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+36

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

5data

6(+1.50181794, +0.115960419), (+1.90760016, +0.334465325), (+1.13850558, +0.281729102), (+1.95291114, +0.135239840), (+1.94294357, +0.403895199), (+1.36937582, +0.644446254), (+1.14799094, +0.168884933), (+1.63172281, +0.222432017E-1), (+1.75567627, +0.357230544), (+1.83243227, +0.573088825), (+1.52864432, +0.913300931), (+1.58670187, +0.848946571E-1), (+1.21496391, +0.935692370), (+1.95143986, +0.858387589), (+1.19935060, +0.697071135), (+1.75127625, +0.876916885), (+1.35976279, +0.881524384), (+1.89837289, +0.164843619), (+1.03405356, +0.560307324), (+1.57021117, +0.930166662), (+1.64328170, +0.286450386E-1), (+1.36786675, +0.437844694), (+1.23686123, +0.514081776), (+1.78564501, +0.472835898), (+1.76537991, +0.686042905), (+1.43298149, +0.613808632), (+1.03116918, +0.349743724), (+1.43122160, +0.935128450), (+1.49257493, +0.730068207), (+1.93957901, +0.249582350), (+1.68207943, +0.430140257), (+1.21768391, +0.447426617), (+1.31641436, +0.267508149), (+1.73206782, +0.255733013), (+1.13330555, +0.956078947), (+1.91885912, +0.531385362)

7

8atad = getFFTI(getFFTF(data))

9atad

10(+1.50181782, +0.115960360), (+1.90760005, +0.334465325), (+1.13850534, +0.281729102), (+1.95291078, +0.135239765), (+1.94294357, +0.403895259), (+1.36937571, +0.644446135), (+1.14799070, +0.168884844), (+1.63172269, +0.222431421E-1), (+1.75567603, +0.357230663), (+1.83243227, +0.573089004), (+1.52864408, +0.913300812), (+1.58670163, +0.848945975E-1), (+1.21496367, +0.935692549), (+1.95143974, +0.858387828), (+1.19935060, +0.697071135), (+1.75127625, +0.876916707), (+1.35976267, +0.881524324), (+1.89837289, +0.164843604), (+1.03405344, +0.560307264), (+1.57021117, +0.930166364), (+1.64328146, +0.286449492E-1), (+1.36786675, +0.437844694), (+1.23686099, +0.514081717), (+1.78564501, +0.472835839), (+1.76537967, +0.686042905), (+1.43298149, +0.613808632), (+1.03116894, +0.349743664), (+1.43122137, +0.935128391), (+1.49257469, +0.730068147), (+1.93957865, +0.249582618), (+1.68207932, +0.430140138), (+1.21768379, +0.447426707), (+1.31641424, +0.267508090), (+1.73206794, +0.255732954), (+1.13330567, +0.956078649), (+1.91885936, +0.531385124), (+0.00000000, -0.119209290E-6), (+0.596046448E-7, -0.298023224E-7), (+0.119209290E-6, +0.670552254E-7), (+0.417232513E-6, +0.00000000), (+0.178813934E-6, -0.193715096E-6), (+0.298023224E-6, -0.119209290E-6), (+0.178813934E-6, +0.596046448E-7), (+0.238418579E-6, +0.119209290E-6), (+0.178813934E-6, -0.268220901E-6), (+0.119209290E-6, -0.208616257E-6), (+0.178813934E-6, -0.596046448E-7), (-0.596046448E-7, -0.596046448E-7), (+0.00000000, +0.298023224E-7), (+0.178813934E-6, +0.447034836E-7), (+0.119209290E-6, +0.149011612E-6), (+0.00000000, +0.238418579E-6), (+0.178813934E-6, -0.298023224E-7), (+0.178813934E-6, -0.596046448E-7), (+0.596046448E-7, +0.596046448E-7), (+0.238418579E-6, +0.163912773E-6), (+0.178813934E-6, -0.298023224E-7), (+0.238418579E-6, +0.00000000), (+0.596046448E-7, +0.178813934E-6), (+0.119209290E-6, +0.00000000), (+0.178813934E-6, +0.00000000), (+0.357627869E-6, -0.119209290E-6), (+0.178813934E-6, +0.104308128E-6), (+0.178813934E-6, +0.894069672E-7)

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

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

17

18lenData = getUnifRand(5, 100)

19lenData

20+77

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

22data

23(+1.3324453817231745, +0.39445214227473935), (+1.3401773135690291, +0.79546795178790930E-1), (+1.3307953570864464, +0.24986155207931149), (+1.0321173133634884, +0.58025024996920926), (+1.9613824217324416, +0.94108395906443754), (+1.9377138592761129, +0.63016130878369325), (+1.6492686894770043, +0.89259614293128164), (+1.0319400752140395, +0.16704673115507063), (+1.2302564969469230, +0.81892908287160660), (+1.5532879864593181, +0.70506573716614251), (+1.5827126380625351, +0.51080122251128179), (+1.8247915626606535, +0.28493540702883935), (+1.9193320542016918, +0.85676253995764373), (+1.3382994297379156, +0.49389561484800470), (+1.8989269695338955, +0.72816788024426926), (+1.5863482010422805, +0.44226389526968657), (+1.0901532903748254, +0.51817587760497785), (+1.8879662545267859, +0.40433239973853696), (+1.8995278657541066, +0.18253783491155828), (+1.7453805895396641, +0.23688017485800328), (+1.8963581668049170, +0.86078597272501645), (+1.5779667601107197, +0.48504174975369141), (+1.1024103989697223, +0.48295144349256991), (+1.8614526533567333, +0.12501837721475173E-1), (+1.8944194313815581, +0.80463284652399258), (+1.2599886989171361, +0.57117553714367419), (+1.8075442986481236, +0.88156843398285856), (+1.4738476824150033, +0.69913361665421037), (+1.2590983335041011, +0.26111436307555635E-1), (+1.6309093952170941, +0.97965763127781857), (+1.7856097552435841, +0.55120309520062860), (+1.3389655647838397, +0.35960803091897431), (+1.4329001111056745, +0.60417629917994697), (+1.1584779012995887, +0.97270132291237732), (+1.5084807275315606, +0.70072125706760191), (+1.1134741975380096, +0.27440768492106460), (+1.6369232733173253, +0.31975889027724624), (+1.4282283004373002, +0.46788610607359116), (+1.9490100498233471, +0.43603329907713428), (+1.8105317033748676, +0.97358713106329831), (+1.7947312009769558, +0.83908531413867060), (+1.7833997945341573, +0.80568080412101983), (+1.7556406029734721, +0.39852378286524293), (+1.4758009269063832, +0.81293510932176594), (+1.5862277359122379, +0.30172944518186207), (+1.5067632167600395, +0.46872045141772090), (+1.1433813422592034, +0.78739601832105532), (+1.2892942174048494, +0.72784143771014753), (+1.2619939620121228, +0.89495410599579717), (+1.3693176017178068, +0.19629911446920301), (+1.2226745297001373, +0.85896556370632204), (+1.1117892572270218, +0.93452794618134205), (+1.2845807290809708, +0.95105740954624773), (+1.2612434045858392, +0.17939000639327274), (+1.1255356767039237, +0.33206051296126837), (+1.4664247081720065, +0.38348582197099690E-2), (+1.0871518007949952, +0.65602463899206132), (+1.0631357367289787, +0.90504158748310670), (+1.6835459404709177, +0.11847105935412960), (+1.9956451552420251, +0.60333916733445681), (+1.1078520641624250, +0.44084518731174172), (+1.3348584679948197, +0.66149367488228616), (+1.3993777426689740, +0.77185232831922024), (+1.0468181367273615, +0.26234200055908963), (+1.7650391303889128, +0.74111790007455935), (+1.4473519500755274, +0.36596907668079115), (+1.4732252623667892, +0.27727543861970616), (+1.4026065529907927, +0.90808209358550107), (+1.6227409434096707, +0.12626147679026645), (+1.1572571972190855, +0.42636850782375413), (+1.8355314953271695, +0.29339167790628473), (+1.2342189356028679, +0.54143557876872683), (+1.2524617580054231, +0.47228071510346692), (+1.1477965815222593, +0.88085377035509194), (+1.8718439321546192, +0.92288574859449068), (+1.8210055972571406, +0.57662903720413272), (+1.1161381461268802, +0.81014875944549591E-1)

24

25atad = getFFTI(getFFTF(data))

26atad

27(+1.3324453817231747, +0.39445214227473929), (+1.3401773135690294, +0.79546795178791041E-1), (+1.3307953570864461, +0.24986155207931171), (+1.0321173133634882, +0.58025024996920982), (+1.9613824217324414, +0.94108395906443754), (+1.9377138592761129, +0.63016130878369325), (+1.6492686894770041, +0.89259614293128187), (+1.0319400752140395, +0.16704673115507079), (+1.2302564969469232, +0.81892908287160648), (+1.5532879864593183, +0.70506573716614263), (+1.5827126380625351, +0.51080122251128235), (+1.8247915626606537, +0.28493540702883979), (+1.9193320542016914, +0.85676253995764373), (+1.3382994297379156, +0.49389561484800493), (+1.8989269695338953, +0.72816788024426971), (+1.5863482010422807, +0.44226389526968696), (+1.0901532903748254, +0.51817587760497796), (+1.8879662545267855, +0.40433239973853685), (+1.8995278657541066, +0.18253783491155812), (+1.7453805895396639, +0.23688017485800350), (+1.8963581668049168, +0.86078597272501600), (+1.5779667601107197, +0.48504174975369135), (+1.1024103989697220, +0.48295144349256980), (+1.8614526533567330, +0.12501837721475187E-1), (+1.8944194313815581, +0.80463284652399270), (+1.2599886989171361, +0.57117553714367442), (+1.8075442986481232, +0.88156843398285867), (+1.4738476824150033, +0.69913361665421037), (+1.2590983335041011, +0.26111436307555580E-1), (+1.6309093952170937, +0.97965763127781824), (+1.7856097552435837, +0.55120309520062838), (+1.3389655647838394, +0.35960803091897420), (+1.4329001111056745, +0.60417629917994664), (+1.1584779012995887, +0.97270132291237710), (+1.5084807275315608, +0.70072125706760158), (+1.1134741975380091, +0.27440768492106460), (+1.6369232733173251, +0.31975889027724591), (+1.4282283004373002, +0.46788610607359110), (+1.9490100498233469, +0.43603329907713373), (+1.8105317033748678, +0.97358713106329797), (+1.7947312009769560, +0.83908531413867038), (+1.7833997945341573, +0.80568080412101972), (+1.7556406029734724, +0.39852378286524243), (+1.4758009269063832, +0.81293510932176583), (+1.5862277359122374, +0.30172944518186173), (+1.5067632167600391, +0.46872045141772078), (+1.1433813422592032, +0.78739601832105510), (+1.2892942174048496, +0.72784143771014731), (+1.2619939620121228, +0.89495410599579683), (+1.3693176017178064, +0.19629911446920281), (+1.2226745297001376, +0.85896556370632171), (+1.1117892572270218, +0.93452794618134172), (+1.2845807290809708, +0.95105740954624718), (+1.2612434045858392, +0.17939000639327238), (+1.1255356767039237, +0.33206051296126798), (+1.4664247081720063, +0.38348582197098441E-2), (+1.0871518007949952, +0.65602463899206076), (+1.0631357367289784, +0.90504158748310659), (+1.6835459404709177, +0.11847105935412941), (+1.9956451552420251, +0.60333916733445658), (+1.1078520641624250, +0.44084518731174133), (+1.3348584679948194, +0.66149367488228550), (+1.3993777426689737, +0.77185232831921957), (+1.0468181367273615, +0.26234200055908924), (+1.7650391303889128, +0.74111790007455913), (+1.4473519500755272, +0.36596907668079109), (+1.4732252623667896, +0.27727543861970605), (+1.4026065529907925, +0.90808209358550085), (+1.6227409434096707, +0.12626147679026617), (+1.1572571972190855, +0.42636850782375396), (+1.8355314953271695, +0.29339167790628445), (+1.2342189356028679, +0.54143557876872683), (+1.2524617580054229, +0.47228071510346692), (+1.1477965815222588, +0.88085377035509160), (+1.8718439321546194, +0.92288574859449057), (+1.8210055972571404, +0.57662903720413272), (+1.1161381461268802, +0.81014875944549314E-1), (-0.11102230246251565E-15, -0.55511151231257827E-15), (+0.55511151231257827E-15, -0.49960036108132044E-15), (+0.33306690738754696E-15, -0.49960036108132044E-15), (+0.11102230246251565E-15, -0.11102230246251565E-15), (+0.22204460492503131E-15, -0.30531133177191805E-15), (+0.22204460492503131E-15, -0.55511151231257827E-16), (+0.22204460492503131E-15, -0.44408920985006262E-15), (+0.55511151231257827E-15, +0.11102230246251565E-15), (+0.11102230246251565E-15, -0.16653345369377348E-15), (+0.44408920985006262E-15, -0.13877787807814457E-15), (+0.44408920985006262E-15, -0.97144514654701197E-16), (-0.11102230246251565E-15, -0.55511151231257827E-16), (+0.11102230246251565E-15, -0.55511151231257827E-15), (+0.22204460492503131E-15, -0.27755575615628914E-15), (+0.22204460492503131E-15, -0.27755575615628914E-15), (+0.33306690738754696E-15, +0.55511151231257827E-16), (+0.22204460492503131E-15, -0.55511151231257827E-16), (+0.55511151231257827E-15, +0.11102230246251565E-15), (+0.88817841970012523E-15, +0.13877787807814457E-15), (-0.44408920985006262E-15, +0.16653345369377348E-15), (-0.33306690738754696E-15, -0.55511151231257827E-16), (+0.11102230246251565E-15, +0.16653345369377348E-15), (-0.11102230246251565E-15, +0.83266726846886741E-16), (+0.11102230246251565E-15, +0.24980018054066022E-15), (-0.11102230246251565E-15, +0.11102230246251565E-15), (+0.0000000000000000, +0.47184478546569153E-15), (+0.0000000000000000, +0.44408920985006262E-15), (-0.11102230246251565E-15, +0.11102230246251565E-15), (-0.11102230246251565E-15, -0.27755575615628914E-15), (+0.22204460492503131E-15, -0.16653345369377348E-15), (-0.44408920985006262E-15, -0.11102230246251565E-15), (+0.11102230246251565E-15, +0.33306690738754696E-15), (+0.11102230246251565E-15, +0.11102230246251565E-15), (+0.22204460492503131E-15, +0.55511151231257827E-16), (+0.33306690738754696E-15, +0.11102230246251565E-15), (-0.11102230246251565E-15, +0.22204460492503131E-15), (+0.11102230246251565E-15, +0.27755575615628914E-16), (-0.11102230246251565E-15, +0.33306690738754696E-15), (+0.11102230246251565E-15, +0.22204460492503131E-15), (-0.11102230246251565E-15, +0.38857805861880479E-15), (+0.22204460492503131E-15, +0.13877787807814457E-15), (+0.11102230246251565E-15, +0.49960036108132044E-15), (+0.33306690738754696E-15, +0.20816681711721685E-15), (+0.11102230246251565E-15, +0.16653345369377348E-15), (+0.22204460492503131E-15, +0.55511151231257827E-16), (+0.11102230246251565E-15, +0.63837823915946501E-15), (+0.22204460492503131E-15, +0.27755575615628914E-15), (+0.11102230246251565E-15, +0.72164496600635175E-15), (+0.22204460492503131E-15, +0.61062266354383610E-15), (+0.0000000000000000, +0.83266726846886741E-15), (+0.55511151231257827E-15, +0.44408920985006262E-15)

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

29reltol

30+0.14901161193847656E-7

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

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

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

34

35lenData = getUnifRand(5, 100)

36lenData

37+42

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

39data

40(+1.27981474740672237584768893196660337, +0.862182744691642054436293147406288598), (+1.20383448745971028189261573073883500, +0.219615416949786286574647589541044594), (+1.26373325483685969309059069019298284, +0.901283012836958477228937988361113549), (+1.84797059111275649957298115624833949, +0.441614652323975609219778770979417350), (+1.83115423241218993726571236913987920, +0.571600559158026696466250601978489905), (+1.43389142054039288096400369950751844, +0.988104752081723163436146978446363521E-1), (+1.35664130362052526425009166386482132, +0.152112018158093453016070166926128895), (+1.03141702031106287893784356543478565, +0.726128294790956291952493206856298643), (+1.72620960578272069652633784101288235, +0.715380160788292509277229417264705951), (+1.00225083813778151329598416949603648, +0.289643846297123872160398205422645941), (+1.82342163724353527634422939076482255, +0.948383248253497240243462261226402154), (+1.98805131210313171429374712835271094, +0.601135225285593654594183445411210577), (+1.96055836042005124546862101398347042, +0.276472437149438829796783895944388884E-1), (+1.29236892458652938110911548527339976, +0.484386715069929483674633845908129259), (+1.52988038709185776405601571810040784, +0.153251681655208831765009658127137137), (+1.98001663970701600177179139314408160, +0.135101588782687124806383323980709238), (+1.99476966890952706381184679873524500, +0.921911161455751360510795397465222428), (+1.42737837698777025686864818353854523, +0.821198036139524101953685753587062397), (+1.14868919571040929185700076158920862, +0.239698308671618898376833381059466924), (+1.07766469562909606966483137664147283, +0.989907208130600439557345687068011305), (+1.14669285212903943764002057277424258, +0.839644556290512271952035081336522096), (+1.69046921113777925364073563113869513, +0.265756414820899317162617189549898334E-1), (+1.17036462538702153620076692085530773, +0.554878276484645326575541185677420408), (+1.50408981008328331634420029429016529, +0.152959169748893410954636116299494955), (+1.25470022724087607522321998926398839, +0.873175434996657629510025012127217457), (+1.10381691165379056109364985041484665, +0.387768548935729644309320796793347177), (+1.83690496889986955923309570841449422, +0.240305660582902723160126161339430942), (+1.07713579481748712228522918310400012, +0.944698535606908859054010216603866717), (+1.01278052864824447667521289924422202, +0.711342997979353402188972446655927162), (+1.97183531952328898637442268094092691, +0.532818198576860003361478864609898586), (+1.52534321677720788158230813704965351, +0.437011305262029053058177907324685908), (+1.40554601162204599166767230035194788, +0.342392120286120388781840017437460865E-1), (+1.48399756521785925254825918534535631, +0.855419357630672631736586698556247103), (+1.41656801590411910909339072365326494, +0.747241546969413243490629423268676975), (+1.59475281412609733241710197305659082, +0.259100497656315535301200205788730127), (+1.31497041944567669264634986329412470, +0.870980492531157534777052945783562988), (+1.90716543120479916286323272357712200, +0.502982895407143925811540837861311435), (+1.42528042020043986342323060427744255, +0.661578434882031012515592551138341531), (+1.14289788492111962656514770422566036, +0.452987987105495251976970700764950955), (+1.47461295315215972346144067030032350, +0.876774488054467196861311132062885832), (+1.60023119301141147779551511073822009, +0.631241770774893542231418642326186166), (+1.80607232234342259908683440723620231, +0.488627353337897276027401402525856182)

41

42atad = getFFTI(getFFTF(data))

43atad

44(+1.27981474740672237584768893196660376, +0.862182744691642054436293147406288598), (+1.20383448745971028189261573073883500, +0.219615416949786286574647589541044690), (+1.26373325483685969309059069019298284, +0.901283012836958477228937988361113645), (+1.84797059111275649957298115624833968, +0.441614652323975609219778770979417399), (+1.83115423241218993726571236913987978, +0.571600559158026696466250601978489616), (+1.43389142054039288096400369950751883, +0.988104752081723163436146978446362077E-1), (+1.35664130362052526425009166386482171, +0.152112018158093453016070166926128655), (+1.03141702031106287893784356543478545, +0.726128294790956291952493206856298547), (+1.72620960578272069652633784101288235, +0.715380160788292509277229417264706143), (+1.00225083813778151329598416949603648, +0.289643846297123872160398205422645989), (+1.82342163724353527634422939076482255, +0.948383248253497240243462261226402250), (+1.98805131210313171429374712835271075, +0.601135225285593654594183445411210866), (+1.96055836042005124546862101398347061, +0.276472437149438829796783895944389125E-1), (+1.29236892458652938110911548527339995, +0.484386715069929483674633845908129355), (+1.52988038709185776405601571810040804, +0.153251681655208831765009658127137016), (+1.98001663970701600177179139314408160, +0.135101588782687124806383323980709286), (+1.99476966890952706381184679873524519, +0.921911161455751360510795397465222332), (+1.42737837698777025686864818353854523, +0.821198036139524101953685753587062300), (+1.14868919571040929185700076158920881, +0.239698308671618898376833381059466924), (+1.07766469562909606966483137664147303, +0.989907208130600439557345687068011305), (+1.14669285212903943764002057277424278, +0.839644556290512271952035081336522289), (+1.69046921113777925364073563113869513, +0.265756414820899317162617189549895686E-1), (+1.17036462538702153620076692085530792, +0.554878276484645326575541185677420600), (+1.50408981008328331634420029429016568, +0.152959169748893410954636116299495051), (+1.25470022724087607522321998926398877, +0.873175434996657629510025012127217457), (+1.10381691165379056109364985041484665, +0.387768548935729644309320796793346888), (+1.83690496889986955923309570841449422, +0.240305660582902723160126161339430870), (+1.07713579481748712228522918310399993, +0.944698535606908859054010216603866139), (+1.01278052864824447667521289924422202, +0.711342997979353402188972446655926970), (+1.97183531952328898637442268094092730, +0.532818198576860003361478864609898682), (+1.52534321677720788158230813704965370, +0.437011305262029053058177907324685908), (+1.40554601162204599166767230035194788, +0.342392120286120388781840017437457374E-1), (+1.48399756521785925254825918534535651, +0.855419357630672631736586698556247199), (+1.41656801590411910909339072365326475, +0.747241546969413243490629423268676975), (+1.59475281412609733241710197305659101, +0.259100497656315535301200205788730031), (+1.31497041944567669264634986329412451, +0.870980492531157534777052945783562892), (+1.90716543120479916286323272357712238, +0.502982895407143925811540837861311627), (+1.42528042020043986342323060427744255, +0.661578434882031012515592551138342013), (+1.14289788492111962656514770422566055, +0.452987987105495251976970700764951195), (+1.47461295315215972346144067030032350, +0.876774488054467196861311132062886314), (+1.60023119301141147779551511073822029, +0.631241770774893542231418642326186070), (+1.80607232234342259908683440723620212, +0.488627353337897276027401402525856134), (+0.962964972193617926527988971292463659E-34, -0.192592994438723585305597794258492732E-33), (-0.962964972193617926527988971292463659E-34, -0.144444745829042688979198345693869549E-33), (-0.962964972193617926527988971292463659E-34, +0.240741243048404481631997242823115915E-34), (-0.385185988877447170611195588516985464E-33, -0.192592994438723585305597794258492732E-33), (-0.192592994438723585305597794258492732E-33, +0.240741243048404481631997242823115915E-33), (-0.674075480535532548569592279904724561E-33, +0.108333559371782016734398759270402162E-33), (+0.192592994438723585305597794258492732E-33, +0.00000000000000000000000000000000000), (-0.962964972193617926527988971292463659E-34, +0.962964972193617926527988971292463659E-34), (+0.288889491658085377958396691387739098E-33, +0.192592994438723585305597794258492732E-33), (+0.00000000000000000000000000000000000, -0.144444745829042688979198345693869549E-33), (+0.00000000000000000000000000000000000, -0.240741243048404481631997242823115915E-33), (-0.288889491658085377958396691387739098E-33, -0.168518870133883137142398069976181140E-33), (+0.00000000000000000000000000000000000, -0.962964972193617926527988971292463659E-34), (-0.288889491658085377958396691387739098E-33, +0.00000000000000000000000000000000000), (+0.385185988877447170611195588516985464E-33, +0.481482486096808963263994485646231830E-34), (+0.192592994438723585305597794258492732E-33, -0.216667118743564033468797518540804323E-33), (+0.00000000000000000000000000000000000, +0.312963615962925826121596415670050689E-33), (+0.962964972193617926527988971292463659E-34, +0.192592994438723585305597794258492732E-33), (+0.288889491658085377958396691387739098E-33, -0.288889491658085377958396691387739098E-33), (-0.962964972193617926527988971292463659E-34, -0.192592994438723585305597794258492732E-33), (-0.192592994438723585305597794258492732E-33, -0.120370621524202240815998621411557957E-33), (+0.00000000000000000000000000000000000, +0.312963615962925826121596415670050689E-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

