Generate a sample of shape (nsam), or (ndim, nsam) or (nsam, ndim) that is normalized by the specified input shift and scale along the specified axis dim.
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Detailed Description

Generate a sample of shape (nsam), or (ndim, nsam) or (nsam, ndim) that is normalized by the specified input shift and scale along the specified axis dim.

Here, ndim stands for the number of dimensions (data attributes) of the input sample and nsam represents the number of data points in the sample.
If the input shift is the negative of the mean of the sample and scale is the square-root of the inverse of the variance of the sample, then the returned sample will be a standard score (i.e., z-score).

Parameters

[in]	sample	: The input `contiguous` array of shape `(nsam)`, `(ndim, nsam)`, or `(nsam, ndim)` 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 sample to be normalized.
[in]	dim	: The input scalar of type `integer` of default kind IK, whose value represents the dimension of the input `sample` containing different `nsam` observations: If `dim = 1`, the input `sample` is assumed to have the shape `(nsam, ndim)`. If `dim = 2`, the input `sample` is assumed to have the shape `(ndim, nsam)`. (optional. It must be present if and only if the input arguments the condition `rank(sample) > 1` holds.)
[in]	shift	: The input scalar or the `contiguous` vector of the same type and kind as `sample`, representing the amount by which the input sample must be shifted. If the input `rank(sample) = 1`, then `shift` must be a scalar. If the input `rank(sample) = 2`, then `shift` must be a vector of size `ndim`. If the sample is to be shifted toward the origin to have a mean of zero, then the input `shift` corresponds to the negative of the current mean of the sample that is returned by procedures collectively represented by the generic interface getMean. Note that the size of the input `shift` must be consistent with the size of the input `sample`: If the input argument `dim = 1` then, `size(shift) == size(sample, 2) == ndim` must hold. If the input argument `dim = 2` then, `size(shift) == size(sample, 1) == ndim` must hold.
[in]	scale	: The input scalar or the `contiguous` vector of, the same type and kind as `sample`, type `real` of the same kind as that of `sample` if `sample` is of type `complex`, representing the amount by which the input sample must be scaled. If the input `rank(sample) = 1`, then `scale` must be a scalar. If the input `rank(sample) = 2`, then `scale` must be a vector of size `ndim`. If the sample is to be scaled to have a unit variance, then the input `scale` corresponds to the square-root of the inverse of the variance of the sample that is returned by procedures collectively represented by the generic interface getVar. Note that the size of the input `scale` must be consistent with the size of the input `sample`: If the input argument `dim = 1` then, `size(scale) == size(sample, 2) == ndim` must hold. If the input argument `dim = 2` then, `size(scale) == size(sample, 1) == ndim` must hold.
[in]	operation	: The input scalar constant that can be any of the following: The constant transHerm implying that a Hermitian transpose of the input sample must be returned. In other words, the actions `getNormed(sample, dim, transHerm)` and `transpose(conjg(getNormed(sample, dim)))` are equivalent. Specifying transHerm for `source` of type other than `complex` is identical to specifying transSymm for `source` of type other than `complex`. (optional, default = `.false.`. It can be present only if the condition `rank(sample) == 2` holds.)

Returns

sampleNormed : The output object of the same type and kind and rank as sample, containing the normalized sample.

If the input sample is a vector, then sampleNormed has the same shape and size as that of sample.
If the input sample is a matrix of shape (nrow, ncol), then
1. sampleNormed has the shape (nrow, ncol) if operation is missing.
2. sampleNormed has the shape (ncol, nrow) if operation = transHerm.

