E-2), (+1.92374702984788629910326991229112627, +0.843162586631049721707358093623375991), (+1.51209279201841388121501323789348372, +0.794248312264039199169047307441487681), (+1.55118006881084276033961740737611962, +0.543981113801531177196722393016490388), (+1.07916587577282471628454681135981945, +0.882024277415694355750289029631668891), (+1.53819359284139329451744212065724092, +0.260782710352638861610235370290314276), (+1.77315055268688860519403991063856510, +0.140041855175053885296404413348020468), (+1.47870499891694170489354357064539423, +0.723965912496438739971306126782993843), (+1.78530556287267538466570574775584344, +0.122732297804289083200672302006032032), (+1.08678036669267673762090587925127502, +0.482954198679320816891108627429566674), (+1.63504523777724998881099695587017895, +0.632919337027077523770345512880234684), (+1.94226769619637933106422539796265415, +0.181500357885934656256474407545975850), (+1.00778792608212595300399484801014139, +0.246780488598931549663780084545771383), (+1.69124236127920792618346080954971649, +0.499855132780480375342631071131582905), (+1.22760793592676902732869014721885065, +0.583899884978976982051286744434317198), (+1.42435170612294646685425862152063344, +0.365048355137115084479271508023947054), (+1.06386894785612564994225348285300021, +0.397838512144940560233251899721368591), (+1.13051791623769727542007345562783114, +0.574703947493464429734456341488044475), (+1.22872516647729180619895877593038451, +0.247489776990070907563631266074151756), (+1.30909392300253821796972561423609520, +0.874750042302726124385816822848805562E-1), (+1.49394034858329650229977275723383544, +0.427016434870529820108929797227054772), (+1.83469435184257060959331628342883427, +0.968194099908147324327468947070799596E-1), (+1.12828027399081417019069451817033792, +0.462468144428114740236950027941600705), (+1.06610554361403557347148549220778602, +0.509781300047969770409029371123230358), (+1.92874481730044548003256070355688187, +0.802966459680921162226385540535575658), (+1.17719641223573780792303020014958731, +0.303020490991080894365544970049879549), (+1.57378434321949921958328036766383341, +0.558756680917287035967422198499086214), (+1.29973543790489377302844523047093528, +0.545529564230632176299276885377460148), (+1.49984016915180172529675390355831035, +0.469508571672150464055968199362378521), (+1.78640578436554886258526488760931142, +0.109409994802100516613990691054529101), (+1.80807957134526135163225609094180064, +0.233611822535615971463558500999119742), (+1.12844334345605685619730697085746999, +0.471207440304959074397012340671763370), (+1.24598800792134759161347919412930366, +0.158060727830845328579275104261757345), (+1.97813093547929297252075413181270257, +0.924772021501580004420804791088522365), (+1.85023135239550168610742998639293384, +0.533923576835610230633858980771449115E-1), (+1.93498414287165554192180194903618145, +0.903446427026422462044993449479858337), (+1.92856657331754765231580334294180335, +0.384407189402869360562374617520206711), (-0.962964972193617926527988971292463659E-34, +0.00000000000000000000000000000000000), (-0.288889491658085377958396691387739098E-33, +0.240741243048404481631997242823115915E-34), (-0.192592994438723585305597794258492732E-33, -0.144444745829042688979198345693869549E-33), (+0.192592994438723585305597794258492732E-33, -0.842594350669415685711990349880905702E-34)

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, T, 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+13

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

464data

465+1.36515152, +1.75344539, +1.54570019, +1.77291393, +1.17175293, +1.97514987, +1.20307124, +1.01557064, +1.79895008, +1.70801187, +1.08266592, +1.31030667, +1.59875441

466

467atad = getFFTI(getFFTF(data))

468atad

469+1.36515164, +1.75344539, +1.54570007, +1.77291381, +1.17175317, +1.97514987, +1.20307112, +1.01557064, +1.79895020, +1.70801187, +1.08266592, +1.31030643, +1.59875441, +0.178813934E-6, +0.178813934E-6, +0.298023224E-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, T, T, T

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

476

477lenData = getUnifRand(5, 100)