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

51

52lenData = getUnifRand(5, 100)

53lenData

54+48

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

56data

57+1.67343247, +1.64487982, +1.27125895, +1.93363202, +1.29907751, +1.67862391, +1.75069213, +1.89066041, +1.38388371, +1.68207574, +1.26418972, +1.70091939, +1.67065072, +1.09575129, +1.29001975, +1.51800525, +1.96322274, +1.72935104, +1.80956113, +1.12263036, +1.78541017, +1.79913974, +1.51552510, +1.52216244, +1.80719376, +1.50468326, +1.98516691, +1.73070145, +1.95345342, +1.83292389, +1.68648160, +1.79589474, +1.79148531, +1.36568570, +1.22257984, +1.14823890, +1.35807312, +1.99733734, +1.85389566, +1.20944071, +1.39976883, +1.91435719, +1.03514636, +1.21887922, +1.79255271, +1.16540170, +1.11608243, +1.39070272

58

59atad = getFFTI(getFFTF(data))

60atad

61+1.67343235, +1.64487958, +1.27125859, +1.93363202, +1.29907763, +1.67862380, +1.75069165, +1.89066029, +1.38388360, +1.68207550, +1.26418936, +1.70091951, +1.67065060, +1.09575129, +1.29001963, +1.51800537, +1.96322298, +1.72935092, +1.80956113, +1.12263060, +1.78541028, +1.79913962, +1.51552510, +1.52216268, +1.80719376, +1.50468326, +1.98516679, +1.73070157, +1.95345294, +1.83292389, +1.68648148, +1.79589486, +1.79148531, +1.36568570, +1.22257996, +1.14823902, +1.35807312, +1.99733722, +1.85389566, +1.20944071, +1.39976871, +1.91435695, +1.03514636, +1.21887934, +1.79255259, +1.16540170, +1.11608255, +1.39070272, +0.00000000, +0.119209290E-6, -0.119209290E-6, +0.00000000, +0.119209290E-6, -0.119209290E-6, +0.596046448E-7, +0.119209290E-6, +0.596046448E-7, +0.596046448E-7, -0.596046448E-7, +0.357627869E-6, +0.357627869E-6, +0.119209290E-6, -0.178813934E-6, +0.298023224E-6

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

63reltol

64+0.345266977E-3

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

66T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, 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+29

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

73data

74+1.8813933360211275, +1.7883388096090993, +1.6192579422400553, +1.6046850986288801, +1.3396175050365517, +1.8300628988755803, +1.8797593664619265, +1.2443858111291188, +1.1377418914186528, +1.4045543013021962, +1.8423945007008760, +1.3094264349807170, +1.7537100656986204, +1.7632959809113617, +1.2217615685976588, +1.7430494376080119, +1.3092795150876895, +1.9015195387467376, +1.4810010471604289, +1.9319532160864448, +1.4530427133433546, +1.0716855492327719, +1.2050605186739167, +1.9386090987910287, +1.5971108388455937, +1.8809736645755128, +1.5261885752343425, +1.0976039207778849, +1.2264183820624166

75

76atad = getFFTI(getFFTF(data))

77atad

78+1.8813933360211277, +1.7883388096090995, +1.6192579422400553, +1.6046850986288803, +1.3396175050365522, +1.8300628988755805, +1.8797593664619261, +1.2443858111291195, +1.1377418914186532, +1.4045543013021966, +1.8423945007008757, +1.3094264349807174, +1.7537100656986206, +1.7632959809113615, +1.2217615685976591, +1.7430494376080117, +1.3092795150876897, +1.9015195387467376, +1.4810010471604287, +1.9319532160864450, +1.4530427133433550, +1.0716855492327721, +1.2050605186739163, +1.9386090987910285, +1.5971108388455941, +1.8809736645755133, +1.5261885752343420, +1.0976039207778849, +1.2264183820624166, +0.66613381477509392E-15, +0.11102230246251565E-15, +0.55511151231257827E-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

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

85

86lenData = getUnifRand(5, 100)

87lenData

88+34

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

90data

91+1.61706775203305838209178929693004867, +1.14766008505713645451801182372826531, +1.53216498695164134238321001453452142, +1.86296412484217909602140221570785823, +1.43915203000147347258546974611818392, +1.58481504682734146354845165212552913, +1.70679397499359204775636739701649843, +1.74009023950606989124635400842224549, +1.22561457663841653596234771996356027, +1.75699811647365265766838019131129902, +1.35507425250012299908185413219349506, +1.99555168287054591353923883304661277, +1.63427422698951413890364096976183425, +1.56662671107469317816100264526440851, +1.51003964709255886479004977113343223, +1.19777063645017771900856675540722490, +1.47912423213289887203125848155277786, +1.20122937447027798440072936182944441, +1.78879682668040293274387197498763261, +1.99055065048296757554070769116297277, +1.12210256157404655828988689213946588, +1.71281995815285101347849232160026587, +1.09091697863892757245767629123307878, +1.70204836432305036378349499910707618, +1.94578369131329093390932100298194157, +1.61623825861835362523501216454004077, +1.15485238276038903162271881590436362, +1.73753433085405779460918443459635109, +1.59990778086592133126098886505884831, +1.84888476608901318258583374376575953, +1.56945452762235585561670328924455220, +1.56243377858163182820717651408967329, +1.46541624775459752606033991473642347, +1.20762714570647608571911454450851387

92

93atad = getFFTI(getFFTF(data))

94atad

95+1.61706775203305838209178929693004867, +1.14766008505713645451801182372826512, +1.53216498695164134238321001453452104, +1.86296412484217909602140221570785804, +1.43915203000147347258546974611818449, +1.58481504682734146354845165212552952, +1.70679397499359204775636739701649843, +1.74009023950606989124635400842224568, +1.22561457663841653596234771996356046, +1.75699811647365265766838019131129902, +1.35507425250012299908185413219349544, +1.99555168287054591353923883304661277, +1.63427422698951413890364096976183483, +1.56662671107469317816100264526440890, +1.51003964709255886479004977113343223, +1.19777063645017771900856675540722490, +1.47912423213289887203125848155277767, +1.20122937447027798440072936182944422, +1.78879682668040293274387197498763261, +1.99055065048296757554070769116297238, +1.12210256157404655828988689213946550, +1.71281995815285101347849232160026587, +1.09091697863892757245767629123307878, +1.70204836432305036378349499910707637, +1.94578369131329093390932100298194157, +1.61623825861835362523501216454004077, +1.15485238276038903162271881590436400, +1.73753433085405779460918443459635128, +1.59990778086592133126098886505884812, +1.84888476608901318258583374376576011, +1.56945452762235585561670328924455239, +1.56243377858163182820717651408967348, +1.46541624775459752606033991473642347, +1.20762714570647608571911454450851368, +0.481482486096808963263994485646231830E-33, +0.385185988877447170611195588516985464E-33, -0.385185988877447170611195588516985464E-33, -0.385185988877447170611195588516985464E-33, +0.00000000000000000000000000000000000, -0.192592994438723585305597794258492732E-33, -0.192592994438723585305597794258492732E-33, -0.962964972193617926527988971292463659E-34, +0.192592994438723585305597794258492732E-33, +0.192592994438723585305597794258492732E-33, -0.385185988877447170611195588516985464E-33, -0.962964972193617926527988971292463659E-34, +0.962964972193617926527988971292463659E-34, +0.962964972193617926527988971292463659E-34, +0.962964972193617926527988971292463659E-34, +0.00000000000000000000000000000000000, +0.288889491658085377958396691387739098E-33, +0.674075480535532548569592279904724561E-33, +0.288889491658085377958396691387739098E-33, +0.00000000000000000000000000000000000, +0.288889491658085377958396691387739098E-33, +0.962964972193617926527988971292463659E-34, +0.288889491658085377958396691387739098E-33, -0.962964972193617926527988971292463659E-34, +0.00000000000000000000000000000000000, +0.962964972193617926527988971292463659E-34, +0.577778983316170755916793382775478196E-33, -0.385185988877447170611195588516985464E-33, +0.00000000000000000000000000000000000, +0.00000000000000000000000000000000000

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

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

102

103lenData = getUnifRand(5, 100)

104lenData

105+48

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

107data

108(+1.04872501, +0.504522324E-1), (+1.52842236, +0.416509569), (+1.32822752, +0.855860770), (+1.73441505, +0.556950092), (+1.16510010, +0.313898087), (+1.98980820, +0.173110545), (+1.29929471, +0.906772017E-1), (+1.18096435, +0.397098899), (+1.45289886, +0.688606024), (+1.04419518, +0.958772600), (+1.56167459, +0.789553225), (+1.39571440, +0.998471379), (+1.16666913, +0.446261108), (+1.63133526, +0.653022528), (+1.69561434, +0.375422776), (+1.36294651, +0.609731615), (+1.91000009, +0.520605326), (+1.82481647, +0.653725028), (+1.41266000, +0.556563079), (+1.76445317, +0.699774027E-1), (+1.26957846, +0.667725861), (+1.00470328, +0.966892719), (+1.93545568, +0.595810533), (+1.33031344, +0.391473114), (+1.48531258, +0.922189593), (+1.45937359, +0.176292360), (+1.39269006, +0.861941755), (+1.44138801, +0.230386555), (+1.41899872, +0.508401036), (+1.34607935, +0.404766440), (+1.78557515, +0.542855859), (+1.81277323, +0.133631825), (+1.73801494, +0.231632650), (+1.46311378, +0.477816761), (+1.02870440, +0.213294387), (+1.63491285, +0.258458853), (+1.46077132, +0.494463861), (+1.90993822, +0.682605505), (+1.50521541, +0.903200686), (+1.76976490, +0.238560140), (+1.79696560, +0.629968882), (+1.90503299, +0.306149721E-1), (+1.02624750, +0.968809724), (+1.08972740, +0.255665779), (+1.07153141, +0.705233037), (+1.68794417, +0.168841481E-1), (+1.53693676, +0.697678030), (+1.89158297, +0.923357725)

109

110atad = getFFTI(getFFTF(data))

111atad

112(+1.04872489, +0.504521728E-1), (+1.52842236, +0.416509569), (+1.32822716, +0.855860591), (+1.73441505, +0.556949854), (+1.16509998, +0.313898146), (+1.98980808, +0.173110604), (+1.29929459, +0.906771123E-1), (+1.18096459, +0.397098809), (+1.45289862, +0.688606143), (+1.04419518, +0.958772540), (+1.56167436, +0.789553344), (+1.39571452, +0.998471320), (+1.16666901, +0.446261227), (+1.63133514, +0.653022647), (+1.69561446, +0.375422716), (+1.36294675, +0.609731793), (+1.90999985, +0.520605266), (+1.82481647, +0.653724909), (+1.41265976, +0.556563020), (+1.76445293, +0.699773729E-1), (+1.26957822, +0.667725801), (+1.00470304, +0.966892540), (+1.93545556, +0.595810413), (+1.33031344, +0.391472995), (+1.48531222, +0.922189593), (+1.45937347, +0.176292405), (+1.39268982, +0.861941695), (+1.44138801, +0.230386630), (+1.41899848, +0.508401096), (+1.34607911, +0.404766381), (+1.78557515, +0.542855918), (+1.81277323, +0.133631676), (+1.73801470, +0.231632650), (+1.46311378, +0.477816820), (+1.02870429, +0.213294476), (+1.63491297, +0.258458734), (+1.46077120, +0.494463861), (+1.90993786, +0.682605505), (+1.50521529, +0.903200626), (+1.76976526, +0.238559932), (+1.79696524, +0.629968882), (+1.90503287, +0.306150019E-1), (+1.02624750, +0.968809664), (+1.08972740, +0.255665720), (+1.07153118, +0.705233037), (+1.68794405, +0.168842375E-1), (+1.53693664, +0.697678089), (+1.89158297, +0.923357725), (-0.178813934E-6, +0.596046448E-7), (+0.238418579E-6, +0.298023224E-7), (+0.00000000, +0.238418579E-6), (+0.417232513E-6, +0.238418579E-6), (-0.119209290E-6, +0.00000000), (-0.596046448E-7, -0.596046448E-7), (+0.00000000, +0.149011612E-6), (+0.357627869E-6, +0.298023224E-6), (+0.00000000, +0.00000000), (+0.238418579E-6, +0.447034836E-7), (+0.119209290E-6, +0.894069672E-7), (+0.357627869E-6, +0.104308128E-6), (+0.119209290E-6, -0.178813934E-6), (-0.596046448E-7, -0.178813934E-6), (+0.119209290E-6, -0.178813934E-6), (+0.238418579E-6, -0.968575478E-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

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

119

120lenData = getUnifRand(5, 100)

121lenData

122+22

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

124data

125(+1.1522741490421833, +0.29037294858953056), (+1.3304795477049534, +0.62466149353362477), (+1.4520294073056026, +0.75124831586451046), (+1.3672232018971822, +0.49157808777075640), (+1.8790415818849726, +0.92603293633731798), (+1.3258949887754781, +0.70464326356249263), (+1.6731140297719391, +0.46091164402118123), (+1.5581010391434365, +0.29252233522238313), (+1.3923006898089971, +0.79878977620287195), (+1.1296339182937229, +0.88273106720872296E-1), (+1.4222072407065305, +0.18586094924635110), (+1.6561219799631890, +0.30872284014193629), (+1.0112644514449904, +0.24754272235938579), (+1.3747230566489146, +0.69043871234565879), (+1.3452578218939908, +0.59403095348769730), (+1.5660306192896938, +0.16931693710990381), (+1.3473035214761793, +0.72136200438799947), (+1.4930787309659570, +0.83485327660749686), (+1.3181126460214840, +0.27740513444327042E-1), (+1.5840318097795540, +0.24114090923688092), (+1.1620810250043392, +0.85945462139421092), (+1.1017231268502070, +0.59794095107056211)

126

127atad = getFFTI(getFFTF(data))

128atad

129(+1.1522741490421833, +0.29037294858953039), (+1.3304795477049531, +0.62466149353362488), (+1.4520294073056026, +0.75124831586451046), (+1.3672232018971819, +0.49157808777075651), (+1.8790415818849726, +0.92603293633731787), (+1.3258949887754774, +0.70464326356249263), (+1.6731140297719389, +0.46091164402118129), (+1.5581010391434362, +0.29252233522238325), (+1.3923006898089971, +0.79878977620287195), (+1.1296339182937229, +0.88273106720872394E-1), (+1.4222072407065300, +0.18586094924635113), (+1.6561219799631888, +0.30872284014193624), (+1.0112644514449902, +0.24754272235938599), (+1.3747230566489144, +0.69043871234565835), (+1.3452578218939906, +0.59403095348769686), (+1.5660306192896933, +0.16931693710990361), (+1.3473035214761793, +0.72136200438799958), (+1.4930787309659570, +0.83485327660749664), (+1.3181126460214840, +0.27740513444327097E-1), (+1.5840318097795538, +0.24114090923688070), (+1.1620810250043392, +0.85945462139421092), (+1.1017231268502066, +0.59794095107056178), (+0.44408920985006262E-15, -0.55511151231257827E-16), (+0.44408920985006262E-15, -0.27755575615628914E-15), (+0.11102230246251565E-15, +0.16653345369377348E-15), (+0.11102230246251565E-15, +0.13877787807814457E-16), (+0.33306690738754696E-15, +0.27755575615628914E-16), (+0.66613381477509392E-15, +0.55511151231257827E-16), (+0.44408920985006262E-15, +0.36082248300317588E-15), (+0.33306690738754696E-15, +0.49960036108132044E-15), (+0.44408920985006262E-15, +0.38857805861880479E-15), (+0.77715611723760958E-15, +0.47184478546569153E-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

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

136

137lenData = getUnifRand(5, 100)

138lenData

139+79

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

141data

142(+1.19271741165461623619318561425441032, +0.972898986239908897856283983877449268), (+1.50272867996475026377978368751823503, +0.464465884331570958153435657776532728), (+1.92119399229554858106563947255013408, +0.809253047830122779782652731948002880), (+1.15029823744888810912109866217074643, +0.255731284984498307669748792361523321), (+1.17599617852336004243246074065386045, +0.126489754147658237835232751377642150), (+1.21206535380403311189983135450629239, +0.933409120979812604549259730216790761), (+1.14939192633969989627950146572106229, +0.773419028048781808487797205486569261), (+1.65638966468687674203174280633264253, +0.881672125275890271517047430885300732), (+1.03662536020574194380383324837612948, +0.894963733891435258464618288555756253), (+1.56551173029159296881953660765919756, +0.756077041181728171044599836835796290), (+1.67626107952634859260230658635947981, +0.591814246066482511794716788273353666), (+1.38126426800111644329350119084859363, +0.702692275759110840821976768756500352), (+1.26521606293085924291439515144737347, +0.758258558567543687408467978139726098), (+1.01048485149469416821970837171000351, +0.682223025859423423746204925514884263), (+1.08632420469638638545248688076485699, +0.315290529872431056693638493255783644), (+1.66573149333872746219188023080472324, +0.859424547286356201717507483752438826), (+1.54782238983089076966860679451499394, +0.314390573558149369515696522565880940), (+1.45797531581907645578555792876614913, +0.963454665778953589320920158921232912), (+1.20702561599335695828639580345718379, +0.613165083435867799874850839283701366), (+1.43969256977202063918719015017892807, +0.355070301529612757196137193252122760), (+1.89199561697901246177870223693336703, +0.425197021009151326322341071200714954), (+1.90878471539554609335607572477290253, +0.117575303119100005556914050706863240), (+1.94801135086751094894752374358832754, +0.239182233786754409637877804216987999), (+1.93655285300421557994797445349796792, +0.392845717155462970270386994252044787), (+1.80955079760346951736397168606959043, +0.389774084824656088006614345882114975E-1), (+1.59348459450505230754424426504842665, +0.120322876761920521410344312528493245), (+1.70146259767829828990952517383097784, +0.314679796023344973836058117165873416), (+1.67201945139416873878458602150897456, +0.171301260062432660400821824316227756), (+1.22373350856414047903055081486238269, +0.180399280232512370078205001467894251), (+1.94614609669582674677984253351639666, +0.815202151289170514581476731039856038), (+1.71060993029663230653320157816311110, +0.750685140876527811194493034618791012E-1), (+1.87888248097877934073519946925384408, +0.773389658379505318405399969829023701), (+1.02908277029750885652686829085920438, +0.905091080316552468255304649666158966E-2), (+1.74968369307783708329418498527810290, +0.671918833393887932984904815123765424), (+1.32048157367411277810686169349073613, +0.845619108612503094890339504814762797), (+1.36099012325678096919645011418080156, +0.618654897050557941992884731196514435E-1), (+1.82949068826308703820396814664710080, +0.182389474456339236225276782162499311), (+1.12310492502378990001325573861338758, +0.784322904199031443783970855363536366), (+1.09932130563146622210357775478775683, +0.233049864471303501569259491426452315E-1), (+1.75906924613288539061609862087746087, +0.183073151848785489966983440061269608E-1), (+1.04907152053297935996719895748905478, +0.272185812361339862281160887874736269), (+1.74155659747320914154984937547756520, +0.389442946568815950002418180844280562), (+1.38712716357185502296417870413657655, +0.783076382585230737242074284951201404), (+1.47601417222421392459824700358793019, +0.333596715511916895240375140635938020), (+1.24087415815504163291121101399546325, +0.524044377912794589834270216876991409), (+1.39358456756844190682033330822267575, +0.673852369293889921217971158667789036), (+1.76854494056200243848529346724043112, +0.950261396599340162071741003027084997), (+1.10195114691538443737457835454963225, +0.654494182901087548423796399319825112), (+1.33310120792062723334815503757149415, +0.635020156700700266863285176446652340), (+1.68754563487105658859560132746559629, +0.881742955628179005660495074258075461E-1), (+1.56029606565314561384281438937783726, +0.459775708400630204632975423394500582), (+1.68788496568015976107021881397065600, +0.692288149417400655692503413488131174), (+1.85110122439130368669628045755718024, +0.832711369270323503497855214306471559), (+1.32702238394190670570963139321867302, +0.378521214202826282532839009551685069), (+1.58819880624550594330482992770766882, +0.313764633066625371223999480302319473), (+1.66456799141639717651806465613554509, +0.616287303410671049924849849976044924), (+1.62952107250770887130529181822366599, +0.384494848060866553644212404194574919), (+1.38462939277880610021218461428842709, +0.748863772437596245568190062310052398), (+1.27931746842636721556684666322197460, +0.388186374187183765662386215532852054), (+1.09750081733357971950836728611580464, +0.952271790772719513844158903781388503), (+1.88331878589911829254560657573344567, +0.650904110452985855158490195595625209), (+1.00998893600950537473381869047737478, +0.712102747839629446888680939470957965), (+1.84746220354627338128932206226798588, +0.492556053615176063617386315545551475), (+1.06193625379800383980624773074908871, +0.396253887052225892727674616079819963), (+1.31323001114670480097198605341483539, +0.111331392090377101670574543468168456), (+1.79770000799970599087143563741036976, +0.844347671044838100119197124952442007), (+1.11488488608198613311726378242995213, +0.223686425794086782862210870254030509), (+1.66115758989994950211405690460906754, +0.457348544332670425288846898396289517), (+1.24794436221879761815829946631196312, +0.454844019872045127964321097642372770E-1), (+1.00097795770779844595987781898957534, +0.243627142885869625260649815160573031E-1), (+1.28237682447648309956482601853848947, +0.465582938102647977623844412012288743), (+1.88873673360714058533391108804785143, +0.307200394902089051677472139629243252), (+1.77430065123855363869068129155702627, +0.251464344333603165166588226692401043), (+1.66364292512489202916121290135826214, +0.144579862331598487671365335860918453E-1), (+1.37267367525232460133934132929676690, +0.213004805622553629512052196969645425), (+1.62725428586855713638938836785460806, +0.154727482834001835843504264190208661), (+1.98023610545216866096487838584761971, +0.464400444417576386260364391532857062), (+1.68295559588144562907563273648965398, +0.919205791672134932798723791402345274), (+1.06870141773761891235658089701833718, +0.454066339853614378130973492573887975)