Possible calling interfaces ⛓

: use pm_sampleNorm, only: getNormed

sampleNormed(:) = getNormed(sample(:), shift, scale)

sampleNormed(:,:) = getNormed(sample(:,:), dim, shift(:), scale(:))

sampleNormed(:,:) = getNormed(sample(:,:), dim, shift(:), scale(:), operation)

pm_sampleNorm::getNormed
Generate a sample of shape (nsam), or (ndim, nsam) or (nsam, ndim) that is normalized by the specifie...
Definition: pm_sampleNorm.F90:281

pm_sampleNorm
This module contains classes and procedures for normalizing univariate or multivariate samples by arb...
Definition: pm_sampleNorm.F90:123

Warning: The condition 1 <= dim .and. dim <= rank(sample) must hold for the corresponding input arguments.
The condition size(scale) == size(sample, 3 - dim) .or. rank(sample) /= 2 must hold for the corresponding input arguments.
The condition size(shift) == size(sample, 3 - dim) .or. rank(sample) /= 2 must hold for the corresponding input arguments.
These conditions are verified only if the library is built with the preprocessor macro CHECK_ENABLED=1.; The pure procedure(s) documented herein become impure when the ParaMonte library is compiled with preprocessor macro CHECK_ENABLED=1.
By default, these procedures are pure in release build and impure in debug and testing builds.

See also: getScaled
setScaled
getNormed
setNormed

Example usage ⛓

: 1program example

2

3 use pm_kind, only: SK, IK, LK

4 use pm_sampleVar, only: getVar

5 use pm_sampleMean, only: getMean

6 use pm_sampleNorm, only: transHerm

7 use pm_sampleNorm, only: getNormed

8 use pm_sampleShift, only: setShifted

9 use pm_arraySpace, only: getLinSpace

10 use pm_io, only: display_type

11

12 implicit none

13

14 integer(IK) :: dim

15 type(display_type) :: disp

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

17

18 call disp%skip()

19 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")

20 call disp%show("!Normalize a 1D zero-mean sample to have a unit variance.")

21 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")

22 call disp%skip()

23

24 block

25 use pm_kind, only: TKG => RKS ! All kinds are supported.

26 real(TKG), allocatable :: sample(:)

27 call disp%show("sample = getLinSpace(x1 = 0., x2 = 10., count = 11_IK)")

28 sample = getLinSpace(x1 = 0., x2 = 10., count = 11_IK)

29 call disp%show("sample")

30 call disp%show( sample )

31 call disp%show("getMean(sample)")

32 call disp%show( getMean(sample) )

33 call disp%show("getVar(sample)")

34 call disp%show( getVar(sample) )

35 call disp%show("sample = getNormed(sample, -getMean(sample), 1._TKG / sqrt(getVar(sample)))")

36 sample = getNormed(sample, -getMean(sample), 1._TKG / sqrt(getVar(sample)))

37 call disp%show("sample")

38 call disp%show( sample )

39 call disp%show("getMean(sample)")

40 call disp%show( getMean(sample) )

41 call disp%show("getVar(sample)")

42 call disp%show( getVar(sample) )

43 call disp%skip()

44 end block

45

46 block

47 use pm_kind, only: TKG => RKS ! All kinds are supported.

48 complex(TKG), allocatable :: sample(:)

49 call disp%show("sample = cmplx(getLinSpace(x1 = 0., x2 = 10., count = 11_IK), -getLinSpace(x1 = 0., x2 = 10., count = 11_IK), TKG)")

50 sample = cmplx(getLinSpace(x1 = 0., x2 = 10., count = 11_IK), -getLinSpace(x1 = 0., x2 = 10., count = 11_IK), TKG)

51 call disp%show("sample")

52 call disp%show( sample )

53 call disp%show("getMean(sample)")

54 call disp%show( getMean(sample) )

55 call disp%show("getVar(sample)")

56 call disp%show( getVar(sample) )

57 call disp%show("sample = getNormed(sample, -getMean(sample), 1._TKG / sqrt(getVar(sample)))")

58 sample = getNormed(sample, -getMean(sample), 1._TKG / sqrt(getVar(sample)))

59 call disp%show("sample")

60 call disp%show( sample )

61 call disp%show("getMean(sample)")

62 call disp%show( getMean(sample) )

63 call disp%show("getVar(sample)")

64 call disp%show( getVar(sample) )

65 call disp%skip()

66 end block

67

68 call disp%skip()

69 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")

70 call disp%show("!Normalize a 2D zero-mean sample to have a unit variance.")

71 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")

72 call disp%skip()

73

74 block

75 use pm_kind, only: TKG => RKS ! All kinds are supported.