478lenData

479+82

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

481data

482+1.1816873983487874, +1.7836672177395272, +1.5347331620072331, +1.5723172489162920, +1.1340776410464715, +1.5274054106610047, +1.4073877028389519, +1.7472886717441614, +1.0359039852085918, +1.2476920846862773, +1.1310923827762362, +1.6477936387208809, +1.5425388141231782, +1.4756260774970702, +1.4026337106886988, +1.3143509874810060, +1.9502386799085940, +1.6439676000111456, +1.5432960626815890, +1.2248393598013543, +1.0647247646697431, +1.0848056920652698, +1.5011614181229991, +1.6766242064828645, +1.4442085273822984, +1.6058918155560367, +1.5555072021501792, +1.3438871462186848, +1.6822001548903840, +1.4474723526580218, +1.7429446837517415, +1.3623945524787890, +1.8499919215966876, +1.4732341456402434, +1.6454123168841432, +1.3765695314780939, +1.0849665208418933, +1.5604952925492932, +1.5868667982823499, +1.6720914110196605, +1.4763719208176884, +1.7142915547169224, +1.6200585428152467, +1.7565755790653501, +1.9391226851769996, +1.7573425818183099, +1.3242547856254605, +1.9621436417743559, +1.8989044705984073, +1.1131280907684467, +1.2771179368438179, +1.5174187047881096, +1.5416934899197900, +1.9724805946538178, +1.8587776413881061, +1.9752709830358202, +1.6389525023004294, +1.3908721650068241, +1.4160813115945974, +1.0076546692831103, +1.5742279956357215, +1.0753200478661944, +1.8862572637070181, +1.6592318141004141, +1.6059837852709260, +1.1011246759164823, +1.5632604140654096, +1.0603184637225047, +1.1333407332089476, +1.4632480059437816, +1.8119459483124922, +1.0988317829467036, +1.3835090162203278, +1.2244671926070043, +1.3893927277059257, +1.6206160598613644, +1.3955389586450764, +1.6655835285545604, +1.5099561964019590, +1.0675818130442107, +1.0667111060162138, +1.1767628865753998

483

484atad = getFFTI(getFFTF(data))

485atad

486+1.1816873983487874, +1.7836672177395272, +1.5347331620072331, +1.5723172489162922, +1.1340776410464710, +1.5274054106610044, +1.4073877028389510, +1.7472886717441614, +1.0359039852085918, +1.2476920846862773, +1.1310923827762358, +1.6477936387208814, +1.5425388141231779, +1.4756260774970700, +1.4026337106886984, +1.3143509874810060, +1.9502386799085938, +1.6439676000111456, +1.5432960626815888, +1.2248393598013545, +1.0647247646697426, +1.0848056920652698, +1.5011614181229984, +1.6766242064828645, +1.4442085273822982, +1.6058918155560364, +1.5555072021501788, +1.3438871462186850, +1.6822001548903835, +1.4474723526580218, +1.7429446837517406, +1.3623945524787893, +1.8499919215966876, +1.4732341456402431, +1.6454123168841435, +1.3765695314780937, +1.0849665208418935, +1.5604952925492928, +1.5868667982823499, +1.6720914110196603, +1.4763719208176889, +1.7142915547169222, +1.6200585428152467, +1.7565755790653506, +1.9391226851770000, +1.7573425818183095, +1.3242547856254610, +1.9621436417743559, +1.8989044705984073, +1.1131280907684462, +1.2771179368438181, +1.5174187047881094, +1.5416934899197905, +1.9724805946538169, +1.8587776413881061, +1.9752709830358197, +1.6389525023004294, +1.3908721650068234, +1.4160813115945974, +1.0076546692831099, +1.5742279956357217, +1.0753200478661942, +1.8862572637070185, +1.6592318141004134, +1.6059837852709262, +1.1011246759164823, +1.5632604140654096, +1.0603184637225043, +1.1333407332089478, +1.4632480059437813, +1.8119459483124922, +1.0988317829467036, +1.3835090162203278, +1.2244671926070043, +1.3893927277059253, +1.6206160598613646, +1.3955389586450770, +1.6655835285545602, +1.5099561964019594, +1.0675818130442103, +1.0667111060162136, +1.1767628865753994, +0.0000000000000000, -0.66613381477509392E-15, +0.77715611723760958E-15, +0.11102230246251565E-15, +0.66613381477509392E-15, -0.44408920985006262E-15, +0.22204460492503131E-15, -0.22204460492503131E-15, +0.22204460492503131E-15, -0.44408920985006262E-15, +0.44408920985006262E-15, +0.33306690738754696E-15, +0.88817841970012523E-15, -0.22204460492503131E-15, -0.44408920985006262E-15, +0.33306690738754696E-15, -0.22204460492503131E-15, -0.22204460492503131E-15, -0.22204460492503131E-15, +0.44408920985006262E-15, -0.22204460492503131E-15, +0.22204460492503131E-15, -0.22204460492503131E-15, -0.22204460492503131E-15, -0.44408920985006262E-15, +0.11102230246251565E-15, +0.22204460492503131E-15, +0.55511151231257827E-15, +0.0000000000000000, +0.22204460492503131E-15, +0.22204460492503131E-15, +0.77715611723760958E-15, -0.33306690738754696E-15, +0.0000000000000000, -0.33306690738754696E-15, +0.77715611723760958E-15, +0.11102230246251565E-15, +0.22204460492503131E-15, +0.44408920985006262E-15, +0.22204460492503131E-15, +0.22204460492503131E-15, +0.33306690738754696E-15, -0.22204460492503131E-15, +0.66613381477509392E-15, -0.33306690738754696E-15, +0.13322676295501878E-14