143

144atad = getFFTI(getFFTF(data))

145atad

146(+1.19271741165461623619318561425441032, +0.972898986239908897856283983877449172), (+1.50272867996475026377978368751823522, +0.464465884331570958153435657776532247), (+1.92119399229554858106563947255013427, +0.809253047830122779782652731948002880), (+1.15029823744888810912109866217074643, +0.255731284984498307669748792361523128), (+1.17599617852336004243246074065386045, +0.126489754147658237835232751377641933), (+1.21206535380403311189983135450629259, +0.933409120979812604549259730216790472), (+1.14939192633969989627950146572106210, +0.773419028048781808487797205486569261), (+1.65638966468687674203174280633264311, +0.881672125275890271517047430885300636), (+1.03662536020574194380383324837612928, +0.894963733891435258464618288555756350), (+1.56551173029159296881953660765919775, +0.756077041181728171044599836835796194), (+1.67626107952634859260230658635948020, +0.591814246066482511794716788273353955), (+1.38126426800111644329350119084859440, +0.702692275759110840821976768756500352), (+1.26521606293085924291439515144737347, +0.758258558567543687408467978139726002), (+1.01048485149469416821970837171000351, +0.682223025859423423746204925514884167), (+1.08632420469638638545248688076485699, +0.315290529872431056693638493255783740), (+1.66573149333872746219188023080472363, +0.859424547286356201717507483752438826), (+1.54782238983089076966860679451499394, +0.314390573558149369515696522565880748), (+1.45797531581907645578555792876614932, +0.963454665778953589320920158921233008), (+1.20702561599335695828639580345718417, +0.613165083435867799874850839283701462), (+1.43969256977202063918719015017892826, +0.355070301529612757196137193252122519), (+1.89199561697901246177870223693336703, +0.425197021009151326322341071200714521), (+1.90878471539554609335607572477290292, +0.117575303119100005556914050706862915), (+1.94801135086751094894752374358832735, +0.239182233786754409637877804216987999), (+1.93655285300421557994797445349796830, +0.392845717155462970270386994252044594), (+1.80955079760346951736397168606959043, +0.389774084824656088006614345882114975E-1), (+1.59348459450505230754424426504842723, +0.120322876761920521410344312528493028), (+1.70146259767829828990952517383097803, +0.314679796023344973836058117165873609), (+1.67201945139416873878458602150897533, +0.171301260062432660400821824316227563), (+1.22373350856414047903055081486238269, +0.180399280232512370078205001467894058), (+1.94614609669582674677984253351639743, +0.815202151289170514581476731039856134), (+1.71060993029663230653320157816311129, +0.750685140876527811194493034618792697E-1), (+1.87888248097877934073519946925384446, +0.773389658379505318405399969829023894), (+1.02908277029750885652686829085920438, +0.905091080316552468255304649666166489E-2), (+1.74968369307783708329418498527810348, +0.671918833393887932984904815123765520), (+1.32048157367411277810686169349073613, +0.845619108612503094890339504814762893), (+1.36099012325678096919645011418080195, 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(+1.10195114691538443737457835454963225, +0.654494182901087548423796399319825208), (+1.33310120792062723334815503757149434, +0.635020156700700266863285176446652532), (+1.68754563487105658859560132746559668, +0.881742955628179005660495074258074257E-1), (+1.56029606565314561384281438937783745, +0.459775708400630204632975423394500533), (+1.68788496568015976107021881397065639, +0.692288149417400655692503413488131366), (+1.85110122439130368669628045755718063, +0.832711369270323503497855214306471463), (+1.32702238394190670570963139321867321, +0.378521214202826282532839009551685165), (+1.58819880624550594330482992770766920, +0.313764633066625371223999480302319280), (+1.66456799141639717651806465613554548, +0.616287303410671049924849849976045117), (+1.62952107250770887130529181822366638, +0.384494848060866553644212404194574919), (+1.38462939277880610021218461428842747, +0.748863772437596245568190062310052879), (+1.27931746842636721556684666322197498, +0.388186374187183765662386215532851958), (+1.09750081733357971950836728611580464, +0.952271790772719513844158903781388985), (+1.88331878589911829254560657573344606, +0.650904110452985855158490195595625401), (+1.00998893600950537473381869047737478, +0.712102747839629446888680939470958350), (+1.84746220354627338128932206226798627, +0.492556053615176063617386315545551571), (+1.06193625379800383980624773074908871, +0.396253887052225892727674616079820252), (+1.31323001114670480097198605341483539, +0.111331392090377101670574543468168408), (+1.79770000799970599087143563741036976, +0.844347671044838100119197124952442296), (+1.11488488608198613311726378242995213, +0.223686425794086782862210870254030509), (+1.66115758989994950211405690460906754, +0.457348544332670425288846898396289710), (+1.24794436221879761815829946631196312, +0.454844019872045127964321097642371987E-1), (+1.00097795770779844595987781898957515, +0.243627142885869625260649815160572068E-1), (+1.28237682447648309956482601853848966, +0.465582938102647977623844412012288695), (+1.88873673360714058533391108804785182, +0.307200394902089051677472139629243155), (+1.77430065123855363869068129155702607, +0.251464344333603165166588226692401043), (+1.66364292512489202916121290135826214, +0.144579862331598487671365335860918934E-1), (+1.37267367525232460133934132929676690, +0.213004805622553629512052196969645353), (+1.62725428586855713638938836785460825, +0.154727482834001835843504264190208854), (+1.98023610545216866096487838584761971, +0.464400444417576386260364391532857254), (+1.68295559588144562907563273648965417, +0.919205791672134932798723791402345852), (+1.06870141773761891235658089701833738, +0.454066339853614378130973492573888167), (-0.385185988877447170611195588516985464E-33, +0.240741243048404481631997242823115915E-33), (-0.962964972193617926527988971292463659E-34, +0.00000000000000000000000000000000000), (-0.674075480535532548569592279904724561E-33, -0.192592994438723585305597794258492732E-33), (-0.962964972193617926527988971292463659E-34, -0.962964972193617926527988971292463659E-34), (-0.288889491658085377958396691387739098E-33, +0.240741243048404481631997242823115915E-33), (+0.192592994438723585305597794258492732E-33, +0.240741243048404481631997242823115915E-33), (-0.481482486096808963263994485646231830E-33, +0.156481807981462913060798207835025345E-33), (+0.962964972193617926527988971292463659E-34, +0.180555932286303361223997932117336936E-33), (-0.288889491658085377958396691387739098E-33, +0.120370621524202240815998621411557957E-33), (-0.288889491658085377958396691387739098E-33, -0.288889491658085377958396691387739098E-33), (-0.481482486096808963263994485646231830E-33, -0.120370621524202240815998621411557957E-33), (-0.192592994438723585305597794258492732E-33, -0.168518870133883137142398069976181140E-33), (-0.674075480535532548569592279904724561E-33, -0.325000678115346050203196277811206485E-33), (+0.00000000000000000000000000000000000, +0.481482486096808963263994485646231830E-34), (-0.674075480535532548569592279904724561E-33, -0.192592994438723585305597794258492732E-33), (+0.00000000000000000000000000000000000, -0.240741243048404481631997242823115915E-34), (-0.481482486096808963263994485646231830E-33, -0.144444745829042688979198345693869549E-33), (-0.962964972193617926527988971292463659E-34, -0.752316384526264005099991383822237234E-34), (-0.674075480535532548569592279904724561E-33, -0.481482486096808963263994485646231830E-34), (+0.00000000000000000000000000000000000, -0.192592994438723585305597794258492732E-33), (-0.577778983316170755916793382775478196E-33, -0.108333559371782016734398759270402162E-33), (-0.962964972193617926527988971292463659E-34, -0.240741243048404481631997242823115915E-34), (-0.481482486096808963263994485646231830E-33, -0.962964972193617926527988971292463659E-34), (+0.00000000000000000000000000000000000, +0.481482486096808963263994485646231830E-34), (-0.385185988877447170611195588516985464E-33, -0.962964972193617926527988971292463659E-34), (-0.192592994438723585305597794258492732E-33, -0.120370621524202240815998621411557957E-33), (-0.288889491658085377958396691387739098E-33, -0.385185988877447170611195588516985464E-33), (+0.00000000000000000000000000000000000, -0.192592994438723585305597794258492732E-33), (-0.385185988877447170611195588516985464E-33, -0.457408361791968515100794761363920238E-33), (-0.192592994438723585305597794258492732E-33, -0.192592994438723585305597794258492732E-33), (-0.674075480535532548569592279904724561E-33, -0.144444745829042688979198345693869549E-33), (-0.288889491658085377958396691387739098E-33, -0.144444745829042688979198345693869549E-33), (-0.385185988877447170611195588516985464E-33, -0.144444745829042688979198345693869549E-33), (-0.192592994438723585305597794258492732E-33, -0.240741243048404481631997242823115915E-33), (-0.770371977754894341222391177033970927E-33, -0.216667118743564033468797518540804323E-33), (-0.192592994438723585305597794258492732E-33, -0.144444745829042688979198345693869549E-33), (-0.866668474974256133875190074163217293E-33, -0.144444745829042688979198345693869549E-33), (-0.192592994438723585305597794258492732E-33, +0.962964972193617926527988971292463659E-34), (-0.481482486096808963263994485646231830E-33, +0.722223729145213444895991728469347744E-34), (-0.962964972193617926527988971292463659E-34, +0.240741243048404481631997242823115915E-33), (-0.288889491658085377958396691387739098E-33, -0.481482486096808963263994485646231830E-34), (-0.385185988877447170611195588516985464E-33, -0.120370621524202240815998621411557957E-33), (-0.481482486096808963263994485646231830E-33, -0.481482486096808963263994485646231830E-33), (+0.962964972193617926527988971292463659E-34, +0.00000000000000000000000000000000000), (-0.962964972193617926527988971292463659E-34, -0.529630734706489859590393934210855013E-33), (-0.385185988877447170611195588516985464E-33, -0.240741243048404481631997242823115915E-33), (-0.577778983316170755916793382775478196E-33, -0.481482486096808963263994485646231830E-33), (-0.385185988877447170611195588516985464E-33, +0.722223729145213444895991728469347744E-34), (-0.481482486096808963263994485646231830E-33, -0.457408361791968515100794761363920238E-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

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

153

154lenData = getUnifRand(5, 100)

155lenData

156+94

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

158data

159+1.04627085, +1.23716736, +1.66350961, +1.87879193, +1.00440001, +1.42632210, +1.80210447, +1.94689631, +1.20031977, +1.77744675, +1.98941636, +1.15201104, +1.76435697, +1.72134507, +1.27957344, +1.39044380, +1.23682475, +1.72543979, +1.80299687, +1.12958288, +1.93224573, +1.53978014, +1.34212422, +1.64113927, +1.45682490, +1.35646367, +1.15128803, +1.87838745, +1.12382448, +1.73371959, +1.22006035, +1.33765018, +1.08756638, +1.80342674, +1.05687523, +1.65513897, +1.41248775, +1.54770160, +1.28854799, +1.91085649, +1.04273629, +1.32828474, +1.91922331, +1.24934900, +1.57529712, +1.20729864, +1.60531616, +1.90637374, +1.18156552, +1.57036686, +1.31842971, +1.66502881, +1.62939954, +1.06630027, +1.42190754, +1.23268962, +1.54487109, +1.16179991, +1.66953743, +1.04617608, +1.06164217, +1.31680369, +1.51512408, +1.96202672, +1.53766692, +1.82680917, +1.64487243, +1.32101083, +1.07180274, +1.08897066, +1.35595870, +1.98477697, +1.27401137, +1.65786922, +1.61868680, +1.24207413, +1.90501189, +1.87355804, +1.05366826, +1.82122755, +1.22312260, +1.50518060, +1.54922152, +1.51588345, +1.71269727, +1.96273196, +1.23426104, +1.46154273, +1.69247425, +1.89460731, +1.76092458, +1.57987320, +1.69817734, +1.18754053

160

161atad = getFFTI(getFFTF(data))

162atad

163+1.04627109, +1.23716760, +1.66350937, +1.87879229, +1.00439990, +1.42632198, +1.80210459, +1.94689620, +1.20032001, +1.77744710, +1.98941648, +1.15201128, +1.76435721, +1.72134507, +1.27957356, +1.39044368, +1.23682487, +1.72544014, +1.80299699, +1.12958324, +1.93224549, +1.53978026, +1.34212434, +1.64113951, +1.45682490, +1.35646403, +1.15128803, +1.87838757, +1.12382460, +1.73371971, +1.22006011, +1.33765030, +1.08756638, +1.80342674, +1.05687535, +1.65513909, +1.41248763, +1.54770160, +1.28854823, +1.91085625, +1.04273629, +1.32828462, +1.91922307, +1.24934888, +1.57529724, +1.20729876, +1.60531628, +1.90637338, +1.18156540, +1.57036674, +1.31842971, +1.66502881, +1.62939954, +1.06630015, +1.42190754, +1.23268950, +1.54487085, +1.16180003, +1.66953707, +1.04617608, +1.06164241, +1.31680322, +1.51512408, +1.96202636, +1.53766704, +1.82680917, +1.64487243, +1.32101107, +1.07180274, +1.08897066, +1.35595930, +1.98477709, +1.27401137, +1.65786946, +1.61868680, +1.24207437, +1.90501201, +1.87355793, +1.05366838, +1.82122767, +1.22312272, +1.50518072, +1.54922163, +1.51588356, +1.71269727, +1.96273196, +1.23426139, +1.46154308, +1.69247401, +1.89460742, +1.76092434, +1.57987320, +1.69817734, +1.18754089, +0.298023224E-6, +0.476837158E-6, -0.596046448E-7, +0.178813934E-6, +0.119209290E-6, +0.357627869E-6, +0.00000000, +0.298023224E-6, -0.596046448E-7, +0.238418579E-6, +0.00000000, +0.00000000, -0.238418579E-6, +0.178813934E-6, +0.119209290E-6, +0.357627869E-6, +0.00000000, +0.119209290E-6, +0.238418579E-6, +0.119209290E-6, +0.298023224E-6, +0.238418579E-6, +0.178813934E-6, +0.417232513E-6, +0.119209290E-6, +0.357627869E-6, +0.238418579E-6, +0.00000000, +0.596046448E-7, +0.119209290E-6, +0.298023224E-6, +0.00000000, -0.596046448E-7, +0.417232513E-6

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

165reltol

166+0.345266977E-3

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

168T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, 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+20

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

175data

176+1.3893324643228593, +1.2743746863259111, +1.1858775222591134, +1.0523776676058123, +1.7915936275781856, +1.8589692063209031, +1.0842817092435522, +1.0378193946311103, +1.7491141835223969, +1.0398924196376431, +1.5556902260423167, +1.2532206681556186, +1.6612520558106256, +1.3663176417029614, +1.2648128497378028, +1.6896254851350176, +1.3014580462928316, +1.8808911028576207, +1.3265125015562678, +1.0583779953529575

177

178atad = getFFTI(getFFTF(data))

179atad

180+1.3893324643228593, +1.2743746863259111, +1.1858775222591134, +1.0523776676058125, +1.7915936275781856, +1.8589692063209029, +1.0842817092435519, +1.0378193946311103, +1.7491141835223969, +1.0398924196376429, +1.5556902260423167, +1.2532206681556186, +1.6612520558106261, +1.3663176417029610, +1.2648128497378028, +1.6896254851350170, +1.3014580462928316, +1.8808911028576207, +1.3265125015562673, +1.0583779953529573, +0.33306690738754696E-15, +0.44408920985006262E-15, +0.22204460492503131E-15, -0.33306690738754696E-15, +0.0000000000000000, +0.11102230246251565E-15, +0.0000000000000000, -0.11102230246251565E-15, -0.33306690738754696E-15, +0.77715611723760958E-15, +0.0000000000000000, +0.11102230246251565E-15

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

182reltol

183+0.14901161193847656E-7

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

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

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

187

188lenData = getUnifRand(5, 100)

189lenData

190+63

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

192data

193+1.06972242400290623693354529825672211, +1.93632779299554045723123298265375702, +1.34889747820450132314505003416105432, +1.46627003719007568935276022354215588, +1.53176800342195787872930644102615584, +1.10412562605951648197990967873697723, +1.47067561822309408352137573522696302, +1.54206078666850601235139998143604582, +1.27464711702106865695611588894793152, +1.93699131018331342878853349965073888, +1.53251879729624188304619002582037367, +1.35584017873329308837738019109397665, +1.22490538153655052808697540381073612, +1.03278478213896046254022817607631474, +1.71207526513420563459713490730853411, +1.04716720509490732598546204506879657, +1.95051598382583986717125873980898271, +1.52066904054580418842040607805468327, +1.45913212613480329727267578729590439, +1.23087184796338622843188866094044104, +1.06633846722227052081697904203094435, +1.59567562057982592374387482043465286, +1.23366005988876700957038137150892749, +1.69345508559957029987006576996265850, +1.07573730415174124963595846836334946, +1.88016224840534313352320635247471909, +1.00381647976534199796564462185600806, +1.14599662954811649214112285951826998, +1.34678856084371049280057973318895676, +1.57424873164185032981533633425984913, +1.23871467802383445155645192430493977, +1.29739537782270715010637996081156463, +1.02798029897393074556057860183421742, +1.87881935886473167317533991851245369, +1.69169724506921031844245095794092828, +1.57289516550277371561516016446384362, +1.68188455459671465776456880260626936, +1.10483518439850753556388453496104669, +1.56030669892679159441888832496522033, +1.47838331896750833595535324734856749, +1.14082119482289243836969036514609675, +1.31226148057744625631299001470932866, +1.61145168131620628891015247450833926, +1.84711072699922117836129326065828975, +1.18896632654552909902383820747499455, +1.03405146334354409145102193218729677, +1.52690514775387860018639869458408788, +1.85930355707940559059754890060543316, +1.11545700490494311043284295971628489, +1.46268421819454880511223208661055980, +1.11084352456122274607567362724399760, +1.64069450778779794927420051335805750, +1.94651305303987234028656060224149065, +1.67357075388444115835270136888563520, +1.23237847604926737002965076236523364, +1.03580907156734086928256003321111023, +1.54677078632418935225188077502274663, +1.79202769243543515880439160639397447, +1.57687858043017030442802888427140468, +1.45715611183391821319381864409001600, +1.69664464392487061836120817317577397, +1.76865371651855654510430747205777245, +1.74526866417248515571670596597436411

194

195atad = getFFTI(getFFTF(data))