76 real(TKG), allocatable :: sample(:,:)

77 call disp%show("sample = reshape(getLinSpace(x1 = 1._TKG, x2 = 10._TKG, count = 10_IK), [2,5])")

78 sample = reshape(getLinSpace(x1 = 1._TKG, x2 = 10._TKG, count = 10_IK), [2,5])

79 call disp%show("dim = 2")

80 dim = 2

81 call disp%show("call setShifted(sample, dim, -getMean(sample, dim))")

82 call setShifted(sample, dim, -getMean(sample, dim))

83 call disp%show("sample")

84 call disp%show( sample )

85 call disp%show("getMean(sample, dim)")

86 call disp%show( getMean(sample, dim) )

87 call disp%show("getVar(sample, dim)")

88 call disp%show( getVar(sample, dim) )

89 call disp%show("sample = getNormed(sample, dim, -getMean(sample, dim), 1._TKG / sqrt(getVar(sample, dim)))")

90 sample = getNormed(sample, dim, -getMean(sample, dim), 1._TKG / sqrt(getVar(sample, dim)))

91 call disp%show("sample")

92 call disp%show( sample )

93 call disp%show("getMean(sample, dim)")

94 call disp%show( getMean(sample, dim) )

95 call disp%show("getVar(sample, dim)")

96 call disp%show( getVar(sample, dim) )

97 call disp%skip()

98 end block

99

100 block

101 use pm_kind, only: TKG => RKS ! All kinds are supported.

102 complex(TKG), allocatable :: sample(:,:)

103 call disp%show("sample = cmplx(reshape(getLinSpace(x1 = 1._TKG, x2 = 10._TKG, count = 10_IK), [2,5]), -reshape(getLinSpace(x1 = 1._TKG, x2 = 10._TKG, count = 10_IK), [2,5]))")

104 sample = cmplx(reshape(getLinSpace(x1 = 1._TKG, x2 = 10._TKG, count = 10_IK), [2,5]), -reshape(getLinSpace(x1 = 1._TKG, x2 = 10._TKG, count = 10_IK), [2,5]))

105 call disp%show("dim = 2")

106 dim = 2

107 call disp%show("call setShifted(sample, dim, -getMean(sample, dim))")

108 call setShifted(sample, dim, -getMean(sample, dim))

109 call disp%show("sample")

110 call disp%show( sample )

111 call disp%show("getMean(sample, dim)")

112 call disp%show( getMean(sample, dim) )

113 call disp%show("getVar(sample, dim)")

114 call disp%show( getVar(sample, dim) )

115 call disp%show("sample = getNormed(sample, dim, -getMean(sample, dim), 1._TKG / sqrt(getVar(sample, dim)))")

116 sample = getNormed(sample, dim, -getMean(sample, dim), 1._TKG / sqrt(getVar(sample, dim)))

117 call disp%show("sample")

118 call disp%show( sample )

119 call disp%show("getMean(sample, dim)")

120 call disp%show( getMean(sample, dim) )

121 call disp%show("getVar(sample, dim)")

122 call disp%show( getVar(sample, dim) )

123 call disp%skip()

124 end block

125

126 call disp%skip()

127 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")

128 call disp%show("!Normalize a 2D zero-mean sample to have a unit variance and transpose the result upon return.")

129 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")

130 call disp%skip()

131

132 block

133 use pm_kind, only: TKG => RKS ! All kinds are supported.

134 real(TKG), allocatable :: sample(:,:)

135 call disp%show("sample = reshape(getLinSpace(x1 = 1._TKG, x2 = 10._TKG, count = 10_IK), [2,5])")

136 sample = reshape(getLinSpace(x1 = 1._TKG, x2 = 10._TKG, count = 10_IK), [2,5])

137 call disp%show("dim = 2")

138 dim = 2

139 call disp%show("call setShifted(sample, dim, -getMean(sample, dim))")

140 call setShifted(sample, dim, -getMean(sample, dim))

141 call disp%show("sample")

142 call disp%show( sample )

143 call disp%show("getMean(sample, dim)")

144 call disp%show( getMean(sample, dim) )

145 call disp%show("getVar(sample, dim)")

