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

Detailed Description

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

See the documentation of pm_fftnr for more details.

Parameters

[in]

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: getFFTR

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

fft(:) = getFFTR(data(:))

pm_fftnr::getFFTR
Generate and return the Reverse (unnormalized) Fourier Transform of a periodic sequence of type compl...
Definition: pm_fftnr.F90:611

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

Warning: The condition 1 < size(data) must hold for the corresponding input arguments.
This condition is verified only if the library is built with the preprocessor macro CHECK_ENABLED=1.

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 setFFTR.
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, getFFTR

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 = getFFTR(getFFTF(data))")

32 atad = getFFTR(getFFTF(data))

33 call disp%show("atad = atad / size(atad)")

34 atad = atad / size(atad)

35 call disp%show("atad")

36 call disp%show( atad )

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

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

39 call disp%show("reltol")

40 call disp%show( reltol )

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

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

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

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

45 call disp%skip()

46 end block

47

48 block

49 use pm_kind, only: TKG => CKD

50 real(TKG) :: reltol

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

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

53 lenData = getUnifRand(5, 100)

54 call disp%show("lenData")

55 call disp%show( lenData )

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

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

58 call disp%show("data")

59 call disp%show( data )

60 call disp%skip()

61 call disp%show("atad = getFFTR(getFFTF(data))")

62 atad = getFFTR(getFFTF(data))

63 call disp%show("atad = atad / size(atad)")

64 atad = atad / size(atad)

65 call disp%show("atad")

66 call disp%show( atad )

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

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

69 call disp%show("reltol")

70 call disp%show( reltol )

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

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

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

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

75 call disp%skip()

76 end block

77

78 block

79 use pm_kind, only: TKG => CKH

80 real(TKG) :: reltol

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

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

83 lenData = getUnifRand(5, 100)

84 call disp%show("lenData")

85 call disp%show( lenData )

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

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

88 call disp%show("data")

89 call disp%show( data )

90 call disp%skip()

91 call disp%show("atad = getFFTR(getFFTF(data))")

92 atad = getFFTR(getFFTF(data))

93 call disp%show("atad = atad / size(atad)")

94 atad = atad / size(atad)

95 call disp%show("atad")

96 call disp%show( atad )

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

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

99 call disp%show("reltol")

100 call disp%show( reltol )

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

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

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

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

105 call disp%skip()

106 end block

107

108 block

109 use pm_kind, only: TKG => RKS

110 real(TKG) :: reltol

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

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

113 lenData = getUnifRand(5, 100)

114 call disp%show("lenData")

115 call disp%show( lenData )

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

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

118 call disp%show("data")

119 call disp%show( data )

120 call disp%skip()

121 call disp%show("atad = getFFTR(getFFTF(data))")

122 atad = getFFTR(getFFTF(data))

123 call disp%show("atad = atad * 2 / size(atad)")

124 atad = atad * 2 / size(atad)

125 call disp%show("atad")

126 call disp%show( atad )

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

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

129 call disp%show("reltol")

130 call disp%show( reltol )

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

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

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

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

135 call disp%skip()

136 end block

137

138 block

139 use pm_kind, only: TKG => RKD

140 real(TKG) :: reltol

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

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

143 lenData = getUnifRand(5, 100)

144 call disp%show("lenData")

145 call disp%show( lenData )

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

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

148 call disp%show("data")

149 call disp%show( data )

150 call disp%skip()

151 call disp%show("atad = getFFTR(getFFTF(data))")

152 atad = getFFTR(getFFTF(data))

153 call disp%show("atad = atad * 2 / size(atad)")

154 atad = atad * 2 / size(atad)

155 call disp%show("atad")

156 call disp%show( atad )

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

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

159 call disp%show("reltol")

160 call disp%show( reltol )

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

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

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

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

165 call disp%skip()

166 end block

167

168 block

169 use pm_kind, only: TKG => RKH

170 real(TKG) :: reltol

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

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

173 lenData = getUnifRand(5, 100)

174 call disp%show("lenData")

175 call disp%show( lenData )

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

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

178 call disp%show("data")

179 call disp%show( data )

180 call disp%skip()

181 call disp%show("atad = getFFTR(getFFTF(data))")

182 atad = getFFTR(getFFTF(data))

183 call disp%show("atad = atad * 2 / size(atad)")

184 atad = atad * 2 / size(atad)

185 call disp%show("atad")

186 call disp%show( atad )

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

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

189 call disp%show("reltol")

190 call disp%show( reltol )

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

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

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

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

195 call disp%skip()

196 end block

197 end do

198

199end 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::getFFTF
Generate and return the Forward Fourier Transform (a.k.a. Fourier Analysis) of a periodic sequence of...
Definition: pm_fftnr.F90:250

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+52

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

5data

6(+1.61368406, +0.654225349E-1), (+1.19083261, +0.940628171), (+1.67558646, +0.937595606), (+1.31847739, +0.932643950), (+1.55749488, +0.377682626), (+1.24174333, +0.452294588), (+1.29846215, +0.190005302E-1), (+1.88556671, +0.658495367), (+1.53819823, +0.839302540), (+1.90280008, +0.942555130), (+1.58312356, +0.445834398E-1), (+1.98105121, +0.600401700), (+1.98306322, +0.580414176), (+1.00115585, +0.120039880), (+1.81048965, +0.260151029E-1), (+1.19385910, +0.153998077), (+1.25176990, +0.130250931), (+1.04936481, +0.989136398), (+1.28833365, +0.653184772), (+1.93274665, +0.897489190), (+1.38575149, +0.342547476), (+1.55673337, +0.999942422E-1), (+1.18029845, +0.375036955), (+1.88120532, +0.389101744), (+1.85994959, +0.863745630), (+1.44652486, +0.853441536), (+1.47773862, +0.893547773), (+1.03444695, +0.822583258), (+1.75758684, +0.356809199), (+1.72709823, +0.143720031), (+1.83520913, +0.699783027), (+1.43279982, +0.130150735), (+1.02815175, +0.840682745), (+1.54114342, +0.951689482E-2), (+1.41512465, +0.160423934), (+1.47288799, +0.717074215), (+1.88853836, +0.511980295), (+1.20436597, +0.588646054), (+1.73607135, +0.376064122), (+1.96007633, +0.320416808), (+1.24530888, +0.433535516), (+1.85164595, +0.189068675), (+1.06671417, +0.529213548E-1), (+1.36590815, +0.547775269), (+1.29882240, +0.389097512), (+1.21258450, +0.759805441E-1), (+1.26463413, +0.835534930), (+1.14723647, +0.673832893), (+1.75493646, +0.553384483), (+1.82087052, +0.986869872), (+1.72736549, +0.583958328), (+1.90030885, +0.427784681)

7

8atad = getFFTR(getFFTF(data))

9atad = atad / size(atad)

10atad

11(+1.61368418, +0.654225647E-1), (+1.19083261, +0.940628052), (+1.67558634, +0.937595606), (+1.31847703, +0.932643890), (+1.55749512, +0.377682656), (+1.24174345, +0.452294707), (+1.29846203, +0.190005749E-1), (+1.88556647, +0.658495307), (+1.53819811, +0.839302599), (+1.90280008, +0.942555130), (+1.58312345, +0.445836037E-1), (+1.98105097, +0.600401580), (+1.98306322, +0.580414414), (+1.00115597, +0.120039940), (+1.81048942, +0.260152519E-1), (+1.19385886, +0.153998256), (+1.25177002, +0.130250961), (+1.04936481, +0.989136457), (+1.28833354, +0.653184652), (+1.93274653, +0.897489071), (+1.38575172, +0.342547476), (+1.55673361, +0.999943465E-1), (+1.18029845, +0.375036836), (+1.88120508, +0.389101654), (+1.85994935, +0.863745630), (+1.44652486, +0.853441477), (+1.47773838, +0.893547773), (+1.03444672, +0.822583318), (+1.75758696, +0.356809199), (+1.72709799, +0.143720269), (+1.83520889, +0.699782968), (+1.43279958, +0.130150914), (+1.02815175, +0.840682745), (+1.54114342, +0.951692462E-2), (+1.41512454, +0.160424024), (+1.47288787, +0.717074156), (+1.88853860, +0.511980295), (+1.20436609, +0.588646173), (+1.73607123, +0.376064181), (+1.96007633, +0.320416808), (+1.24530876, +0.433535516), (+1.85164595, +0.189068735), (+1.06671405, +0.529213697E-1), (+1.36590791, +0.547775090), (+1.29882240, +0.389097571), (+1.21258438, +0.759805143E-1), (+1.26463389, +0.835534811), (+1.14723611, +0.673833013), (+1.75493646, +0.553384423), (+1.82087064, +0.986869812), (+1.72736561, +0.583958149), (+1.90030873, +0.427784473), (+0.238418579E-6, -0.149011612E-7), (+0.357627869E-6, -0.149011612E-7), (+0.119209290E-6, +0.894069672E-7), (+0.238418579E-6, +0.894069672E-7), (+0.238418579E-6, +0.596046448E-7), (+0.417232513E-6, +0.596046448E-7), (+0.178813934E-6, +0.894069672E-7), (+0.178813934E-6, +0.894069672E-7), (+0.417232513E-6, -0.298023224E-6), (+0.357627869E-6, -0.894069672E-7), (+0.596046448E-7, +0.00000000), (+0.596046448E-7, -0.819563866E-7)

12reltol = sqrt(epsilon(1._TKG))

13reltol

14+0.345266977E-3

15isClose(data, atad(1:size(data)), reltol = reltol)

16T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

17call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

18

19lenData = getUnifRand(5, 100)

20lenData

21+21

22data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

23data

24(+1.0357347955145046, +0.92594928238660856), (+1.8259944572736275, +0.87658717906294914), (+1.4544971224646290, +0.52422455261980916), (+1.6589644734542657, +0.76149476165773000), (+1.6482662014179432, +0.67890832928285083), (+1.1913630780891353, +0.46286642104127584E-1), (+1.3148894365340116, +0.86339419003619433), (+1.5341689536606480, +0.19493706765898677E-1), (+1.7569890483111164, +0.31988721174509782), (+1.3620577991507117, +0.76610575234505207), (+1.7629697950180079, +0.33107604990228734), (+1.5090763872357269, +0.24139235326963393), (+1.5473448706988391, +0.32381062144701656), (+1.5033209766221935, +0.79326592474470603E-1), (+1.8179220988075706, +0.95238287942176358), (+1.3969204118419001, +0.94311116750375856), (+1.5196112002950750, +0.17489243915942454), (+1.6003229648620021, +0.54017352729224621), (+1.0354241525060592, +0.83223506017664106), (+1.1989293544136177, +0.30578057507047496), (+1.3771066590496628, +0.33974977810089102)

25

26atad = getFFTR(getFFTF(data))

27atad = atad / size(atad)

28atad

29(+1.0357347955145044, +0.92594928238660845), (+1.8259944572736275, +0.87658717906294925), (+1.4544971224646288, +0.52422455261980916), (+1.6589644734542652, +0.76149476165772989), (+1.6482662014179432, +0.67890832928285083), (+1.1913630780891351, +0.46286642104127820E-1), (+1.3148894365340111, +0.86339419003619411), (+1.5341689536606475, +0.19493706765898872E-1), (+1.7569890483111161, +0.31988721174509782), (+1.3620577991507115, +0.76610575234505185), (+1.7629697950180074, +0.33107604990228739), (+1.5090763872357265, +0.24139235326963376), (+1.5473448706988389, +0.32381062144701644), (+1.5033209766221929, +0.79326592474470478E-1), (+1.8179220988075704, +0.95238287942176303), (+1.3969204118419003, +0.94311116750375779), (+1.5196112002950748, +0.17489243915942460), (+1.6003229648620021, +0.54017352729224599), (+1.0354241525060590, +0.83223506017664095), (+1.1989293544136177, +0.30578057507047451), (+1.3771066590496628, +0.33974977810089096), (+0.33306690738754696E-15, -0.31918911957973251E-15), (+0.33306690738754696E-15, +0.55511151231257827E-16), (+0.88817841970012523E-15, -0.27755575615628914E-16), (+0.0000000000000000, +0.22204460492503131E-15), (+0.44408920985006262E-15, +0.22204460492503131E-15), (+0.22204460492503131E-15, +0.55511151231257827E-16), (+0.44408920985006262E-15, -0.55511151231257827E-16), (+0.66613381477509392E-15, +0.33306690738754696E-15), (+0.33306690738754696E-15, +0.97144514654701197E-16), (+0.44408920985006262E-15, +0.55511151231257827E-15), (+0.55511151231257827E-15, +0.61062266354383610E-15)

30reltol = sqrt(epsilon(1._TKG))

31reltol

32+0.14901161193847656E-7

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

34T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

35call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

36

37lenData = getUnifRand(5, 100)

38lenData

39+69

40data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

41data

42(+1.14550154486670481228487049238010256, +0.137804609872366983275998400602062422E-1), (+1.51034299527552626114594638473802444, +0.468457878558344747020711468821407555), (+1.56671001893587697470042806343021542, +0.655674646366053875794473369269666294), (+1.70677254403386082434665722245225195, +0.918757836004708192305034130851484454), (+1.81124342615394295350172368734984818, +0.347648160286339147618839524225420690E-1), (+1.43088948908333446301099497316509003, +0.269101493098986942684962122437864990), (+1.60297726480488216876187899972991505, +0.951053454490898651846978710502654719), (+1.05430371297123999792764981127482130, +0.317072755263924505350643081011117610), (+1.76830718652982591332593510739848540, +0.193046939943327347350782603309651690), (+1.73022996237171313583717970067237607, +0.772841202761389842637163028887341711), (+1.39897522111928624841141579021045800, +0.467881331218414364890475285352279332), (+1.40092035810828918488446490607933812, +0.502987660523732594180326994619439318), (+1.53488005486929748855973274934162637, +0.781122993640296940078420807299855879E-1), (+1.51341548646267399080175709643631396, +0.402796041406038667540062788968608951), (+1.74653029370908113474577210693360122, +0.580617624626589469449904976608114618), (+1.29705260196664736264080602571221000, +0.689988285622526183341504369683877543E-1), (+1.53561667890903428017292661281288874, +0.216896211213068673437605349702154562), (+1.53748450958218736170602796425998899, +0.451751509031929304742385216001463918), (+1.85091330467665284597891953855846808, +0.901228994148521719984452914549949679), (+1.60836855653420246454067326889082769, +0.993797214300646384666627083902378982), (+1.68899689597360514613522335292009960, +0.300201800176324713203858730423782508), (+1.87155797134487538711154395123744274, +0.745853481184971901467646951997825493E-1), (+1.09169146029414452541373199658643576, +0.269003293406237955363686202647376376), (+1.98742611306799054581612030984583867, +0.293642607664343563795330818753840779), (+1.09755877562814056689588368959810766, +0.909539592871376763574746720065575639), (+1.32834811435291600481297393667750117, +0.722725744284960880355897463073960388), (+1.39226141372908298608926983406217891, +0.688015013616403753968788628856341409), (+1.61576599826256811370705304325350655, +0.559747279952123455352910151798767634E-1), (+1.29097643540622752595929646553300381, +0.328083692692068538997872239422635126), (+1.35647412021259751599418596905870732, +0.252111330828928616438679792377747025), (+1.59384808047828125145158529036797971, +0.374808083344234222896447007690967695), (+1.71438503449512216119541995422435455, +0.134912714137833574722300104443506881), (+1.15626648416164340166531171013065293, +0.868157877829071828953639411103653839E-2), (+1.81286504208240157503671883860817069, +0.909827879693314400955931690632828549), (+1.44951054842991416405811269204492026, 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+0.315150545129112267914723805395764411), (+1.41014957876159098446260942923590042, +0.814563870925030705149156890830039318), (+1.49591956539925267582018320750935762, +0.239043454628307450443369193527476012E-1), (+1.67328594168727208018230213418683853, +0.292422819277734176432027619505389355), (+1.18895070745353631862284404136470790, +0.795949018794606596114958357888004794), (+1.80632472309024208187023722674210539, +0.417964924598159517721800960303680772), (+1.31414714865392711863279976921032775, +0.378255815238766578534518477103995206), (+1.04993070496228011315296703740878519, +0.974824087679805682361885888746052838), (+1.91176412330982618663866056361988194, +0.250406230779305374245816316758023189), (+1.98600120109123051052085814269850977, +0.612125889076128476947881677361620422), (+1.91757369585328913747806440622578829, +0.723649082926554548147795529503503532), (+1.02199295566495289506925849532927201, +0.746245123577217932061872138900505108), (+1.27360641061896230867732270982699520, +0.686516551733401522628501442333606479), (+1.77346799925772516147179125593760143, +0.525414157667867766653058313728247877E-1), (+1.25358468480547002602966126982923674, +0.192325863999980375377779473278131780), (+1.37456704785623043487823352235668930, +0.252427251360473717222445592514820709), (+1.85861532572084253203027692593017472, +0.988595348780370453881342808196639611), (+1.70628385757330584234018760283506515, +0.161016130262190363744401827794390058), (+1.04653757124573899493193435863673384, +0.916607694909230917105049067959686523), (+1.83667957124581303045874867636925780, +0.884162555062641343612780347209369341), (+1.78759455768293294247817237373946032, +0.375952812887157444317699632176630549), (+1.44085886421271657690352821911396337, +0.650177860200679479295112939796062200), (+1.58434613020540686596056803522676242, +0.248039655293998297932141727252206597)

43

44atad = getFFTR(getFFTF(data))

45atad = atad / size(atad)