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, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, 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+81

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

498data

499+1.57202534416971138936919995570285389, +1.85549765799059884742576754207404546, +1.89810886940984934044597661677955610, +1.95743391045803861132856983236050937, +1.98882058426272172988284165837835221, +1.91927995727748940270677912291645397, +1.78743272206986052211507122584740509, +1.60298172009350239409162288844754563, +1.34814001298317823422673308120149345, +1.64560586974976771887600401982754927, +1.88232259435047589563624512547560935, +1.25149878259661732345388163508047930, +1.89065736160814293903561068913421480, +1.50634813626162359695897209543730842, +1.28974052823090411085295291734129965, +1.74647416915150761535293319363487066, +1.49012111590929956450207552265625706, +1.46769668970866911591977108012820375, +1.04250849908486599057741298817966980, +1.12851242735328250552519554497024814, +1.21237524998472121135221776291795889, +1.58211460490312805895696396460081345, +1.05825802199034981944156870349898652, +1.72452162843946576112287154462075078, +1.04072738830799780378561988869632677, +1.39541801851087082266169947892061696, +1.04637315469385240893319571506626915, +1.89962012667504423524406112834344920, +1.95624200069300078387094358560752059, +1.70672516926589062508316398088854170, +1.53405353323403167582056303858228843, +1.43962699848645575376010002316660708, +1.84360859565342945470527844714913562, +1.40392185112027938587136423037451131, +1.37321259656592228860840450188713174, +1.13787237577564566049358414143499890, +1.12355367361705886542372440030977688, +1.22555878842716031403316038994392872, +1.13630495800715519258531587335960292, +1.19538457137047961132876344556103946, +1.98323740636057069808061497144666837, +1.83451076401208024345423957288536991, +1.95741788575935239871329254491090190, +1.84568467722112864966364044005402622, +1.02363199773220676845024622814817000, +1.65673941464958174953465361213530281, +1.75017179446283542942515767402990020, +1.72290050818408487852282449897725101, +1.35890924600259982139010218195223505, +1.61824988870929486413981292152884025, +1.46759819342002445801086290193892091, +1.30683034292653761392804083064871071, +1.41690664666373464540689856521752739, +1.73741451544020801978329796873607270, +1.09973945367266525079119328690012223, +1.95467767055048079087850368334583955, +1.49437107490393080951119754663901575, +1.08719548938403910688668794166156122, +1.13125145421098225885546151959889885, +1.59282464061114538927946594115473691, +1.29232044814007044744486400602426301, +1.26969616136664523495621231369320242, +1.39058848427075251532231834618395473, +1.83632849980432277911635555572663265, +1.39796982661955731908037099830925592, +1.28919071348492847301615576153470313, +1.28577790174770982441525177272490110, +1.96080183011625285968279254304195887, +1.34753763086530585326948381015649557, +1.24086510427020860718046671388264910, +1.58935732461226833672665819212326539, +1.01252996108735221900290211050407171, +1.13171538062632404915264727025132999, +1.56389786436143385258300403990656961, +1.60997339362436172168609395478425641, +1.17565400349754127452482179123388522, +1.31775807181916798167690378650429194, +1.73105801176509732990452919660898812, +1.46601768239632343709112944353542004, +1.99648803165720275580673138157055287, +1.13810386704525548704174158977920179

500

501atad = getFFTI(getFFTF(data))