196atad

197+1.06972242400290623693354529825672231, +1.93632779299554045723123298265375702, +1.34889747820450132314505003416105412, +1.46627003719007568935276022354215607, +1.53176800342195787872930644102615584, +1.10412562605951648197990967873697723, +1.47067561822309408352137573522696321, +1.54206078666850601235139998143604621, +1.27464711702106865695611588894793171, +1.93699131018331342878853349965073927, +1.53251879729624188304619002582037386, +1.35584017873329308837738019109397723, +1.22490538153655052808697540381073573, +1.03278478213896046254022817607631474, +1.71207526513420563459713490730853450, +1.04716720509490732598546204506879696, +1.95051598382583986717125873980898271, +1.52066904054580418842040607805468308, +1.45913212613480329727267578729590420, +1.23087184796338622843188866094044123, +1.06633846722227052081697904203094435, +1.59567562057982592374387482043465305, +1.23366005988876700957038137150892730, +1.69345508559957029987006576996265850, +1.07573730415174124963595846836334965, +1.88016224840534313352320635247471909, +1.00381647976534199796564462185600806, +1.14599662954811649214112285951827037, +1.34678856084371049280057973318895657, +1.57424873164185032981533633425984932, +1.23871467802383445155645192430493977, +1.29739537782270715010637996081156482, +1.02798029897393074556057860183421742, +1.87881935886473167317533991851245350, +1.69169724506921031844245095794092809, +1.57289516550277371561516016446384382, +1.68188455459671465776456880260626936, +1.10483518439850753556388453496104669, +1.56030669892679159441888832496522033, +1.47838331896750833595535324734856768, +1.14082119482289243836969036514609675, +1.31226148057744625631299001470932885, +1.61145168131620628891015247450833965, +1.84711072699922117836129326065828995, +1.18896632654552909902383820747499417, +1.03405146334354409145102193218729677, +1.52690514775387860018639869458408788, +1.85930355707940559059754890060543336, +1.11545700490494311043284295971628508, +1.46268421819454880511223208661055980, +1.11084352456122274607567362724399760, +1.64069450778779794927420051335805769, +1.94651305303987234028656060224149065, +1.67357075388444115835270136888563558, +1.23237847604926737002965076236523344, +1.03580907156734086928256003321111043, +1.54677078632418935225188077502274683, +1.79202769243543515880439160639397467, +1.57687858043017030442802888427140468, +1.45715611183391821319381864409001639, +1.69664464392487061836120817317577378, +1.76865371651855654510430747205777245, +1.74526866417248515571670596597436411, +0.962964972193617926527988971292463659E-34

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

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

204

205lenData = getUnifRand(5, 100)

206lenData

207+94

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

209data

210(+1.00472951, +0.257473826), (+1.86805367, +0.109934211), (+1.19786096, +0.930017889), (+1.80722427, +0.363323331), (+1.26726818, +0.602169514), (+1.26504517, +0.672523618), (+1.15634418, +0.763292909), (+1.81784296, +0.109660625), (+1.41292763, +0.630842447), (+1.97561336, +0.667227209), (+1.26177979, +0.256344557), (+1.21070576, +0.646264136), (+1.02777433, +0.519611895), (+1.27125871, +0.852590203E-1), (+1.46499574, +0.514805198), (+1.09101462, +0.729842186), (+1.92613173, +0.302976429), (+1.66559458, +0.459932864), (+1.71705103, +0.436029792), (+1.85200930, +0.122238994), (+1.29882669, +0.571139634), (+1.63991809, +0.904473603), (+1.16568327, +0.920008659), (+1.17433035, +0.333266377), (+1.71211505, +0.653069854), (+1.90063000, +0.167991996), (+1.35086596, +0.117824435), (+1.89656019, +0.221393406), (+1.24911070, +0.943973660), (+1.51707172, +0.815358043), (+1.70698822, +0.539733469), (+1.27190101, +0.889832556), (+1.17241526, +0.773193240), (+1.27427816, +0.393080473), (+1.79319096, +0.525608838), (+1.84462357, +0.847084880), (+1.25336266, +0.301927209), (+1.33079171, +0.565029979E-1), (+1.31160522, +0.531917632), (+1.63085818, +0.228594959), (+1.64302802, +0.582161307), (+1.73454785, +0.697402418), (+1.17922449, +0.716376722), (+1.83988023, +0.834784210), (+1.43608356, +0.752584100), (+1.92311001, +0.177634835), (+1.53605437, +0.404357314E-1), (+1.56553555, +0.437086880), (+1.37768757, +0.350850105), (+1.99362421, +0.365545809), (+1.65634298, +0.111740410), (+1.51468730, +0.619105637), (+1.98221946, +0.266296685), (+1.56281066, +0.987014651), (+1.38031387, +0.298638046), (+1.39845586, +0.705956995), (+1.50069916, +0.203221977), (+1.48963690, +0.795418262), (+1.20823574, +0.124538183), (+1.52159381, +0.980682075), (+1.67251337, +0.981312394), (+1.23148823, +0.620031893), (+1.85334277, +0.964828730), (+1.50715160, +0.393328369), (+1.29973066, +0.166556954), (+1.01082397, +0.778027773E-1), (+1.44677281, +0.129067719), (+1.23747420, +0.882884979), (+1.77475953, +0.607860744), (+1.27854657, +0.135178447), (+1.68681335, +0.570170164), (+1.38527298, +0.803066492), (+1.66217899, +0.370047688), (+1.02617097, +0.756265998), (+1.34608197, +0.401077390), (+1.33189321, +0.124323368E-2), (+1.48607707, +0.751505494), (+1.76802135, +0.948333979), (+1.00771928, +0.165151477), (+1.88914573, +0.428426385), (+1.77861142, +0.418047965), (+1.63705397, +0.266395092), (+1.69666505, +0.891538441), (+1.23878157, +0.252418578), (+1.65522861, +0.353537738), (+1.63407350, +0.489637077), (+1.55798912, +0.508608222E-1), (+1.63347507, +0.547100842), (+1.70381331, +0.649823606), (+1.88239956, +0.665990651), (+1.14403427, +0.859594226), (+1.95737123, +0.260997176), (+1.11818552, +0.505274236), (+1.18537569, +0.922632217)

211

212atad = getFFTI(getFFTF(data))

213atad

214(+1.00472939, +0.257473856), (+1.86805367, +0.109934330), (+1.19786072, +0.930017829), (+1.80722392, +0.363323301), (+1.26726794, +0.602169394), (+1.26504517, +0.672523618), (+1.15634394, +0.763292849), (+1.81784272, +0.109660476), (+1.41292775, +0.630842566), (+1.97561336, +0.667227149), (+1.26177967, +0.256344676), (+1.21070588, +0.646264017), (+1.02777421, +0.519612074), (+1.27125907, +0.852590799E-1), (+1.46499550, +0.514805198), (+1.09101474, +0.729842305), (+1.92613161, +0.302976489), (+1.66559458, +0.459932923), (+1.71705043, +0.436029822), (+1.85200918, +0.122238994), (+1.29882634, +0.571139574), (+1.63991809, +0.904473543), (+1.16568315, +0.920008540), (+1.17433035, +0.333266467), (+1.71211493, +0.653069913), (+1.90063024, +0.167992309), (+1.35086560, +0.117824703), (+1.89656019, +0.221393734), (+1.24911046, +0.943973660), (+1.51707172, +0.815358281), (+1.70698810, +0.539733648), (+1.27190101, +0.889832616), (+1.17241526, +0.773193121), (+1.27427816, +0.393080354), (+1.79319060, +0.525608599), (+1.84462368, +0.847084582), (+1.25336230, +0.301927090), (+1.33079159, +0.565027744E-1), (+1.31160510, +0.531917572), (+1.63085806, +0.228594899), (+1.64302778, +0.582161188), (+1.73454785, +0.697402358), (+1.17922425, +0.716376662), (+1.83988023, +0.834784150), (+1.43608332, +0.752583981), (+1.92311025, +0.177634746), (+1.53605413, +0.404358804E-1), (+1.56553555, +0.437086850), (+1.37768745, +0.350850016), (+1.99362421, +0.365545750), (+1.65634251, +0.111740410), (+1.51468730, +0.619105458), (+1.98221922, +0.266296446), (+1.56281090, +0.987014532), (+1.38031363, +0.298637778), (+1.39845586, +0.705956817), (+1.50069916, +0.203221992), (+1.48963702, +0.795418262), (+1.20823550, +0.124538153), (+1.52159369, +0.980681658), (+1.67251325, +0.981312275), (+1.23148823, +0.620031953), (+1.85334229, +0.964828551), (+1.50715160, +0.393328190), (+1.29973042, +0.166557044), (+1.01082397, +0.778027475E-1), (+1.44677258, +0.129067779), (+1.23747432, +0.882884860), (+1.77475953, +0.607860684), (+1.27854657, +0.135178417), (+1.68681335, +0.570170105), (+1.38527298, +0.803066492), (+1.66217887, +0.370047688), (+1.02617073, +0.756265998), (+1.34608185, +0.401077330), (+1.33189332, +0.124329329E-2), (+1.48607695, +0.751505494), (+1.76802135, +0.948334098), (+1.00771892, +0.165151641), (+1.88914573, +0.428426474), (+1.77861130, +0.418048024), (+1.63705373, +0.266395092), (+1.69666445, +0.891538382), (+1.23878157, +0.252418518), (+1.65522850, +0.353537649), (+1.63407350, +0.489637136), (+1.55798900, +0.508608222E-1), (+1.63347518, +0.547100782), (+1.70381296, +0.649823725), (+1.88239932, +0.665990710), (+1.14403391, +0.859594107), (+1.95737123, +0.260997176), (+1.11818552, +0.505274177), (+1.18537569, +0.922632337), (+0.596046448E-7, +0.298023224E-7), (+0.238418579E-6, -0.596046448E-7), (-0.178813934E-6, +0.894069672E-7), (+0.596046448E-7, +0.163912773E-6), (+0.00000000, +0.238418579E-6), (+0.238418579E-6, +0.178813934E-6), (+0.00000000, +0.298023224E-6), (+0.119209290E-6, +0.342726707E-6), (+0.00000000, +0.268220901E-6), (+0.119209290E-6, +0.298023224E-6), (-0.596046448E-7, +0.119209290E-6), (+0.00000000, +0.894069672E-7), (-0.178813934E-6, +0.596046448E-7), (+0.178813934E-6, +0.00000000), (+0.00000000, +0.119209290E-6), (+0.238418579E-6, +0.298023224E-7), (+0.00000000, +0.894069672E-7), (+0.178813934E-6, +0.894069672E-7), (+0.178813934E-6, +0.894069672E-7), (+0.238418579E-6, +0.119209290E-6), (+0.00000000, +0.596046448E-7), (+0.298023224E-6, +0.149011612E-6), (+0.00000000, +0.178813934E-6), (+0.357627869E-6, +0.208616257E-6), (+0.00000000, +0.268220901E-6), (+0.178813934E-6, +0.149011612E-6), (+0.357627869E-6, -0.149011612E-7), (+0.476837158E-6, -0.268220901E-6), (-0.596046448E-7, +0.298023224E-7), (+0.357627869E-6, -0.298023224E-7), (+0.596046448E-7, +0.00000000), (+0.417232513E-6, -0.298023224E-7), (+0.00000000, +0.596046448E-7), (+0.596046448E-7, +0.178813934E-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, T, T, T, T, T, T, T, T, 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+62

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

226data

227(+1.2760011441261265, +0.32636385387245359), (+1.2380502346287976, +0.73092013158967073E-1), (+1.6073888452371743, +0.30607307983552678), (+1.1682587556400956, +0.30873867962800505), (+1.1804855088212585, +0.24143928477283938), (+1.7615071376805072, +0.23933569686629041), (+1.4178273776556707, +0.44772959806307899), (+1.8701745638803382, +0.83568890989544697), (+1.9095218497118149, +0.23414023439754372), (+1.1371526526871956, +0.44024133040012470), (+1.3761013081327440, +0.27351293701757784), (+1.9103103192224100, +0.88722099871671301), (+1.6207769562358063, +0.14322829457956721), (+1.6664554234007465, +0.10831325468429087), (+1.6956846137650854, +0.79091169843316755), (+1.7255278144264976, +0.88609709596038866), (+1.1599572811784560, +0.87163948712662653), (+1.1519414037621138, +0.87442997936915834), (+1.5763020583010261, +0.41889547495662038), (+1.0559938405426270, +0.99932706322591469), (+1.8744976715497492, +0.82171018005105734), (+1.4504929237121869, +0.83843125514061412), (+1.3339147371776106, +0.90191618342840163), (+1.6468132184100734, +0.16103808835162792), (+1.3308132750200894, +0.43843340353480265), (+1.1511043828969427, +0.28019106610601852), (+1.0861995059995175, +0.12617771854452153), (+1.8104469361597220, +0.11894620839608072), (+1.6247008028211423, +0.63530207268090777E-1), (+1.1551007220674832, +0.91756171784561846), (+1.6474947763207144, +0.67456207477017538), (+1.0655830288069641, +0.80368405892709194), (+1.2744965901909435, +0.40585998456940997E-1), (+1.5615055641699922, +0.57605536196371709), (+1.8834049207295087, +0.82210923990163709), (+1.4331560799839673, +0.65469850814701658), (+1.0010229844354410, +0.84618182323654101), (+1.6446126850553460, +0.20456475604236457), (+1.9074494355662583, +0.25613351164329057), (+1.7906915957220986, +0.85837857627764036), (+1.9303169388211181, +0.86834126500570208E-1), (+1.3753973137054065, +0.19432615632598749), (+1.6953106361120103, +0.31278012712291947), (+1.4067773151079832, +0.77081496105055769E-1), (+1.7690455896075656, +0.61401449634027738), (+1.9669370337084997, +0.20717071554762889), (+1.7155893450225448, +0.42449489315297650), (+1.9531609118369082, +0.24484022260242944), (+1.2970590308132319, +0.44605102621111814), (+1.6809674957405611, +0.55515773706228944), (+1.4183404197966705, +0.62024748495467630), (+1.5173361623866766, +0.45322107107555465), (+1.8026073949357315, +0.31207945749881683), (+1.7975649324664866, +0.81504787149128533), (+1.7231470428046669, +0.10193740382702354), (+1.8802913497049629, +0.31036490655745896), (+1.8702112348154096, +0.91859018427400074E-1), (+1.3207935474210206, +0.74148232965125038), (+1.3171746275518723, +0.19000164227889849), (+1.4759844315642310, +0.70909913646375133), (+1.0728709455972887, +0.74109936154831313), (+1.7274794719493027, +0.51972075770638615)

228

229atad = getFFTI(getFFTF(data))

230atad

231(+1.2760011441261268, +0.32636385387245370), (+1.2380502346287974, +0.73092013158966962E-1), (+1.6073888452371743, +0.30607307983552706), (+1.1682587556400954, +0.30873867962800533), (+1.1804855088212587, +0.24143928477283944), (+1.7615071376805076, +0.23933569686629050), (+1.4178273776556709, +0.44772959806307883), (+1.8701745638803378, +0.83568890989544686), (+1.9095218497118152, +0.23414023439754392), (+1.1371526526871956, +0.44024133040012464), (+1.3761013081327442, +0.27351293701757806), (+1.9103103192224102, +0.88722099871671301), (+1.6207769562358065, +0.14322829457956734), (+1.6664554234007465, +0.10831325468429104), (+1.6956846137650854, +0.79091169843316789), (+1.7255278144264972, +0.88609709596038910), (+1.1599572811784562, +0.87163948712662664), (+1.1519414037621132, +0.87442997936915834), (+1.5763020583010261, +0.41889547495662044), (+1.0559938405426272, +0.99932706322591469), (+1.8744976715497492, +0.82171018005105745), (+1.4504929237121871, +0.83843125514061412), (+1.3339147371776108, +0.90191618342840152), (+1.6468132184100732, +0.16103808835162803), (+1.3308132750200896, +0.43843340353480287), (+1.1511043828969425, +0.28019106610601840), (+1.0861995059995180, +0.12617771854452187), (+1.8104469361597222, +0.11894620839608067), (+1.6247008028211423, +0.63530207268090944E-1), (+1.1551007220674832, +0.91756171784561835), (+1.6474947763207144, +0.67456207477017527), (+1.0655830288069645, +0.80368405892709160), (+1.2744965901909440, +0.40585998456941025E-1), (+1.5615055641699922, +0.57605536196371721), (+1.8834049207295092, +0.82210923990163698), (+1.4331560799839675, +0.65469850814701669), (+1.0010229844354412, +0.84618182323654101), (+1.6446126850553464, +0.20456475604236449), (+1.9074494355662586, +0.25613351164329040), (+1.7906915957220984, +0.85837857627764025), (+1.9303169388211183, +0.86834126500570458E-1), (+1.3753973137054063, +0.19432615632598754), (+1.6953106361120105, +0.31278012712291947), (+1.4067773151079837, +0.77081496105055880E-1), (+1.7690455896075654, +0.61401449634027749), (+1.9669370337084997, +0.20717071554762906), (+1.7155893450225448, +0.42449489315297639), (+1.9531609118369080, +0.24484022260242960), (+1.2970590308132321, +0.44605102621111814), (+1.6809674957405607, +0.55515773706228932), (+1.4183404197966707, +0.62024748495467630), (+1.5173361623866766, +0.45322107107555454), (+1.8026073949357315, +0.31207945749881694), (+1.7975649324664869, +0.81504787149128521), (+1.7231470428046671, +0.10193740382702349), (+1.8802913497049627, +0.31036490655745896), (+1.8702112348154099, +0.91859018427400102E-1), (+1.3207935474210204, +0.74148232965125038), (+1.3171746275518728, +0.19000164227889826), (+1.4759844315642312, +0.70909913646375111), (+1.0728709455972889, +0.74109936154831302), (+1.7274794719493025, +0.51972075770638582), (+0.77715611723760958E-15, +0.61062266354383610E-15), (+0.44408920985006262E-15, +0.0000000000000000)

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

233reltol

234+0.14901161193847656E-7

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

236T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, 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+61

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

243data

244(+1.84873987135795342437274702159582293, +0.503153049187723480876669953923081055), (+1.51447478094444258119287332583281111, +0.186498209631227502535459102387656911), (+1.39535793267678411889812429592656977, +0.705267497428877159927976069738259962), (+1.31255260223492884699588144712696149, +0.615593621347920905444790193900384713), (+1.99562372723739396438982963278940211, +0.935000153458209913749756018808103478), (+1.76289134741152406975366345761829381, +0.652045968173500449568677027865263152), (+1.85756983683130038329789475014406747, +0.432405271345984834862977723151026529), (+1.56959698618987095174517498888087618, +0.560652823587969968895470180776416671), (+1.23633503272815815418808115054942014, +0.349920409229717464295710532911930732), (+1.93345209751492471126167780860729811, +0.573043777658138173633558216885536027), (+1.64680635265846445032508791448591558, +0.728476420490311782173310969349482037E-1), (+1.21928452186803118943700932280411850, +0.732648771262397136324674657380969352), (+1.22096250718767433951502657490130495, +0.847000861849003995027112265862634732), (+1.49156254944024822689574299119302518, +0.395748665365579755033421155599684725E-1), (+1.37162276712910151265698669969790678, +0.139658588700843846953060555693071711), (+1.53190324032976425963884074067482838, +0.741901893103139929499984419177599016), (+1.29143623934613502718163517950841662, +0.351732161372730183387231426951718254), (+1.20444763483233854724176190613248799, +0.828497538612232183899477444022528433), (+1.55223038893659100710406202001822734, +0.112834931512390741634086451338110776), (+1.54225999379153340354064600191351674, +0.506669452631128486386003484217122836), (+1.21994863898779009106406942207113421, +0.737493263800332057337136974397225224), (+1.59834703507421500157855673181194394, +0.267811205783128038107991363113760974), (+1.01651361709738626569839542221658194, +0.301409668551342032685556835399555830), (+1.46701609699059697676282834060746019, +0.727477808884166771351821080890728930), (+1.14156350249251623223186855816235359, +0.255337261518008118546822516074624950), (+1.04082758974523301005734949817163776, +0.157918995731619478503752334085262158), (+1.97938449915704369361696521752069551, +0.248695359340165316947016109368527125), (+1.36224076094962254728925461059130627, +0.913152476072684574377994502739838034), (+1.79195196651843487730962385852672732, +0.822845111896963825720142759378191008), (+1.12609463617860210907251582177102732, +0.579719721146431599802764770460374826), (+1.44882880118244582868047587646130670, +0.146363016685731940961179588969864197), (+1.75521905349501817001238733695533625, +0.841871373992627727271467042877628698E-1), (+1.38023994008857593201363375030107442, +0.597863873505470870587393565665800618), (+1.69855244641304915246540257429401680, +0.106470937051432287534646300450679357), (+1.46592968904498105491854270140999031, +0.590591342716591895766218001742534268), (+1.12667718569025383372079114008588542, +0.893174762590811204657782857574614309), (+1.01455166365340362477576390111429913, +0.352973453104309536354677387774487145), (+1.21566906271470376317814971250387307, +0.873054071153041351328677892312639728), (+1.55024849136981815811014064583374488, +0.881023316418192249438550728788183812), (+1.95308700183244899120187224026646354, +0.920571866377429045079638875549984366), (+1.48468674221717245598428013974272080, +0.873200591339964623648489336443442206), (+1.06110927549894902746109833278358252, +0.714466184400188519683754493180271772), (+1.56078747954082555366854308067964780, +0.224329024573201427065845762303654700), (+1.22284645700860472235996720095133309, +0.180150851892457049839108136391613429), (+1.41346201599805361068323413921580298, +0.621193836371240087651681593778659047), (+1.03336389150481490267405659654737688, +0.131851921771398205450304805952389713), (+1.69261677401243285392643917909131490, +0.812226393372000236954656795661522176), (+1.96356249958985923064227660060086913, +0.483550363583958658312423492834293125), (+1.15160354459103525983796682084092681, +0.601462633734641126992760588882162269), (+1.75527975228273274856075612862415315, +0.178032506365398640704262824193531022E-1), (+1.61008453458566307911948560684254471, +0.320602732135224651613000494532452767), (+1.33757852044424976582840596659471325, +0.905553090074544571868283575801999633), (+1.78629678555180962052176136694128597, +0.344753821421909913459903224427384132), (+1.64396068621145082789421736647850051, +0.156532874085804832444053838473136331), (+1.58116738315752584629602066362238609, +0.879974422279827950130301546100454710), (+1.06027294097316091082159743020015404, +0.642643575798723475448856800166572420), (+1.52687329644335813096982909300687080, +0.743378138554291080959924802261416871), (+1.16500443842275574384974326897841382, +0.734088466125032428972288685822136380), (+1.35892379034429850296102746163152542, +0.486543809177301313770967608107917422), (+1.46872671229381162969548417140196623, +0.169510610763329729978785127173822010), (+1.23436792381450831919806671180963424, +0.332172984274562174872472130340763756)

245

246atad = getFFTI(getFFTF(data))