46atad

47(+1.14550154486670481228487049238010256, +0.137804609872366983275998400602064829E-1), (+1.51034299527552626114594638473802444, +0.468457878558344747020711468821407411), (+1.56671001893587697470042806343021580, +0.655674646366053875794473369269666391), (+1.70677254403386082434665722245225233, +0.918757836004708192305034130851484454), (+1.81124342615394295350172368734984818, +0.347648160286339147618839524225420329E-1), (+1.43088948908333446301099497316509003, +0.269101493098986942684962122437864653), (+1.60297726480488216876187899972991505, +0.951053454490898651846978710502654815), (+1.05430371297123999792764981127482111, +0.317072755263924505350643081011117514), (+1.76830718652982591332593510739848540, +0.193046939943327347350782603309651786), (+1.73022996237171313583717970067237664, +0.772841202761389842637163028887341903), (+1.39897522111928624841141579021045839, +0.467881331218414364890475285352279524), (+1.40092035810828918488446490607933812, 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(-0.385185988877447170611195588516985464E-33, -0.722223729145213444895991728469347744E-34), (+0.00000000000000000000000000000000000, +0.144444745829042688979198345693869549E-33), (-0.288889491658085377958396691387739098E-33, +0.481482486096808963263994485646231830E-34), (-0.962964972193617926527988971292463659E-34, -0.481482486096808963263994485646231830E-34), (-0.385185988877447170611195588516985464E-33, +0.385185988877447170611195588516985464E-33), (+0.192592994438723585305597794258492732E-33, -0.240741243048404481631997242823115915E-34), (-0.385185988877447170611195588516985464E-33, +0.481482486096808963263994485646231830E-33), (-0.192592994438723585305597794258492732E-33, -0.192592994438723585305597794258492732E-33), (-0.385185988877447170611195588516985464E-33, -0.962964972193617926527988971292463659E-34), (+0.00000000000000000000000000000000000, -0.192592994438723585305597794258492732E-33), (-0.385185988877447170611195588516985464E-33, -0.105324293833676960713998793735113213E-33), (+0.962964972193617926527988971292463659E-34, -0.722223729145213444895991728469347744E-34), (-0.288889491658085377958396691387739098E-33, +0.481482486096808963263994485646231830E-34), (-0.962964972193617926527988971292463659E-34, -0.192592994438723585305597794258492732E-33), (-0.192592994438723585305597794258492732E-33, +0.601853107621011204079993107057789787E-34), (-0.962964972193617926527988971292463659E-34, +0.180555932286303361223997932117336936E-34), (-0.288889491658085377958396691387739098E-33, -0.144444745829042688979198345693869549E-33), (-0.192592994438723585305597794258492732E-33, -0.288889491658085377958396691387739098E-33), (-0.385185988877447170611195588516985464E-33, -0.240741243048404481631997242823115915E-34), (-0.962964972193617926527988971292463659E-34, +0.00000000000000000000000000000000000), (-0.288889491658085377958396691387739098E-33, +0.168518870133883137142398069976181140E-33), (-0.962964972193617926527988971292463659E-34, -0.962964972193617926527988971292463659E-34), (-0.385185988877447170611195588516985464E-33, +0.144444745829042688979198345693869549E-33), (-0.288889491658085377958396691387739098E-33, -0.240741243048404481631997242823115915E-33), (-0.192592994438723585305597794258492732E-33, -0.481482486096808963263994485646231830E-33), (+0.962964972193617926527988971292463659E-34, -0.288889491658085377958396691387739098E-33), (-0.385185988877447170611195588516985464E-33, -0.481482486096808963263994485646231830E-33), (-0.962964972193617926527988971292463659E-34, -0.240741243048404481631997242823115915E-34), (-0.577778983316170755916793382775478196E-33, -0.216667118743564033468797518540804323E-33), (-0.192592994438723585305597794258492732E-33, -0.337037740267766274284796139952362281E-33), (-0.288889491658085377958396691387739098E-33, -0.288889491658085377958396691387739098E-33), (+0.00000000000000000000000000000000000, +0.264815367353244929795196967105427506E-33), (-0.385185988877447170611195588516985464E-33, -0.168518870133883137142398069976181140E-33), (+0.962964972193617926527988971292463659E-34, -0.288889491658085377958396691387739098E-33), (-0.288889491658085377958396691387739098E-33, -0.288889491658085377958396691387739098E-33), (-0.192592994438723585305597794258492732E-33, +0.240741243048404481631997242823115915E-33), (-0.192592994438723585305597794258492732E-33, -0.962964972193617926527988971292463659E-34), (+0.00000000000000000000000000000000000, +0.481482486096808963263994485646231830E-34), (-0.577778983316170755916793382775478196E-33, +0.00000000000000000000000000000000000), (-0.192592994438723585305597794258492732E-33, -0.192592994438723585305597794258492732E-33), (+0.962964972193617926527988971292463659E-34, -0.385185988877447170611195588516985464E-33), (+0.192592994438723585305597794258492732E-33, -0.337037740267766274284796139952362281E-33), (-0.385185988877447170611195588516985464E-33, -0.616899435311536484181992934734234532E-33), (-0.962964972193617926527988971292463659E-34, +0.481482486096808963263994485646231830E-34), (-0.385185988877447170611195588516985464E-33, -0.337037740267766274284796139952362281E-33), (-0.962964972193617926527988971292463659E-34, -0.385185988877447170611195588516985464E-33), (-0.674075480535532548569592279904724561E-33, -0.192592994438723585305597794258492732E-33)

48reltol = sqrt(epsilon(1._TKG))

49reltol

50+0.138777878078144567552953958511352539E-16

51isClose(data, atad(1:size(data)), reltol = reltol)

52T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

53call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

54

55lenData = getUnifRand(5, 100)

56lenData

57+66

58data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

59data

60+1.00829077, +1.22157145, +1.45627904, +1.25002933, +1.89474392, +1.66434669, +1.63262773, +1.01381290, +1.09944463, +1.38174272, +1.76567888, +1.58814836, +1.17005801, +1.22888863, +1.28920174, +1.18183255, +1.98998117, +1.56513286, +1.81650221, +1.29708314, +1.47393966, +1.00876999, +1.39366841, +1.83379459, +1.83882356, +1.70531511, +1.82238626, +1.46683347, +1.78373909, +1.85447001, +1.46778631, +1.54521143, +1.83365047, +1.63982606, +1.08023143, +1.49671507, +1.67797327, +1.39179444, +1.98483086, +1.41462207, +1.60589886, +1.44007063, +1.50399220, +1.03599739, +1.19293690, +1.40704370, +1.07201958, +1.89822531, +1.01675677, +1.20436442, +1.17751169, +1.71320689, +1.38984799, +1.39919543, +1.41106415, +1.06901670, +1.44472897, +1.13386178, +1.53681231, +1.34706306, +1.93301821, +1.21533298, +1.44251013, +1.48933530, +1.29799628, +1.19267166

61

62atad = getFFTR(getFFTF(data))

63atad = atad * 2 / size(atad)

64atad

65+1.00829077, +1.22157180, +1.45627880, +1.25002909, +1.89474368, +1.66434646, +1.63262725, +1.01381254, +1.09944463, +1.38174272, +1.76567876, +1.58814836, +1.17005801, +1.22888851, +1.28920162, +1.18183243, +1.98998094, +1.56513286, +1.81650186, +1.29708314, +1.47393954, +1.00876999, +1.39366817, +1.83379436, +1.83882368, +1.70531535, +1.82238603, +1.46683383, +1.78373909, +1.85447001, +1.46778619, +1.54521143, +1.83365059, +1.63982618, +1.08023143, +1.49671495, +1.67797327, +1.39179420, +1.98483062, +1.41462159, +1.60589886, +1.44007063, +1.50399196, +1.03599739, +1.19293678, +1.40704370, +1.07201958, +1.89822507, +1.01675665, +1.20436430, +1.17751169, +1.71320653, +1.38984776, +1.39919519, +1.41106391, +1.06901658, +1.44472885, +1.13386178, +1.53681195, +1.34706283, +1.93301809, +1.21533287, +1.44250989, +1.48933506, +1.29799628, +1.19267190, +0.119209290E-6, +0.596046448E-7, +0.178813934E-6, +0.298023224E-6, +0.178813934E-6, +0.238418579E-6, +0.596046448E-7, +0.596046448E-7, -0.119209290E-6, +0.00000000, -0.178813934E-6, +0.119209290E-6, -0.119209290E-6, +0.119209290E-6, +0.178813934E-6, +0.178813934E-6, +0.596046448E-7, -0.178813934E-6, +0.00000000, -0.596046448E-7, +0.596046448E-7, +0.596046448E-7, +0.119209290E-6, -0.119209290E-6, +0.00000000, -0.298023224E-6, +0.00000000, -0.238418579E-6, +0.00000000, +0.00000000, -0.596046448E-7, +0.238418579E-6, -0.596046448E-7, +0.00000000, -0.596046448E-7, +0.298023224E-6, -0.596046448E-7, +0.178813934E-6, +0.119209290E-6, +0.178813934E-6, -0.119209290E-6, +0.00000000, +0.00000000, +0.178813934E-6, +0.596046448E-7, +0.298023224E-6, +0.357627869E-6, +0.298023224E-6, -0.596046448E-7, +0.178813934E-6, +0.119209290E-6, +0.178813934E-6, +0.00000000, +0.357627869E-6, +0.417232513E-6, +0.119209290E-6, +0.119209290E-6, +0.596046448E-7, +0.119209290E-6, +0.119209290E-6, +0.596046448E-7, +0.596046448E-7

66reltol = sqrt(epsilon(1._TKG))

67reltol

68+0.345266977E-3

69isClose(data, atad(1:size(data)), reltol = reltol)

70T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

71call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

72

73lenData = getUnifRand(5, 100)

74lenData

75+5

76data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

77data

78+1.1406431501447831, +1.3354951561814052, +1.2928183336275023, +1.5490854749558078, +1.1883439725843368

79

80atad = getFFTR(getFFTF(data))

81atad = atad * 2 / size(atad)

82atad

83+1.1406431501447831, +1.3354951561814052, +1.2928183336275023, +1.5490854749558078, +1.1883439725843368, +0.22204460492503131E-15, -0.22204460492503131E-15, +0.11102230246251565E-15

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

85reltol

86+0.14901161193847656E-7

87isClose(data, atad(1:size(data)), reltol = reltol)

88T, T, T, T, T

89call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

90

91lenData = getUnifRand(5, 100)

92lenData

93+56

94data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

95data

96+1.75440796741736041903148699119444670, +1.37572073305706262541989422038980676, +1.71804678883535106799065200290214526, +1.75578443556894323550312021835313895, +1.44735293467142860128966923020053319, +1.22907078766092863347511472452800662, +1.86842353501316584398310550893168281, +1.55696564325464503166411759588171227, +1.88581436402106616276944974433952324, +1.42487385483705565413465966003365473, +1.20264844221037038094585668190982674, +1.41616583344867122672434530715254113, +1.59933700483716550809498530837281588, +1.15876378996295924490911436594747605, +1.63064545695997770603215612908984921, +1.29029825407337118064758501984138431, +1.05815300265892217805638814690871621, +1.53581311603216101000770743313647241, +1.52347356421024674749532262621494773, +1.64583778622685816139980791053766099, +1.56019585818134059088040199460583259, +1.65451261836367458388635510887003751, +1.93229820138579326618162175430704765, +1.46033360168534458761655834444815806, +1.64819455501278654291905363965264359, +1.88156894502870856267783927245773905, +1.66603638105232818121608580957949987, +1.81262900843529837851556728487230299, +1.20312717421698428500763442833762257, +1.65285961474224310357598087225075947, +1.84522464659617841993573399643918624, +1.40977918427572005632875519580255376, +1.51592220999342537224012168589666777, +1.63037706022487899208545192905062426, +1.45088995904387135198431307792702914, +1.65963238709272392021083241157147833, +1.68156163216775913129868358621376054, +1.92358184153449764867849219744246705, +1.66471849541268424268526271072240115, +1.68855584204178105008728309816755437, +1.03968317622462905486895664088857209, +1.81698664579241372667280194893369803, +1.16999880591779742598562474902700636, +1.19988945947747580186069595202322848, +1.05151523280569377088882132617065922, +1.51737653199207511310753748877150652, +1.42160693300405699810005255002854446, +1.35760753122346104666640261926103602, +1.13503260062227176344997752176859049, +1.92733410293207358121941650087745646, +1.71289750534173612801663408560029398, +1.69375060746715505756423035245120489, +1.24950795148433336683126486067716799, +1.01393078078790292443725924293753893, +1.02170965273741525841936882258667868, +1.29794781326668576429407754703941274

97

98atad = getFFTR(getFFTF(data))

99atad = atad * 2 / size(atad)

100atad

101+1.75440796741736041903148699119444689, +1.37572073305706262541989422038980695, +1.71804678883535106799065200290214487, +1.75578443556894323550312021835313856, +1.44735293467142860128966923020053338, +1.22907078766092863347511472452800623, +1.86842353501316584398310550893168320, +1.55696564325464503166411759588171227, +1.88581436402106616276944974433952363, +1.42487385483705565413465966003365454, +1.20264844221037038094585668190982674, +1.41616583344867122672434530715254094, +1.59933700483716550809498530837281627, +1.15876378996295924490911436594747586, +1.63064545695997770603215612908984959, +1.29029825407337118064758501984138392, +1.05815300265892217805638814690871640, +1.53581311603216101000770743313647260, +1.52347356421024674749532262621494735, +1.64583778622685816139980791053766099, +1.56019585818134059088040199460583259, +1.65451261836367458388635510887003771, +1.93229820138579326618162175430704746, +1.46033360168534458761655834444815844, +1.64819455501278654291905363965264378, +1.88156894502870856267783927245773886, +1.66603638105232818121608580957949948, +1.81262900843529837851556728487230299, +1.20312717421698428500763442833762218, +1.65285961474224310357598087225075947, +1.84522464659617841993573399643918605, +1.40977918427572005632875519580255376, +1.51592220999342537224012168589666816, +1.63037706022487899208545192905062426, +1.45088995904387135198431307792702895, +1.65963238709272392021083241157147775, +1.68156163216775913129868358621376054, +1.92358184153449764867849219744246705, +1.66471849541268424268526271072240115, +1.68855584204178105008728309816755475, +1.03968317622462905486895664088857228, +1.81698664579241372667280194893369822, +1.16999880591779742598562474902700636, +1.19988945947747580186069595202322867, +1.05151523280569377088882132617065922, +1.51737653199207511310753748877150672, +1.42160693300405699810005255002854446, +1.35760753122346104666640261926103622, +1.13503260062227176344997752176859068, +1.92733410293207358121941650087745646, +1.71289750534173612801663408560029378, +1.69375060746715505756423035245120450, +1.24950795148433336683126486067716818, +1.01393078078790292443725924293753874, +1.02170965273741525841936882258667868, +1.29794781326668576429407754703941274, +0.192592994438723585305597794258492732E-33, +0.288889491658085377958396691387739098E-33, +0.962964972193617926527988971292463659E-34, +0.192592994438723585305597794258492732E-33, -0.288889491658085377958396691387739098E-33, -0.385185988877447170611195588516985464E-33, +0.00000000000000000000000000000000000, -0.192592994438723585305597794258492732E-33

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

103reltol

104+0.138777878078144567552953958511352539E-16

105isClose(data, atad(1:size(data)), reltol = reltol)

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

107call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

108

109lenData = getUnifRand(5, 100)

110lenData

111+89

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

113data

114(+1.31102109, +0.757225513), (+1.71525836, +0.215270221), (+1.10544848, +0.278623819), (+1.99447680, +0.900681496), (+1.79355049, +0.275364041), (+1.53165722, +0.941103041), (+1.97395015, +0.384381235), (+1.00721121, +0.752579451), (+1.64961886, +0.128082454), (+1.67663658, +0.856807411), (+1.71169186, +0.277390003), (+1.46627867, +0.802962184E-1), (+1.55648184, +0.728902161), (+1.94388580, +0.714847207), (+1.07826114, +0.755888999), (+1.95375800, +0.396801889), (+1.43315363, +0.176451445), (+1.04513109, +0.771216452), (+1.73742414, +0.578356743), (+1.83237410, +0.199857116), (+1.47664547, +0.909258246), (+1.67014706, +0.959771276E-1), (+1.45134807, +0.221768320), (+1.00972629, +0.952544212), (+1.48987031, +0.311609507), (+1.19435096, +0.603837430), (+1.53688169, +0.208338678), (+1.42823398, +0.226907372), (+1.27582455, +0.535555303), (+1.92600262, +0.146405101E-1), (+1.29083538, +0.206523657), (+1.72006464, +0.263048708), (+1.09386420, +0.221479535), (+1.78698039, +0.586674213), (+1.13025331, +0.172055125), (+1.08482718, +0.903653979), (+1.90682793, +0.568373799), (+1.16915035, +0.383570969), (+1.60341978, +0.847031713), (+1.58990240, +0.783954978), (+1.39408696, +0.724919498), (+1.80643475, +0.898195565), (+1.67395389, +0.501606941), (+1.67731667, +0.455545247), (+1.25647295, +0.715970397), (+1.89582193, +0.620481253), (+1.42056978, +0.619821548E-1), (+1.28499389, +0.496908844), (+1.05806231, +0.910172760), (+1.40984786, +0.967889071), (+1.33340609, +0.237192690), (+1.73024917, +0.162451923), (+1.76573873, +0.609782159), (+1.94721293, +0.984765172), (+1.46817541, +0.892524421), (+1.93303645, +0.452120960), (+1.66016281, +0.629022419), (+1.87530661, +0.164658129), (+1.78333831, +0.750520945), (+1.79960990, +0.757913470), (+1.34946156, +0.838714659), (+1.71182430, +0.441066921), (+1.24161088, +0.904054761), (+1.57922268, +0.632016301), (+1.45890117, +0.186497986), (+1.66434360, +0.936535358), (+1.27242541, +0.602265060), (+1.31976759, +0.980745196), (+1.27077472, +0.182730079), (+1.20480680, +0.492879510), (+1.72344899, +0.789520383), (+1.30846667, +0.164015889E-1), (+1.29231501, +0.422759414), (+1.03665614, +0.227379382), (+1.23495960, +0.364741206), (+1.15536034, +0.321222603), (+1.62139201, +0.802840114), (+1.68799067, +0.652909100), (+1.73573041, +0.373855054), (+1.18619049, +0.354571700), (+1.92190170, +0.527439415), (+1.01148367, +0.365948081E-1), (+1.80684948, +0.455643475), (+1.54571486, +0.178189099), (+1.80437255, +0.195587277), (+1.11838198, +0.649090111), (+1.38779640, +0.843261361), (+1.66926515, +0.233065128), (+1.88988948, +0.902323127E-1)