146 call disp%show( getVar(sample, dim) )

147 call disp%show("sample = getNormed(sample, dim, -getMean(sample, dim), 1._TKG / sqrt(getVar(sample, dim)), transHerm)")

148 sample = getNormed(sample, dim, -getMean(sample, dim), 1._TKG / sqrt(getVar(sample, dim)), transHerm)

149 call disp%show("sample")

150 call disp%show( sample )

151 call disp%show("getMean(sample, 3_IK - dim)")

152 call disp%show( getMean(sample, 3_IK - dim) )

153 call disp%show("getVar(sample, 3_IK - dim)")

154 call disp%show( getVar(sample, 3_IK - dim) )

155 call disp%skip()

156 end block

157

158 block

159 use pm_kind, only: TKG => RKS ! All kinds are supported.

160 complex(TKG), allocatable :: sample(:,:)

161 call disp%show("sample = cmplx(reshape(getLinSpace(x1 = 1._TKG, x2 = 10._TKG, count = 10_IK), [2,5]), -reshape(getLinSpace(x1 = 1._TKG, x2 = 10._TKG, count = 10_IK), [2,5]))")

162 sample = cmplx(reshape(getLinSpace(x1 = 1._TKG, x2 = 10._TKG, count = 10_IK), [2,5]), -reshape(getLinSpace(x1 = 1._TKG, x2 = 10._TKG, count = 10_IK), [2,5]))

163 call disp%show("dim = 2")

164 dim = 2

165 call disp%show("call setShifted(sample, dim, -getMean(sample, dim))")

166 call setShifted(sample, dim, -getMean(sample, dim))

167 call disp%show("sample")

168 call disp%show( sample )

169 call disp%show("getMean(sample, dim)")

170 call disp%show( getMean(sample, dim) )

171 call disp%show("getVar(sample, dim)")

172 call disp%show( getVar(sample, dim) )

173 call disp%show("sample = getNormed(sample, dim, -getMean(sample, dim), 1._TKG / sqrt(getVar(sample, dim)), transHerm)")

174 sample = getNormed(sample, dim, -getMean(sample, dim), 1._TKG / sqrt(getVar(sample, dim)), transHerm)

175 call disp%show("sample")

176 call disp%show( sample )

177 call disp%show("getMean(sample, 3_IK - dim)")

178 call disp%show( getMean(sample, 3_IK - dim) )

179 call disp%show("getVar(sample, 3_IK - dim)")

180 call disp%show( getVar(sample, 3_IK - dim) )

181 call disp%skip()

182 end block

183

184end program example

pm_arraySpace::getLinSpace
Generate count evenly spaced points over the interval [x1, x2] if x1 < x2, or [x2,...
Definition: pm_arraySpace.F90:108

pm_io::show
This is a generic method of the derived type display_type with pass attribute.
Definition: pm_io.F90:11726

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

pm_sampleMean::getMean
Generate and return the (weighted) mean of an input sample of nsam observations with ndim = 1 or 2 at...
Definition: pm_sampleMean.F90:229

pm_sampleShift::setShifted
Return a sample of shape (nsam), or (ndim, nsam) or (nsam, ndim) that is shifted by the specified inp...
Definition: pm_sampleShift.F90:1133

pm_sampleVar::getVar
Generate and return the variance of the input sample of type complex or real of shape (nsam) or (ndim...
Definition: pm_sampleVar.F90:715

pm_arraySpace
This module contains procedures and generic interfaces for generating arrays with linear or logarithm...
Definition: pm_arraySpace.F90:33

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::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::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::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_sampleMean
This module contains classes and procedures for computing the first moment (i.e., the statistical mea...
Definition: pm_sampleMean.F90:104

pm_sampleShift
This module contains classes and procedures for shifting univariate or multivariate samples by arbitr...
Definition: pm_sampleShift.F90:59

pm_sampleVar
This module contains classes and procedures for computing the properties related to the covariance ma...
Definition: pm_sampleVar.F90:394

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 ⛓
1

2!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

3!Normalize a 1D zero-mean sample to have a unit variance.