502atad

503+1.57202534416971138936919995570285408, +1.85549765799059884742576754207404603, +1.89810886940984934044597661677955649, +1.95743391045803861132856983236050975, +1.98882058426272172988284165837835202, +1.91927995727748940270677912291645416, +1.78743272206986052211507122584740490, +1.60298172009350239409162288844754583, +1.34814001298317823422673308120149384, +1.64560586974976771887600401982754965, +1.88232259435047589563624512547561012, +1.25149878259661732345388163508047930, +1.89065736160814293903561068913421538, +1.50634813626162359695897209543730842, +1.28974052823090411085295291734130023, +1.74647416915150761535293319363487066, +1.49012111590929956450207552265625667, +1.46769668970866911591977108012820375, +1.04250849908486599057741298817967019, +1.12851242735328250552519554497024814, +1.21237524998472121135221776291795870, +1.58211460490312805895696396460081345, +1.05825802199034981944156870349898614, +1.72452162843946576112287154462075078, +1.04072738830799780378561988869632677, +1.39541801851087082266169947892061696, +1.04637315469385240893319571506626896, +1.89962012667504423524406112834344940, +1.95624200069300078387094358560752059, +1.70672516926589062508316398088854189, +1.53405353323403167582056303858228823, +1.43962699848645575376010002316660689, +1.84360859565342945470527844714913543, +1.40392185112027938587136423037451131, +1.37321259656592228860840450188713213, +1.13787237577564566049358414143499870, +1.12355367361705886542372440030977726, +1.22555878842716031403316038994392853, +1.13630495800715519258531587335960312, +1.19538457137047961132876344556103888, +1.98323740636057069808061497144666876, +1.83451076401208024345423957288537029, +1.95741788575935239871329254491090228, +1.84568467722112864966364044005402661, +1.02363199773220676845024622814817000, +1.65673941464958174953465361213530281, +1.75017179446283542942515767402990039, +1.72290050818408487852282449897725101, +1.35890924600259982139010218195223486, +1.61824988870929486413981292152884006, +1.46759819342002445801086290193892091, +1.30683034292653761392804083064871071, +1.41690664666373464540689856521752777, +1.73741451544020801978329796873607251, +1.09973945367266525079119328690012223, +1.95467767055048079087850368334583878, +1.49437107490393080951119754663901575, +1.08719548938403910688668794166156122, +1.13125145421098225885546151959889847, +1.59282464061114538927946594115473729, +1.29232044814007044744486400602426340, +1.26969616136664523495621231369320185, +1.39058848427075251532231834618395453, +1.83632849980432277911635555572663246, +1.39796982661955731908037099830925592, +1.28919071348492847301615576153470333, +1.28577790174770982441525177272490110, +1.96080183011625285968279254304195926, +1.34753763086530585326948381015649557, +1.24086510427020860718046671388264929, +1.58935732461226833672665819212326558, +1.01252996108735221900290211050407152, +1.13171538062632404915264727025132961, +1.56389786436143385258300403990657019, +1.60997339362436172168609395478425621, +1.17565400349754127452482179123388580, +1.31775807181916798167690378650429213, +1.73105801176509732990452919660898890, +1.46601768239632343709112944353541985, +1.99648803165720275580673138157055344, +1.13810386704525548704174158977920179, -0.288889491658085377958396691387739098E-33, -0.962964972193617926527988971292463659E-34, -0.385185988877447170611195588516985464E-33, +0.288889491658085377958396691387739098E-33, +0.385185988877447170611195588516985464E-33, +0.674075480535532548569592279904724561E-33, +0.962964972193617926527988971292463659E-34, -0.288889491658085377958396691387739098E-33, -0.385185988877447170611195588516985464E-33, -0.577778983316170755916793382775478196E-33, -0.192592994438723585305597794258492732E-33, -0.385185988877447170611195588516985464E-33, +0.962964972193617926527988971292463659E-34, -0.192592994438723585305597794258492732E-33, -0.962964972193617926527988971292463659E-34, -0.192592994438723585305597794258492732E-33, +0.192592994438723585305597794258492732E-33, -0.288889491658085377958396691387739098E-33, +0.962964972193617926527988971292463659E-34, -0.962964972193617926527988971292463659E-34, +0.674075480535532548569592279904724561E-33, +0.962964972193617926527988971292463659E-34, +0.288889491658085377958396691387739098E-33, -0.288889491658085377958396691387739098E-33, -0.385185988877447170611195588516985464E-33, -0.288889491658085377958396691387739098E-33, -0.288889491658085377958396691387739098E-33, -0.962964972193617926527988971292463659E-34, +0.288889491658085377958396691387739098E-33, +0.192592994438723585305597794258492732E-33, +0.962964972193617926527988971292463659E-34, -0.192592994438723585305597794258492732E-33, +0.00000000000000000000000000000000000, +0.962964972193617926527988971292463659E-34, -0.962964972193617926527988971292463659E-34, -0.192592994438723585305597794258492732E-33, +0.481482486096808963263994485646231830E-33, +0.00000000000000000000000000000000000, +0.674075480535532548569592279904724561E-33, +0.00000000000000000000000000000000000, -0.962964972193617926527988971292463659E-34, +0.00000000000000000000000000000000000, -0.385185988877447170611195588516985464E-33, -0.385185988877447170611195588516985464E-33, -0.962964972193617926527988971292463659E-34, +0.00000000000000000000000000000000000, -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, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, 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