115

116atad = getFFTR(getFFTF(data))

117atad = atad / size(atad)

118atad

119(+1.31102109, +0.757225513), (+1.71525824, +0.215270400), (+1.10544825, +0.278623968), (+1.99447656, +0.900681436), (+1.79355037, +0.275363863), (+1.53165710, +0.941103041), (+1.97395003, +0.384381056), (+1.00721109, +0.752579331), (+1.64961910, +0.128082544), (+1.67663658, +0.856807470), (+1.71169198, +0.277390122), (+1.46627879, +0.802963078E-1), (+1.55648196, +0.728902221), (+1.94388580, +0.714847386), (+1.07826138, +0.755888999), (+1.95375764, +0.396801889), (+1.43315339, +0.176451534), (+1.04513121, +0.771216512), (+1.73742390, +0.578356683), (+1.83237386, +0.199856937), (+1.47664559, +0.909258127), (+1.67014682, +0.959773958E-1), (+1.45134807, +0.221768409), (+1.00972629, +0.952543974), (+1.48987043, +0.311609745), (+1.19435108, +0.603837609), (+1.53688192, +0.208338976), (+1.42823398, +0.226907656), (+1.27582467, +0.535555542), (+1.92600274, +0.146407112E-1), (+1.29083562, +0.206523821), (+1.72006440, +0.263048738), (+1.09386420, +0.221479416), (+1.78698039, +0.586674094), (+1.13025331, +0.172055155), (+1.08482718, +0.903653860), (+1.90682817, +0.568373561), (+1.16915035, +0.383570910), (+1.60341990, +0.847031593), (+1.58990264, +0.783954799), (+1.39408708, +0.724919438), (+1.80643475, +0.898195386), (+1.67395401, +0.501606941), (+1.67731678, +0.455545247), (+1.25647306, +0.715970397), (+1.89582193, +0.620481253), (+1.42056990, +0.619822443E-1), (+1.28499365, +0.496908784), (+1.05806208, +0.910172701), (+1.40984774, +0.967888832), (+1.33340609, +0.237192586), (+1.73024917, +0.162451833), (+1.76573884, +0.609781861), (+1.94721270, +0.984764993), (+1.46817541, +0.892524302), (+1.93303621, +0.452120632), (+1.66016281, +0.629022479), (+1.87530661, +0.164658397), (+1.78333819, +0.750520825), (+1.79960966, +0.757913351), (+1.34946179, +0.838714600), (+1.71182418, +0.441066951), (+1.24161100, +0.904054701), (+1.57922244, +0.632016063), (+1.45890117, +0.186498076), (+1.66434348, +0.936535358), (+1.27242565, +0.602265000), (+1.31976771, +0.980745018), (+1.27077496, +0.182730079), (+1.20480669, +0.492879450), (+1.72344911, +0.789520264), (+1.30846655, +0.164016187E-1), (+1.29231501, +0.422759503), (+1.03665602, +0.227379411), (+1.23495972, +0.364741206), (+1.15536022, +0.321222544), (+1.62139189, +0.802840233), (+1.68799019, +0.652909219), (+1.73573041, +0.373855054), (+1.18619025, +0.354571640), (+1.92190146, +0.527439475), (+1.01148391, +0.365947187E-1), (+1.80684948, +0.455643207), (+1.54571486, +0.178188980), (+1.80437243, +0.195587367), (+1.11838186, +0.649090052), (+1.38779664, +0.843261123), (+1.66926503, +0.233065099), (+1.88988936, +0.902324095E-1), (+0.119209290E-6, -0.387430191E-6), (+0.298023224E-6, -0.186264515E-6), (+0.119209290E-6, -0.372529030E-6), (+0.357627869E-6, -0.178813934E-6), (-0.596046448E-7, +0.521540642E-7), (+0.298023224E-6, +0.134110451E-6), (+0.596046448E-7, -0.298023224E-7), (-0.178813934E-6, +0.596046448E-7), (+0.00000000, +0.894069672E-7), (+0.119209290E-6, +0.149011612E-6), (+0.178813934E-6, +0.894069672E-7), (+0.178813934E-6, +0.327825546E-6), (+0.00000000, +0.223517418E-6), (+0.238418579E-6, +0.327825546E-6), (-0.596046448E-7, +0.298023224E-6), (+0.596046448E-7, +0.00000000), (+0.238418579E-6, -0.298023224E-7), (+0.298023224E-6, +0.119209290E-6), (+0.119209290E-6, +0.149011612E-7), (+0.178813934E-6, +0.00000000), (+0.00000000, +0.298023224E-7), (+0.238418579E-6, +0.894069672E-7), (-0.596046448E-7, +0.134110451E-6), (-0.596046448E-7, +0.596046448E-7), (+0.298023224E-6, +0.149011612E-6), (+0.238418579E-6, +0.134110451E-6), (+0.417232513E-6, +0.223517418E-7), (+0.357627869E-6, +0.149011612E-6), (+0.178813934E-6, +0.596046448E-7), (+0.298023224E-6, +0.178813934E-6), (+0.119209290E-6, +0.327825546E-6), (+0.238418579E-6, -0.208616257E-6), (+0.238418579E-6, -0.968575478E-7), (+0.357627869E-6, -0.298023224E-7), (+0.178813934E-6, +0.00000000), (+0.298023224E-6, +0.00000000), (+0.178813934E-6, -0.149011612E-6), (+0.00000000, +0.119209290E-6), (+0.596046448E-7, +0.894069672E-7)

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

121reltol

122+0.345266977E-3

123isClose(data, atad(1:size(data)), reltol = reltol)

124T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

125call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

126

127lenData = getUnifRand(5, 100)

128lenData

129+73

130data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

131data

132(+1.0133682491995351, +0.82294907780062732), (+1.9024104565794437, +0.53916586468086625), (+1.7756539255686694, +0.80973194880630928E-1), (+1.6718218565570313, +0.32982647629079320), (+1.7516132732730325, +0.17890708152775447), (+1.7866884501193350, +0.80977247508891947), (+1.9287251357090125, +0.16575741730237836), (+1.5847607256316292, +0.46324088526372198), (+1.0084704425177886, +0.97167423982035617), (+1.4139185108487622, +0.98075389227632459), (+1.1628725270405729, +0.30989661737900343), (+1.9279754433404512, +0.94269304141298016), (+1.5008777986170485, +0.15268970067077869), (+1.6542039218393707, +0.65701077594535728), (+1.2393798093446149, +0.42218027755749277), (+1.2033862118793897, +0.74700829539485814), (+1.6139176872217758, +0.97524003921241142), (+1.2500677459184772, +0.77425144250493072E-1), (+1.3479830859776833, +0.10035717552174006), (+1.2022275582029769, +0.25511923613274967), (+1.9761839836169224, +0.79546815113774438), (+1.3602698473951200, +0.77837225767182439), (+1.8364670169206101, +0.27124295832092349), (+1.5252012600173441, +0.70225787050906763E-1), (+1.8378300896966837, +0.48842958647985002), (+1.8603392152940266, +0.79093456673273055), (+1.7270450255590801, +0.22301068227236887), (+1.2770920896453664, +0.68152836830807695), (+1.5539004118065942, +0.34574471669120332), (+1.7571593466344750, +0.67483467573731859), (+1.0958611836301935, +0.31880433175289158), (+1.3761899669160935, +0.27959104845772575E-1), (+1.1413100478046685, +0.65836885119645927), (+1.9142224074971064, +0.21044141925646642), (+1.2464268670400303, +0.46736338289558621), (+1.7237111469579944, +0.69507365989408876), (+1.9976464091775696, +0.33661321576381031), (+1.1393749403427385, +0.64664945625212522), (+1.5769382868757753, +0.35384639949415386), (+1.2506531843207482, +0.71267254664917989), (+1.9495278759214016, +0.33372766085887695), (+1.3795583141248131, +0.15225649291140531), (+1.5391586710168439, +0.94086062228041445), (+1.4230177220360418, +0.80465993858956919), (+1.7995535483930434, +0.43553998778751724), (+1.8521962349394503, +0.13287710271503128), (+1.3309295711560059, +0.24299755566481607), (+1.1730744878670227, +0.40652749990207626E-1), (+1.6613285751622926, +0.79478083040776637), (+1.4809326964555125, +0.45746126589059033), (+1.2316161619839401, +0.37423433925032956), (+1.2206643367281504, +0.48693681229206920), (+1.7377002061486171, +0.15449115074374942), (+1.4191993533274507, +0.44108186649777226E-2), (+1.2369878767415441, +0.61334792043646191), (+1.9695444095089440, +0.90568163131662127), (+1.6324365903715905, +0.98936655271599649), (+1.6307640916610016, +0.68529341522633114), (+1.4096982791474233, +0.87680043966629873E-1), (+1.0712083040794953, +0.45527565815773274), (+1.7415819792691036, +0.51709011825168461), (+1.4773732785426339, +0.95171694291742104), (+1.7636150104928543, +0.26563922601806667), (+1.3179293002631534, +0.80967595316718632), (+1.1389740345708517, +0.54393013595313111), (+1.1886421706399775, +0.84619009966001801E-1), (+1.7920309463042434, +0.59285393575268253), (+1.4152907075264978, +0.51246800240152035), (+1.1486938510734339, +0.56971443854185189), (+1.6196218186397835, +0.92384803633339019), (+1.3653982335856152, +0.25442101014637619E-1), (+1.0593216280923521, +0.74605260545996810E-2), (+1.7841708102826979, +0.81808316811602422)

133

134atad = getFFTR(getFFTF(data))

135atad = atad / size(atad)

136atad

137(+1.0133682491995348, +0.82294907780062720), (+1.9024104565794440, +0.53916586468086658), (+1.7756539255686694, +0.80973194880630928E-1), (+1.6718218565570315, +0.32982647629079365), (+1.7516132732730318, +0.17890708152775436), (+1.7866884501193345, +0.80977247508891947), (+1.9287251357090123, +0.16575741730237786), (+1.5847607256316292, +0.46324088526372231), (+1.0084704425177884, +0.97167423982035650), (+1.4139185108487622, +0.98075389227632481), (+1.1628725270405731, +0.30989661737900343), (+1.9279754433404508, +0.94269304141298060), (+1.5008777986170481, +0.15268970067077897), (+1.6542039218393707, +0.65701077594535762), (+1.2393798093446149, +0.42218027755749288), (+1.2033862118793897, +0.74700829539485825), (+1.6139176872217753, +0.97524003921241131), (+1.2500677459184772, +0.77425144250493003E-1), (+1.3479830859776833, +0.10035717552174005), (+1.2022275582029769, +0.25511923613274984), (+1.9761839836169217, +0.79546815113774394), (+1.3602698473951200, +0.77837225767182439), (+1.8364670169206097, +0.27124295832092316), (+1.5252012600173444, +0.70225787050906763E-1), (+1.8378300896966833, +0.48842958647984996), (+1.8603392152940266, +0.79093456673273055), (+1.7270450255590801, +0.22301068227236887), (+1.2770920896453664, +0.68152836830807695), (+1.5539004118065938, +0.34574471669120327), (+1.7571593466344750, +0.67483467573731848), (+1.0958611836301935, +0.31880433175289141), (+1.3761899669160935, +0.27959104845772503E-1), (+1.1413100478046685, +0.65836885119645894), (+1.9142224074971066, +0.21044141925646626), (+1.2464268670400303, +0.46736338289558588), (+1.7237111469579944, +0.69507365989408876), (+1.9976464091775692, +0.33661321576380976), (+1.1393749403427385, +0.64664945625212522), (+1.5769382868757753, +0.35384639949415353), (+1.2506531843207487, +0.71267254664917967), (+1.9495278759214012, +0.33372766085887673), (+1.3795583141248131, +0.15225649291140519), (+1.5391586710168441, +0.94086062228041423), (+1.4230177220360414, +0.80465993858956919), (+1.7995535483930429, +0.43553998778751690), (+1.8521962349394501, +0.13287710271503139), (+1.3309295711560059, +0.24299755566481579), (+1.1730744878670225, +0.40652749990207598E-1), (+1.6613285751622926, +0.79478083040776615), (+1.4809326964555125, +0.45746126589059022), (+1.2316161619839403, +0.37423433925032928), (+1.2206643367281504, +0.48693681229206914), (+1.7377002061486166, +0.15449115074374892), (+1.4191993533274507, +0.44108186649777226E-2), (+1.2369878767415443, +0.61334792043646169), (+1.9695444095089443, +0.90568163131662083), (+1.6324365903715901, +0.98936655271599627), (+1.6307640916610011, +0.68529341522633080), (+1.4096982791474233, +0.87680043966629789E-1), (+1.0712083040794951, +0.45527565815773247), (+1.7415819792691032, +0.51709011825168372), (+1.4773732785426335, +0.95171694291742037), (+1.7636150104928539, +0.26563922601806622), (+1.3179293002631534, +0.80967595316718555), (+1.1389740345708514, +0.54393013595313100), (+1.1886421706399772, +0.84619009966002079E-1), (+1.7920309463042434, +0.59285393575268241), (+1.4152907075264980, +0.51246800240152035), (+1.1486938510734339, +0.56971443854185178), (+1.6196218186397831, +0.92384803633339008), (+1.3653982335856154, +0.25442101014637508E-1), (+1.0593216280923521, +0.74605260545993479E-2), (+1.7841708102826976, +0.81808316811602444), (-0.22204460492503131E-15, -0.38857805861880479E-15), (+0.0000000000000000, -0.36082248300317588E-15), (-0.22204460492503131E-15, -0.44408920985006262E-15), (+0.11102230246251565E-15, -0.38857805861880479E-15), (+0.22204460492503131E-15, -0.22204460492503131E-15), (+0.22204460492503131E-15, -0.33306690738754696E-15), (+0.33306690738754696E-15, -0.22204460492503131E-15), (+0.11102230246251565E-15, -0.11102230246251565E-15), (+0.0000000000000000, -0.69388939039072284E-16), (+0.55511151231257827E-15, -0.12490009027033011E-15), (+0.11102230246251565E-15, -0.16653345369377348E-15), (+0.22204460492503131E-15, +0.55511151231257827E-16), (-0.11102230246251565E-15, +0.16653345369377348E-15), (+0.44408920985006262E-15, +0.11102230246251565E-15), (+0.22204460492503131E-15, +0.22204460492503131E-15), (+0.11102230246251565E-15, -0.27755575615628914E-15), (+0.0000000000000000, +0.55511151231257827E-16), (+0.22204460492503131E-15, -0.16653345369377348E-15), (+0.0000000000000000, -0.11102230246251565E-15), (+0.33306690738754696E-15, -0.55511151231257827E-16), (+0.22204460492503131E-15, +0.22204460492503131E-15), (+0.11102230246251565E-15, +0.55511151231257827E-16), (+0.55511151231257827E-15, +0.23939183968479938E-15), (-0.11102230246251565E-15, +0.55511151231257827E-16), (-0.22204460492503131E-15, +0.33306690738754696E-15), (-0.22204460492503131E-15, +0.83266726846886741E-16), (-0.11102230246251565E-15, +0.11102230246251565E-15), (+0.0000000000000000, +0.33306690738754696E-15), (-0.55511151231257827E-15, +0.22204460492503131E-15), (-0.22204460492503131E-15, +0.13877787807814457E-15), (+0.11102230246251565E-15, +0.22204460492503131E-15), (-0.22204460492503131E-15, +0.0000000000000000), (+0.11102230246251565E-15, -0.11102230246251565E-15), (-0.22204460492503131E-15, +0.11102230246251565E-15), (-0.11102230246251565E-15, -0.22204460492503131E-15), (+0.11102230246251565E-15, +0.22204460492503131E-15), (+0.22204460492503131E-15, +0.22204460492503131E-15), (+0.22204460492503131E-15, +0.55511151231257827E-16), (+0.44408920985006262E-15, +0.83266726846886741E-16), (-0.22204460492503131E-15, +0.0000000000000000), (+0.0000000000000000, +0.83266726846886741E-16), (+0.33306690738754696E-15, +0.27755575615628914E-15), (+0.11102230246251565E-15, +0.55511151231257827E-16), (+0.11102230246251565E-15, +0.38857805861880479E-15), (+0.0000000000000000, +0.33306690738754696E-15), (-0.33306690738754696E-15, +0.33306690738754696E-15), (+0.22204460492503131E-15, +0.44408920985006262E-15), (+0.22204460492503131E-15, +0.55511151231257827E-16), (+0.11102230246251565E-15, +0.49960036108132044E-15), (+0.44408920985006262E-15, +0.24980018054066022E-15), (+0.22204460492503131E-15, +0.38857805861880479E-15), (-0.22204460492503131E-15, +0.77715611723760958E-15), (+0.11102230246251565E-15, +0.44408920985006262E-15), (+0.11102230246251565E-15, +0.69388939039072284E-15), (+0.33306690738754696E-15, +0.94368957093138306E-15)