4!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

5

6sample = getLinSpace(x1 = 0., x2 = 10., count = 11_IK)

7sample

8+0.00000000, +1.00000000, +2.00000000, +3.00000000, +4.00000000, +5.00000000, +6.00000000, +7.00000000, +8.00000000, +9.00000000, +10.0000000

9getMean(sample)

10+5.00000000

11getVar(sample)

12+10.0000000

13sample = getNormed(sample, -getMean(sample), 1._TKG / sqrt(getVar(sample)))

14sample

15-1.58113885, -1.26491106, -0.948683262, -0.632455528, -0.316227764, +0.00000000, +0.316227764, +0.632455528, +0.948683262, +1.26491106, +1.58113885

16getMean(sample)

17+0.325116254E-7

18getVar(sample)

19+1.00000000

20

21sample = cmplx(getLinSpace(x1 = 0., x2 = 10., count = 11_IK), -getLinSpace(x1 = 0., x2 = 10., count = 11_IK), TKG)

22sample

23(+0.00000000, -0.00000000), (+1.00000000, -1.00000000), (+2.00000000, -2.00000000), (+3.00000000, -3.00000000), (+4.00000000, -4.00000000), (+5.00000000, -5.00000000), (+6.00000000, -6.00000000), (+7.00000000, -7.00000000), (+8.00000000, -8.00000000), (+9.00000000, -9.00000000), (+10.0000000, -10.0000000)

24getMean(sample)

25(+5.00000000, -5.00000000)

26getVar(sample)

27+20.0000000

28sample = getNormed(sample, -getMean(sample), 1._TKG / sqrt(getVar(sample)))

29sample

30(-1.11803401, +1.11803401), (-0.894427180, +0.894427180), (-0.670820355, +0.670820355), (-0.447213590, +0.447213590), (-0.223606795, +0.223606795), (+0.00000000, +0.00000000), (+0.223606795, -0.223606795), (+0.447213590, -0.447213590), (+0.670820355, -0.670820355), (+0.894427180, -0.894427180), (+1.11803401, -1.11803401)

31getMean(sample)

32(+0.00000000, +0.00000000)

33getVar(sample)

34+1.00000000

35

36

37!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

38!Normalize a 2D zero-mean sample to have a unit variance.

39!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

40

41sample = reshape(getLinSpace(x1 = 1._TKG, x2 = 10._TKG, count = 10_IK), [2,5])

42dim = 2

43call setShifted(sample, dim, -getMean(sample, dim))

44sample

45-4.00000000, -2.00000000, +0.00000000, +2.00000000, +4.00000000

46-4.00000000, -2.00000000, +0.00000000, +2.00000000, +4.00000000

47getMean(sample, dim)

48+0.00000000, +0.00000000

49getVar(sample, dim)

50+8.00000000, +8.00000000

51sample = getNormed(sample, dim, -getMean(sample, dim), 1._TKG / sqrt(getVar(sample, dim)))

52sample

53-1.41421354, -0.707106769, +0.00000000, +0.707106769, +1.41421354

54-1.41421354, -0.707106769, +0.00000000, +0.707106769, +1.41421354

55getMean(sample, dim)

56+0.238418583E-7, +0.238418583E-7

57getVar(sample, dim)

58+0.999999940, +0.999999940

59

60sample = cmplx(reshape(getLinSpace(x1 = 1._TKG, x2 = 10._TKG, count = 10_IK), [2,5]), -reshape(getLinSpace(x1 = 1._TKG, x2 = 10._TKG, count = 10_IK), [2,5]))

61dim = 2

62call setShifted(sample, dim, -getMean(sample, dim))

63sample

64(-4.00000000, +4.00000000), (-2.00000000, +2.00000000), (+0.00000000, +0.00000000), (+2.00000000, -2.00000000), (+4.00000000, -4.00000000)

65(-4.00000000, +4.00000000), (-2.00000000, +2.00000000), (+0.00000000, +0.00000000), (+2.00000000, -2.00000000), (+4.00000000, -4.00000000)

66getMean(sample, dim)

67(+0.00000000, +0.00000000), (+0.00000000, +0.00000000)

68getVar(sample, dim)