247atad

248(+1.84873987135795342437274702159582293, +0.503153049187723480876669953923081055), (+1.51447478094444258119287332583281130, +0.186498209631227502535459102387657008), (+1.39535793267678411889812429592657015, +0.705267497428877159927976069738260058), (+1.31255260223492884699588144712696130, +0.615593621347920905444790193900384809), (+1.99562372723739396438982963278940230, +0.935000153458209913749756018808103478), (+1.76289134741152406975366345761829420, +0.652045968173500449568677027865263152), (+1.85756983683130038329789475014406786, +0.432405271345984834862977723151026481), (+1.56959698618987095174517498888087638, +0.560652823587969968895470180776416575), (+1.23633503272815815418808115054941975, +0.349920409229717464295710532911930636), (+1.93345209751492471126167780860729849, +0.573043777658138173633558216885536123), (+1.64680635265846445032508791448591577, +0.728476420490311782173310969349482879E-1), (+1.21928452186803118943700932280411850, +0.732648771262397136324674657380969352), (+1.22096250718767433951502657490130456, +0.847000861849003995027112265862634828), (+1.49156254944024822689574299119302538, +0.395748665365579755033421155599686951E-1), (+1.37162276712910151265698669969790697, +0.139658588700843846953060555693071808), (+1.53190324032976425963884074067482800, +0.741901893103139929499984419177599209), (+1.29143623934613502718163517950841643, +0.351732161372730183387231426951718302), (+1.20444763483233854724176190613248818, +0.828497538612232183899477444022528530), (+1.55223038893659100710406202001822792, +0.112834931512390741634086451338110812), (+1.54225999379153340354064600191351674, +0.506669452631128486386003484217122836), (+1.21994863898779009106406942207113421, +0.737493263800332057337136974397225031), (+1.59834703507421500157855673181194452, +0.267811205783128038107991363113761022), (+1.01651361709738626569839542221658232, +0.301409668551342032685556835399555926), (+1.46701609699059697676282834060746019, +0.727477808884166771351821080890729026), (+1.14156350249251623223186855816235359, +0.255337261518008118546822516074624950), (+1.04082758974523301005734949817163795, +0.157918995731619478503752334085262206), (+1.97938449915704369361696521752069551, +0.248695359340165316947016109368527197), (+1.36224076094962254728925461059130646, +0.913152476072684574377994502739837937), (+1.79195196651843487730962385852672694, +0.822845111896963825720142759378191008), (+1.12609463617860210907251582177102751, +0.579719721146431599802764770460375019), (+1.44882880118244582868047587646130708, +0.146363016685731940961179588969864004), (+1.75521905349501817001238733695533644, +0.841871373992627727271467042877627012E-1), (+1.38023994008857593201363375030107461, +0.597863873505470870587393565665800618), (+1.69855244641304915246540257429401699, +0.106470937051432287534646300450679550), (+1.46592968904498105491854270140999069, +0.590591342716591895766218001742534268), (+1.12667718569025383372079114008588523, +0.893174762590811204657782857574614309), (+1.01455166365340362477576390111429874, +0.352973453104309536354677387774486953), (+1.21566906271470376317814971250387307, +0.873054071153041351328677892312639920), (+1.55024849136981815811014064583374526, +0.881023316418192249438550728788184101), (+1.95308700183244899120187224026646373, +0.920571866377429045079638875549984366), (+1.48468674221717245598428013974272041, +0.873200591339964623648489336443442206), (+1.06110927549894902746109833278358252, +0.714466184400188519683754493180271676), (+1.56078747954082555366854308067964799, +0.224329024573201427065845762303654700), (+1.22284645700860472235996720095133329, +0.180150851892457049839108136391613429), (+1.41346201599805361068323413921580259, +0.621193836371240087651681593778658951), (+1.03336389150481490267405659654737688, +0.131851921771398205450304805952389641), (+1.69261677401243285392643917909131509, +0.812226393372000236954656795661522272), (+1.96356249958985923064227660060086875, +0.483550363583958658312423492834293173), (+1.15160354459103525983796682084092681, +0.601462633734641126992760588882162269), (+1.75527975228273274856075612862415353, +0.178032506365398640704262824193531504E-1), (+1.61008453458566307911948560684254548, +0.320602732135224651613000494532452767), (+1.33757852044424976582840596659471325, +0.905553090074544571868283575801999440), (+1.78629678555180962052176136694128617, +0.344753821421909913459903224427383892), (+1.64396068621145082789421736647850071, +0.156532874085804832444053838473136572), (+1.58116738315752584629602066362238647, +0.879974422279827950130301546100454903), (+1.06027294097316091082159743020015404, +0.642643575798723475448856800166572902), (+1.52687329644335813096982909300687061, +0.743378138554291080959924802261416775), (+1.16500443842275574384974326897841401, +0.734088466125032428972288685822136380), (+1.35892379034429850296102746163152581, +0.486543809177301313770967608107917422), (+1.46872671229381162969548417140196604, +0.169510610763329729978785127173821866), (+1.23436792381450831919806671180963424, +0.332172984274562174872472130340763708), (+0.00000000000000000000000000000000000, -0.337037740267766274284796139952362281E-33), (+0.00000000000000000000000000000000000, +0.361111864572606722447995864234673872E-34), (-0.385185988877447170611195588516985464E-33, -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, 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+82

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

260data

261+1.68182170, +1.05450058, +1.32272983, +1.56983018, +1.45717156, +1.64860606, +1.73930573, +1.48438501, +1.83034992, +1.79785335, +1.94368017, +1.79981232, +1.31684017, +1.63994908, +1.00646138, +1.05550504, +1.67415309, +1.80609941, +1.23986924, +1.75913906, +1.00581932, +1.16750944, +1.08313751, +1.90474844, +1.11310482, +1.58232522, +1.19990802, +1.81037700, +1.86773741, +1.86767817, +1.14382195, +1.69947696, +1.15332472, +1.79613256, +1.24678814, +1.10631669, +1.68252277, +1.47481465, +1.58186829, +1.99980402, +1.64679170, +1.36538124, +1.42401958, +1.81699753, +1.28046596, +1.05396748, +1.00744307, +1.15684795, +1.38092375, +1.10988975, +1.43774319, +1.07286322, +1.74897242, +1.21059263, +1.35869861, +1.19413531, +1.47379303, +1.07057691, +1.77897942, +1.08278513, +1.81935740, +1.03133702, +1.11678910, +1.31434059, +1.94407678, +1.67291296, +1.29842663, +1.96520519, +1.30933285, +1.06503892, +1.70008457, +1.21993160, +1.26228833, +1.03731346, +1.21075988, +1.39818525, +1.08854067, +1.49922729, +1.46695435, +1.41249096, +1.73608899, +1.02293551

262

263atad = getFFTI(getFFTF(data))

264atad

265+1.68182158, +1.05450070, +1.32272935, +1.56983018, +1.45717132, +1.64860606, +1.73930526, +1.48438489, +1.83035016, +1.79785371, +1.94368005, +1.79981244, +1.31684017, +1.63994932, +1.00646138, +1.05550492, +1.67415309, +1.80609953, +1.23986876, +1.75913894, +1.00581908, +1.16750979, +1.08313727, +1.90474844, +1.11310482, +1.58232546, +1.19990778, +1.81037736, +1.86773729, +1.86767840, +1.14382172, +1.69947708, +1.15332484, +1.79613268, +1.24678826, +1.10631692, +1.68252289, +1.47481453, +1.58186841, +1.99980390, +1.64679205, +1.36538136, +1.42401958, +1.81699753, +1.28046608, +1.05396748, +1.00744343, +1.15684795, +1.38092375, +1.10988975, +1.43774319, +1.07286322, +1.74897242, +1.21059263, +1.35869861, +1.19413495, +1.47379303, +1.07057667, +1.77897906, +1.08278513, +1.81935716, +1.03133678, +1.11678910, +1.31434035, +1.94407678, +1.67291296, +1.29842687, +1.96520495, +1.30933297, +1.06503868, +1.70008469, +1.21993148, +1.26228833, +1.03731346, +1.21075988, +1.39818513, +1.08854055, +1.49922729, +1.46695495, +1.41249073, +1.73608899, +1.02293527, +0.357627869E-6, -0.119209290E-6, +0.178813934E-6, -0.596046448E-7, +0.536441803E-6, +0.00000000, -0.596046448E-7, -0.298023224E-6, +0.00000000, -0.178813934E-6, -0.238418579E-6, +0.00000000, +0.238418579E-6, +0.00000000, -0.238418579E-6, -0.119209290E-6, -0.178813934E-6, +0.00000000, -0.119209290E-6, +0.119209290E-6, -0.596046448E-7, +0.357627869E-6, -0.119209290E-6, +0.119209290E-6, +0.178813934E-6, +0.119209290E-6, -0.596046448E-7, +0.238418579E-6, -0.596046448E-7, +0.00000000, -0.596046448E-7, +0.00000000, +0.596046448E-7, +0.119209290E-6, -0.178813934E-6, +0.238418579E-6, -0.178813934E-6, +0.417232513E-6, +0.178813934E-6, +0.178813934E-6, +0.178813934E-6, +0.596046448E-7, -0.596046448E-7, +0.238418579E-6, -0.238418579E-6, +0.357627869E-6

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

267reltol

268+0.345266977E-3

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

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

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

272

273lenData = getUnifRand(5, 100)

274lenData

275+81

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

277data

278+1.8821498027154577, +1.6888585018277378, +1.8575419283091454, +1.4969719666312926, +1.5512394133767646, +1.9212334697459539, +1.2654882776553209, +1.3257587151688699, +1.7535083452313964, +1.7942789695569290, +1.4540630040138189, +1.9486335312514944, +1.1685613452745545, +1.7278582604517934, +1.8471571842162544, +1.1282517360752071, +1.0170867791549048, +1.3590549858447829, +1.3259338745690643, +1.2490449511803317, +1.0787275267041996, +1.5250256337931434, +1.5759402606938946, +1.3344067650894715, +1.2871860618577506, +1.0663340177551801, +1.4943200611447045, +1.5896518818803218, +1.1454158866087210, +1.1777498622988378, +1.7625934172483073, +1.7610242858718907, +1.2052853773463443, +1.4112270501105146, +1.8936673296943214, +1.7613581342578053, +1.9286301859657000, +1.1318908666244709, +1.5266466670717058, +1.5692076236979826, +1.3456029877884168, +1.3899576574626320, +1.2188086816732437, +1.2109710235466209, +1.4450666443744695, +1.7388951379765998, +1.4110852351475980, +1.9934240100132308, +1.0231684178162546, +1.8433775076014092, +1.9161536790212652, +1.6217535804591594, +1.1601776419413818, +1.1715125585280615, +1.8933326592168878, +1.9224470142071204, +1.4768921774879047, +1.9979109977710641, +1.0563675459495268, +1.1983371400078382, +1.7106405032536123, +1.9329658799572009, +1.3128769431809830, +1.4511295899508005, +1.0724178845588859, +1.7984565998823248, +1.1631912992213040, +1.9727453936437218, +1.2502894392745156, +1.3865461472683571, +1.7671376623579742, +1.2828583803756421, +1.9859060774604900, +1.8679838833234794, +1.7351021486407767, +1.1489013854201060, +1.5280879225012713, +1.1092236493505161, +1.8410444389673237, +1.2787454277691412, +1.0817706266100597

279

280atad = getFFTI(getFFTF(data))

281atad

282+1.8821498027154575, +1.6888585018277380, +1.8575419283091457, +1.4969719666312931, +1.5512394133767644, +1.9212334697459541, +1.2654882776553200, +1.3257587151688701, +1.7535083452313964, +1.7942789695569290, +1.4540630040138187, +1.9486335312514949, +1.1685613452745542, +1.7278582604517934, +1.8471571842162542, +1.1282517360752069, +1.0170867791549043, +1.3590549858447833, +1.3259338745690643, +1.2490449511803321, +1.0787275267041991, +1.5250256337931436, +1.5759402606938937, +1.3344067650894713, +1.2871860618577504, +1.0663340177551803, +1.4943200611447036, +1.5896518818803216, +1.1454158866087205, +1.1777498622988385, +1.7625934172483064, +1.7610242858718903, +1.2052853773463443, +1.4112270501105146, +1.8936673296943214, +1.7613581342578051, +1.9286301859656998, +1.1318908666244707, +1.5266466670717058, +1.5692076236979817, +1.3456029877884168, +1.3899576574626318, +1.2188086816732437, +1.2109710235466209, +1.4450666443744700, +1.7388951379765998, +1.4110852351475982, +1.9934240100132308, +1.0231684178162546, +1.8433775076014092, +1.9161536790212650, +1.6217535804591594, +1.1601776419413818, +1.1715125585280610, +1.8933326592168873, +1.9224470142071197, +1.4768921774879047, +1.9979109977710636, +1.0563675459495268, +1.1983371400078378, +1.7106405032536123, +1.9329658799572000, +1.3128769431809830, +1.4511295899508001, +1.0724178845588856, +1.7984565998823248, +1.1631912992213038, +1.9727453936437218, +1.2502894392745161, +1.3865461472683567, +1.7671376623579742, +1.2828583803756419, +1.9859060774604895, +1.8679838833234796, +1.7351021486407765, +1.1489013854201060, +1.5280879225012716, +1.1092236493505161, +1.8410444389673237, +1.2787454277691410, +1.0817706266100597, +0.22204460492503131E-15, +0.22204460492503131E-15, -0.44408920985006262E-15, +0.88817841970012523E-15, -0.11102230246251565E-15, +0.44408920985006262E-15, -0.11102230246251565E-15, +0.66613381477509392E-15, -0.44408920985006262E-15, +0.33306690738754696E-15, -0.33306690738754696E-15, +0.33306690738754696E-15, +0.11102230246251565E-15, +0.33306690738754696E-15, +0.22204460492503131E-15, -0.11102230246251565E-15, +0.0000000000000000, -0.11102230246251565E-15, -0.22204460492503131E-15, +0.0000000000000000, +0.55511151231257827E-15, -0.22204460492503131E-15, +0.33306690738754696E-15, -0.22204460492503131E-15, -0.44408920985006262E-15, +0.11102230246251565E-15, -0.11102230246251565E-15, -0.33306690738754696E-15, +0.55511151231257827E-15, +0.0000000000000000, +0.0000000000000000, -0.11102230246251565E-15, +0.55511151231257827E-15, +0.22204460492503131E-15, +0.33306690738754696E-15, -0.11102230246251565E-15, +0.55511151231257827E-15, -0.11102230246251565E-15, +0.66613381477509392E-15, -0.11102230246251565E-15, +0.0000000000000000, +0.11102230246251565E-15, +0.22204460492503131E-15, -0.88817841970012523E-15, +0.66613381477509392E-15, -0.22204460492503131E-15, +0.88817841970012523E-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, 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+53

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

294data

295+1.46177757645977964639392690173990318, +1.24465359825432966651364963097808626, +1.87483303744148333321926844783028069, +1.56681793974056777616833392787260860, +1.23842936939074587086499690321336138, +1.29575687459757235650965456370411799, +1.57241878445186974850050672751540609, +1.75393492436378033219498126757940810, +1.57565307535275128112612467810246871, +1.05234856392962391810239067019689519, +1.15201517598324270422336406648305286, +1.47001975470725653453437529961704810, +1.31293710253187758662657203737583643, +1.09596794604702609344711859689574738, +1.19637600726382039850042072385499123, +1.71043508837873635718736697094435228, +1.75487456833005469896716990887139314, +1.60656014058298701193679015787503089, +1.85934461711796020295896596570704585, +1.74107971375456027271122063902140262, +1.14987160038684056379912735994514511, +1.27065558805494966796943909113531083, +1.91177948414038178465675253867749504, +1.53916669424425735635773453908774234, +1.44581128963944068432427236274085667, +1.81975401199809523267979818992702774, +1.49691374615083233362109574817531139, +1.17111399180216952625900044143812560, +1.02320968167120136878453711420684828, +1.52283187501493164805706924962610980, +1.59792684776362057297923635143824172, +1.31706276213775854826299912021684476, +1.40764985136826480540846715927827633, +1.01122490695211425446049202617700713, +1.75082281769045729212051320731456720, +1.66708503070780725329292854066869785, +1.34585541135753903517866779682459592, +1.60540350637910491193953352917609093, +1.52944780803584429829574858891445704, +1.64216672530995656485605260247901942, +1.35631395949290374329926690009320992, +1.42653471924534617682516523313064142, +1.97089695395332468121602149485565695, +1.68530137400889429701316381923196264, +1.14700227469321448441869191484257130, +1.00192922322997166526894026243876609, +1.24443620915826796139646454799170894, +1.38636948163635199010241492976258098, +1.69073799073734662904624057914983454, +1.90594889875369940023864350791095768, +1.55660944729871537247006885792654088, +1.16614542909340236879106343482153012, +1.66040990811538452127005767970661956

296

297atad = getFFTI(getFFTF(data))

298atad

299+1.46177757645977964639392690173990337, +1.24465359825432966651364963097808645, +1.87483303744148333321926844783028030, +1.56681793974056777616833392787260860, +1.23842936939074587086499690321336196, +1.29575687459757235650965456370411799, +1.57241878445186974850050672751540647, +1.75393492436378033219498126757940791, +1.57565307535275128112612467810246890, +1.05234856392962391810239067019689500, +1.15201517598324270422336406648305305, +1.47001975470725653453437529961704810, +1.31293710253187758662657203737583701, +1.09596794604702609344711859689574699, +1.19637600726382039850042072385499161, +1.71043508837873635718736697094435209, +1.75487456833005469896716990887139314, +1.60656014058298701193679015787503108, +1.85934461711796020295896596570704585, +1.74107971375456027271122063902140224, +1.14987160038684056379912735994514550, +1.27065558805494966796943909113531083, +1.91177948414038178465675253867749504, +1.53916669424425735635773453908774176, +1.44581128963944068432427236274085667, +1.81975401199809523267979818992702774, +1.49691374615083233362109574817531100, +1.17111399180216952625900044143812521, +1.02320968167120136878453711420684867, +1.52283187501493164805706924962610980, +1.59792684776362057297923635143824172, +1.31706276213775854826299912021684418, +1.40764985136826480540846715927827652, +1.01122490695211425446049202617700694, +1.75082281769045729212051320731456720, +1.66708503070780725329292854066869747, +1.34585541135753903517866779682459612, +1.60540350637910491193953352917609093, +1.52944780803584429829574858891445704, +1.64216672530995656485605260247901961, +1.35631395949290374329926690009321031, +1.42653471924534617682516523313064142, +1.97089695395332468121602149485565714, +1.68530137400889429701316381923196245, +1.14700227469321448441869191484257169, +1.00192922322997166526894026243876609, +1.24443620915826796139646454799170952, +1.38636948163635199010241492976258079, +1.69073799073734662904624057914983512, +1.90594889875369940023864350791095788, +1.55660944729871537247006885792654126, +1.16614542909340236879106343482153012, +1.66040990811538452127005767970662034, +0.00000000000000000000000000000000000, +0.385185988877447170611195588516985464E-33, -0.288889491658085377958396691387739098E-33, +0.00000000000000000000000000000000000, +0.192592994438723585305597794258492732E-33, -0.192592994438723585305597794258492732E-33, +0.192592994438723585305597794258492732E-33, +0.288889491658085377958396691387739098E-33, +0.00000000000000000000000000000000000, +0.192592994438723585305597794258492732E-33, -0.192592994438723585305597794258492732E-33

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

301reltol

302+0.138777878078144567552953958511352539E-16

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

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

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

306

307lenData = getUnifRand(5, 100)

308lenData

309+85

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

311data

312(+1.94086146, +0.660122633E-1), (+1.22176158, +0.671337426), (+1.61378467, +0.153834939), (+1.87572587, +0.735391080), (+1.75813484, +0.531821191), (+1.19481707, +0.646567643), (+1.53105092, +0.514353752), (+1.60828996, +0.372825742), (+1.98265052, +0.380960763), (+1.11644542, +0.519262314), (+1.12057233, +0.488566518), (+1.43421102, +0.658128977), (+1.78669906, +0.570488453), (+1.36446226, +0.991018951), (+1.94214845, +0.379252911), (+1.84484148, +0.532591045), (+1.04677820, +0.889641404), (+1.18359995, +0.798364937), (+1.36317945, +0.654760003E-1), (+1.39705813, +0.163736105), (+1.11549783, +0.769100010), (+1.14214587, +0.618069530), (+1.60679352, +0.233259022), (+1.44687307, +0.146306932), (+1.78411794, +0.633711219E-1), (+1.82940984, +0.359229386), (+1.85311973, +0.185015261), (+1.71760917, +0.775926650), (+1.52079165, +0.207643330), (+1.89748788, +0.698186398), (+1.68893945, +0.472708166), (+1.49288487, +0.462803245), (+1.97341585, +0.847120106), (+1.09662199, +0.393188059), (+1.18358779, +0.242239416), (+1.48875344, +0.395506263), (+1.22274518, +0.102129519), (+1.02089047, +0.497356653E-1), (+1.85309649, +0.140454948), (+1.13876486, +0.946884871), (+1.44868875, +0.702405989), (+1.55956244, +0.930106401), (+1.95649409, +0.652033687E-1), (+1.45325780, +0.664832175), (+1.83150744, +0.791601539E-1), (+1.54903162, +0.854009271), (+1.79165864, +0.845868707), (+1.57170260, +0.142235756), (+1.77560329, +0.339883089), (+1.14391923, +0.459241629), (+1.27598405, +0.591191649), (+1.42703986, +0.757573307), (+1.31541467, +0.283415854), (+1.91211915, +0.839607596), (+1.28943086, +0.479193330E-1), (+1.39558566, +0.238840580), (+1.16975546, +0.692834616), (+1.72964311, +0.761533976), (+1.72911894, +0.106761873), (+1.87241578, +0.158507288), (+1.27778804, +0.809883177), (+1.81498623, +0.752451658), (+1.13467991, +0.550861120), (+1.76117682, +0.448437452), (+1.02352428, +0.923029602), (+1.32111669, +0.950801790), (+1.37626600, +0.351850450), (+1.54666877, +0.958443880E-1), (+1.31119502, +0.615471005), (+1.65289438, +0.144819558), (+1.41499949, +0.998634279), (+1.87465405, +0.132952631), (+1.97768235, +0.525278151), (+1.31711972, +0.664581776), (+1.15504074, +0.174889863), (+1.07335544, +0.917252123), (+1.74068928, +0.531303823), (+1.98650753, +0.816617727), (+1.85463297, +0.847381771), (+1.13286185, +0.730823278E-1), (+1.98104715, +0.992974877), (+1.73084700, +0.187973082), (+1.64833879, +0.400197268), (+1.98242521, +0.975282013), (+1.73350859, +0.774241686)