138reltol = sqrt(epsilon(1._TKG))

139reltol

140+0.14901161193847656E-7

141isClose(data, atad(1:size(data)), reltol = reltol)

142T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

143call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

144

145lenData = getUnifRand(5, 100)

146lenData

147+64

148data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

149data

150(+1.70853336300687200654182478202292647, +0.522433835743235909846236049559993974), (+1.83329810955915914500048525500995211, +0.429693193707598566715314878079697268), (+1.68922631332709068832298553519564867, +0.839795682846277581859407773886499328), (+1.42103451212658197005555456366972364, +0.583572626764809175715678142655276845), (+1.05637105083556975641947393962582692, +0.497279399830100176618965224796328314), (+1.92981095332507137922812610365538030, +0.688551790426724893787920658406898538), (+1.64110383676549888039852514797200841, +0.787940930595649440790148233143304249), (+1.77582059013297112968611412955067165, +0.886185536277443130942380818737505005), (+1.15410685398788299189842340895869744, +0.553391397208414410963593211341949687E-1), (+1.50561604987718368345496829287501257, +0.398889682483041860813323588960089974), (+1.71839348700599969013281361427968064, +0.696153474267596725896102483361201574), (+1.82891641566834917607669405234869852, +0.262253454787572903924941754216504136), (+1.09390548758625076220520320455978555, +0.735858105392458051041994833792952107), (+1.51639321253417309186967638163475441, +0.120426333350273068418146240043089741), (+1.31629069738261122239303400656386462, +0.450217913241366404073539576945556020), (+1.75546859703795854425446918774635946, +0.730662287603823150529922385669295727), (+1.91785648770669798333865109256169079, +0.228194835464678849376295329200699715), (+1.36632660002340221186783183448396699, +0.391313259146726724951616808683768863), (+1.62302735775678560302817356533558025, +0.143812476775195134939425909809259521), (+1.17366417645959024945487171831579800, +0.488791730394627148608035940757422138), (+1.00155963521536886091039996934125512, +0.669825498227278472699562564262313899), (+1.69045560483879349801545748892623409, +0.446312561550062969537187129619415702), (+1.05821988606757807336773589877053606, +0.811120330788047754044791741627546072), (+1.45579692559402745087950207641582761, +0.688721047587959640511202241156682890), (+1.74737312990175533389138110087525305, +0.892842504224258313807818690487685053), (+1.80566316502269375971387024439217403, +0.173360908223423493089900508916664776), (+1.29229087441856240696541493665383741, +0.555528381312845784285643222217985095), (+1.25297220875458742847215733758802701, +0.907609087804783761858858198926498458), (+1.11571839276534740625935697899758231, +0.758526991822167137711493104328436464), (+1.45284821955746132845541369341147980, +0.931567634811417983212301334127607077), (+1.19456437857812437139109582774509136, +0.589041131948266411766005809626825034), (+1.58153386572616712797513576657625165, +0.219470405735821838874428706055724909), (+1.76062743071964364622684042854115872, +0.639703602641452899712253352041032124), (+1.75249238219801249807195480709033695, +0.160510076640480428875052074443673699), (+1.20677975871916521163810068839737097, +0.624761200996602625429578463315621985), (+1.54711503632548457357037003735766767, +0.713707914750149598032585825129397597), (+1.22062923291338096834920378047185184, +0.913035783209926672385228500525506872), (+1.34383922549193798475620766576472645, +0.306374098667186360951411575929487110), (+1.91535722048030582814024305998118912, +0.523942842261568004646588175151050206), (+1.64425946369105866060892483816508385, +0.604888242888537781550328900549585603), (+1.34918490537839925515176157993751389, +0.369007224803521103012980959651490911E-2), (+1.90491309463975226002021080129457604, +0.348152437474439364891890372772298687), (+1.68292371561686448034982633377870465, +0.482211633956387261196410074531428981E-1), (+1.44228214889893348332835522967606759, +0.827833888850478583126138654304791214), (+1.30273113311063844981401909331504716, +0.559108490199977754152354709808516454), (+1.72857704600621753855155658486367287, +0.608716330118645137939278049645900697), (+1.98283536535387288887517338450322498, +0.472644427298958319105962198310303782), (+1.90539606477040593989820347791746938, +0.846173281059143641717639346407215343E-1), (+1.53623701227767715057142455578343800, +0.488888841782070069207007664448704327), (+1.21067627839374500352877499736120729, +0.941497788754005171517783908643345782), (+1.17028456479261149071774358932130517, +0.468487284098991015161294322659913475), (+1.26338381567238487837272117427871580, +0.509515312555310695160761816702428893), (+1.00996134270911751072633269146830910, +0.499549650548032332952600272079710834), (+1.92078391331474323365256346386309011, +0.492509105363772250471294143782174559), (+1.29237491736831454470963278959085074, +0.689098683034519700890424499589791488), (+1.58509183617583815931442580271966369, +0.814122437356574115972384188974211329), (+1.00861931390472671935043607768487017, +0.407218013324204642944357350194377641), (+1.70824028900681649051584948370972738, +0.596656071333050897732655146470633232), (+1.38959849239390573893773998695111642, +0.848700885792372582830177296182371256), (+1.92526389918499489912561872225969351, +0.644912527022776487988376706303717391), (+1.12874627664335566945033691494454940, +0.173077340211148615640332402508379609), (+1.37316165087949922934764969905556220, +0.452527150615216003648548150822071516), (+1.32872164709358755345833420244978622, +0.521153637947681369440477091315890833E-1), (+1.46556271064410442235613389915903295, +0.346259994241609225125245377289671857)

151

152atad = getFFTR(getFFTF(data))

153atad = atad / size(atad)

154atad

155(+1.70853336300687200654182478202292647, +0.522433835743235909846236049559993878), (+1.83329810955915914500048525500995230, +0.429693193707598566715314878079697268), (+1.68922631332709068832298553519564867, +0.839795682846277581859407773886499136), (+1.42103451212658197005555456366972345, +0.583572626764809175715678142655276942), (+1.05637105083556975641947393962582692, +0.497279399830100176618965224796328121), (+1.92981095332507137922812610365538050, +0.688551790426724893787920658406898634), (+1.64110383676549888039852514797200841, +0.787940930595649440790148233143304153), (+1.77582059013297112968611412955067165, +0.886185536277443130942380818737505101), (+1.15410685398788299189842340895869763, +0.553391397208414410963593211341948965E-1), (+1.50561604987718368345496829287501276, +0.398889682483041860813323588960089926), (+1.71839348700599969013281361427968064, +0.696153474267596725896102483361201478), (+1.82891641566834917607669405234869814, +0.262253454787572903924941754216504087), (+1.09390548758625076220520320455978555, +0.735858105392458051041994833792952011), (+1.51639321253417309186967638163475460, +0.120426333350273068418146240043089789), (+1.31629069738261122239303400656386462, +0.450217913241366404073539576945555924), (+1.75546859703795854425446918774635927, +0.730662287603823150529922385669295727), (+1.91785648770669798333865109256169060, +0.228194835464678849376295329200699570), (+1.36632660002340221186783183448396699, +0.391313259146726724951616808683768815), (+1.62302735775678560302817356533558044, +0.143812476775195134939425909809259569), (+1.17366417645959024945487171831579800, +0.488791730394627148608035940757422138), (+1.00155963521536886091039996934125493, +0.669825498227278472699562564262313707), (+1.69045560483879349801545748892623448, +0.446312561550062969537187129619415702), (+1.05821988606757807336773589877053606, +0.811120330788047754044791741627546072), (+1.45579692559402745087950207641582742, +0.688721047587959640511202241156682986), (+1.74737312990175533389138110087525305, +0.892842504224258313807818690487684861), (+1.80566316502269375971387024439217442, +0.173360908223423493089900508916664825), (+1.29229087441856240696541493665383761, +0.555528381312845784285643222217985287), (+1.25297220875458742847215733758802682, +0.907609087804783761858858198926498458), (+1.11571839276534740625935697899758231, +0.758526991822167137711493104328436367), (+1.45284821955746132845541369341147999, +0.931567634811417983212301334127607174), (+1.19456437857812437139109582774509136, +0.589041131948266411766005809626824745), (+1.58153386572616712797513576657625184, +0.219470405735821838874428706055724716), (+1.76062743071964364622684042854115872, +0.639703602641452899712253352041031932), (+1.75249238219801249807195480709033715, +0.160510076640480428875052074443673699), (+1.20677975871916521163810068839737097, +0.624761200996602625429578463315622081), (+1.54711503632548457357037003735766748, +0.713707914750149598032585825129397693), (+1.22062923291338096834920378047185165, +0.913035783209926672385228500525506872), (+1.34383922549193798475620766576472645, +0.306374098667186360951411575929487014), (+1.91535722048030582814024305998118912, +0.523942842261568004646588175151049917), (+1.64425946369105866060892483816508385, +0.604888242888537781550328900549585699), (+1.34918490537839925515176157993751408, +0.369007224803521103012980959651469245E-2), (+1.90491309463975226002021080129457624, +0.348152437474439364891890372772298639), (+1.68292371561686448034982633377870465, +0.482211633956387261196410074531430906E-1), (+1.44228214889893348332835522967606759, +0.827833888850478583126138654304791214), (+1.30273113311063844981401909331504735, +0.559108490199977754152354709808516357), (+1.72857704600621753855155658486367326, +0.608716330118645137939278049645900794), (+1.98283536535387288887517338450322479, +0.472644427298958319105962198310303685), (+1.90539606477040593989820347791746919, +0.846173281059143641717639346407214862E-1), (+1.53623701227767715057142455578343781, +0.488888841782070069207007664448704183), (+1.21067627839374500352877499736120748, +0.941497788754005171517783908643345782), (+1.17028456479261149071774358932130517, +0.468487284098991015161294322659913523), (+1.26338381567238487837272117427871580, +0.509515312555310695160761816702428893), (+1.00996134270911751072633269146830890, +0.499549650548032332952600272079710593), (+1.92078391331474323365256346386309050, +0.492509105363772250471294143782174655), (+1.29237491736831454470963278959085054, +0.689098683034519700890424499589791488), (+1.58509183617583815931442580271966369, +0.814122437356574115972384188974211522), (+1.00861931390472671935043607768487056, +0.407218013324204642944357350194377497), (+1.70824028900681649051584948370972777, +0.596656071333050897732655146470633135), (+1.38959849239390573893773998695111661, +0.848700885792372582830177296182371256), (+1.92526389918499489912561872225969332, +0.644912527022776487988376706303717391), (+1.12874627664335566945033691494454920, +0.173077340211148615640332402508379513), (+1.37316165087949922934764969905556258, +0.452527150615216003648548150822071468), (+1.32872164709358755345833420244978603, +0.521153637947681369440477091315887944E-1), (+1.46556271064410442235613389915903295, +0.346259994241609225125245377289671761)

156reltol = sqrt(epsilon(1._TKG))

157reltol

158+0.138777878078144567552953958511352539E-16

159isClose(data, atad(1:size(data)), reltol = reltol)

160T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

161call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

162

163lenData = getUnifRand(5, 100)

164lenData

165+11

166data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

167data

168+1.82269776, +1.00820327, +1.51413941, +1.19090438, +1.11147666, +1.01579499, +1.55092752, +1.59855902, +1.38079977, +1.19610751, +1.50574398

169

170atad = getFFTR(getFFTF(data))

171atad = atad * 2 / size(atad)

172atad

173+1.82269764, +1.00820327, +1.51413918, +1.19090438, +1.11147666, +1.01579475, +1.55092728, +1.59855866, +1.38079977, +1.19610739, +1.50574374, +0.178813934E-6, -0.119209290E-6, +0.238418579E-6, +0.119209290E-6, +0.357627869E-6

174reltol = sqrt(epsilon(1._TKG))

175reltol

176+0.345266977E-3

177isClose(data, atad(1:size(data)), reltol = reltol)

178T, T, T, T, T, T, T, T, T, T, T

179call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

180

181lenData = getUnifRand(5, 100)

182lenData

183+55

184data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

185data

186+1.5347294960611793, +1.7294131920991829, +1.5623557225654903, +1.0836875375648938, +1.1023259389804763, +1.3395751841842636, +1.6084261445501049, +1.7695249729857376, +1.1412655649994847, +1.3735227443901241, +1.2198204486769266, +1.5703537340581071, +1.0563561472055647, +1.2882103284389406, +1.5011793447616604, +1.0285771529408363, +1.5331857894615086, +1.2008134585319175, +1.5009186572463125, +1.9591400832678927, +1.6156023554488246, +1.2764799209439710, +1.1950124878413659, +1.2508790761109205, +1.5247068717886012, +1.0871341241254613, +1.3397946353115260, +1.3163828394120385, +1.0705107087606736, +1.5707495410798948, +1.9078006306551831, +1.0561784798610518, +1.9550818554000355, +1.1082736960882165, +1.7242301811884313, +1.7853711509897994, +1.2295711210253217, +1.3510342314637418, +1.7497770653695102, +1.4181403413354965, +1.8008179091504095, +1.9069265819441354, +1.7911851278738666, +1.8394865661133064, +1.5961140469311172, +1.9549080717348177, +1.7971559681868681, +1.4134374900011366, +1.7914224535223924, +1.8867975391868799, +1.3178728531961039, +1.9959254985999793, +1.1610034689654796, +1.2143880420164694, +1.0024518049087252

187

188atad = getFFTR(getFFTF(data))

189atad = atad * 2 / size(atad)

190atad

191+1.5347294960611795, +1.7294131920991833, +1.5623557225654903, +1.0836875375648942, +1.1023259389804767, +1.3395751841842636, +1.6084261445501051, +1.7695249729857374, +1.1412655649994847, +1.3735227443901243, +1.2198204486769266, +1.5703537340581071, +1.0563561472055649, +1.2882103284389408, +1.5011793447616608, +1.0285771529408365, +1.5331857894615086, +1.2008134585319177, +1.5009186572463129, +1.9591400832678929, +1.6156023554488246, +1.2764799209439712, +1.1950124878413662, +1.2508790761109205, +1.5247068717886008, +1.0871341241254613, +1.3397946353115260, +1.3163828394120385, +1.0705107087606736, +1.5707495410798948, +1.9078006306551827, +1.0561784798610516, +1.9550818554000358, +1.1082736960882169, +1.7242301811884317, +1.7853711509897998, +1.2295711210253220, +1.3510342314637420, +1.7497770653695104, +1.4181403413354965, +1.8008179091504095, +1.9069265819441357, +1.7911851278738666, +1.8394865661133064, +1.5961140469311175, +1.9549080717348177, +1.7971559681868683, +1.4134374900011364, +1.7914224535223924, +1.8867975391868799, +1.3178728531961044, +1.9959254985999795, +1.1610034689654798, +1.2143880420164692, +1.0024518049087257, -0.11102230246251565E-15, +0.22204460492503131E-15, +0.44408920985006262E-15, +0.88817841970012523E-15, +0.55511151231257827E-15, +0.66613381477509392E-15, +0.44408920985006262E-15, +0.12212453270876722E-14, +0.66613381477509392E-15

192reltol = sqrt(epsilon(1._TKG))

193reltol

194+0.14901161193847656E-7

195isClose(data, atad(1:size(data)), reltol = reltol)

196T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

197call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

198

199lenData = getUnifRand(5, 100)

200lenData

201+60

202data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

203data

204+1.30990427443429664509515289488732135, +1.55477905262944578828262578389216659, +1.14327638072919906767295878319864276, +1.63218091843242557532558703951913130, +1.38324617850074045344733126553099266, +1.25568413546844432101681203351881396, +1.72025489142269349507165266790775479, +1.02462804906166734331443525108503070, +1.92432080529120603895568640653828055, +1.55183759751263730119457930353810458, +1.61393233430758428842567537410141582, +1.75401559683122508012660078513096052, +1.17552185572437091770180106512706490, +1.35712669990745868071258700273415533, +1.81413882877905184757603557927348211, +1.60033155793275455576049173264293160, +1.76634204372500052654839994576755460, +1.22588103059036023394738855404171573, +1.47868147685783044000072089362925265, +1.12596586424496658108273323643027623, +1.84440230076837476466878766136706871, +1.06840668299427994223082958847054814, +1.28373408254257596982620686445357665, +1.24408307343480690823637276103969187, +1.73680821548234540410628060550586816, +1.43714663217456828579328837154980566, +1.04545871306546098661936903359741541, +1.90601753252847014743990241401758300, +1.39679604984631297991595529241418398, +1.97363456752210568269068398630696975, +1.75543909041729359483779431725854511, +1.24936519554567156997287522588824272, +1.80967738478753837514107817426564379, +1.20144163755024095755149566963127227, +1.42708044872241841983733283817725869, +1.06142430567801584874258256763900445, +1.30487775146353424225416279147995877, +1.51960273758239792913871648320223244, +1.30043714019038082854964904049577901, +1.24561264748478911842161946875484678, +1.19766140875841356535234055882364101, +1.26520850319628879416326105782469642, +1.70775890442015728226447035792678182, +1.91475321446454401998322228203796332, +1.39895063008336853145961912971478260, +1.33537488583710021217822959884914930, +1.73172335823315555556173450983440400, +1.30583378221918397936640026877084651, +1.76577214561939118813834369839250552, +1.05564007648869571237585096392646604, +1.48515384552657776081910382867584925, +1.09319107555397341242889844978683478, +1.15794461022358126543726726694011286, +1.70571226823718752290254095924964439, +1.03581307032049049455727741434065788, +1.17012383115738500511613802372949858, +1.18001228561915420478278417507446596, +1.35821974721431565000083125107352174, +1.58337140298845682258523225471229995, +1.30458658479456338946429860343972991