69+16.0000000, +16.0000000

70sample = getNormed(sample, dim, -getMean(sample, dim), 1._TKG / sqrt(getVar(sample, dim)))

71sample

72(-1.00000000, +1.00000000), (-0.500000000, +0.500000000), (+0.00000000, +0.00000000), (+0.500000000, -0.500000000), (+1.00000000, -1.00000000)

73(-1.00000000, +1.00000000), (-0.500000000, +0.500000000), (+0.00000000, +0.00000000), (+0.500000000, -0.500000000), (+1.00000000, -1.00000000)

74getMean(sample, dim)

75(+0.00000000, +0.00000000), (+0.00000000, +0.00000000)

76getVar(sample, dim)

77+1.00000000, +1.00000000

78

79

80!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

81!Normalize a 2D zero-mean sample to have a unit variance and transpose the result upon return.

82!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

83

84sample = reshape(getLinSpace(x1 = 1._TKG, x2 = 10._TKG, count = 10_IK), [2,5])

85dim = 2

86call setShifted(sample, dim, -getMean(sample, dim))

87sample

88-4.00000000, -2.00000000, +0.00000000, +2.00000000, +4.00000000

89-4.00000000, -2.00000000, +0.00000000, +2.00000000, +4.00000000

90getMean(sample, dim)

91+0.00000000, +0.00000000

92getVar(sample, dim)

93+8.00000000, +8.00000000

94sample = getNormed(sample, dim, -getMean(sample, dim), 1._TKG / sqrt(getVar(sample, dim)), transHerm)

95sample

96-1.41421354, -1.41421354

97-0.707106769, -0.707106769

98+0.00000000, +0.00000000

99+0.707106769, +0.707106769

100+1.41421354, +1.41421354

101getMean(sample, 3_IK - dim)

102+0.238418583E-7, +0.238418583E-7

103getVar(sample, 3_IK - dim)

104+0.999999940, +0.999999940

105

106sample = cmplx(reshape(getLinSpace(x1 = 1._TKG, x2 = 10._TKG, count = 10_IK), [2,5]), -reshape(getLinSpace(x1 = 1._TKG, x2 = 10._TKG, count = 10_IK), [2,5]))

107dim = 2

108call setShifted(sample, dim, -getMean(sample, dim))

109sample

110(-4.00000000, +4.00000000), (-2.00000000, +2.00000000), (+0.00000000, +0.00000000), (+2.00000000, -2.00000000), (+4.00000000, -4.00000000)

111(-4.00000000, +4.00000000), (-2.00000000, +2.00000000), (+0.00000000, +0.00000000), (+2.00000000, -2.00000000), (+4.00000000, -4.00000000)

112getMean(sample, dim)

113(+0.00000000, +0.00000000), (+0.00000000, +0.00000000)

114getVar(sample, dim)

115+16.0000000, +16.0000000

116sample = getNormed(sample, dim, -getMean(sample, dim), 1._TKG / sqrt(getVar(sample, dim)), transHerm)

117sample

118(-1.00000000, -1.00000000), (-1.00000000, -1.00000000)

119(-0.500000000, -0.500000000), (-0.500000000, -0.500000000)

120(+0.00000000, -0.00000000), (+0.00000000, -0.00000000)

121(+0.500000000, +0.500000000), (+0.500000000, +0.500000000)

122(+1.00000000, +1.00000000), (+1.00000000, +1.00000000)

123getMean(sample, 3_IK - dim)

124(+0.00000000, +0.00000000), (+0.00000000, +0.00000000)

125getVar(sample, 3_IK - dim)

126+1.00000000, +1.00000000

127

128

Test:: test_pm_sampleNorm

Todo:: Very Low Priority: The functionality of this interface can be expanded to include normalizing of higher dimensional input sample and whole sample input arrays of arbitrary shape, although the latter is trivial using the Fortran array syntax.

Final Remarks ⛓

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Copyright: Computational Data Science Lab

Author:: Amir Shahmoradi, Saturday 2:48 AM, August 22, 2021, Dallas, TX

Definition at line 281 of file pm_sampleNorm.F90.

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

src/fortran/main/pm_sampleNorm.F90