313

314atad = getFFTI(getFFTF(data))

315atad

316(+1.94086134, +0.660123229E-1), (+1.22176170, +0.671337485), (+1.61378431, +0.153834969), (+1.87572575, +0.735391140), (+1.75813472, +0.531821012), (+1.19481707, +0.646567464), (+1.53105068, +0.514353573), (+1.60828996, +0.372825623), (+1.98265052, +0.380960971), (+1.11644554, +0.519262433), (+1.12057233, +0.488566488), (+1.43421113, +0.658129036), (+1.78669906, +0.570488513), (+1.36446238, +0.991018891), (+1.94214845, +0.379252911), (+1.84484172, +0.532591164), (+1.04677832, +0.889641404), (+1.18359995, +0.798365057), (+1.36317921, +0.654760599E-1), (+1.39705825, +0.163736135), (+1.11549747, +0.769100070), (+1.14214575, +0.618069470), (+1.60679340, +0.233258888), (+1.44687307, +0.146306917), (+1.78411782, +0.633714348E-1), (+1.82940996, +0.359229624), (+1.85311961, +0.185015291), (+1.71760917, +0.775926769), (+1.52079129, +0.207643524), (+1.89748812, +0.698186576), (+1.68893981, +0.472708225), (+1.49288511, +0.462803245), (+1.97341585, +0.847120047), (+1.09662199, +0.393188000), (+1.18358779, +0.242239356), (+1.48875356, +0.395506024), (+1.22274494, +0.102129407), (+1.02089047, +0.497356281E-1), (+1.85309625, +0.140454650), (+1.13876486, +0.946884751), (+1.44868851, +0.702406049), (+1.55956233, +0.930106342), (+1.95649385, +0.652032793E-1), (+1.45325792, +0.664832115), (+1.83150709, +0.791600645E-1), (+1.54903162, +0.854009092), (+1.79165888, +0.845868587), (+1.57170272, +0.142235696), (+1.77560318, +0.339883089), (+1.14391923, +0.459241390), (+1.27598405, +0.591191530), (+1.42704010, +0.757573247), (+1.31541467, +0.283415616), (+1.91211915, +0.839607477), (+1.28943086, +0.479193777E-1), (+1.39558578, +0.238840476), (+1.16975510, +0.692834496), (+1.72964287, +0.761534035), (+1.72911870, +0.106761970), (+1.87241566, +0.158507481), (+1.27778769, +0.809883058), (+1.81498611, +0.752451777), (+1.13468003, +0.550860882), (+1.76117671, +0.448437363), (+1.02352417, +0.923029602), (+1.32111669, +0.950801730), (+1.37626600, +0.351850480), (+1.54666901, +0.958444178E-1), (+1.31119502, +0.615470886), (+1.65289450, +0.144819558), (+1.41499949, +0.998634279), (+1.87465405, +0.132952526), (+1.97768211, +0.525278330), (+1.31711960, +0.664581895), (+1.15504050, +0.174890131), (+1.07335532, +0.917252004), (+1.74068904, +0.531303823), (+1.98650742, +0.816617966), (+1.85463309, +0.847381949), (+1.13286185, +0.730825067E-1), (+1.98104703, +0.992974758), (+1.73084688, +0.187973201), (+1.64833879, +0.400197089), (+1.98242497, +0.975281715), (+1.73350847, +0.774241567), (+0.238418579E-6, +0.00000000), (+0.536441803E-6, +0.283122063E-6), (+0.476837158E-6, +0.193715096E-6), (+0.00000000, -0.223517418E-6), (+0.00000000, -0.223517418E-6), (+0.178813934E-6, -0.670552254E-7), (+0.119209290E-6, -0.596046448E-7), (+0.596046448E-7, +0.149011612E-7), (+0.00000000, -0.298023224E-6), (+0.298023224E-6, -0.149011612E-7), (+0.178813934E-6, -0.298023224E-7), (-0.119209290E-6, +0.149011612E-6), (+0.178813934E-6, +0.00000000), (+0.178813934E-6, +0.275671482E-6), (+0.238418579E-6, +0.283122063E-6), (+0.00000000, +0.290572643E-6), (+0.596046448E-7, +0.216066837E-6), (+0.596046448E-7, +0.417232513E-6), (+0.596046448E-7, +0.298023224E-6), (-0.178813934E-6, +0.00000000), (+0.119209290E-6, +0.596046448E-7), (+0.00000000, +0.894069672E-7), (+0.119209290E-6, -0.894069672E-7), (+0.119209290E-6, +0.149011612E-6), (+0.119209290E-6, -0.596046448E-7), (+0.00000000, +0.149011612E-6), (+0.298023224E-6, +0.00000000), (+0.238418579E-6, +0.119209290E-6), (+0.298023224E-6, +0.134110451E-6), (+0.178813934E-6, +0.178813934E-6), (+0.417232513E-6, +0.894069672E-7), (+0.00000000, +0.119209290E-6), (+0.178813934E-6, +0.178813934E-6), (+0.298023224E-6, +0.223517418E-6), (+0.178813934E-6, +0.163912773E-6), (+0.238418579E-6, +0.00000000), (+0.357627869E-6, -0.119209290E-6), (+0.119209290E-6, +0.968575478E-7), (+0.476837158E-6, -0.447034836E-7), (+0.596046448E-7, +0.596046448E-7), (+0.357627869E-6, -0.894069672E-7), (+0.178813934E-6, +0.208616257E-6), (+0.238418579E-6, +0.596046448E-7)

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

318reltol

319+0.345266977E-3

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

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

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

323

324lenData = getUnifRand(5, 100)

325lenData

326+54

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

328data

329(+1.2119537100678568, +0.14141166934142380), (+1.3246627963302169, +0.22331057146310695), (+1.7796103237299246, +0.10878523641688409), (+1.8300255733094444, +0.21064412876100480), (+1.4164686959249937, +0.31902770056359331E-1), (+1.0033036843663381, +0.65663941798700420), (+1.7171291171350220, +0.61719720886741058), (+1.2859636493596485, +0.18427916700038671), (+1.8197264226881100, +0.98035689492006650), (+1.7142034889597415, +0.58148809111892219), (+1.9116196828580121, +0.39797735661273759), (+1.6978210497999835, +0.58476023993570070), (+1.2546325542214658, +0.55553810104660206E-1), (+1.5575764427226038, +0.71011535670005455), (+1.1733325056973711, +0.56565165447502130), (+1.9673714578264674, +0.82541387293671820), (+1.2460385274289880, +0.53519644440364500E-1), (+1.8652393264417655, +0.32862460459004517), (+1.7155318694568895, +0.91970141167294894), (+1.0271214761077374, +0.13577179704764386), (+1.6346431798355752, +0.83632240962015181), (+1.6223389001677540, +0.55183032854384728), (+1.3414105729990744, +0.46928099028914361), (+1.6255140274423887, +0.68792206718298765), (+1.4111886154560913, +0.36716792355897099), (+1.8015359985388022, +0.27215947842256516), (+1.7597200276666725, +0.60599380534974223), (+1.4543607009979318, +0.90001247198214096), (+1.5505351405160068, +0.46651514027168706), (+1.8048835468670139, +0.21873230701109470E-1), (+1.8755846743823712, +0.91464960255935612), (+1.9744313467150567, +0.82205077501235890), (+1.8945993951682412, +0.22537015604987620), (+1.2970764209263206, +0.93553438861609439), (+1.3567485931645167, +0.84318228095032255), (+1.2114815673750605, +0.94639679936474419), (+1.1284248488663278, +0.56032379424274725), (+1.4973744963276225, +0.75650334933957886), (+1.2599345613500290, +0.29786084065889429), (+1.4177031467176091, +0.17673010784351284), (+1.4895501328113849, +0.69249413397751780), (+1.1709431230332779, +0.98762626146498300), (+1.0965611770118273, +0.81729274672240848), (+1.2212066141747115, +0.45611260712403445), (+1.0234278066998068, +0.23903795701142083), (+1.9575444180918806, +0.61210689647444283), (+1.6163341279578596, +0.99497587918482611), (+1.6124306857256741, +0.64596609687232365), (+1.9270670366853380, +0.40865902999704640), (+1.2823089839410624, +0.81724631294999295E-2), (+1.5354285594913024, +0.26615476280893757), (+1.9553496699259314, +0.55801283796543177), (+1.6818784844767172, +0.31773037153841777), (+1.6439937952644414, +0.13085203728638295)

330

331atad = getFFTI(getFFTF(data))

332atad

333(+1.2119537100678568, +0.14141166934142385), (+1.3246627963302169, +0.22331057146310695), (+1.7796103237299241, +0.10878523641688448), (+1.8300255733094446, +0.21064412876100524), (+1.4164686959249941, +0.31902770056359220E-1), (+1.0033036843663381, +0.65663941798700409), (+1.7171291171350216, +0.61719720886741070), (+1.2859636493596482, +0.18427916700038691), (+1.8197264226881100, +0.98035689492006683), (+1.7142034889597413, +0.58148809111892241), (+1.9116196828580114, +0.39797735661273781), (+1.6978210497999833, +0.58476023993570103), (+1.2546325542214660, +0.55553810104660539E-1), (+1.5575764427226038, +0.71011535670005466), (+1.1733325056973709, +0.56565165447502175), (+1.9673714578264669, +0.82541387293671820), (+1.2460385274289880, +0.53519644440364555E-1), (+1.8652393264417653, +0.32862460459004511), (+1.7155318694568893, +0.91970141167294872), (+1.0271214761077374, +0.13577179704764403), (+1.6346431798355754, +0.83632240962015181), (+1.6223389001677542, +0.55183032854384750), (+1.3414105729990740, +0.46928099028914327), (+1.6255140274423887, +0.68792206718298732), (+1.4111886154560918, +0.36716792355897065), (+1.8015359985388022, +0.27215947842256505), (+1.7597200276666720, +0.60599380534974179), (+1.4543607009979320, +0.90001247198214041), (+1.5505351405160068, +0.46651514027168695), (+1.8048835468670146, +0.21873230701109525E-1), (+1.8755846743823712, +0.91464960255935590), (+1.9744313467150563, +0.82205077501235868), (+1.8945993951682412, +0.22537015604987615), (+1.2970764209263201, +0.93553438861609428), (+1.3567485931645167, +0.84318228095032244), (+1.2114815673750610, +0.94639679936474397), (+1.1284248488663278, +0.56032379424274736), (+1.4973744963276228, +0.75650334933957875), (+1.2599345613500286, +0.29786084065889423), (+1.4177031467176093, +0.17673010784351298), (+1.4895501328113849, +0.69249413397751758), (+1.1709431230332774, +0.98762626146498267), (+1.0965611770118273, +0.81729274672240826), (+1.2212066141747118, +0.45611260712403423), (+1.0234278066998068, +0.23903795701142072), (+1.9575444180918804, +0.61210689647444272), (+1.6163341279578596, +0.99497587918482588), (+1.6124306857256738, +0.64596609687232331), (+1.9270670366853384, +0.40865902999704645), (+1.2823089839410622, +0.81724631294998740E-2), (+1.5354285594913024, +0.26615476280893752), (+1.9553496699259321, +0.55801283796543144), (+1.6818784844767172, +0.31773037153841771), (+1.6439937952644414, +0.13085203728638287), (+0.22204460492503131E-15, +0.38857805861880479E-15), (+0.0000000000000000, -0.11102230246251565E-15), (+0.66613381477509392E-15, +0.22204460492503131E-15), (-0.11102230246251565E-15, +0.0000000000000000), (+0.22204460492503131E-15, +0.72164496600635175E-15), (+0.55511151231257827E-15, +0.33306690738754696E-15), (+0.33306690738754696E-15, +0.11102230246251565E-15), (+0.77715611723760958E-15, +0.27755575615628914E-15), (+0.44408920985006262E-15, +0.55511151231257827E-15), (+0.44408920985006262E-15, +0.72164496600635175E-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

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

340

341lenData = getUnifRand(5, 100)

342lenData

343+93

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

345data

346(+1.45947271946347894239260217120063273, +0.750702372759703751951855395427086111), (+1.77653361107919655784587656041290977, +0.137097063422459692083514173638970736E-2), (+1.71049394965057782484091384734412586, +0.875301301216476976047378229657987768), (+1.62197415915953436109984934979674045, +0.494860960483814736648311963523333269E-1), (+1.86665081542200591280270489670574983, +0.611679591394300645498798860177120831), (+1.48089930809526085221214954279157311, +0.865475056228344831320199073540086815), (+1.32787366438736405545369919618330618, +0.297981703014479111984747145317048883E-1), (+1.03525846519999070102404358004830355, +0.898046604383781848941491101315304449), (+1.63617906167769362547483356011573036, +0.289883759544211873580627581927102658), (+1.82611144064919787301211884848671408, +0.110448407557973468409871054033502007E-1), (+1.13087258784327374015900721439759108, +0.512045430142111389060245559566841609E-1), (+1.24928405185550983473360880739961227, +0.552234304053732904050884453934937976), (+1.62853942084859731714617809851256908, +0.191539068409011096281239848309692144), (+1.34765960565511343713161107466792792, +0.284472459941772389733742645293443142), (+1.93726677448652567933561539411460915, +0.132760550543133242735351868108562471), (+1.47523869809920507600532496780159418, +0.905547334985748069118510115155114022), (+1.34858907486638746673273150504632347, +0.234564613502250728682810005928877320), (+1.29243487607206360027303086661618497, +0.160458530032438149917470896732607074), (+1.52263175836907399690866825343565914, +0.776553775145694518337834260972016796E-1), (+1.36938301825375290713708336231950739, +0.463421538225635497179149556038830055), (+1.61042486095943104045992931056370012, +0.745870021906586009640773038563053063), (+1.49545049582439378829759919494440710, +0.915215802006741520204598092881228264), (+1.58457679941623351701704379766921574, +0.155616174293625329621093213908671933), (+1.85854954271483579009654156329115349, +0.245753947411880187686259998305938117), (+1.97180670669462226943822762498839781, +0.228044250496391873169506608532829383), (+1.00092578217861576222569558145932537, +0.737123692526862261885421171768985892), (+1.95765143842417213862939279938109513, +0.706964066877635955511735926901782494), (+1.06749469124083328370759748875967595, +0.437641838064070994082223710198817355E-1), (+1.67703158366918870349464140410988106, +0.141235976982929338083205488078613755), (+1.72015336083234525821980040638615047, +0.583256938563554375978917601725902643), (+1.93978246831203347118855756804337640, +0.790032976493780373847924484631388238), (+1.62657925315400933718866437270239321, +0.243621721415343410461562995232878083), (+1.83653931012538615968054534917282013, +0.256371525117757094018918092819522930), (+1.83969800837838395850071706670092147, +0.240510026667377463352420734045132815E-2), (+1.46017601995429922893231101005984619, +0.266679096758056871785450428236902234), (+1.64114105978503534372437108627038916, +0.943730394593139175352048629863876169), (+1.81260145519060046424308865830664996, +0.864923323769281780455615322030734208), (+1.39123202057924473060258003288595094, +0.679507960546856703659903585216906053), (+1.98066875788865756330381380899058902, +0.807430985910990944856570168329539206), (+1.55933740258050489106052670291422929, +0.955148095505582986952606390015041225), (+1.51226359640013160745864476329292637, +0.392010531338933903727920797865158083), (+1.22040226210176618387860403780028999, +0.792795549443111505827325265774329533), (+1.44092908678067158722269910567163248, +0.488442165723337831804963707616612699E-1), (+1.98197696569072302347251983252005642, +0.202593656431111798659916262432275748), (+1.60721341531848514366226164939459349, +0.714643482674593442100650551850861477), (+1.71069928181687553667155858722118798, +0.174877290069755296591205057257396739E-1), (+1.44651557470610665857479495730742162, +0.696056813947427977276845461757062250), (+1.28616052320725870102412032756832058, +0.715814096685994759769427192231797626), (+1.74112041724482739569525028443429438, +0.132157020027294228958634149526076748), (+1.02801925013172724994263438027410272, +0.548511578833305441453977227915891947), (+1.73882765717329292351204098959033079, +0.834031392192900283938858624731749960), (+1.05884150212971464538020577390392214, +0.707407713579825279171532403973231407), (+1.28691960707590662815516347363006419, +0.446145215630116193088745846842774494), (+1.30784719461811054406101643460822420, +0.669980652900379842521418587663018763), (+1.43595412463100024245887880457835585, +0.369354709948044623364371827768977628), (+1.36357738838535180432768382886037954, +0.115074550458740858380073875130840492), (+1.56722426687241333796161185385698327, +0.430337836125406797566085777327147123), (+1.59676915122165823123478778621419316, +0.368847845522768018286888947321011033), (+1.93078637763080926708461712122934003, 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347

348atad = getFFTI(getFFTF(data))

349atad

350(+1.45947271946347894239260217120063292, +0.750702372759703751951855395427086111), (+1.77653361107919655784587656041291016, +0.137097063422459692083514173638940794E-2), (+1.71049394965057782484091384734412586, +0.875301301216476976047378229657987671), (+1.62197415915953436109984934979674103, +0.494860960483814736648311963523333269E-1), (+1.86665081542200591280270489670575003, +0.611679591394300645498798860177120638), (+1.48089930809526085221214954279157311, +0.865475056228344831320199073540086815), (+1.32787366438736405545369919618330598, +0.297981703014479111984747145317048642E-1), (+1.03525846519999070102404358004830355, +0.898046604383781848941491101315304353), (+1.63617906167769362547483356011573055, +0.289883759544211873580627581927102706), (+1.82611144064919787301211884848671466, +0.110448407557973468409871054033498998E-1), (+1.13087258784327374015900721439759128, +0.512045430142111389060245559566838961E-1), (+1.24928405185550983473360880739961227, 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(-0.192592994438723585305597794258492732E-33, -0.385185988877447170611195588516985464E-33), (-0.481482486096808963263994485646231830E-33, +0.168518870133883137142398069976181140E-33), (+0.962964972193617926527988971292463659E-34, -0.481482486096808963263994485646231830E-34), (-0.385185988877447170611195588516985464E-33, +0.252778305200824705713597104964271711E-33), (-0.288889491658085377958396691387739098E-33, -0.337037740267766274284796139952362281E-33), (+0.00000000000000000000000000000000000, -0.962964972193617926527988971292463659E-34), (+0.192592994438723585305597794258492732E-33, +0.962964972193617926527988971292463659E-34), (-0.481482486096808963263994485646231830E-33, +0.144444745829042688979198345693869549E-33), (+0.00000000000000000000000000000000000, -0.192592994438723585305597794258492732E-33), (-0.288889491658085377958396691387739098E-33, +0.962964972193617926527988971292463659E-34), (-0.481482486096808963263994485646231830E-33, -0.312963615962925826121596415670050689E-33), (-0.577778983316170755916793382775478196E-33, -0.192592994438723585305597794258492732E-33), (-0.481482486096808963263994485646231830E-33, -0.312963615962925826121596415670050689E-33), (-0.866668474974256133875190074163217293E-33, -0.433334237487128066937595037081608647E-33), (-0.962964972193617926527988971292463659E-34, -0.240741243048404481631997242823115915E-33), (-0.770371977754894341222391177033970927E-33, -0.481482486096808963263994485646231830E-34), (-0.192592994438723585305597794258492732E-33, -0.385185988877447170611195588516985464E-33), (-0.577778983316170755916793382775478196E-33, -0.144444745829042688979198345693869549E-33), (-0.192592994438723585305597794258492732E-33, +0.481482486096808963263994485646231830E-34), (-0.192592994438723585305597794258492732E-33, -0.481482486096808963263994485646231830E-34), (-0.288889491658085377958396691387739098E-33, -0.192592994438723585305597794258492732E-33), (-0.192592994438723585305597794258492732E-33, -0.337037740267766274284796139952362281E-33), (-0.385185988877447170611195588516985464E-33, +0.192592994438723585305597794258492732E-33), (-0.385185988877447170611195588516985464E-33, -0.481482486096808963263994485646231830E-34), (-0.385185988877447170611195588516985464E-33, +0.240741243048404481631997242823115915E-34), (-0.385185988877447170611195588516985464E-33, +0.240741243048404481631997242823115915E-34), (-0.192592994438723585305597794258492732E-33, -0.144444745829042688979198345693869549E-33), (+0.00000000000000000000000000000000000, -0.312963615962925826121596415670050689E-33), (-0.481482486096808963263994485646231830E-33, -0.433334237487128066937595037081608647E-33), (-0.288889491658085377958396691387739098E-33, -0.529630734706489859590393934210855013E-33), (+0.962964972193617926527988971292463659E-34, -0.204630056591143809387197656399648528E-33), (-0.674075480535532548569592279904724561E-33, -0.481482486096808963263994485646231830E-33), (-0.192592994438723585305597794258492732E-33, -0.276852429505665153876796829246583302E-33), (-0.481482486096808963263994485646231830E-33, -0.385185988877447170611195588516985464E-33)

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

352reltol

353+0.138777878078144567552953958511352539E-16

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

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

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

357

358lenData = getUnifRand(5, 100)