205

206atad = getFFTR(getFFTF(data))

207atad = atad * 2 / size(atad)

208atad

209+1.30990427443429664509515289488732135, +1.55477905262944578828262578389216679, +1.14327638072919906767295878319864276, +1.63218091843242557532558703951913168, +1.38324617850074045344733126553099247, +1.25568413546844432101681203351881396, +1.72025489142269349507165266790775479, +1.02462804906166734331443525108503070, +1.92432080529120603895568640653828036, +1.55183759751263730119457930353810458, +1.61393233430758428842567537410141582, +1.75401559683122508012660078513096052, +1.17552185572437091770180106512706490, +1.35712669990745868071258700273415513, +1.81413882877905184757603557927348250, +1.60033155793275455576049173264293160, +1.76634204372500052654839994576755460, +1.22588103059036023394738855404171592, +1.47868147685783044000072089362925284, +1.12596586424496658108273323643027661, +1.84440230076837476466878766136706851, +1.06840668299427994223082958847054814, +1.28373408254257596982620686445357665, +1.24408307343480690823637276103969225, +1.73680821548234540410628060550586777, +1.43714663217456828579328837154980566, +1.04545871306546098661936903359741541, +1.90601753252847014743990241401758300, +1.39679604984631297991595529241418360, +1.97363456752210568269068398630696975, +1.75543909041729359483779431725854473, +1.24936519554567156997287522588824310, +1.80967738478753837514107817426564359, +1.20144163755024095755149566963127246, +1.42708044872241841983733283817725888, +1.06142430567801584874258256763900464, +1.30487775146353424225416279147995857, +1.51960273758239792913871648320223244, +1.30043714019038082854964904049577863, +1.24561264748478911842161946875484678, +1.19766140875841356535234055882364082, +1.26520850319628879416326105782469642, +1.70775890442015728226447035792678182, +1.91475321446454401998322228203796332, +1.39895063008336853145961912971478240, +1.33537488583710021217822959884914949, +1.73172335823315555556173450983440400, +1.30583378221918397936640026877084670, +1.76577214561939118813834369839250533, +1.05564007648869571237585096392646604, +1.48515384552657776081910382867584944, +1.09319107555397341242889844978683478, +1.15794461022358126543726726694011247, +1.70571226823718752290254095924964439, +1.03581307032049049455727741434065768, +1.17012383115738500511613802372949877, +1.18001228561915420478278417507446576, +1.35821974721431565000083125107352155, +1.58337140298845682258523225471229976, +1.30458658479456338946429860343973010, -0.288889491658085377958396691387739098E-33, -0.288889491658085377958396691387739098E-33, -0.674075480535532548569592279904724561E-33, -0.288889491658085377958396691387739098E-33

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

211reltol

212+0.138777878078144567552953958511352539E-16

213isClose(data, atad(1:size(data)), reltol = reltol)

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

215call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

216

217lenData = getUnifRand(5, 100)

218lenData

219+15

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

221data

222(+1.20908642, +0.990785837), (+1.59353924, +0.758457780E-1), (+1.51655650, +0.463270724), (+1.13107729, +0.613232195), (+1.64414358, +0.940283477), (+1.99446559, +0.393959880E-1), (+1.12604856, +0.464112937), (+1.56641471, +0.955671668), (+1.68582940, +0.856388330), (+1.70615458, +0.549200475), (+1.08319092, +0.641266644), (+1.94630313, +0.424390972), (+1.92281520, +0.559256315), (+1.99413478, +0.852257550), (+1.92341614, +0.257786810)

223

224atad = getFFTR(getFFTF(data))

225atad = atad / size(atad)

226atad

227(+1.20908630, +0.990785837), (+1.59353936, +0.758458078E-1), (+1.51655638, +0.463270634), (+1.13107717, +0.613232136), (+1.64414370, +0.940283537), (+1.99446547, +0.393960476E-1), (+1.12604833, +0.464112937), (+1.56641483, +0.955671489), (+1.68582928, +0.856388330), (+1.70615447, +0.549200535), (+1.08319080, +0.641266584), (+1.94630301, +0.424390882), (+1.92281520, +0.559256315), (+1.99413455, +0.852257669), (+1.92341590, +0.257786810), (+0.596046448E-7, -0.596046448E-7)

228reltol = sqrt(epsilon(1._TKG))

229reltol

230+0.345266977E-3

231isClose(data, atad(1:size(data)), reltol = reltol)

232T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

233call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

234

235lenData = getUnifRand(5, 100)

236lenData

237+18

238data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

239data

240(+1.0328091319124610, +0.83220361712123758), (+1.1242434978187501, +0.33839801667317893), (+1.9920852790513086, +0.46811067035321341), (+1.0091172524809509, +0.36020914848679819), (+1.5169061683791099, +0.90541229340895146E-1), (+1.8516217772790797, +0.64919479701391158), (+1.6599073729898390, +0.14037914450816635), (+1.8232928610837691, +0.39807944033808762), (+1.5705719449807338, +0.46424445327538755E-1), (+1.3398789943560221, +0.85710954194869726), (+1.8379216150752176, +0.92010817532033262), (+1.3234568836264533, +0.98526001750473458), (+1.8626078230662801, +0.21107445443618933), (+1.6070806376483402, +0.61202520519322801), (+1.2019935837456743, +0.41392225146186867), (+1.8174566146558098, +0.19687557799861999), (+1.1674514894452930, +0.33872609457422620), (+1.6624184894242688, +0.26962021759572696)

241

242atad = getFFTR(getFFTF(data))

243atad = atad / size(atad)

244atad

245(+1.0328091319124608, +0.83220361712123747), (+1.1242434978187499, +0.33839801667317915), (+1.9920852790513086, +0.46811067035321358), (+1.0091172524809506, +0.36020914848679869), (+1.5169061683791099, +0.90541229340895188E-1), (+1.8516217772790793, +0.64919479701391181), (+1.6599073729898390, +0.14037914450816652), (+1.8232928610837686, +0.39807944033808795), (+1.5705719449807338, +0.46424445327538609E-1), (+1.3398789943560219, +0.85710954194869715), (+1.8379216150752173, +0.92010817532033240), (+1.3234568836264531, +0.98526001750473424), (+1.8626078230662799, +0.21107445443618927), (+1.6070806376483400, +0.61202520519322767), (+1.2019935837456741, +0.41392225146186845), (+1.8174566146558093, +0.19687557799861954), (+1.1674514894452930, +0.33872609457422626), (+1.6624184894242686, +0.26962021759572674), (+0.11102230246251565E-15, -0.16653345369377348E-15), (+0.33306690738754696E-15, -0.55511151231257827E-15), (+0.11102230246251565E-15, +0.41633363423443370E-16), (+0.44408920985006262E-15, -0.22204460492503131E-15), (+0.22204460492503131E-15, +0.55511151231257827E-16), (+0.55511151231257827E-15, -0.30531133177191805E-15), (+0.11102230246251565E-15, +0.34694469519536142E-16), (+0.22204460492503131E-15, +0.16653345369377348E-15), (+0.22204460492503131E-15, +0.16653345369377348E-15), (+0.33306690738754696E-15, +0.11102230246251565E-15), (+0.22204460492503131E-15, +0.69388939039072284E-16), (+0.44408920985006262E-15, +0.55511151231257827E-15), (+0.44408920985006262E-15, +0.41633363423443370E-15), (+0.55511151231257827E-15, +0.70776717819853729E-15)

246reltol = sqrt(epsilon(1._TKG))

247reltol

248+0.14901161193847656E-7

249isClose(data, atad(1:size(data)), reltol = reltol)

250T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

251call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

252

253lenData = getUnifRand(5, 100)

254lenData

255+26

256data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

257data

258(+1.23991471786691051992558363033501432, +0.901389228131210797661286177865110682E-1), (+1.81614782695467956529419540767342519, +0.289832017967398059463942442216507632E-1), (+1.47777583639495753065065955069004230, +0.566538880384652589205630418878258603), (+1.62929668194051879227020865745443980, +0.902690010325043992670116135349133962), (+1.64612740090426474925243668526988730, +0.952387631231456877180630145619875577), (+1.28692938918593202218646697255267531, +0.654714138399707776308833327510310506), (+1.83576229239101313895903575409483867, +0.288192867846956521185564609497053349), (+1.53762889732876376130564060959053894, +0.812357790602423048720825558686773395), (+1.49353656527091815259768750803755611, +0.208982103801309268786717582635453056), (+1.93655215044276519247016322354083190, +0.934848386373361005667245638610900265), (+1.95428571147425244655011559280205553, +0.144825830881051188476552223785894632), (+1.80611126987721062021492255311555720, +0.818597542789299237489046400621741748), (+1.17442745257053286336853069440041299, +0.296323055153042813743447318225519976), (+1.70933917400869235727187256135408073, +0.664392498245629910722373829901594640), (+1.92769367666388981433638873995566042, +0.230007021947218352974667754750591883), (+1.16155819587510499881216093171629839, +0.881545327748106624693283662850858877), (+1.46746182878525746781134044199289392, +0.204160964249330057098106765713727446), (+1.34945253549310128634492092559340982, +0.507959524269381843447369098133322466), (+1.71639535340501584490362422259894688, +0.384876013302870900922317393245285655), (+1.38722348371399203061501111750472257, +0.323035873964670277925185322778985398), (+1.60070300319603723041598694622292162, +0.654598700489191175716837783821094166), (+1.11211952828394345596369999346089452, +0.931797526490102619633838536655728478), (+1.12224050636156317729670075805597767, +0.127746472301198976577393054344499805), (+1.50442713843467845179101407468188358, +0.370783654923287404557515317254556028), (+1.76485850720318980341190094992330120, +0.836540732529611732673156200327724423), (+1.76154782705362712850194821895903263, +0.486022133946078082370654453402064907)

259

260atad = getFFTR(getFFTF(data))

261atad = atad / size(atad)

262atad

263(+1.23991471786691051992558363033501413, +0.901389228131210797661286177865111164E-1), (+1.81614782695467956529419540767342519, +0.289832017967398059463942442216509798E-1), (+1.47777583639495753065065955069004249, +0.566538880384652589205630418878258507), (+1.62929668194051879227020865745444019, +0.902690010325043992670116135349134059), (+1.64612740090426474925243668526988730, +0.952387631231456877180630145619875673), (+1.28692938918593202218646697255267550, +0.654714138399707776308833327510310217), (+1.83576229239101313895903575409483906, +0.288192867846956521185564609497053253), (+1.53762889732876376130564060959053932, +0.812357790602423048720825558686773299), (+1.49353656527091815259768750803755573, +0.208982103801309268786717582635453104), (+1.93655215044276519247016322354083209, +0.934848386373361005667245638610900169), (+1.95428571147425244655011559280205553, +0.144825830881051188476552223785894777), (+1.80611126987721062021492255311555720, +0.818597542789299237489046400621741748), (+1.17442745257053286336853069440041299, +0.296323055153042813743447318225519928), (+1.70933917400869235727187256135408073, +0.664392498245629910722373829901594447), (+1.92769367666388981433638873995566042, +0.230007021947218352974667754750592075), (+1.16155819587510499881216093171629839, +0.881545327748106624693283662850858877), (+1.46746182878525746781134044199289372, +0.204160964249330057098106765713727495), (+1.34945253549310128634492092559340982, +0.507959524269381843447369098133322370), (+1.71639535340501584490362422259894707, +0.384876013302870900922317393245286040), (+1.38722348371399203061501111750472296, +0.323035873964670277925185322778985591), (+1.60070300319603723041598694622292162, +0.654598700489191175716837783821094166), (+1.11211952828394345596369999346089490, +0.931797526490102619633838536655728285), (+1.12224050636156317729670075805597767, +0.127746472301198976577393054344499998), (+1.50442713843467845179101407468188416, +0.370783654923287404557515317254556124), (+1.76485850720318980341190094992330081, +0.836540732529611732673156200327724327), (+1.76154782705362712850194821895903301, +0.486022133946078082370654453402065052), (-0.288889491658085377958396691387739098E-33, -0.481482486096808963263994485646231830E-34), (+0.385185988877447170611195588516985464E-33, +0.144444745829042688979198345693869549E-33), (-0.962964972193617926527988971292463659E-34, +0.481482486096808963263994485646231830E-34), (+0.192592994438723585305597794258492732E-33, +0.240741243048404481631997242823115915E-33), (+0.962964972193617926527988971292463659E-34, -0.180555932286303361223997932117336936E-33), (+0.00000000000000000000000000000000000, +0.337037740267766274284796139952362281E-33)

264reltol = sqrt(epsilon(1._TKG))

265reltol

266+0.138777878078144567552953958511352539E-16

267isClose(data, atad(1:size(data)), reltol = reltol)

268T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

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

270

271lenData = getUnifRand(5, 100)

272lenData

273+50

274data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

275data

276+1.53441644, +1.44134545, +1.44633806, +1.84235239, +1.65313411, +1.60422730, +1.34454989, +1.15074277, +1.16948485, +1.86132860, +1.99439609, +1.46186018, +1.02753115, +1.12648964, +1.72704077, +1.46437621, +1.97449160, +1.17283821, +1.18612421, +1.68453920, +1.64654422, +1.89208269, +1.63005829, +1.48880911, +1.96113265, +1.00462544, +1.49084997, +1.99633884, +1.30929208, +1.17928696, +1.21268916, +1.30956364, +1.16688919, +1.55548668, +1.10994840, +1.08486414, +1.35520768, +1.69668484, +1.53748560, +1.55482101, +1.39700687, +1.75042129, +1.90695858, +1.47414970, +1.51890993, +1.57852387, +1.55378199, +1.72817397, +1.19643402, +1.37755263

277

278atad = getFFTR(getFFTF(data))

279atad = atad * 2 / size(atad)

280atad

281+1.53441668, +1.44134569, +1.44633794, +1.84235215, +1.65313435, +1.60422719, +1.34454978, +1.15074253, +1.16948485, +1.86132848, +1.99439597, +1.46185982, +1.02753139, +1.12648940, +1.72704065, +1.46437621, +1.97449172, +1.17283809, +1.18612432, +1.68453908, +1.64654422, +1.89208257, +1.63005829, +1.48880911, +1.96113253, +1.00462544, +1.49084973, +1.99633884, +1.30929208, +1.17928672, +1.21268916, +1.30956376, +1.16688943, +1.55548668, +1.10994816, +1.08486390, +1.35520768, +1.69668472, +1.53748548, +1.55482101, +1.39700699, +1.75042093, +1.90695858, +1.47414958, +1.51890993, +1.57852364, +1.55378211, +1.72817397, +1.19643414, +1.37755263, +0.00000000, +0.119209290E-6, +0.596046448E-7, +0.00000000, +0.596046448E-7, +0.357627869E-6, +0.178813934E-6, +0.119209290E-6, +0.596046448E-7, +0.178813934E-6, +0.238418579E-6, -0.596046448E-7, +0.178813934E-6, +0.357627869E-6

282reltol = sqrt(epsilon(1._TKG))

283reltol

284+0.345266977E-3

285isClose(data, atad(1:size(data)), reltol = reltol)

286T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

287call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

288

289lenData = getUnifRand(5, 100)

290lenData

291+76

292data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

293data

294+1.5870352037237689, +1.3001334452998010, +1.2615654030936378, +1.2387885243153807, +1.3720722755754751, +1.1502154592735669, +1.0849590111020528, +1.4399960860461600, +1.5194795657195883, +1.2265697590174445, +1.1243229230608898, +1.4928455018971156, +1.9392282756350383, +1.4655342678531631, +1.5241766354579849, +1.6545003185812051, +1.9838938677357330, +1.8572384279537486, +1.7915385792565042, +1.4212731948708330, +1.6866063948112437, +1.9383233562276807, +1.2011439715330985, +1.0834268781429535, +1.9529608192746375, +1.0312006639075051, +1.1293356355389621, +1.6351185864991233, +1.5902040025449795, +1.6407025794625913, +1.2713637235945929, +1.6810766652751417, +1.9774141514513546, +1.3557726038821021, +1.2918132944814280, +1.2584201734736209, +1.5753563788647598, +1.5026296591650523, +1.1428292402715425, +1.5145639897993759, +1.4868576105916858, +1.5507750847496582, +1.1640663757675505, +1.2423527509360726, +1.6917086344621795, +1.8942638410565804, +1.1869507151911853, +1.0591837768563566, +1.0225259289879940, +1.9597674679764634, +1.6764031316082795, +1.0908757953307739, +1.6426724902340275, +1.8734702773415637, +1.5613514195735108, +1.0305435937456626, +1.6257198282669911, +1.0299869708218572, +1.3709833846091435, +1.7623305174372486, +1.9641060819722242, +1.9712929166014168, +1.1268896526882997, +1.5261002867503115, +1.5699377949307958, +1.5987186611108819, +1.5406302289283584, +1.3471030906761929, +1.8982271077306023, +1.1696582349503513, +1.0664928436302172, +1.5633852158558752, +1.0778395215332395, +1.1223611404467218, +1.3874104492923180, +1.4596305560544449

295

296atad = getFFTR(getFFTF(data))

297atad = atad * 2 / size(atad)

298atad

299+1.5870352037237692, +1.3001334452998008, +1.2615654030936378, +1.2387885243153809, +1.3720722755754746, +1.1502154592735672, +1.0849590111020526, +1.4399960860461600, +1.5194795657195885, +1.2265697590174445, +1.1243229230608895, +1.4928455018971161, +1.9392282756350376, +1.4655342678531627, +1.5241766354579849, +1.6545003185812053, +1.9838938677357327, +1.8572384279537488, +1.7915385792565037, +1.4212731948708333, +1.6866063948112431, +1.9383233562276807, +1.2011439715330978, +1.0834268781429535, +1.9529608192746373, +1.0312006639075055, +1.1293356355389612, +1.6351185864991236, +1.5902040025449793, +1.6407025794625913, +1.2713637235945923, +1.6810766652751414, +1.9774141514513546, +1.3557726038821016, +1.2918132944814278, +1.2584201734736205, +1.5753563788647602, +1.5026296591650521, +1.1428292402715428, +1.5145639897993750, +1.4868576105916862, +1.5507750847496586, +1.1640663757675507, +1.2423527509360723, +1.6917086344621799, +1.8942638410565795, +1.1869507151911858, +1.0591837768563559, +1.0225259289879944, +1.9597674679764630, +1.6764031316082795, +1.0908757953307731, +1.6426724902340277, +1.8734702773415628, +1.5613514195735108, +1.0305435937456617, +1.6257198282669909, +1.0299869708218568, +1.3709833846091435, +1.7623305174372479, +1.9641060819722242, +1.9712929166014157, +1.1268896526882999, +1.5261002867503106, +1.5699377949307958, +1.5987186611108819, +1.5406302289283580, +1.3471030906761925, +1.8982271077306025, +1.1696582349503510, +1.0664928436302179, +1.5633852158558745, +1.0778395215332393, +1.1223611404467220, +1.3874104492923178, +1.4596305560544451, +0.11102230246251565E-14, +0.11102230246251565E-15, +0.22204460492503131E-15, -0.22204460492503131E-15, -0.33306690738754696E-15, -0.22204460492503131E-15, +0.33306690738754696E-15, -0.66613381477509392E-15, +0.66613381477509392E-15, +0.33306690738754696E-15, +0.88817841970012523E-15, +0.0000000000000000, +0.0000000000000000, +0.0000000000000000, +0.99920072216264089E-15, -0.66613381477509392E-15, +0.88817841970012523E-15, +0.0000000000000000, +0.99920072216264089E-15, +0.44408920985006262E-15, -0.33306690738754696E-15, +0.11102230246251565E-15, +0.0000000000000000, -0.33306690738754696E-15, -0.11102230246251565E-15, +0.44408920985006262E-15, +0.22204460492503131E-15, +0.22204460492503131E-15, +0.0000000000000000, +0.11102230246251565E-15, +0.22204460492503131E-15, -0.11102230246251565E-15, -0.11102230246251565E-15, +0.55511151231257827E-15, +0.11102230246251565E-15, +0.66613381477509392E-15, -0.11102230246251565E-15, +0.22204460492503131E-15, +0.22204460492503131E-15, +0.22204460492503131E-15, -0.22204460492503131E-15, +0.11102230246251565E-14, +0.22204460492503131E-15, +0.11102230246251565E-14, +0.44408920985006262E-15, +0.44408920985006262E-15, +0.33306690738754696E-15, +0.66613381477509392E-15, -0.11102230246251565E-15, +0.88817841970012523E-15, -0.22204460492503131E-15, +0.99920072216264089E-15

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

301reltol

302+0.14901161193847656E-7

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, 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+18

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

311data

312+1.20360035906283603475080724657766479, +1.32618248902909721696389161662851330, +1.26355631043373212171269292102607901, +1.18874329523318502980469703003797459, +1.46853190001053469563098233761862466, +1.32506098817400413541474516769473792, +1.28844833357163178163601963154443841, +1.42263070854249726868337274397132476, +1.67297704251552935459417225403368167, +1.89062291231918641256326569951742066, +1.12220158471305534275368444525003765, +1.48001907759673638279591219938163986, +1.30949370937520804822926045581497104, +1.35673982065284801165251299175772990, +1.63220968120965529109413668479056964, +1.15469858139419935029895243614482668, +1.88842895405549078897076293052347627, +1.27624983413008311340924516950709079

313

314atad = getFFTR(getFFTF(data))

315atad = atad * 2 / size(atad)

316atad

317+1.20360035906283603475080724657766479, +1.32618248902909721696389161662851330, +1.26355631043373212171269292102607920, +1.18874329523318502980469703003797497, +1.46853190001053469563098233761862466, +1.32506098817400413541474516769473792, +1.28844833357163178163601963154443841, +1.42263070854249726868337274397132515, +1.67297704251552935459417225403368167, +1.89062291231918641256326569951742066, +1.12220158471305534275368444525003765, +1.48001907759673638279591219938164005, +1.30949370937520804822926045581497142, +1.35673982065284801165251299175772990, +1.63220968120965529109413668479056983, +1.15469858139419935029895243614482687, +1.88842895405549078897076293052347607, +1.27624983413008311340924516950709079, -0.385185988877447170611195588516985464E-33, -0.962964972193617926527988971292463659E-34, -0.962964972193617926527988971292463659E-34, +0.00000000000000000000000000000000000, -0.962964972193617926527988971292463659E-34, -0.192592994438723585305597794258492732E-33, -0.481482486096808963263994485646231830E-33, -0.962964972193617926527988971292463659E-34, -0.288889491658085377958396691387739098E-33, -0.288889491658085377958396691387739098E-33, -0.577778983316170755916793382775478196E-33, +0.00000000000000000000000000000000000, -0.288889491658085377958396691387739098E-33, +0.00000000000000000000000000000000000

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

319reltol

320+0.138777878078144567552953958511352539E-16

321isClose(data, atad(1:size(data)), reltol = reltol)

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

323call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

324

325lenData = getUnifRand(5, 100)

326lenData

327+11

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

329data

330(+1.04773283, +0.949883461E-2), (+1.06665766, +0.444492877), (+1.76439524, +0.908906341), (+1.59882367, +0.776413798), (+1.41962242, +0.666528940E-1), (+1.21530056, +0.439028382), (+1.77925062, +0.973439693), (+1.92819285, +0.198876858), (+1.79299521, +0.826918483E-1), (+1.42200100, +0.381344795), (+1.72921133, +0.962966383)

331

332atad = getFFTR(getFFTF(data))

333atad = atad / size(atad)

334atad

335(+1.04773271, +0.949874520E-2), (+1.06665778, +0.444492936), (+1.76439488, +0.908906341), (+1.59882367, +0.776413798), (+1.41962242, +0.666527450E-1), (+1.21530056, +0.439028263), (+1.77925062, +0.973439515), (+1.92819285, +0.198876724), (+1.79299510, +0.826918185E-1), (+1.42200089, +0.381344914), (+1.72921121, +0.962966084), (+0.119209290E-6, -0.119209290E-6), (-0.596046448E-7, +0.856816769E-7), (+0.00000000, -0.149011612E-7), (+0.00000000, +0.178813934E-6), (+0.178813934E-6, +0.163912773E-6)

336reltol = sqrt(epsilon(1._TKG))

337reltol

338+0.345266977E-3

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

340T, T, T, T, T, T, T, T, T, T, T

341call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

342

343lenData = getUnifRand(5, 100)

344lenData

345+48

346data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

347data

348(+1.7576397667694925, +0.87105650789217082), (+1.7838407232013438, +0.35690842392319122E-1), (+1.5421445884578575, +0.18516738357313511), (+1.4512048445636845, +0.11999915457473953), (+1.9119915141643435, +0.99745457868623699), (+1.1473091147833374, +0.91857065598424503), (+1.1771584073374934, +0.33863296945905863), (+1.0155214711856910, +0.16609962284653923), (+1.0755130929369503, +0.62700025866368148), (+1.4565967958084070, +0.88212588185331819), (+1.5311770225025088, +0.14090601267997727), (+1.9546239812032251, +0.26031193942970876), (+1.4258753039129781, +0.52315929114944526), (+1.1592108803306560, +0.62394883553769143), (+1.4322616298460140, +0.40304524631601413), (+1.9449787139004924, +0.37532400235674201), (+1.7115089203076947, +0.97366317183068452), (+1.1208290960917242, +0.12474089131319344), (+1.8242571393975457, +0.49735074244948496), (+1.6608885466544003, +0.28601269454506117), (+1.5424576137715111, +0.92609263996637126), (+1.1211800471213544, +0.48999227913548049E-1), (+1.0008613571070728, +0.19803667774901890), (+1.8926239748570368, +0.89143002401243254), (+1.3242278544845378, +0.58871854978088167), (+1.0011436296426783, +0.44291262687588995), (+1.7259464162065690, +0.88774019417845684E-1), (+1.7575605570289210, +0.24677548930005277), (+1.2317069265827021, +0.86417213511163404), (+1.0649836836772621, +0.40895747937417137), (+1.7364115527323758, +0.57572151374878144), (+1.6980221270593359, +0.88118660136927829), (+1.0864141692826133, +0.95428653178127787), (+1.7337152037165833, +0.69886761791738183), (+1.0200589544421961, +0.33034908867062396), (+1.6303227524651485, +0.77106805825008184), (+1.9851062824753325, +0.28276931242049896), (+1.4528520516448269, +0.66185153841770328), (+1.8811164085555281, +0.47532291263675941), (+1.2751694340397619, +0.58836584415091930), (+1.0061604546081533, +0.36522600975255304), (+1.0831762021528453, +0.64479714983778313), (+1.9490329224667575, +0.75239268294880601), (+1.8084074323833907, +0.66863902859221802), (+1.6410919963267787, +0.42893735322542392), (+1.4684202856403534, +0.78820665139061563), (+1.5421758124349805, +0.64837378801377354), (+1.0728193535761661, +0.23985187833946986E-1)

349

350atad = getFFTR(getFFTF(data))

351atad = atad / size(atad)

352atad

353(+1.7576397667694925, +0.87105650789217082), (+1.7838407232013438, +0.35690842392319344E-1), (+1.5421445884578573, +0.18516738357313534), (+1.4512048445636845, +0.11999915457473975), (+1.9119915141643433, +0.99745457868623721), (+1.1473091147833374, +0.91857065598424492), (+1.1771584073374934, +0.33863296945905863), (+1.0155214711856910, +0.16609962284653931), (+1.0755130929369503, +0.62700025866368148), (+1.4565967958084072, +0.88212588185331831), (+1.5311770225025088, +0.14090601267997743), (+1.9546239812032247, +0.26031193942970920), (+1.4258753039129777, +0.52315929114944559), (+1.1592108803306558, +0.62394883553769165), (+1.4322616298460136, +0.40304524631601435), (+1.9449787139004919, +0.37532400235674224), (+1.7115089203076947, +0.97366317183068407), (+1.1208290960917244, +0.12474089131319317), (+1.8242571393975460, +0.49735074244948452), (+1.6608885466544003, +0.28601269454506106), (+1.5424576137715111, +0.92609263996637070), (+1.1211800471213547, +0.48999227913547994E-1), (+1.0008613571070735, +0.19803667774901884), (+1.8926239748570373, +0.89143002401243265), (+1.3242278544845378, +0.58871854978088156), (+1.0011436296426783, +0.44291262687588989), (+1.7259464162065687, +0.88774019417845712E-1), (+1.7575605570289210, +0.24677548930005247), (+1.2317069265827021, +0.86417213511163382), (+1.0649836836772621, +0.40895747937417143), (+1.7364115527323760, +0.57572151374878089), (+1.6980221270593356, +0.88118660136927773), (+1.0864141692826133, +0.95428653178127787), (+1.7337152037165833, +0.69886761791738206), (+1.0200589544421963, +0.33034908867062407), (+1.6303227524651485, +0.77106805825008151), (+1.9851062824753323, +0.28276931242049907), (+1.4528520516448271, +0.66185153841770339), (+1.8811164085555281, +0.47532291263675941), (+1.2751694340397619, +0.58836584415091919), (+1.0061604546081531, +0.36522600975255293), (+1.0831762021528448, +0.64479714983778302), (+1.9490329224667571, +0.75239268294880546), (+1.8084074323833907, +0.66863902859221758), (+1.6410919963267780, +0.42893735322542381), (+1.4684202856403528, +0.78820665139061541), (+1.5421758124349805, +0.64837378801377277), (+1.0728193535761661, +0.23985187833946653E-1), (-0.33306690738754696E-15, +0.55511151231257827E-16), (-0.11102230246251565E-15, -0.40245584642661925E-15), (+0.66613381477509392E-15, +0.13877787807814457E-15), (+0.44408920985006262E-15, -0.27755575615628914E-16), (-0.44408920985006262E-15, +0.55511151231257827E-16), (-0.11102230246251565E-15, -0.16653345369377348E-15), (+0.44408920985006262E-15, +0.55511151231257827E-16), (+0.33306690738754696E-15, -0.55511151231257827E-16), (-0.44408920985006262E-15, +0.0000000000000000), (+0.0000000000000000, +0.55511151231257827E-16), (+0.55511151231257827E-15, +0.24980018054066022E-15), (+0.55511151231257827E-15, +0.13877787807814457E-15), (+0.0000000000000000, +0.11102230246251565E-15), (+0.33306690738754696E-15, -0.16653345369377348E-15), (+0.44408920985006262E-15, +0.55511151231257827E-15), (+0.44408920985006262E-15, +0.27755575615628914E-15)

354reltol = sqrt(epsilon(1._TKG))

355reltol

356+0.14901161193847656E-7

357isClose(data, atad(1:size(data)), reltol = reltol)

358T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

359call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

360

361lenData = getUnifRand(5, 100)

362lenData

363+30

364data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

365data

366(+1.09345781640191486150689147303850442, +0.936732574027314555078003975521024046), (+1.53904437004455829861577233326522017, +0.819670198014762161305045486920485141), (+1.60027368388894454607323983384979740, +0.306382330007985851344261088615455983), (+1.98342742490870508626546484387376767, +0.846003582764567560000182527328595863), (+1.46837997549404189148768826210496044, +0.457766202218983019654253898024841967), (+1.07079921878203093761949378274285108, +0.696193654979305367512065306402046118), (+1.80850946826771764787054392115437092, +0.588621871793443195409145347857822775), (+1.07815984759451703219411942281011276, +0.600711830245359758537075459749510799), (+1.68509777639377548778148814344123324, +0.329287060119074827793075220580580746), (+1.32907970896348953269803551859160448, +0.125006791560789299804510297171530479), (+1.02827124235372984469848782698614379, +0.207238477336605276696402635855550142), (+1.80876468867616601151452827373329977, +0.852101841737348902175942555445567385), (+1.11714994356753993969517217409994217, +0.671560296611666991367868980456115024), (+1.86794860562448609090768740624385397, +0.332528635220933966853941902386840732), (+1.07682991209174428685951828868581309, +0.707815237053168244363668774708366516), (+1.55969242034927576870303539457646225, +0.378931846241272660825111226696397847), (+1.13551353998324689059593593498876560, +0.838566906475360934947151908587252989E-1), (+1.58176325503384314126782424186825574, +0.598971925641665422873599965522993174), (+1.07864426246118906596147686278780715, +0.467878238178994585634073508871141510E-2), (+1.76497775802370113477082152531450791, +0.337829503015887850229126217334191240), (+1.00836036222436757402866480083296124, +0.347228345251492926393283458450052946), (+1.67948947171155807123836784441449147, +0.516465307017798460086165135982965240), (+1.67219329206393827790889452982100566, +0.538353802126835296894336006310188317), (+1.47011128629727511295898598821734634, +0.358286219528710556085437308487731534), (+1.07681935461435242249125119049638465, +0.479450204590717104143851796421746468), (+1.26679143616930175589522364116510890, +0.887256485276382824939580061027812561), (+1.19759747524183194578683153401526251, +0.155729708789616026198095705891737516), (+1.23923335214501712807769817458337208, +0.803888506583946004544483067486430216), (+1.96110740386248367857827985728667563, +0.392472119987030181190843815961377416), (+1.39734851544389501948895588646422131, +0.544690428560677766636385015787304908)

367

368atad = getFFTR(getFFTF(data))

369atad = atad / size(atad)