359lenData

360+93

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

362data

363+1.13850904, +1.95491791, +1.85419130, +1.82718682, +1.58583021, +1.18171787, +1.00596857, +1.26864600, +1.01355410, +1.43078935, +1.62421298, +1.21372676, +1.99465525, +1.55088353, +1.96069801, +1.96416950, +1.07181740, +1.64247262, +1.39377391, +1.91579247, +1.47248125, +1.57259691, +1.50017881, +1.02426934, +1.30560470, +1.58991218, +1.31399608, +1.70087576, +1.39508748, +1.80336332, +1.90897298, +1.23942471, +1.39576745, +1.57059383, +1.10676599, +1.78420734, +1.13752699, +1.84457111, +1.80457091, +1.92172122, +1.07500541, +1.09811258, +1.94984221, +1.35001898, +1.30496716, +1.65054011, +1.70717335, +1.99966216, +1.94406319, +1.20037222, +1.07742977, +1.15350580, +1.04348254, +1.25931704, +1.59803975, +1.97462106, +1.11699343, +1.66734529, +1.70975852, +1.62794912, +1.96163201, +1.89711285, +1.38171768, +1.90086746, +1.28629518, +1.20449889, +1.00222659, +1.66660273, +1.93827844, +1.49345112, +1.49318635, +1.06188047, +1.39544511, +1.42855239, +1.45769954, +1.56696844, +1.75901723, +1.33271146, +1.47850966, +1.89697123, +1.29701877, +1.85236025, +1.80672812, +1.82106161, +1.68976736, +1.76729107, +1.92830324, +1.60762668, +1.12434602, +1.19036007, +1.04834962, +1.30908704, +1.03278303

364

365atad = getFFTI(getFFTF(data))

366atad

367+1.13850927, +1.95491791, +1.85419106, +1.82718658, +1.58582997, +1.18171763, +1.00596833, +1.26864600, +1.01355422, +1.43078935, +1.62421310, +1.21372676, +1.99465549, +1.55088329, +1.96069813, +1.96416938, +1.07181764, +1.64247262, +1.39377367, +1.91579235, +1.47248125, +1.57259679, +1.50017846, +1.02426946, +1.30560446, +1.58991241, +1.31399596, +1.70087576, +1.39508748, +1.80336344, +1.90897274, +1.23942471, +1.39576769, +1.57059360, +1.10676599, +1.78420722, +1.13752723, +1.84457088, +1.80457091, +1.92172098, +1.07500541, +1.09811234, +1.94984198, +1.35001898, +1.30496705, +1.65053988, +1.70717347, +1.99966192, +1.94406319, +1.20037198, +1.07742977, +1.15350556, +1.04348254, +1.25931668, +1.59803939, +1.97462082, +1.11699343, +1.66734505, +1.70975828, +1.62794876, +1.96163154, +1.89711261, +1.38171744, +1.90086722, +1.28629541, +1.20449877, +1.00222659, +1.66660261, +1.93827844, +1.49345088, +1.49318647, +1.06188059, +1.39544499, +1.42855227, +1.45769942, +1.56696820, +1.75901711, +1.33271146, +1.47850966, +1.89697111, +1.29701877, +1.85235989, +1.80672801, +1.82106125, +1.68976760, +1.76729083, +1.92830312, +1.60762632, +1.12434578, +1.19036007, +1.04834974, +1.30908680, +1.03278327, +0.119209290E-6, +0.357627869E-6, +0.596046448E-7, +0.178813934E-6, -0.119209290E-6, +0.596046448E-7, +0.00000000, +0.178813934E-6, +0.238418579E-6, +0.00000000, +0.417232513E-6, +0.119209290E-6, +0.119209290E-6, +0.119209290E-6, -0.178813934E-6, +0.00000000, +0.298023224E-6, +0.119209290E-6, +0.178813934E-6, +0.596046448E-6, +0.596046448E-7, +0.238418579E-6, +0.119209290E-6, +0.476837158E-6, +0.596046448E-7, +0.596046448E-7, +0.298023224E-6, +0.655651093E-6, +0.178813934E-6, +0.476837158E-6, -0.119209290E-6, +0.178813934E-6, +0.178813934E-6, +0.178813934E-6, +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, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

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

374

375lenData = getUnifRand(5, 100)

376lenData

377+63

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

379data

380+1.6160103039552633, +1.6541140120509306, +1.0040869417908698, +1.4542974132457216, +1.6947377067325697, +1.2075372192141871, +1.4631610716038574, +1.1406040226247374, +1.9348615881914295, +1.2879567233905402, +1.4945042255400804, +1.8469099118991217, +1.7919929119418903, +1.1360395222122714, +1.2318772881752520, +1.3799270555306662, +1.1143029677669491, +1.2609452729986552, +1.9828388242790043, +1.6821135210490183, +1.2170934383844718, +1.0883369833068128, +1.2062805907015570, +1.0037009983077463, +1.2916324076758112, +1.0638605392361611, +1.3470989481675817, +1.8328416410296340, +1.4891419812278208, +1.6986893542508232, +1.0524784505542923, +1.1516956910816971, +1.3144223801216626, +1.6937200535883421, +1.2698080270717715, +1.7318047049031911, +1.2244981351451196, +1.9886230387911041, +1.8610479558349535, +1.5060290588218486, +1.7552078846196424, +1.7111013064367684, +1.9324150528038397, +1.9433878977036156, +1.4576857447095994, +1.7662051714402041, +1.1433310092892315, +1.3740818794837124, +1.1067823108351864, +1.2722864494390880, +1.8546842059664248, +1.3101720940958037, +1.4108722759626842, +1.6310654420905699, +1.8083563859441165, +1.7329818537473569, +1.1571740537173192, +1.8996684785387783, +1.7795058199280493, +1.8600169907946225, +1.4904216502523564, +1.7382186457803095, +1.6497612000696416

381

382atad = getFFTI(getFFTF(data))

383atad

384+1.6160103039552636, +1.6541140120509306, +1.0040869417908698, +1.4542974132457216, +1.6947377067325700, +1.2075372192141876, +1.4631610716038574, +1.1406040226247369, +1.9348615881914297, +1.2879567233905405, +1.4945042255400804, +1.8469099118991219, +1.7919929119418905, +1.1360395222122719, +1.2318772881752522, +1.3799270555306657, +1.1143029677669496, +1.2609452729986554, +1.9828388242790045, +1.6821135210490181, +1.2170934383844720, +1.0883369833068133, +1.2062805907015575, +1.0037009983077461, +1.2916324076758114, +1.0638605392361613, +1.3470989481675817, +1.8328416410296340, +1.4891419812278210, +1.6986893542508235, +1.0524784505542928, +1.1516956910816969, +1.3144223801216628, +1.6937200535883423, +1.2698080270717718, +1.7318047049031908, +1.2244981351451198, +1.9886230387911041, +1.8610479558349535, +1.5060290588218486, +1.7552078846196426, +1.7111013064367684, +1.9324150528038397, +1.9433878977036156, +1.4576857447095999, +1.7662051714402045, +1.1433310092892321, +1.3740818794837120, +1.1067823108351869, +1.2722864494390882, +1.8546842059664252, +1.3101720940958035, +1.4108722759626842, +1.6310654420905704, +1.8083563859441165, +1.7329818537473565, +1.1571740537173196, +1.8996684785387783, +1.7795058199280493, +1.8600169907946222, +1.4904216502523566, +1.7382186457803097, +1.6497612000696416, +0.0000000000000000

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

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

391

392lenData = getUnifRand(5, 100)

393lenData

394+44

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

396data

397+1.00214030136991751696912507531567393, +1.41427367863912389602816069373570595, +1.55393612683366519717679809605737567, +1.08794711931300109110483589732710114, +1.31469294020686756343437101203671537, +1.59077151040069684226496096016998598, +1.07713115330800752124977448734176767, +1.41611162398150088445917213182182578, +1.53748464324203838780933876580052792, +1.94370377484312109253856960655102525, +1.67348976120816961842846871954792535, +1.20222716891033445164139702713199226, +1.29071259409580272392558445515891605, +1.63132850526542004897214521819168921, +1.99576386193998199441365239211554651, +1.55594708527599628576746528797680883, +1.91355930429175495150473528051905477, +1.54908642900770490351098749145782073, +1.82118538056700444510712867185009797, +1.97780483579163422331987597491511525, +1.90815576700018396369504531808678348, +1.49058555904194437223440281796739695, +1.94940498466937705186257913062795008, +1.43077639387946187787595967903371118, +1.86261084414923582279583763873936268, +1.23950712657882487162619882721987351, +1.67206656279025038107040790177222330, +1.21712891976297316584711508579699023, +1.60223269971586723850433348950759050, +1.97637530132567462539421644252074467, +1.43677002812842494973984111177331996, +1.59101691207905151807386845313228001, +1.95016477209798423575088737046880542, +1.39470334488124837867191547925607277, +1.53538719371839144264182985315383002, +1.45170494312221457343883878706281743, +1.50384348038276888998781473502156948, +1.70369943060310219817144384553834178, +1.14724310563883452555537769599512514, +1.89219422126040039545021386401807067, +1.95185788822246066032065255470987014, +1.50066844746253644153548597239797499, +1.52921689099017786924056966638398257, +1.81068100739815701055567426547210082

398

399atad = getFFTI(getFFTF(data))

400atad

401+1.00214030136991751696912507531567354, +1.41427367863912389602816069373570556, +1.55393612683366519717679809605737548, +1.08794711931300109110483589732710075, +1.31469294020686756343437101203671557, +1.59077151040069684226496096016998579, +1.07713115330800752124977448734176787, +1.41611162398150088445917213182182559, +1.53748464324203838780933876580052792, +1.94370377484312109253856960655102486, +1.67348976120816961842846871954792555, +1.20222716891033445164139702713199245, +1.29071259409580272392558445515891605, +1.63132850526542004897214521819168883, +1.99576386193998199441365239211554671, +1.55594708527599628576746528797680864, +1.91355930429175495150473528051905439, +1.54908642900770490351098749145782034, +1.82118538056700444510712867185009778, +1.97780483579163422331987597491511506, +1.90815576700018396369504531808678348, +1.49058555904194437223440281796739695, +1.94940498466937705186257913062795047, +1.43077639387946187787595967903371099, +1.86261084414923582279583763873936268, +1.23950712657882487162619882721987293, +1.67206656279025038107040790177222330, +1.21712891976297316584711508579698985, +1.60223269971586723850433348950759050, +1.97637530132567462539421644252074486, +1.43677002812842494973984111177331996, +1.59101691207905151807386845313228020, +1.95016477209798423575088737046880504, +1.39470334488124837867191547925607277, +1.53538719371839144264182985315383021, +1.45170494312221457343883878706281723, +1.50384348038276888998781473502156928, +1.70369943060310219817144384553834197, +1.14724310563883452555537769599512533, +1.89219422126040039545021386401807086, +1.95185788822246066032065255470987014, +1.50066844746253644153548597239797442, +1.52921689099017786924056966638398315, +1.81068100739815701055567426547210082, -0.481482486096808963263994485646231830E-33, -0.577778983316170755916793382775478196E-33, +0.192592994438723585305597794258492732E-33, +0.962964972193617926527988971292463659E-34, -0.385185988877447170611195588516985464E-33, -0.192592994438723585305597794258492732E-33, +0.192592994438723585305597794258492732E-33, -0.192592994438723585305597794258492732E-33, +0.00000000000000000000000000000000000, -0.770371977754894341222391177033970927E-33, +0.192592994438723585305597794258492732E-33, -0.288889491658085377958396691387739098E-33, -0.288889491658085377958396691387739098E-33, -0.770371977754894341222391177033970927E-33, +0.192592994438723585305597794258492732E-33, -0.962964972193617926527988971292463659E-34, +0.00000000000000000000000000000000000, -0.105926146941297971918078786842171003E-32, +0.962964972193617926527988971292463659E-34, -0.385185988877447170611195588516985464E-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

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

408

409lenData = getUnifRand(5, 100)

410lenData

411+57

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

413data

414(+1.78070045, +0.461442471), (+1.64971399, +0.671645403E-1), (+1.57969546, +0.695726514), (+1.43690825, +0.470665038), (+1.00433207, +0.535529971), (+1.58583927, +0.378952444), (+1.69145989, +0.381616771), (+1.95004642, +0.191478372), (+1.66798949, +0.740885735E-4), (+1.08259439, +0.417011976E-2), (+1.38777447, +0.379514098), (+1.87408328, +0.287635624), (+1.90318418, +0.308253765E-1), (+1.37596643, +0.360579073), (+1.97353208, +0.835707426), (+1.56007648, +0.235085487), (+1.54318428, +0.613026440), (+1.15544546, +0.603195846), (+1.01724339, +0.335798383), (+1.09329498, +0.848679364), (+1.72450602, +0.506694973), (+1.01621723, +0.511708677), (+1.99756980, +0.318912446), (+1.99526203, +0.520367980), (+1.77170527, +0.427832007E-1), (+1.48249555, +0.499551237), (+1.66839623, +0.466739833), (+1.79689157, +0.566666424), (+1.31877875, +0.369573474), (+1.51008141, +0.687099934), (+1.37163770, +0.916197717), (+1.91094351, +0.417398393), (+1.35456920, +0.285857022), (+1.29775071, +0.674656332), (+1.27389884, +0.755856335), (+1.65268540, +0.492864311), (+1.05920577, +0.821733475E-1), (+1.28488994, +0.311521173), (+1.88183331, +0.580952585), (+1.69847453, +0.342561305), (+1.96100664, +0.364868820), (+1.79909754, +0.351487994E-1), (+1.89123976, +0.193100810), (+1.33626652, +0.915951133E-1), (+1.49876904, +0.974286675), (+1.11158252, +0.179010689), (+1.57456374, +0.352008581), (+1.65032434, +0.193040252), (+1.22512686, +0.218436003), (+1.72766149, +0.260624170), (+1.95420027, +0.214014709), (+1.50839758, +0.760960937), (+1.13202381, +0.449895263E-1), (+1.51383698, +0.982521951), (+1.81521320, +0.652696192), (+1.42579257, +0.380623519), (+1.62368417, +0.679522753E-1)

415

416atad = getFFTI(getFFTF(data))

417atad

418(+1.78070056, +0.461442471), (+1.64971387, +0.671646297E-1), (+1.57969546, +0.695726454), (+1.43690801, +0.470665097), (+1.00433218, +0.535529912), (+1.58583939, +0.378952444), (+1.69145977, +0.381616622), (+1.95004606, +0.191478297), (+1.66798949, +0.740140676E-4), (+1.08259439, +0.417021662E-2), (+1.38777447, +0.379514128), (+1.87408316, +0.287635654), (+1.90318429, +0.308255553E-1), (+1.37596643, +0.360579193), (+1.97353184, +0.835707486), (+1.56007648, +0.235085517), (+1.54318440, +0.613026381), (+1.15544558, +0.603195906), (+1.01724350, +0.335798383), (+1.09329498, +0.848679423), (+1.72450614, +0.506695032), (+1.01621747, +0.511708736), (+1.99756980, +0.318912357), (+1.99526179, +0.520367920), (+1.77170539, +0.427831709E-1), (+1.48249555, +0.499551237), (+1.66839623, +0.466739714), (+1.79689121, +0.566666305), (+1.31877863, +0.369573504), (+1.51008129, +0.687099874), (+1.37163758, +0.916197598), (+1.91094339, +0.417398453), (+1.35456932, +0.285856962), (+1.29775083, +0.674656272), (+1.27389908, +0.755856335), (+1.65268540, +0.492864311), (+1.05920589, +0.821733028E-1), (+1.28489006, +0.311521232), (+1.88183320, +0.580952525), (+1.69847441, +0.342561305), (+1.96100664, +0.364868760), (+1.79909754, +0.351489261E-1), (+1.89123964, +0.193100899), (+1.33626640, +0.915950835E-1), (+1.49876893, +0.974286616), (+1.11158240, +0.179010734), (+1.57456338, +0.352008522), (+1.65032411, +0.193040371), (+1.22512686, +0.218435988), (+1.72766137, +0.260624081), (+1.95420039, +0.214014515), (+1.50839770, +0.760960937), (+1.13202405, +0.449894965E-1), (+1.51383710, +0.982521892), (+1.81521320, +0.652696133), (+1.42579257, +0.380623519), (+1.62368441, +0.679522455E-1), (+0.298023224E-6, -0.134110451E-6), (+0.596046448E-6, +0.745058060E-7), (+0.417232513E-6, +0.178813934E-6), (+0.357627869E-6, -0.208616257E-6), (+0.417232513E-6, +0.00000000), (+0.178813934E-6, -0.596046448E-7), (+0.119209290E-6, +0.745058060E-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, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

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

425

426lenData = getUnifRand(5, 100)

427lenData

428+39

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

430data

431(+1.0710537125794901, +0.38435673824482430), (+1.4308308753175725, +0.80892293848962094), (+1.0890017472647038, +0.36099374980963772), (+1.8864552480901673, +0.43569585794292232), (+1.7145466202495543, +0.36169565135376369), (+1.4075730976316132, +0.37563434744192847), (+1.6270741483725240, +0.23859567751500965), (+1.3343675048532311, +0.58315066953613282), (+1.7691967697560083, +0.74392229485494976), (+1.2372785958371761, +0.89335920846246086), (+1.9431586074060068, +0.75989690736030724), (+1.9258116342238638, +0.11377337971530710), (+1.2504319844259206, +0.55067793215399685), (+1.4471202816329862, +0.55595963903755985E-1), (+1.2854982720195691, +0.15978896891605054), (+1.9369710069136226, +0.11894293444148629), (+1.0380803600923174, +0.74798081993426546), (+1.8884328454525572, +0.34402571765483103), (+1.7655259695472969, +0.41268668652512674), (+1.2440441658312851, +0.21083475734841550), (+1.1164086740876171, +0.62171033395347386), (+1.1503222251909053, +0.93732385451705336), (+1.5058974394795732, +0.73255238148507440), (+1.3089320160830211, +0.92093532222884233), (+1.5835135092390971, +0.43624643305698041), (+1.1013590617498998, +0.98833469120178985E-1), (+1.4470621895305333, +0.85411198267321908E-1), (+1.3224657660773911, +0.62269861206457933), (+1.2484243982362468, +0.57889722471554927), (+1.6194902184538078, +0.96632651209122200), (+1.7401923171150444, +0.64435046112351080), (+1.5104715987839963, +0.56240316324334905E-1), (+1.0517953924626136, +0.73193799318956843), (+1.4195179855737285, +0.63125907138917359), (+1.0258466655282699, +0.93380987628804157), (+1.1594803449200248, +0.22722281825911372), (+1.4205459289356632, +0.79538111104244025E-1), (+1.9589285881484320, +0.31695858475510374), (+1.6565346735953170, +0.41252564289452565)

432

433atad = getFFTI(getFFTF(data))

434atad

435(+1.0710537125794901, +0.38435673824482441), (+1.4308308753175725, +0.80892293848962127), (+1.0890017472647033, +0.36099374980963783), (+1.8864552480901671, +0.43569585794292259), (+1.7145466202495543, +0.36169565135376397), (+1.4075730976316134, +0.37563434744192870), (+1.6270741483725235, +0.23859567751500985), (+1.3343675048532311, +0.58315066953613293), (+1.7691967697560083, +0.74392229485494998), (+1.2372785958371759, +0.89335920846246086), (+1.9431586074060059, +0.75989690736030691), (+1.9258116342238636, +0.11377337971530749), (+1.2504319844259206, +0.55067793215399741), (+1.4471202816329858, +0.55595963903756485E-1), (+1.2854982720195687, +0.15978896891605093), (+1.9369710069136221, +0.11894293444148654), (+1.0380803600923176, +0.74798081993426535), (+1.8884328454525567, +0.34402571765483075), (+1.7655259695472967, +0.41268668652512647), (+1.2440441658312849, +0.21083475734841522), (+1.1164086740876171, +0.62171033395347375), (+1.1503222251909055, +0.93732385451705325), (+1.5058974394795732, +0.73255238148507407), (+1.3089320160830211, +0.92093532222884167), (+1.5835135092390968, +0.43624643305698030), (+1.1013590617498996, +0.98833469120178846E-1), (+1.4470621895305329, +0.85411198267321936E-1), (+1.3224657660773911, +0.62269861206457888), (+1.2484243982362466, +0.57889722471554927), (+1.6194902184538071, +0.96632651209122122), (+1.7401923171150440, +0.64435046112351024), (+1.5104715987839961, +0.56240316324334481E-1), (+1.0517953924626133, +0.73193799318956831), (+1.4195179855737283, +0.63125907138917348), (+1.0258466655282696, +0.93380987628804157), (+1.1594803449200251, +0.22722281825911345), (+1.4205459289356632, +0.79538111104244080E-1), (+1.9589285881484317, +0.31695858475510386), (+1.6565346735953170, +0.41252564289452531), (+0.33306690738754696E-15, -0.33306690738754696E-15), (-0.11102230246251565E-15, -0.55511151231257827E-16), (+0.0000000000000000, -0.22204460492503131E-15), (+0.55511151231257827E-15, -0.11102230246251565E-15), (+0.33306690738754696E-15, -0.27755575615628914E-15), (+0.11102230246251565E-15, -0.55511151231257827E-16), (+0.33306690738754696E-15, -0.33306690738754696E-15), (+0.33306690738754696E-15, +0.12490009027033011E-15), (+0.44408920985006262E-15, -0.34000580129145419E-15), (+0.0000000000000000, +0.22204460492503131E-15), (-0.11102230246251565E-15, +0.16653345369377348E-15), (+0.0000000000000000, +0.33306690738754696E-15), (+0.55511151231257827E-15, +0.0000000000000000), (-0.33306690738754696E-15, +0.0000000000000000), (+0.0000000000000000, -0.22204460492503131E-15), (+0.11102230246251565E-15, +0.16653345369377348E-15), (+0.33306690738754696E-15, +0.22204460492503131E-15), (+0.22204460492503131E-15, +0.22204460492503131E-15), (+0.22204460492503131E-15, +0.30531133177191805E-15), (+0.11102230246251565E-15, +0.36082248300317588E-15), (+0.22204460492503131E-15, +0.11102230246251565E-15), (+0.11102230246251565E-15, +0.16653345369377348E-15), (+0.22204460492503131E-15, +0.16653345369377348E-15), (-0.11102230246251565E-15, +0.61062266354383610E-15), (+0.55511151231257827E-15, +0.74246164771807344E-15)