370atad

371(+1.09345781640191486150689147303850442, +0.936732574027314555078003975521024046), (+1.53904437004455829861577233326521997, +0.819670198014762161305045486920485237), (+1.60027368388894454607323983384979778, +0.306382330007985851344261088615455983), (+1.98342742490870508626546484387376747, +0.846003582764567560000182527328595959), (+1.46837997549404189148768826210496063, +0.457766202218983019654253898024842015), (+1.07079921878203093761949378274285108, +0.696193654979305367512065306402046118), (+1.80850946826771764787054392115437130, +0.588621871793443195409145347857822678), (+1.07815984759451703219411942281011257, +0.600711830245359758537075459749510607), (+1.68509777639377548778148814344123324, +0.329287060119074827793075220580580842), (+1.32907970896348953269803551859160428, +0.125006791560789299804510297171530528), (+1.02827124235372984469848782698614398, +0.207238477336605276696402635855550190), (+1.80876468867616601151452827373329958, +0.852101841737348902175942555445567481), (+1.11714994356753993969517217409994236, +0.671560296611666991367868980456115216), (+1.86794860562448609090768740624385397, +0.332528635220933966853941902386840684), (+1.07682991209174428685951828868581290, +0.707815237053168244363668774708366612), (+1.55969242034927576870303539457646187, +0.378931846241272660825111226696397799), (+1.13551353998324689059593593498876560, +0.838566906475360934947151908587252989E-1), (+1.58176325503384314126782424186825555, +0.598971925641665422873599965522993174), (+1.07864426246118906596147686278780734, +0.467878238178994585634073508871134288E-2), (+1.76497775802370113477082152531450772, +0.337829503015887850229126217334191288), (+1.00836036222436757402866480083296124, +0.347228345251492926393283458450052995), (+1.67948947171155807123836784441449147, +0.516465307017798460086165135982965143), (+1.67219329206393827790889452982100624, +0.538353802126835296894336006310188413), (+1.47011128629727511295898598821734634, +0.358286219528710556085437308487731582), (+1.07681935461435242249125119049638484, +0.479450204590717104143851796421746372), (+1.26679143616930175589522364116510909, +0.887256485276382824939580061027812465), (+1.19759747524183194578683153401526270, +0.155729708789616026198095705891737516), (+1.23923335214501712807769817458337189, +0.803888506583946004544483067486430409), (+1.96110740386248367857827985728667582, +0.392472119987030181190843815961377512), (+1.39734851544389501948895588646422131, +0.544690428560677766636385015787304908), (-0.962964972193617926527988971292463659E-34, -0.481482486096808963263994485646231830E-34), (-0.962964972193617926527988971292463659E-34, -0.240741243048404481631997242823115915E-33)

372reltol = sqrt(epsilon(1._TKG))

373reltol

374+0.138777878078144567552953958511352539E-16

375isClose(data, atad(1:size(data)), reltol = reltol)

376T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

377call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

378

379lenData = getUnifRand(5, 100)

380lenData

381+63

382data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

383data

384+1.39837039, +1.24280429, +1.08450627, +1.55254197, +1.99915504, +1.79519427, +1.23962152, +1.62556553, +1.02700496, +1.08699703, +1.50190544, +1.16013360, +1.23942876, +1.64094138, +1.64273691, +1.82044744, +1.56101584, +1.98991346, +1.86751306, +1.01152754, +1.13986278, +1.32322967, +1.78706992, +1.51325679, +1.91573572, +1.98321140, +1.99335694, +1.24322033, +1.36124897, +1.08991647, +1.98888242, +1.14855444, +1.15576625, +1.28128171, +1.82010055, +1.05468273, +1.26678824, +1.22607791, +1.72010565, +1.05605209, +1.26545668, +1.79809809, +1.72791362, +1.12480068, +1.24920011, +1.06674910, +1.85259664, +1.79621792, +1.73945725, +1.22882342, +1.79373789, +1.54482079, +1.38086343, +1.74486017, +1.41735792, +1.82500446, +1.28640342, +1.77581191, +1.30445778, +1.60766602, +1.94513011, +1.20962703, +1.86542702

385

386atad = getFFTR(getFFTF(data))

387atad = atad * 2 / size(atad)

388atad

389+1.39837039, +1.24280417, +1.08450627, +1.55254197, +1.99915516, +1.79519403, +1.23962152, +1.62556529, +1.02700496, +1.08699703, +1.50190520, +1.16013348, +1.23942888, +1.64094090, +1.64273691, +1.82044721, +1.56101584, +1.98991323, +1.86751294, +1.01152742, +1.13986301, +1.32322955, +1.78706980, +1.51325655, +1.91573572, +1.98321116, +1.99335682, +1.24322009, +1.36124897, +1.08991611, +1.98888230, +1.14855421, +1.15576637, +1.28128159, +1.82010031, +1.05468273, +1.26678836, +1.22607768, +1.72010577, +1.05605197, +1.26545668, +1.79809785, +1.72791338, +1.12480056, +1.24920022, +1.06674886, +1.85259652, +1.79621768, +1.73945737, +1.22882318, +1.79373789, +1.54482067, +1.38086367, +1.74485993, +1.41735792, +1.82500410, +1.28640342, +1.77581179, +1.30445778, +1.60766578, +1.94513011, +1.20962679, +1.86542702, +0.00000000

390reltol = sqrt(epsilon(1._TKG))

391reltol

392+0.345266977E-3

393isClose(data, atad(1:size(data)), reltol = reltol)

394T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

395call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

396

397lenData = getUnifRand(5, 100)

398lenData

399+36

400data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

401data

402+1.2947604449810504, +1.6198874889166022, +1.0383929173059250, +1.7337071800342940, +1.7568966457940729, +1.4233652007738922, +1.5063266671445792, +1.9095272112586064, +1.8442389966577153, +1.1625307357582182, +1.1202713179942687, +1.7668365684109764, +1.7922046841839161, +1.3919998361688497, +1.6305937780224620, +1.8427274377827274, +1.7575154159808872, +1.4926924823622518, +1.2421821460806139, +1.7522039723171343, +1.6885059789999581, +1.5825949792870859, +1.0286059698915628, +1.7806576108027299, +1.7591891707965543, +1.9400253693319494, +1.3195277109854826, +1.6309090345897999, +1.3674864832215312, +1.9800318351498256, +1.8737962164032036, +1.6645011259218383, +1.5830714400814794, +1.9090154815499609, +1.1390234741734746, +1.2075696900166006

403

404atad = getFFTR(getFFTF(data))

405atad = atad * 2 / size(atad)

406atad

407+1.2947604449810501, +1.6198874889166024, +1.0383929173059248, +1.7337071800342942, +1.7568966457940722, +1.4233652007738926, +1.5063266671445785, +1.9095272112586068, +1.8442389966577151, +1.1625307357582182, +1.1202713179942683, +1.7668365684109761, +1.7922046841839152, +1.3919998361688495, +1.6305937780224613, +1.8427274377827274, +1.7575154159808868, +1.4926924823622518, +1.2421821460806139, +1.7522039723171341, +1.6885059789999575, +1.5825949792870859, +1.0286059698915626, +1.7806576108027294, +1.7591891707965543, +1.9400253693319491, +1.3195277109854826, +1.6309090345897994, +1.3674864832215312, +1.9800318351498252, +1.8737962164032034, +1.6645011259218374, +1.5830714400814794, +1.9090154815499611, +1.1390234741734748, +1.2075696900166004, +0.77715611723760958E-15, -0.44408920985006262E-15, +0.66613381477509392E-15, -0.33306690738754696E-15, +0.44408920985006262E-15, +0.0000000000000000, +0.66613381477509392E-15, -0.33306690738754696E-15, +0.33306690738754696E-15, -0.33306690738754696E-15, +0.88817841970012523E-15, +0.0000000000000000, +0.55511151231257827E-15, +0.11102230246251565E-15, +0.44408920985006262E-15, -0.11102230246251565E-15, +0.44408920985006262E-15, +0.11102230246251565E-15, +0.22204460492503131E-15, +0.44408920985006262E-15, +0.22204460492503131E-15, +0.22204460492503131E-15, +0.22204460492503131E-15, +0.33306690738754696E-15, +0.11102230246251565E-15, +0.33306690738754696E-15, +0.11102230246251565E-15, +0.77715611723760958E-15

408reltol = sqrt(epsilon(1._TKG))

409reltol

410+0.14901161193847656E-7

411isClose(data, atad(1:size(data)), reltol = reltol)

412T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

413call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

414

415lenData = getUnifRand(5, 100)

416lenData

417+38

418data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

419data

420+1.55682109468767361182747518861147237, +1.36005479737632253566729019256101501, +1.31137356813262150199955860808677701, +1.99017422658779561738408561621880803, +1.67758745477234128184594891858187643, +1.41486694040957466637980361062220407, +1.15107454556031143539841570493760196, +1.62673902883025133044603264765163778, +1.59895677460671916163717320372005224, +1.67077743318208165518587104140406048, +1.31227892279235499370095732762412059, +1.91146712575382678722246956792106881, +1.63230627650847199055515712765681636, +1.68892389575147065114936515465187069, +1.59064293183417739478660726625173533, +1.21531916964420765189382748342253571, +1.82460712951486209909774729537222374, +1.48016427735421361048547374887134039, +1.58626945856103030030219058482204793, +1.68274160391279560172746236372118379, +1.37286583220790578091384068168911783, +1.32431826166721625240634115510821367, +1.26837835025108755046181453296249539, +1.56755029350535740066674273316228064, +1.30039532567070356537823361235240932, +1.65399780035294366064147342188046483, +1.11709355244118938244259080733682611, +1.61179903239669059965970258998343632, +1.22969210106290578125581645928589913, +1.50178545989158713751413989827960257, +1.34175908136105127723123377514450754, +1.00126426061765076199720661522587644, +1.83842396162827815415203525446074571, +1.43829702354651479209545621139969766, +1.37506860794168360699854894716404972, +1.58575433505711880969189976081013435, +1.03219703104599462873124568979428595, +1.87856970840150613076221683569723964

421

422atad = getFFTR(getFFTF(data))

423atad = atad * 2 / size(atad)

424atad

425+1.55682109468767361182747518861147217, +1.36005479737632253566729019256101501, +1.31137356813262150199955860808677701, +1.99017422658779561738408561621880803, +1.67758745477234128184594891858187682, +1.41486694040957466637980361062220426, +1.15107454556031143539841570493760196, +1.62673902883025133044603264765163778, +1.59895677460671916163717320372005281, +1.67077743318208165518587104140406068, +1.31227892279235499370095732762412098, +1.91146712575382678722246956792106881, +1.63230627650847199055515712765681694, +1.68892389575147065114936515465187108, +1.59064293183417739478660726625173533, +1.21531916964420765189382748342253571, +1.82460712951486209909774729537222393, +1.48016427735421361048547374887134039, +1.58626945856103030030219058482204793, +1.68274160391279560172746236372118379, +1.37286583220790578091384068168911822, +1.32431826166721625240634115510821386, +1.26837835025108755046181453296249539, +1.56755029350535740066674273316228064, +1.30039532567070356537823361235240970, +1.65399780035294366064147342188046483, +1.11709355244118938244259080733682630, +1.61179903239669059965970258998343652, +1.22969210106290578125581645928589933, +1.50178545989158713751413989827960296, +1.34175908136105127723123377514450754, +1.00126426061765076199720661522587663, +1.83842396162827815415203525446074571, +1.43829702354651479209545621139969766, +1.37506860794168360699854894716404972, +1.58575433505711880969189976081013435, +1.03219703104599462873124568979428595, +1.87856970840150613076221683569724021, +0.192592994438723585305597794258492732E-33, -0.288889491658085377958396691387739098E-33, -0.385185988877447170611195588516985464E-33, +0.00000000000000000000000000000000000, -0.962964972193617926527988971292463659E-34, -0.962964972193617926527988971292463659E-34, -0.481482486096808963263994485646231830E-33, +0.00000000000000000000000000000000000, +0.962964972193617926527988971292463659E-34, -0.288889491658085377958396691387739098E-33, +0.00000000000000000000000000000000000, +0.962964972193617926527988971292463659E-34, -0.962964972193617926527988971292463659E-34, +0.288889491658085377958396691387739098E-33, +0.962964972193617926527988971292463659E-34, -0.192592994438723585305597794258492732E-33, +0.962964972193617926527988971292463659E-34, -0.192592994438723585305597794258492732E-33, -0.962964972193617926527988971292463659E-34, -0.962964972193617926527988971292463659E-34, +0.00000000000000000000000000000000000, -0.192592994438723585305597794258492732E-33, +0.00000000000000000000000000000000000, -0.385185988877447170611195588516985464E-33, -0.962964972193617926527988971292463659E-34, -0.192592994438723585305597794258492732E-33

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

427reltol

428+0.138777878078144567552953958511352539E-16

429isClose(data, atad(1:size(data)), reltol = reltol)

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

431call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

432

433lenData = getUnifRand(5, 100)

434lenData

435+23

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

437data

438(+1.31246758, +0.795602918), (+1.67182112, +0.817714453), (+1.24260426, +0.737477660), (+1.27881634, +0.730496585), (+1.86260545, +0.131622255), (+1.15171361, +0.924093306), (+1.85238123, +0.253730357), (+1.39050078, +0.255794406), (+1.64449930, +0.375803530), (+1.01106715, +0.231191814), (+1.51696038, +0.893736303), (+1.61279559, +0.246228635), (+1.57345223, +0.898953438), (+1.74226570, +0.771595359), (+1.75501847, +0.437854409), (+1.81947994, +0.474314928), (+1.99601221, +0.736883938), (+1.76096416, +0.343750477), (+1.04103374, +0.693101346), (+1.62998760, +0.634929478), (+1.42511988, +0.407687783), (+1.60073161, +0.464218795), (+1.84986925, +0.469426513)

439

440atad = getFFTR(getFFTF(data))

441atad = atad / size(atad)

442atad

443(+1.31246746, +0.795602918), (+1.67182100, +0.817714512), (+1.24260414, +0.737477660), (+1.27881634, +0.730496526), (+1.86260521, +0.131622240), (+1.15171361, +0.924093246), (+1.85238111, +0.253730476), (+1.39050055, +0.255794406), (+1.64449918, +0.375803471), (+1.01106691, +0.231191725), (+1.51696026, +0.893736362), (+1.61279559, +0.246228576), (+1.57345200, +0.898953438), (+1.74226534, +0.771595240), (+1.75501823, +0.437854528), (+1.81947982, +0.474314898), (+1.99601209, +0.736883998), (+1.76096404, +0.343750417), (+1.04103363, +0.693101287), (+1.62998760, +0.634929419), (+1.42511976, +0.407687783), (+1.60073161, +0.464218736), (+1.84986889, +0.469426453), (+0.178813934E-6, -0.447034836E-7), (-0.119209290E-6, -0.149011612E-7), (+0.00000000, +0.201165676E-6), (-0.119209290E-6, +0.298023224E-7), (+0.596046448E-7, +0.119209290E-6), (+0.00000000, -0.298023224E-7), (+0.00000000, +0.119209290E-6), (-0.596046448E-7, +0.149011612E-7), (+0.119209290E-6, +0.596046448E-7)

444reltol = sqrt(epsilon(1._TKG))

445reltol

446+0.345266977E-3

447isClose(data, atad(1:size(data)), reltol = reltol)

448T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

449call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

450

451lenData = getUnifRand(5, 100)

452lenData

453+68

454data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

455data

456(+1.0864375956505656, +0.46099427589297126), (+1.2619602120799696, +0.57782277836289653), (+1.3494661453220940, +0.64049779017064035), (+1.5248007741991869, +0.49201536504365784), (+1.2414661448272448, +0.74867578755959563), (+1.4278200668950130, +0.80695455457937149), (+1.1206718118926018, +0.99393399267041593), (+1.9264870120685260, +0.79645608079133567), (+1.5826211496316418, +0.44914167344231370), (+1.1811102919288015, +0.30702537551775433E-1), (+1.3242014347957614, +0.59865816225440627E-1), (+1.3844570535866954, +0.29535279245302459), (+1.5792718634509699, +0.70279745475833821E-1), (+1.1166585100560820, +0.51766269252640362), (+1.6263306409864202, +0.53036040463475720), (+1.2034566684412062, +0.26736985546788816), (+1.9443052405949031, +0.44993985448277551), (+1.2302839046436684, +0.87621526021903062), (+1.4446785674258189, +0.33779356856931630), (+1.2761037607788304, +0.94774228389907311), (+1.9442116474863174, +0.54630794768682600), (+1.0680058445692682, +0.39225806919900186), (+1.7013523676439850, +0.11262775969603611), (+1.2914644043958705, +0.14452544818713031), (+1.8993283902672840, +0.12158248966105800), (+1.4789805073764004, +0.21937337518300726), (+1.7760043327062689, +0.73667250362308545), (+1.6612247734507277, +0.92861192793347758), (+1.2188353383718782, +0.76969168961127887), (+1.2430578539232970, +0.75314302319074145), (+1.2246810772248289, +0.80635340458845073), (+1.6886267439320477, +0.24359837254256200), (+1.0487836722930139, +0.97113912875485886), (+1.2518051927254272, +0.23860728362286043), (+1.3260172337766845, +0.17158380060335354), (+1.0983787170475150, +0.59574813576335806), (+1.9476796005755679, +0.28558731302259099), (+1.1916641715648995, +0.60802855620799823), (+1.6356850230007862, +0.89541977804915374), (+1.0856297432453110, +0.84626581547033730E-1), (+1.8767263426313794, +0.72367872369290143), (+1.0393643162401589, +0.49092849328047283), (+1.5304188350724706, +0.64487539904396973), (+1.0966349515596048, +0.22891525416296887), (+1.9056435311935758, +0.45555078000518612E-1), (+1.0252361032435786, +0.12241786087176665), (+1.6716589660692387, +0.49336939571396421), (+1.5437419206377769, +0.15249890523659826), (+1.6354071048986807, +0.23524871740254305E-1), (+1.8825590028955395, +0.16407187769883480), (+1.6793419040096493, +0.57778269647386649), (+1.1018168790103238, +0.54127685389081603), (+1.6338536138823332, +0.16539485926593245), (+1.1759641554160218, +0.65721060088736705), (+1.9101575312876833, +0.70213567130563193), (+1.8880419313829195, +0.91963007117307871), (+1.4846393464556655, +0.65673170384235036E-1), (+1.1275198330154517, +0.72934896194294496E-1), (+1.5395748449771745, +0.93088511870862667), (+1.9998892369152861, +0.36623700304098572), (+1.9002736230595669, +0.18819750894248977), (+1.1667279885779842, +0.94378955820097710), (+1.3210664432878836, +0.88152330371628462), (+1.2684523462622217, +0.32048068381181261), (+1.2139286742276776, +0.32661738625887093), (+1.5006646589581480, +0.50250381712540226), (+1.6883839022301812, +0.25689674392659456E-1), (+1.1048057360612491, +0.24112569143145213)

457

458atad = getFFTR(getFFTF(data))

459atad = atad / size(atad)

460atad

461(+1.0864375956505654, +0.46099427589297137), (+1.2619602120799698, +0.57782277836289686), (+1.3494661453220937, +0.64049779017064057), (+1.5248007741991871, +0.49201536504365817), (+1.2414661448272448, +0.74867578755959552), (+1.4278200668950132, +0.80695455457937171), (+1.1206718118926020, +0.99393399267041616), (+1.9264870120685258, +0.79645608079133567), (+1.5826211496316418, +0.44914167344231370), (+1.1811102919288019, +0.30702537551775530E-1), (+1.3242014347957614, +0.59865816225440877E-1), (+1.3844570535866958, +0.29535279245302465), (+1.5792718634509697, +0.70279745475833849E-1), (+1.1166585100560815, +0.51766269252640384), (+1.6263306409864198, +0.53036040463475775), (+1.2034566684412062, +0.26736985546788850), (+1.9443052405949031, +0.44993985448277557), (+1.2302839046436684, +0.87621526021903040), (+1.4446785674258187, +0.33779356856931630), (+1.2761037607788299, +0.94774228389907278), (+1.9442116474863171, +0.54630794768682556), (+1.0680058445692682, +0.39225806919900175), (+1.7013523676439846, +0.11262775969603628), (+1.2914644043958705, +0.14452544818713042), (+1.8993283902672840, +0.12158248966105820), (+1.4789805073764004, +0.21937337518300756), (+1.7760043327062687, +0.73667250362308556), (+1.6612247734507273, +0.92861192793347769), (+1.2188353383718780, +0.76969168961127887), (+1.2430578539232968, +0.75314302319074145), (+1.2246810772248287, +0.80635340458845062), (+1.6886267439320473, +0.24359837254256189), (+1.0487836722930139, +0.97113912875485875), (+1.2518051927254272, +0.23860728362286018), (+1.3260172337766845, +0.17158380060335338), (+1.0983787170475148, +0.59574813576335806), (+1.9476796005755674, +0.28558731302259066), (+1.1916641715648995, +0.60802855620799812), (+1.6356850230007864, +0.89541977804915351), (+1.0856297432453110, +0.84626581547033702E-1), (+1.8767263426313794, +0.72367872369290132), (+1.0393643162401589, +0.49092849328047272), (+1.5304188350724706, +0.64487539904396995), (+1.0966349515596048, 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(+1.5006646589581480, +0.50250381712540237), (+1.6883839022301810, +0.25689674392659401E-1), (+1.1048057360612489, +0.24112569143145177), (+0.11102230246251565E-15, +0.11102230246251565E-15), (+0.11102230246251565E-15, -0.22204460492503131E-15), (+0.22204460492503131E-15, -0.22204460492503131E-15), (+0.22204460492503131E-15, -0.22204460492503131E-15), (-0.22204460492503131E-15, -0.13877787807814457E-15), (-0.11102230246251565E-15, -0.18041124150158794E-15), (+0.22204460492503131E-15, -0.83266726846886741E-16), (-0.11102230246251565E-15, -0.27755575615628914E-15), (+0.0000000000000000, -0.76327832942979512E-16), (+0.11102230246251565E-15, +0.0000000000000000), (+0.22204460492503131E-15, -0.44408920985006262E-15), (+0.22204460492503131E-15, -0.19428902930940239E-15), (-0.11102230246251565E-15, -0.27755575615628914E-15), (+0.0000000000000000, +0.11102230246251565E-15), (+0.22204460492503131E-15, +0.0000000000000000), (+0.22204460492503131E-15, -0.55511151231257827E-16), (+0.55511151231257827E-15, +0.22204460492503131E-15), (+0.33306690738754696E-15, +0.83266726846886741E-16), (+0.44408920985006262E-15, +0.16653345369377348E-15), (+0.33306690738754696E-15, +0.0000000000000000), (+0.11102230246251565E-15, -0.13877787807814457E-15), (+0.11102230246251565E-15, -0.27755575615628914E-16), (+0.44408920985006262E-15, +0.0000000000000000), (+0.11102230246251565E-15, -0.22204460492503131E-15), (+0.44408920985006262E-15, -0.22204460492503131E-15), (+0.33306690738754696E-15, +0.55511151231257827E-16), (+0.22204460492503131E-15, +0.0000000000000000), (+0.33306690738754696E-15, +0.55511151231257827E-16), (+0.0000000000000000, +0.11102230246251565E-15), (-0.11102230246251565E-15, +0.19428902930940239E-15), (-0.11102230246251565E-15, +0.16653345369377348E-15), (-0.22204460492503131E-15, -0.16653345369377348E-15), (-0.11102230246251565E-15, +0.19428902930940239E-15), (+0.0000000000000000, +0.0000000000000000), (-0.22204460492503131E-15, +0.38857805861880479E-15), (-0.11102230246251565E-15, +0.24980018054066022E-15), (-0.22204460492503131E-15, +0.22204460492503131E-15), (-0.11102230246251565E-15, -0.27755575615628914E-16), (+0.22204460492503131E-15, +0.0000000000000000), (+0.33306690738754696E-15, +0.41633363423443370E-16), (+0.33306690738754696E-15, +0.13183898417423734E-15), (+0.22204460492503131E-15, +0.18041124150158794E-15), (+0.11102230246251565E-15, +0.24980018054066022E-15), (+0.22204460492503131E-15, +0.22204460492503131E-15), (+0.11102230246251565E-15, +0.22204460492503131E-15), (+0.22204460492503131E-15, +0.30531133177191805E-15), (+0.22204460492503131E-15, +0.27755575615628914E-15), (+0.22204460492503131E-15, +0.16653345369377348E-15), (+0.22204460492503131E-15, +0.22204460492503131E-15), (+0.22204460492503131E-15, +0.33306690738754696E-15), (+0.11102230246251565E-15, +0.88817841970012523E-15), (+0.22204460492503131E-15, +0.49960036108132044E-15), (+0.33306690738754696E-15, +0.27755575615628914E-15), (+0.55511151231257827E-15, -0.20816681711721685E-16), (+0.22204460492503131E-15, +0.33306690738754696E-15), (+0.22204460492503131E-15, +0.49960036108132044E-15), (+0.22204460492503131E-15, +0.37470027081099033E-15), (+0.11102230246251565E-15, +0.66613381477509392E-15), (-0.11102230246251565E-15, +0.83266726846886741E-15), (+0.55511151231257827E-15, +0.74940054162198066E-15)

462reltol = sqrt(epsilon(1._TKG))

463reltol

464+0.14901161193847656E-7

465isClose(data, atad(1:size(data)), reltol = reltol)

466T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

467call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

468

469lenData = getUnifRand(5, 100)

470lenData

471+19

472data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

473data

474(+1.85318242754190707224814511057448628, +0.878963447647814442476997608526661562), (+1.52449348851597491076397820826004679, +0.689015076269346961859401189080740239), (+1.43897239878255527717101905511854146, +0.478108419302382524776338937181923737), (+1.18911229162747598334190264760775479, +0.302741584954293935795881931636674999), (+1.56311211834271548623091154452551181, +0.979159478268048337995458997955651438), (+1.97323675136431450854949107293398360, +0.307045614425020904517067985060076470), (+1.85028642038415699879876057308306530, +0.622167923948900775076464262571221787), (+1.40668772949137115796297524945114855, +0.990012162375960841152029261521764775), (+1.49103835471476582603197908101563215, +0.144698720810721918963463097137159549), (+1.31522061627949730248274123600546574, +0.243988352044510151523025826282847399), (+1.29741094195787232495790856033653195, +0.729716170140747666707542510587791456), (+1.33421971147426101198188812880726785, +0.557141399041541144382972169820410176), (+1.55218835676051044120450534173743680, +0.772553634469752016267459493785192386), (+1.26450371819978972106881452565140723, +0.650854082596168682915055662531037916), (+1.16032632629449045586481545836673607, +0.563468198288003813628448304797937213E-1), (+1.81633559342679668800529775684455890, +0.808480679655051536245712310898808392), (+1.23531985830957900169129569467558794, +0.629001345689344320079128387278084568), (+1.44921859222519110130359487386129023, +0.190104676838052503988509767110651750), (+1.67575550538188852307189974169684423, +0.439571730260436958295248159789758404E-1)

475

476atad = getFFTR(getFFTF(data))

477atad = atad / size(atad)

478atad

479(+1.85318242754190707224814511057448628, +0.878963447647814442476997608526661562), (+1.52449348851597491076397820826004660, +0.689015076269346961859401189080740335), (+1.43897239878255527717101905511854223, +0.478108419302382524776338937181923833), (+1.18911229162747598334190264760775479, +0.302741584954293935795881931636674903), (+1.56311211834271548623091154452551181, +0.979159478268048337995458997955651438), (+1.97323675136431450854949107293398379, +0.307045614425020904517067985060076277), (+1.85028642038415699879876057308306569, +0.622167923948900775076464262571221883), (+1.40668772949137115796297524945114855, +0.990012162375960841152029261521764679), (+1.49103835471476582603197908101563196, +0.144698720810721918963463097137159525), (+1.31522061627949730248274123600546555, +0.243988352044510151523025826282847423), (+1.29741094195787232495790856033653195, +0.729716170140747666707542510587791552), (+1.33421971147426101198188812880726765, +0.557141399041541144382972169820410176), (+1.55218835676051044120450534173743661, +0.772553634469752016267459493785192386), (+1.26450371819978972106881452565140723, +0.650854082596168682915055662531038012), (+1.16032632629449045586481545836673607, +0.563468198288003813628448304797937935E-1), (+1.81633559342679668800529775684455871, +0.808480679655051536245712310898808585), (+1.23531985830957900169129569467558813, +0.629001345689344320079128387278084376), (+1.44921859222519110130359487386129043, +0.190104676838052503988509767110651606), (+1.67575550538188852307189974169684462, +0.439571730260436958295248159789758645E-1), (-0.962964972193617926527988971292463659E-34, -0.481482486096808963263994485646231830E-34), (-0.962964972193617926527988971292463659E-34, +0.481482486096808963263994485646231830E-34), (+0.00000000000000000000000000000000000, +0.120370621524202240815998621411557957E-33), (+0.00000000000000000000000000000000000, +0.192592994438723585305597794258492732E-33), (+0.00000000000000000000000000000000000, +0.962964972193617926527988971292463659E-34), (-0.962964972193617926527988971292463659E-34, +0.240741243048404481631997242823115915E-34), (+0.00000000000000000000000000000000000, +0.722223729145213444895991728469347744E-34), (+0.192592994438723585305597794258492732E-33, +0.00000000000000000000000000000000000), (+0.192592994438723585305597794258492732E-33, +0.00000000000000000000000000000000000), (+0.00000000000000000000000000000000000, -0.481482486096808963263994485646231830E-34), (+0.00000000000000000000000000000000000, +0.144444745829042688979198345693869549E-33), (+0.962964972193617926527988971292463659E-34, -0.264815367353244929795196967105427506E-33), (+0.00000000000000000000000000000000000, -0.288889491658085377958396691387739098E-33)

480reltol = sqrt(epsilon(1._TKG))

481reltol

482+0.138777878078144567552953958511352539E-16

483isClose(data, atad(1:size(data)), reltol = reltol)

484T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

485call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

486

487lenData = getUnifRand(5, 100)

488lenData

489+37

490data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

491data

492+1.00449252, +1.01166320, +1.02609682, +1.62982297, +1.18645716, +1.89417243, +1.42225599, +1.98752248, +1.63982081, +1.61843586, +1.56789517, +1.92118502, +1.13793254, +1.75313795, +1.54184675, +1.64464092, +1.64382982, +1.90487790, +1.49366653, +1.08914578, +1.15879846, +1.83333826, +1.26411891, +1.12453818, +1.70387828, +1.45995021, +1.14125180, +1.43479180, +1.39529145, +1.83706665, +1.23659015, +1.57235146, +1.36371756, +1.12023675, +1.65370750, +1.01146007, +1.49418330

493

494atad = getFFTR(getFFTF(data))

495atad = atad * 2 / size(atad)

496atad

497+1.00449276, +1.01166308, +1.02609670, +1.62982273, +1.18645728, +1.89417231, +1.42225564, +1.98752213, +1.63982069, +1.61843586, +1.56789494, +1.92118490, +1.13793230, +1.75313783, +1.54184651, +1.64464092, +1.64383006, +1.90487790, +1.49366665, +1.08914590, +1.15879846, +1.83333838, +1.26411891, +1.12453830, +1.70387828, +1.45995021, +1.14125180, +1.43479180, +1.39529133, +1.83706665, +1.23659003, +1.57235146, +1.36371779, +1.12023675, +1.65370762, +1.01146007, +1.49418342, +0.357627869E-6, +0.119209290E-6, +0.298023224E-6, +0.238418579E-6, +0.119209290E-6, +0.298023224E-6, +0.119209290E-6, +0.298023224E-6, +0.298023224E-6, +0.119209290E-6, +0.596046448E-7, +0.596046448E-7, +0.596046448E-7, +0.596046448E-7, +0.596046448E-7, +0.596046448E-7, +0.119209290E-6, +0.00000000, -0.119209290E-6, +0.00000000, +0.119209290E-6, +0.00000000, +0.298023224E-6, +0.357627869E-6, +0.298023224E-6, +0.00000000, +0.596046448E-7

498reltol = sqrt(epsilon(1._TKG))

499reltol

500+0.345266977E-3

501isClose(data, atad(1:size(data)), reltol = reltol)

502T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

503call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

504

505lenData = getUnifRand(5, 100)

506lenData

507+6

508data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

509data

510+1.6523022804080045, +1.2072092236223018, +1.6374959351252076, +1.0315717571772522, +1.1257292838833011, +1.4847274621499744

511

512atad = getFFTR(getFFTF(data))

513atad = atad * 2 / size(atad)

514atad

515+1.6523022804080048, +1.2072092236223020, +1.6374959351252079, +1.0315717571772522, +1.1257292838833013, +1.4847274621499744, +0.33306690738754696E-15, +0.22204460492503131E-15

516reltol = sqrt(epsilon(1._TKG))

517reltol

518+0.14901161193847656E-7

519isClose(data, atad(1:size(data)), reltol = reltol)

520T, T, T, T, T, T

521call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

522

523lenData = getUnifRand(5, 100)

524lenData

525+25

526data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

527data

528+1.66955833611673020129119478510510062, +1.05751444982064252733910410397558273, +1.53010278222049895186574316159383616, +1.24472774918488407080829579588490215, +1.26546161188990124300552153333635473, +1.58946358663082613378827042418906345, +1.25814083289231814693904383104925850, +1.71574809371822244680484306642534446, +1.66195562767304562526084732819649713, +1.90826160661569533443786511989932773, +1.88001711414974063790995454310204706, +1.00915373100620910412222113033771813, +1.05403096569574199654732339366069115, +1.25358377474925655609118921463925514, +1.51936718166105581690622935170286448, +1.83861691538744322298867020575560974, +1.42495728096608792854629107949884653, +1.86213808863234291332499786806229986, +1.53420831471926469813003603709254158, +1.87085507745843669811836686003604318, +1.67992196542638057191389995500000639, +1.18795282574670916173547845200875380, +1.47272886404151404928979912586085281, +1.89352133207190390703590579124509940, +1.22253270887781813971267939257302193

529

530atad = getFFTR(getFFTF(data))

531atad = atad * 2 / size(atad)

532atad

533+1.66955833611673020129119478510510081, +1.05751444982064252733910410397558293, +1.53010278222049895186574316159383673, +1.24472774918488407080829579588490273, +1.26546161188990124300552153333635473, +1.58946358663082613378827042418906384, +1.25814083289231814693904383104925850, +1.71574809371822244680484306642534446, +1.66195562767304562526084732819649770, +1.90826160661569533443786511989932792, +1.88001711414974063790995454310204764, +1.00915373100620910412222113033771775, +1.05403096569574199654732339366069134, +1.25358377474925655609118921463925514, +1.51936718166105581690622935170286448, +1.83861691538744322298867020575561013, +1.42495728096608792854629107949884672, +1.86213808863234291332499786806230005, +1.53420831471926469813003603709254177, +1.87085507745843669811836686003604356, +1.67992196542638057191389995500000658, +1.18795282574670916173547845200875418, +1.47272886404151404928979912586085262, +1.89352133207190390703590579124509883, +1.22253270887781813971267939257302212, -0.192592994438723585305597794258492732E-33, -0.577778983316170755916793382775478196E-33, -0.577778983316170755916793382775478196E-33, -0.385185988877447170611195588516985464E-33, +0.288889491658085377958396691387739098E-33, -0.192592994438723585305597794258492732E-33, -0.385185988877447170611195588516985464E-33

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

535reltol

536+0.138777878078144567552953958511352539E-16

537isClose(data, atad(1:size(data)), reltol = reltol)

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

539call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

540

541

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 611 of file pm_fftnr.F90.

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

src/fortran/main/pm_fftnr.F90