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

437reltol

438+0.14901161193847656E-7

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

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

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

442

443lenData = getUnifRand(5, 100)

444lenData

445+57

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

447data

448(+1.39833447418358902665180450601791758, +0.523888315608087100577247777754604802), (+1.64790921959100100948626855868469883, +0.445365684226324347513629060811144322), (+1.82794973444166025472651815741101882, +0.874833626105459275481398577819817510), (+1.24541223183492434352046714679769737, +0.169431800711786955262080983330115826), (+1.00144936559472392892882696298314343, +0.663726583780523379029088254891428171E-3), (+1.80062267094936854165805782119868366, +0.971428981894860867132457379965180791), (+1.70356301053396656955934505228758214, +0.924111876404753924054211912391687967), (+1.47330946197854619379970717411855903, +0.207338498071644377407880929910603632), (+1.00126352213011520907360188121972397, +0.588849905852747097622704165017740157), (+1.46531769490749580615857388278369716, +0.241249014916329151794995323258878934), (+1.59316600796295189796028427643601554, +0.268313000802955673358288293767287086), (+1.94775222995160449043896831381115139, +0.308894891802914069553332392725634213), (+1.28708383256707436807680742925753756, +0.806383181638781046086828879396476307), (+1.07859850964921461315975930484729282, +0.609518438864146845478011389924169998), (+1.04335901712372104352453030218270475, +0.952967257961881348012707012403596962), (+1.40387360868813067314373369229616740, +0.207581617215326741645776252059932250), (+1.96005951276964562379488231437097464, +0.981210474580553641870597038482902277), (+1.43832730914749945372616285367123166, +0.303087765238124192859892990897206381), (+1.88257944191962020483490448011947942, +0.373594641585700745920635013934185854E-1), (+1.28648147114673504635110346645750344, +0.350902581861395549179002064583679163), (+1.05070344853638401381589779417505165, +0.256904631833074321827629937601655692), (+1.94611803480777827940353222894782843, +0.584216947406961856414170834240964691), (+1.40431463066609781507989766200709550, +0.520969389034094936766789717625667074), (+1.63626512426139176875252924337204714, +0.523872000240849012477878086924622523), (+1.55306187112652539047131558157954573, +0.774265119875328227503348847171895339), (+1.89498550318386979197924449558248982, +0.477840943565191158430974079611463823), (+1.62455037023504934232035526115163942, +0.321281279603695434214921763676159138), (+1.74450169509044701690662863091632031, +0.816233261395529398461805599692387662), (+1.61962339134725612534739843236360329, +0.658843773919786319039512465581083085), (+1.97394744586845905750556133570415310, +0.194855584573130955309374155663325033), (+1.49560417373718296218119092681085024, +0.700304532965064235286604527262635397), (+1.29978175112776758636814148593138079, +0.429350434567518402642078490022289226E-2), (+1.17190004608241889484989933640519006, +0.910663645617747570036969960354092111), (+1.66941202745200565612529580637433216, +0.359019531241161702251687194016033283), (+1.30083639237216421490340717412698111, +0.743992193820027907294365224059502580), (+1.25655044359452384601676393902385535, +0.370071094828311436071335987509893731), (+1.66059093474353704554759512611962668, +0.834445249085694004251504964745780498), (+1.88302669879046477139980437364863961, +0.750206644965578969357093480580422652), (+1.76528668084466497155141408380684574, +0.888818480754871777470497609706892823), (+1.41204349655550179282018336822667140, +0.292324550633653997804002738590870448), (+1.30877687191783402489677723440329093, +0.589379029196366283436997217494524172), (+1.35107908757086195728949281947468389, +0.895278161990966576434937861319514475), (+1.43908920623546989737617104940330793, +0.771721758117615331292205651483275173), (+1.84946933597264257078312361487460095, +0.468168272637729484882548584419310965E-1), (+1.39405644367911003798540398011851754, +0.864316399678531722162187850336210322), (+1.41227079892162111312192589162054771, +0.228398049009379850158873375174166657), (+1.24358220071192010717926592293583981, +0.511989312973058729815439389035067020), (+1.77010209538760790853415215875794678, +0.438482061655957610365964457617299565), (+1.52449506193935698126199221882658360, +0.236630305552854697979562369457786624), (+1.52173579157007723724451420873727558, +0.330495200058322918662809133017363641), (+1.77569225294366197950804657784736467, +0.281626757386243769095543734579815652), (+1.31606976068797439345128855116372624, +0.667410592012264198239571611544311737), (+1.97277018370783422638041418009317035, +0.614002500913539304110899103200528609), (+1.39367625105744229038119604485764085, +0.915787637639835489822032349441129479), (+1.01319988769825282649191081733124496, +0.717071826117791372172662028669140603), (+1.64342878671753070012022371463437662, +0.700071486284849968239426687969309169), (+1.58426974060152630758775977431924900, +0.763399280164976651811943064090056469)

449

450atad = getFFTI(getFFTF(data))

451atad

452(+1.39833447418358902665180450601791758, +0.523888315608087100577247777754604609), (+1.64790921959100100948626855868469864, +0.445365684226324347513629060811144226), (+1.82794973444166025472651815741101882, +0.874833626105459275481398577819817510), (+1.24541223183492434352046714679769718, +0.169431800711786955262080983330115898), (+1.00144936559472392892882696298314382, +0.663726583780523379029088254891042985E-3), (+1.80062267094936854165805782119868385, +0.971428981894860867132457379965180984), (+1.70356301053396656955934505228758291, +0.924111876404753924054211912391687967), (+1.47330946197854619379970717411855922, +0.207338498071644377407880929910603536), (+1.00126352213011520907360188121972416, +0.588849905852747097622704165017740157), (+1.46531769490749580615857388278369677, +0.241249014916329151794995323258879078), (+1.59316600796295189796028427643601573, +0.268313000802955673358288293767287327), (+1.94775222995160449043896831381115139, +0.308894891802914069553332392725634310), (+1.28708383256707436807680742925753776, +0.806383181638781046086828879396476404), (+1.07859850964921461315975930484729282, +0.609518438864146845478011389924170287), (+1.04335901712372104352453030218270455, +0.952967257961881348012707012403597251), (+1.40387360868813067314373369229616740, +0.207581617215326741645776252059932418), (+1.96005951276964562379488231437097444, +0.981210474580553641870597038482902181), (+1.43832730914749945372616285367123146, +0.303087765238124192859892990897206333), (+1.88257944191962020483490448011947961, +0.373594641585700745920635013934185372E-1), (+1.28648147114673504635110346645750325, +0.350902581861395549179002064583679163), (+1.05070344853638401381589779417505184, +0.256904631833074321827629937601655548), (+1.94611803480777827940353222894782862, +0.584216947406961856414170834240964691), (+1.40431463066609781507989766200709570, +0.520969389034094936766789717625667074), (+1.63626512426139176875252924337204733, +0.523872000240849012477878086924622523), (+1.55306187112652539047131558157954573, +0.774265119875328227503348847171895436), (+1.89498550318386979197924449558248963, +0.477840943565191158430974079611463775), (+1.62455037023504934232035526115163942, +0.321281279603695434214921763676158994), (+1.74450169509044701690662863091632050, +0.816233261395529398461805599692387277), (+1.61962339134725612534739843236360348, +0.658843773919786319039512465581082893), (+1.97394744586845905750556133570415348, +0.194855584573130955309374155663325081), (+1.49560417373718296218119092681085044, +0.700304532965064235286604527262635204), (+1.29978175112776758636814148593138079, +0.429350434567518402642078490022282606E-2), (+1.17190004608241889484989933640519025, +0.910663645617747570036969960354091918), (+1.66941202745200565612529580637433197, +0.359019531241161702251687194016033283), (+1.30083639237216421490340717412698111, +0.743992193820027907294365224059502676), (+1.25655044359452384601676393902385535, +0.370071094828311436071335987509893924), (+1.66059093474353704554759512611962707, +0.834445249085694004251504964745780594), (+1.88302669879046477139980437364863942, +0.750206644965578969357093480580423134), (+1.76528668084466497155141408380684632, +0.888818480754871777470497609706893015), (+1.41204349655550179282018336822667159, +0.292324550633653997804002738590870496), (+1.30877687191783402489677723440329131, +0.589379029196366283436997217494524172), (+1.35107908757086195728949281947468350, +0.895278161990966576434937861319514379), (+1.43908920623546989737617104940330812, +0.771721758117615331292205651483274981), (+1.84946933597264257078312361487460095, +0.468168272637729484882548584419310724E-1), (+1.39405644367911003798540398011851754, +0.864316399678531722162187850336210033), (+1.41227079892162111312192589162054751, +0.228398049009379850158873375174166488), (+1.24358220071192010717926592293583981, +0.511989312973058729815439389035067020), (+1.77010209538760790853415215875794678, +0.438482061655957610365964457617299276), (+1.52449506193935698126199221882658341, +0.236630305552854697979562369457786527), (+1.52173579157007723724451420873727538, +0.330495200058322918662809133017363497), (+1.77569225294366197950804657784736486, +0.281626757386243769095543734579815604), (+1.31606976068797439345128855116372605, +0.667410592012264198239571611544311640), (+1.97277018370783422638041418009317054, +0.614002500913539304110899103200528706), (+1.39367625105744229038119604485764066, +0.915787637639835489822032349441129864), (+1.01319988769825282649191081733124515, +0.717071826117791372172662028669140796), (+1.64342878671753070012022371463437662, +0.700071486284849968239426687969309361), (+1.58426974060152630758775977431924900, +0.763399280164976651811943064090056373), (-0.288889491658085377958396691387739098E-33, -0.481482486096808963263994485646231830E-34), (+0.674075480535532548569592279904724561E-33, +0.144444745829042688979198345693869549E-33), (+0.385185988877447170611195588516985464E-33, +0.962964972193617926527988971292463659E-34), (-0.288889491658085377958396691387739098E-33, +0.481482486096808963263994485646231830E-34), (-0.288889491658085377958396691387739098E-33, -0.192592994438723585305597794258492732E-33), (-0.192592994438723585305597794258492732E-33, +0.00000000000000000000000000000000000), (-0.192592994438723585305597794258492732E-33, +0.162500339057673025101598138905603243E-33)

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

454reltol

455+0.138777878078144567552953958511352539E-16

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

457T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, 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+38

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

464data

465+1.21066880, +1.31886697, +1.55928266, +1.82274508, +1.77002764, +1.57746673, +1.47221124, +1.48124194, +1.41402006, +1.74920559, +1.28508186, +1.70448923, +1.87923741, +1.11306322, +1.43925130, +1.81287432, +1.67682612, +1.13462615, +1.89004326, +1.31945276, +1.48869491, +1.81611156, +1.37266016, +1.56683564, +1.71063328, +1.68923497, +1.94561839, +1.82946587, +1.23035049, +1.86347342, +1.95660043, +1.81421912, +1.71293163, +1.58607721, +1.91894436, +1.41113281, +1.42989302, +1.09435153

466

467atad = getFFTI(getFFTF(data))

468atad

469+1.21066892, +1.31886673, +1.55928254, +1.82274497, +1.77002752, +1.57746661, +1.47221112, +1.48124170, +1.41401958, +1.74920547, +1.28508139, +1.70448935, +1.87923717, +1.11306357, +1.43925095, +1.81287432, +1.67682600, +1.13462615, +1.89004326, +1.31945264, +1.48869503, +1.81611156, +1.37266016, +1.56683576, +1.71063292, +1.68923485, +1.94561839, +1.82946587, +1.23035026, +1.86347353, +1.95660043, +1.81421900, +1.71293175, +1.58607721, +1.91894460, +1.41113269, +1.42989314, +1.09435141, +0.596046448E-7, +0.596046448E-7, +0.238418579E-6, +0.119209290E-6, +0.178813934E-6, +0.119209290E-6, +0.178813934E-6, -0.178813934E-6, +0.596046448E-7, +0.00000000, +0.596046448E-7, +0.119209290E-6, -0.596046448E-7, +0.119209290E-6, +0.119209290E-6, -0.298023224E-6, -0.119209290E-6, -0.119209290E-6, +0.119209290E-6, +0.119209290E-6, -0.596046448E-7, +0.596046448E-7, +0.238418579E-6, -0.119209290E-6, -0.596046448E-7, -0.238418579E-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, T, T, T, T, T, T, T, T, T, T, T, T, T, 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+74

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

481data

482+1.6432558328354809, +1.3654546600076485, +1.6656187971322232, +1.9127385933971552, +1.0364008368145659, +1.6522435825186625, +1.1832082406035442, +1.3901391095100135, +1.6224787609609730, +1.3427244625109653, +1.8359444830840661, +1.2867389560724052, +1.6215809885334025, +1.8240833920717687, +1.2320092717009166, +1.4539540999177216, +1.1537230371910649, +1.6035712066723340, +1.6453438456774367, +1.1497440133430494, +1.8188158471286120, +1.4051220376217777, +1.7920896080519901, +1.7928975565426339, +1.4224854792337660, +1.1136850985942908, +1.2444394012836733, +1.3237888095449366, +1.9137792244152383, +1.9850677553422094, +1.1393668468216951, +1.3557941336910171, +1.8815308518340201, +1.7249434445596834, +1.0343502619204736, +1.9808777952411221, +1.2032420763415090, +1.4807286972550746, +1.2491064944374863, +1.4297639355621108, +1.6290354481891551, +1.2114998281817941, +1.5172699068613671, +1.2942073489339299, +1.4080895474936046, +1.9242609782410005, +1.0992718234442911, +1.7176097174033678, +1.3118069599086539, +1.2657210054989889, +1.3921759185348066, +1.7415985256122810, +1.3834541209298445, +1.4532919827691724, +1.9650945290546877, +1.4160599833329710, +1.9769288416374624, +1.9606233546100109, +1.5240309096119118, +1.8402458662628960, +1.9681946586063583, +1.8624021172529877, +1.5653227109376688, +1.6723363722314373, +1.7147943100345064, +1.2079873571574207, +1.0783658578894415, +1.8917999504505476, +1.2083341912335166, +1.5965591335917328, +1.5634046535909003, +1.9737848936727000, +1.5282339909814917, +1.7807512874853064

483

484atad = getFFTI(getFFTF(data))

485atad

486+1.6432558328354807, +1.3654546600076487, +1.6656187971322229, +1.9127385933971555, +1.0364008368145652, +1.6522435825186625, +1.1832082406035438, +1.3901391095100135, +1.6224787609609728, +1.3427244625109656, +1.8359444830840661, +1.2867389560724054, +1.6215809885334020, +1.8240833920717687, +1.2320092717009159, +1.4539540999177216, +1.1537230371910647, +1.6035712066723340, +1.6453438456774361, +1.1497440133430499, +1.8188158471286116, +1.4051220376217775, +1.7920896080519886, +1.7928975565426342, +1.4224854792337656, +1.1136850985942912, +1.2444394012836726, +1.3237888095449373, +1.9137792244152378, +1.9850677553422094, +1.1393668468216940, +1.3557941336910169, +1.8815308518340204, +1.7249434445596830, +1.0343502619204732, +1.9808777952411218, +1.2032420763415093, +1.4807286972550742, +1.2491064944374863, +1.4297639355621108, +1.6290354481891554, +1.2114998281817937, +1.5172699068613671, +1.2942073489339294, +1.4080895474936050, +1.9242609782410003, +1.0992718234442913, +1.7176097174033673, +1.3118069599086541, +1.2657210054989885, +1.3921759185348068, +1.7415985256122806, +1.3834541209298452, +1.4532919827691719, +1.9650945290546873, +1.4160599833329703, +1.9769288416374624, +1.9606233546100102, +1.5240309096119118, +1.8402458662628955, +1.9681946586063586, +1.8624021172529868, +1.5653227109376688, +1.6723363722314359, +1.7147943100345067, +1.2079873571574207, +1.0783658578894417, +1.8917999504505469, +1.2083341912335177, +1.5965591335917324, +1.5634046535909008, +1.9737848936726992, +1.5282339909814915, +1.7807512874853062, -0.11102230246251565E-15, -0.88817841970012523E-15, +0.55511151231257827E-15, -0.11102230246251565E-15, +0.88817841970012523E-15, -0.88817841970012523E-15, -0.11102230246251565E-15, -0.22204460492503131E-15, +0.44408920985006262E-15, -0.77715611723760958E-15, +0.33306690738754696E-15, +0.22204460492503131E-15, +0.99920072216264089E-15, -0.33306690738754696E-15, +0.66613381477509392E-15, -0.44408920985006262E-15, +0.66613381477509392E-15, -0.44408920985006262E-15, +0.33306690738754696E-15, -0.22204460492503131E-15, +0.77715611723760958E-15, -0.33306690738754696E-15, -0.33306690738754696E-15, +0.11102230246251565E-15, +0.0000000000000000, -0.11102230246251565E-15, -0.22204460492503131E-15, +0.44408920985006262E-15, -0.11102230246251565E-15, +0.0000000000000000, -0.22204460492503131E-15, -0.11102230246251565E-15, -0.11102230246251565E-15, -0.11102230246251565E-15, -0.11102230246251565E-15, +0.0000000000000000, -0.11102230246251565E-15, +0.11102230246251565E-15, -0.44408920985006262E-15, +0.11102230246251565E-15, -0.33306690738754696E-15, +0.11102230246251565E-15, -0.11102230246251565E-15, +0.55511151231257827E-15, -0.22204460492503131E-15, +0.88817841970012523E-15, -0.33306690738754696E-15, +0.44408920985006262E-15, -0.55511151231257827E-15, +0.44408920985006262E-15, -0.66613381477509392E-15, +0.77715611723760958E-15, -0.55511151231257827E-15, +0.88817841970012523E-15

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

488reltol

489+0.14901161193847656E-7

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

491T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, 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+43

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

498data

499+1.86771797327173547043225608976960256, +1.79613463955877659820714819173569711, +1.43953979761430478353306027044390907, +1.53133256362475985705818988348757794, +1.56382502759640583753618760300671927, +1.22207307528627994549204144217418947, +1.61141812579826842901611736942509813, +1.87877798975977661353633546193101165, +1.10032280597192415876968976668680443, +1.55389374273121519307653367654459571, +1.22591622742853006341771421715044008, +1.19179820201907495920500515397627245, +1.39094146418423162570830236888990262, +1.68231427951359665363396543076534996, +1.38685857004091667552576442187354710, +1.79539495865605693273583432647953445, +1.53633751805712879389409684321648844, +1.76528842000778781952471663840051057, +1.13741928108943686791434958924324744, +1.81061873416726227251188350811476490, +1.04620917173802759540657503034647950, +1.89392980866065367042630869071124246, +1.42798295236446370736832198439042274, +1.40270125816364331912192821772819756, +1.43356039617346169086624363507276006, +1.30777275378837533507692235215951667, +1.75258776851735297685457685086186277, +1.86676837016941800202959289594904495, +1.03863306992591572693783908829400452, +1.53535288696317580293638950232809024, +1.24036637946260324738875849496449061, +1.88038901162050486811420068795884974, +1.62072130696269597139000249810728955, +1.61910768479123964915434308047021059, +1.41323627153391146790604588465458738, +1.11165494482781857760895642743089263, +1.56616073168033069146168835967943846, +1.39661899798235076504030436423190616, +1.02853018729844876467506020052524556, +1.59273400956953072512894996646210215, +1.71685686785084575591529646615667788, +1.92263871021477991640099949021328020, +1.12171866898196503558149665401923214

500

501atad = getFFTI(getFFTF(data))

502atad

503+1.86771797327173547043225608976960217, +1.79613463955877659820714819173569692, +1.43953979761430478353306027044390868, +1.53133256362475985705818988348757775, +1.56382502759640583753618760300671927, +1.22207307528627994549204144217418927, +1.61141812579826842901611736942509832, +1.87877798975977661353633546193101146, +1.10032280597192415876968976668680405, +1.55389374273121519307653367654459571, +1.22591622742853006341771421715044008, +1.19179820201907495920500515397627226, +1.39094146418423162570830236888990300, +1.68231427951359665363396543076534996, +1.38685857004091667552576442187354710, +1.79539495865605693273583432647953388, +1.53633751805712879389409684321648786, +1.76528842000778781952471663840051038, +1.13741928108943686791434958924324744, +1.81061873416726227251188350811476451, +1.04620917173802759540657503034647930, +1.89392980866065367042630869071124208, +1.42798295236446370736832198439042274, +1.40270125816364331912192821772819737, +1.43356039617346169086624363507275987, +1.30777275378837533507692235215951628, +1.75258776851735297685457685086186277, +1.86676837016941800202959289594904457, +1.03863306992591572693783908829400413, +1.53535288696317580293638950232809024, +1.24036637946260324738875849496449042, +1.88038901162050486811420068795884955, +1.62072130696269597139000249810728955, +1.61910768479123964915434308047021020, +1.41323627153391146790604588465458738, +1.11165494482781857760895642743089225, +1.56616073168033069146168835967943827, +1.39661899798235076504030436423190616, +1.02853018729844876467506020052524595, +1.59273400956953072512894996646210196, +1.71685686785084575591529646615667827, +1.92263871021477991640099949021328000, +1.12171866898196503558149665401923234, -0.288889491658085377958396691387739098E-33, -0.481482486096808963263994485646231830E-33, -0.770371977754894341222391177033970927E-33, -0.385185988877447170611195588516985464E-33, -0.577778983316170755916793382775478196E-33, -0.192592994438723585305597794258492732E-33, -0.192592994438723585305597794258492732E-33, +0.00000000000000000000000000000000000, -0.192592994438723585305597794258492732E-33, +0.962964972193617926527988971292463659E-34, -0.577778983316170755916793382775478196E-33, +0.00000000000000000000000000000000000, -0.866668474974256133875190074163217293E-33, -0.481482486096808963263994485646231830E-33, -0.577778983316170755916793382775478196E-33, -0.192592994438723585305597794258492732E-33, -0.192592994438723585305597794258492732E-33, -0.288889491658085377958396691387739098E-33, -0.962964972193617926527988971292463659E-33, +0.00000000000000000000000000000000000, -0.481482486096808963263994485646231830E-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

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